Pearson Edexcel International GCSE Mathematics B Paper 2 (2021)

*P66312A0132* Turn over Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information P66312A ©2021 Pearson Educatio ...

*P66312A0132* Turn over Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information P66312A ©2021 Pearson Education Ltd. 1/1/ Instructions • Use black ink or ball-point pen. • Fill in the boxes at the top of this page with your name, centre number and candidate number. • Answer all questions. • Answer the questions in the spaces provided – there may be more space than you need. • Calculators may be used. Information • The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice • Read each question carefully before you start to answer it. • Check your answers if you have time at the end. • Without sufficient working, correct answers may be awarded no marks. You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Mathematics B Paper 2 Afternoon (Time: 2 hours 30 minutes) Paper Reference 4MB1/02 Pearson Edexcel International GCSE Wednesday 13 January 20212 *P66312A0232* Answer ALL TWELVE questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 The following formula can be used to change a temperature f degrees Fahrenheit to a temperature c degrees Celsius. c = 5 32 9 ( ) f − (a) Make f the subject of c = 5 32 9 ( ) f − (3) Sean and Kate measure the temperature of a heated iron bar. Sean measures the temperature of the iron bar as x degrees Fahrenheit. Kate measures the temperature of the iron bar as y degrees Celsius. Given that x = 2y, (b) find the temperature, in degrees Fahrenheit, of the iron bar. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0332* Turn over 3 Question 1 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 1 is 5 marks)4 *P66312A0432* 2 The Earth is assumed to move around the Sun in a circular orbit of radius 1.5 × 108 km. Assuming that the Earth takes 365 days to complete one orbit of the Sun, calculate the average speed, in m/s to 3 significant figures, of the Earth as it orbits the Sun. (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0532* Turn over 5 Question 2 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 2 is 4 marks)6 *P66312A0632* 3 S R Q O T 40mm 50mm 60mm Diagram NOT accurately drawn Figure 1 Figure 1 shows circle QRST with centre O. SQ is a diameter of the circle. QR = 60mm RS = 40mm ST = 50mm Without using a calculator, find the exact length, in mm, of QT. Give your answer in the form a b where a is an integer and b is a prime number. Show your working clearly. (5) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0732* Turn over 7 Question 3 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 3 is 5 marks)8 *P66312A0832* 4 Over the course of a week of seven days, Alan plays a series of games. He plays exactly one game each day. On Sunday, the probability that Alan wins his game is 1 2 On a day other than Sunday, the probability that Alan wins his game is 1 3 The incomplete probability tree diagram below is to give information about Alan’s result on a randomly chosen day in a week of seven days. (a) Complete the probability tree diagram below. Alan wins Alan does not win ............................ ............................ Alan wins Alan does not win ............................ ............................ Sunday Not Sunday ............................ ............................ Day Alan’s result (3) (b) Find the expected number of games Alan will win in a week of seven days. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A0932* Turn over 9 Question 4 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 4 is 5 marks)10 *P66312A01032* 5 E is the universal set and A, B and C are three sets. Here is information about these sets. n( A ) = 45 n( B ) = 48 n( C ) = 55 n( A ∩ B ) = 24 n( A ∩ C ) = 25 n( B ∩ C ) = 27 n( A ∩ B ∩ C ) = x n( A ʹ ∩ B ʹ ∩ C ʹ ) = y (a) Show all this information on the Venn diagram, giving the number of elements in each appropriate subset, in terms of x or y. E A B C (3) Given that n(E ) = 100 (b) find an expression for y in terms of x. Give your answer in its simplest form. (2) (c) Using your Venn diagram and your answer to part (b), find the greatest possible value of x. Give reasons for your answer. (3) An element is selected at random from the 100 elements in the universal set. (d) Find the probability that this element is in the set ( B ∩ C ʹ ) ∪ ( B ʹ ∩ C ). (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A01132* Turn over 11 Question 5 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 5 is 10 marks)12 *P66312A01232* 6 (a) (i) Solve the inequality 3x + 5 > 7x − 9 (2) (ii) Represent your solution on the number line on the next page. (1) (b) (i) Solve the inequality x2 + 5x − 6  0 (3) (ii) Represent your solution on the number line on the next page. (1) (c) Write down the set of values for which both 3x + 5 > 7x − 9 and x2 + 5x − 6  0 (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A01332* Turn over 13 Question 6 continued (a) (ii) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 x (b) (ii) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 x Only use this line if you need to redraw your solution. −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 x .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 6 is 9 marks)14 *P66312A01432* 7 Given that a is inversely proportional to b and b is inversely proportional to c3 complete the following table. a c 16 240 250 135 (6) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A01532* Turn over 15 Question 7 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 7 is 6 marks)16 *P66312A01632* 8 A E D C B 6cm 8cm Diagram NOT accurately drawn Figure 2 Figure 2 shows a kite ABCD in which AB = 6cm BC = 8cm ∠ABC = 90° AEC and BED are straight lines. (a) Calculate the length, in cm, of AC. (2) (b) Calculate the area, in cm2, of ABCD. (2) (c) Show that BE = 4.8cm (2) (d) Prove that triangle ABE is similar to triangle BCE. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A01732* Turn over 17 Question 8 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 8 is 9 marks)18 *P66312A01832* 9 The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A. (a) On the grid, draw and label triangle A. (1) Triangle B is the image of triangle A under a reflection in the line with equation y = −x (b) On the grid, draw and label triangle B. (2) Triangle C is the image of triangle A under the transformation with the matrix M where M = 0 1 1 0  −    (c) Find the matrix product M 1 1 3 2 5 2   (2) (d) Hence, on the grid, draw and label triangle C. (1) (e) Describe fully the single transformation that maps triangle B onto triangle C. (2) The single transformation that maps triangle B onto triangle C is represented by the matrix N (f) State, giving a reason, the matrix N2 (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A01932* Turn over 19 Question 9 continued −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 x y −6 −5 −4 −3 −2 −1 7 6 5 4 3 2 1 .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Turn over for a spare grid if you need to redraw your triangles.20 *P66312A02032* Question 9 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A02132* Turn over 21 Question 9 continued Only use this grid if you need to redraw your triangles. −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 x y −6 −5 −4 −3 −2 −1 7 6 5 4 3 2 1 .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 9 is 10 marks)22 *P66312A02232* 10 A M N P O B Diagram NOT accurately drawn Figure 3 Figure 3 shows the triangle OAB where OA → = 12a and OB → = 6b M is the midpoint of OA and N is the midpoint of AB. The point P on BM is such that BP : BM = 2 : 3 (a) Simplifying your answer, find, in terms of a and b (i) BM → (ii) OP → (3) (b) Hence show that O, P and N are collinear. (4) Given that | a| = | b| = 1cm and that ∠AOB = 70° (c) find the length, in cm to 3 significant figures, of OP. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. [ Cosine rule: a2 = b2 + c2 − 2bc cosA ]*P66312A02332* Turn over 23 Question 10 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................24 *P66312A02432* Question 10 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A02532* Turn over 25 Question 10 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 10 is 10 marks)26 *P66312A02632* 11 The equation of a curve is y = f(x) where f(x) = x3 − 10x2 + 20 (a) Complete the table of values for y = x3 − 10x2 + 20 Give your values of y to one decimal place where necessary. x −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 y −28 −5.9 17.4 20 11 0.9 −12 −43 (3) (b) On the grid opposite, plot the points from your completed table and join them to form a smooth curve. (3) A curve C has equation y = g (x) where B = g (x) and dBdx = f (x) The curve C has two turning points in −2  x  3 (c) Using your graph, find the x coordinates of these two turning points on the curve C. (3) (d) Referring to your graph, determine which of these two turning points is a maximum and which is a minimum. You should explain your reasoning clearly. (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A02732* Turn over 27 Question 11 continued −2 −1 O 1 2 3 x y −30 −40 −50 −20 −10 10 20 30 .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Turn over for a spare grid if you need to redraw your curve.28 *P66312A02832* Question 11 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A02932* Turn over 29 Question 11 continued Only use this grid if you need to redraw your curve. −2 −1 O 1 2 3 x y −30 −40 −50 −20 −10 10 20 30 .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 11 is 13 marks)30 *P66312A03032* 12 Indre buys 1000 Hungarian dolls in Budapest to sell in Austria. She pays in Hungarian forints. Indre pays 1900 forints for each small doll she buys. She pays 10 300 forints for each large doll she buys. The number of small dolls that Indre buys is 4 times the number of large dolls that she buys. (a) Calculate the total cost, in forints, of the 1000 dolls that Indre buys. (3) Indre has to pay 100 euros to transport the dolls from Hungary so that she can sell them in Austria. Initially the price of each small doll that Indre sells is 8 euros and the price of each large doll that Indre sells is 40 euros. She sells 80% of the small dolls and 7 8 of the large dolls at these prices. Indre then reduces the price of each of her remaining dolls by 40% She sells all of the remaining dolls. When Indre bought the dolls, the exchange rate was 1 euro = 327.6 forints. (b) Calculate the total profit, in euros to 2 decimal places, that Indre made by selling all 1000 dolls. (8) (c) (i) Calculate the percentage profit, to 3 significant figures, that Indre made. (2) (ii) State how the percentage profit in part (c) (i) would be affected if the total profit calculated in part (b) had been in forints. (1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................*P66312A03132* Turn over 31 Question 12 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................32 *P66312A03232* Question 12 continued .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 12 is 14 marks) TOTAL FOR PAPER IS 100 MARKS