GCSE (9–1) Mathematics J560/05 Paper 5 (Higher Tier) Practice Paper – Set 3

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GCSE (9–1) Mathematics J560/05 Paper 5 (Higher Tier) Practice Paper – Set 3 INSTRUCTIONS • Use black ink. You may use an HB pencil for graphs and diagrams. • Complete the boxes above wi... th your name, centre number and candidate number. • Answer all the questions. • Read each question carefully before you start your answer. • Where appropriate, your answers should be supported with working. Marks may be given for a correct method even if the answer is incorrect. • Write your answer to each question in the space provided. • Additional paper may be used if required but you must clearly show your candidate number, centre number and question number(s). • Do not write in the barcodes. INFORMATION • The total mark for this paper is 100. • The marks for each question are shown in brackets [ ]. • This document consists of 20 pages. Turn over © OCR 2016 Practice paper DC (LEG/CGW) 143846/3 Last name First name Candidate number Centre number Oxford Cambridge and RSA GCSE (9–1) Mathematics J560/05 Paper 5 (Higher Tier) Practice Paper – Set 3 Time allowed: 1 hour 30 minutes You may use: • Geometrical instruments • Tracing paper Do not use: • a Calculator * 2 0 1 6 * H OCR is an exempt Charity * J 5 6 0 0 5 *2 © OCR 2016 Practice paper J560/05 Answer all the questions 1 Describe the correlation shown in each of these scatter graphs. Where there is correlation, state the strength. .......................................................... .......................................................... .......................................................... .......................................................... [3] 2 (a) Tom invests £2000 at 5% per year simple interest. How much interest has been paid after 6 years? (a) £ ......................................................... [2] (b) Tom receives a 20% wage increase. His new weekly wage is £360. Calculate his weekly wage before the increase. (b) £ ......................................................... [3]3 © OCR 2016 Practice paper J560/05 Turn over 3 Demi gives her dog 23 of a tin of food each day. Work out the smallest number of tins of food that she needs to feed her dog for 10 days. ........................................................... [3] 4 Adil, Katie and Rebecca share £160 in the ratio 2 : 5 : 3. (a) How much does Rebecca receive? (a) £ ......................................................... [2] (b) Katie says she receives 60% more than Rebecca. Here is her reasoning. I receive 5 parts and Rebecca receives 3 parts. 35 = 60% So I receive 60% more than Rebecca. (i) Explain what is wrong with Katie’s reasoning. ........................................................................................................................................... ...................................................................................................................................... [1] (ii) Complete the following to give the correct percentage. I receive 5 parts and Rebecca receives 3 parts. ............... = ............... % So I receive ............... % more than Rebecca. [2]4 © OCR 2016 Practice paper J560/05 5 ABC is a triangle. B A C (a) Construct the locus of points inside the triangle that are equidistant from BA and BC. Show all your construction lines. [2] (b) Indicate the point on the locus inside the triangle which is 3cm from A. [1]5 © OCR 2016 Practice paper J560/05 Turn over 6 (a) The distance from the Sun to the Earth is approximately 150000000km. Write this distance in standard form. (a) ......................................................km [1] (b) Light travels at 299792km per second. Neil estimates that light takes approximately 20 minutes to reach the Earth from the Sun. Show that his estimate is incorrect. [4] 7 Shape A is similar to shape B. A 7.5cm B 5.5 cm h cm 16.5 cm Not to scale Work out the value of h. h = .......................................................... [3]6 © OCR 2016 Practice paper J560/05 8 The diagram shows two views of a solid made from 14 one-centimetre cubes. Front view Rear view Not to scale (a) On the centimetre grid below, draw a plan of the solid. [2] (b) Work out the smallest number of cubes that need to be added to the solid to make a cube. (b) ........................................................... [2]7 © OCR 2016 Practice paper J560/05 Turn over 9 (a) Rearrange this formula to make x the subject. y = x 5 2 (a) ........................................................... [2] (b) Solve. 5x - 6 = 3x + 13 (b) x = ..................................................... [3]8 © OCR 2016 Practice paper J560/05 10 Danny sells pens and notebooks in his shop. On Monday, he sold 5 pens and 8 notebooks for £44.50. On Tuesday, he sold 10 pens and 3 notebooks for £37. Work out the cost of a pen and the cost of a notebook. pen £ ........................................................ notebook £ ........................................................ [5]9 © OCR 2016 Practice paper J560/05 Turn over 11 The diagram shows triangle ABC. D is a point on AB such that DB = 6cm. BC = 10cm, angle CAD = 30° and angle BDC = 90°. 10 cm D 6cm B Not to scale A C 30° Work out the ratio length of AC : length of DB in its simplest form. ........................ : ........................ [5]10 © OCR 2016 Practice paper J560/05 12 A tank in the shape of a cuboid rests on a horizontal surface. The graph shows the depth of water, in cm, in the tank over a period of time. 160 140 120 100 80 60 10 am 11am 12 am Time of day Depth of water (cm) 1 pm 2 pm 40 20 0 (a) What fraction of the water is left in the tank at 1230pm? Give your answer in its simplest form. (a) ........................................................... [2] (b) This is how Mike worked out the average rate of change in the depth of water per hour between 10am and 2pm. 160 ÷ 4 = 40cm/h What error has Mike made? ................................................................................................................................................... .............................................................................................................................................. [1]11 © OCR 2016 Practice paper J560/05 Turn over (c) Mike estimates that the rate of change in the depth of water at 11am is 45cm/h. Is his estimate reasonable? Show your method. .............................................................................................................................................. [4] 13 There are 5 blue sweets, 3 red sweets, 2 green sweets and no other sweets in a box. Waleed chooses 3 sweets at random from the box and puts them in his pocket. (a) Waleed calculates the probability of choosing 3 red sweets as 10 3 10 3 10 3 1000 27 # # = . What incorrect assumption has he made? .............................................................................................................................................. [1] (b) Show that the probability of Waleed choosing three sweets of the same colour is 120 11 . [5]12 © OCR 2016 Practice paper J560/05 14 (a) Write 11 7 as a recurring decimal. (a) ........................................................... [2] (b) Convert 0 3 . 6o to a fraction. Give your answer in its lowest terms. (b) ........................................................... [3]13 © OCR 2016 Practice paper J560/05 Turn over 15 The histogram shows information about the times, in minutes, that trains arrived late at a station one day. 0 10 20 Time (minutes) t Frequency density (trains per minute) 30 40 50 (a) David says that the range of times these trains arrived late is actually 48 minutes. Could he be correct? Explain your reasoning. ................................................................................................................................................... .............................................................................................................................................. [1] (b) 10 of these trains were between 30 minutes and 50 minutes late on that day. Work out the number of trains that were at most 15 minutes late. (b) ........................................................... [3]14 © OCR 2016 Practice paper J560/05 16 Sarah buys x apples and y oranges. She buys • at least 4 apples • at most 9 oranges • more oranges than apples. (a) (i) One of the inequalities for this information is x H 4. Write down two more inequalities for this information. (a)(i) ................................................................ ........................................................... [2] (ii) On the grid, show the region represented by the three inequalities in part (a)(i). Shade the region that is not required. 0 8 6 4 2 2 4 x y 1 3 5 6 7 8 9 10 7 5 3 1 10 9 [4] (b) Apples cost 45p each and oranges cost 30p each. Sarah spends £4.05 on apples and oranges. How many apples and how many oranges does she buy? (b) apples ............... , oranges ............... [2]15 © OCR 2016 Practice paper J560/05 Turn over 17 (a) Simplify. (i) 3 2 # 6 (a)(i) ........................................................... [2] (ii) 2 6 (ii) ........................................................... [2] (b) Evaluate. 162 1 (b) ........................................................... [1]16 © OCR 2016 Practice paper J560/05 18 Ryan is using the quadratic formula to solve an equation of the form ax2 + bx + c = 0. After substituting values into the quadratic formula, he gets - x 2 3 3 ! 5 = . (a) Find a set of possible values for a, b and c. (a) a = ............................................................... b = ............................................................... c = ......................................................... [5] (b) Explain why there are other sets of possible values for a, b and c. ................................................................................................................................................... .............................................................................................................................................. [1]17 © OCR 2016 Practice paper J560/05 Turn over 19 The diagram shows the circle x2 + y2 = 5. y x O P A Not to scale (a) Mandy says that the point (2, 1.5) lies inside the circle. Is she correct? Show how you decide. .............................................................................................................................................. [2] (b) The tangent to the circle at the point P (-2, 1) intersects the y-axis at A. Show that the area of the triangle APO is 5 square units. [6]18 © OCR 2016 Practice paper J560/05 20 OABC is a square. OA = a and OC = b. M is the midpoint of AB. L is a point on MC such that LC = 2ML. B C Not to scale L M A b a O Use vectors to prove that point L lies on the line OB. [5] END OF QUESTION PAPER19 © OCR 2016 Practice paper J560/05 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE20 © OCR 2016 Practice paper J560/05 Oxford Cambridge and RSA Copyright Information OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series. If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity. 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