GCSE (9–1) Mathematics J560/04 Paper 4 (Higher Tier) Practice Paper – Set 3

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GCSE (9–1) Mathematics J560/04 Paper 4 (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 [ ]. • Use the r button on your calculator or take r to be 3.142 unless the question says otherwise. • This document consists of 20 pages. Turn over © OCR 2016 Practice paper DC (LK/JG) 142854/2 Last name First name Candidate number Centre number Oxford Cambridge and RSA GCSE (9–1) Mathematics J560/04 Paper 4 (Higher Tier) Practice Paper – Set 3 Time allowed: 1 hour 30 minutes You may use: • A scientific or graphical calculator • Geometrical instruments • Tracing paper * 2 0 1 6 * H OCR is an exempt Charity * J 5 6 0 0 4 *2 © OCR 2016 Practice paper J560/04 Answer all the questions. 1 Between January 2015 and January 2016 the price of diesel increased from £1.12 per litre to £1.19 per litre. Calculate the percentage increase in price. ...................................................... % [3] 2 (a) Write the ratio 6mm : 180cm in the form 1 : n. (a) ........................................................... [2] (b) An athlete runs 240 metres in 45 seconds. Work out her average speed in kilometres per hour. (b) .................................................. km/h [3]3 © OCR 2016 Practice paper J560/04 Turn over 3 (a) Write down the equation of a line parallel to y x = + 5 3 that passes through the point (0, -7). (a) .......................................................... [2] (b) Find the equation of the line through the points (-3, -17) and (0, 1). (b) ........................................................... [3] 4 Solve. 3 6 _ i x - = 5 48 x = .......................................................... [3]4 © OCR 2016 Practice paper J560/04 5 An alloy is made from 28cm3 of copper and 41cm3 of gold. The density of copper is 9g/cm3. The density of gold is 19g/cm3. (a) Work out the mass of copper used. (a) ....................................................... g [2] (b) Work out the density of the alloy. (b) ................................................ g/cm3 [4] 6 Hannah’s race time, t seconds, was recorded as 53.48, correct to 2 decimal places. Complete the error interval for Hannah’s race time. ............................ G t 1 ............................[2]5 © OCR 2016 Practice paper J560/04 Turn over 7 (a) Here are the first five terms of two sequences. Write down the next term in each of these sequences. (i) 1 1 2 3 5 (a)(i) ........................................................... [1] (ii) 5 8 13 20 29 (ii) ........................................................... [1] (b) The nth term of a sequence is given by n n 2 - 3 . Write down the second and fifth terms of the sequence. (b) second term = ................................... fifth term = ................................... [2]6 © OCR 2016 Practice paper J560/04 8 A railway station has two platforms. Trains stop at the northbound platform every 15 minutes. Trains stop at the southbound platform every 18 minutes. Two trains stopped together at 1512. (a) Work out the next time two trains stop together at this station. (a) ........................................................... [4] (b) Write down two assumptions that were necessary to solve this problem. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ................................................................................................................................................... [2]7 © OCR 2016 Practice paper J560/04 Turn over 9 The diagram shows all the paths in a park. ABCD is a square of side 40 metres. E is the midpoint of AB. F is the midpoint of CD. The circular path is in the centre of the square and has radius 5 metres. B E A C F D 40 m Not to scale (a) Work out the percentage of the square ABCD that is shaded. (a) ...................................................... % [6] (b) Work out the shortest distance from E to F across the park, using only the paths shown. (b) ...................................................... m [4]8 © OCR 2016 Practice paper J560/04 10 In a class of 34 students • 12 study German • 25 study Spanish • 6 do not study either language. One student in the class is selected at random. Find the probability that this student studies both languages. ........................................................... [4]9 © OCR 2016 Practice paper J560/04 Turn over 11 A triangle T is drawn on a coordinate grid. y 0 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 1 T 6 5 4 3 2 (a) Translate triangle T by the vector -- 25 JKKL NOOP . Label your answer V. [2] (b) Describe fully the single transformation that is equivalent to: • a reflection in the line y = x, followed by • a rotation of 90° anti-clockwise about (0, 0). You may use the grid to help you. ................................................................................................................................................... .............................................................................................................................................. [3]10 © OCR 2016 Practice paper J560/04 12 The rectangle has a length (2x + 5) cm and width (x – 2) cm. (2x +5) cm (x– 2) cm Not to scale The rectangle has an area of 35cm2. Use algebra to find the value of x. x = .......................................................... [7]11 © OCR 2016 Practice paper J560/04 Turn over 13 The diagram shows points A, B and C on the circumference of a circle. Line DAE is a tangent to the circle. DE is parallel to BC. Not to scale B A D E C Prove that triangle ABC is an isosceles triangle. Give the reason for each step in your proof. [5]12 © OCR 2016 Practice paper J560/04 14 Jenny is practising the long jump. The table summarises the distances jumped by Jenny. Distance, d (metres) 5 2 . . 1 d G 5 4 5 5 . . 4 6 1 d G 5 5 . . 6 8 1 d G 5 8 . . 1 d G 6 0 6 0 . . 1 d G 6 2 6 6 . . 2 4 1 d G Frequency 3 4 6 8 7 4 (a) Complete the cumulative frequency table. Distance, d (metres) d G 5 4 . d G 5 6 . d G 5 8 . d G 6 0 . d G 6 2 . d G 6.4 Cumulative frequency 3 [2] (b) The cumulative frequency graph below summarises the distances jumped by Fran. (i) How many of Fran’s jumps were less than 5.9 metres long? (b)(i) ........................................................... [1] 35 30 25 20 15 10 5 0 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 Length (metres) Cumulative frequency (ii) On the same diagram, draw the cumulative frequency graph for the distances jumped by Jenny. [2]13 © OCR 2016 Practice paper J560/04 Turn over (c) The box plot shows the distribution of the distances jumped by Jenny. Draw the box plot for the distances jumped by Fran. 5.2 5.3 5.4 5.5 5.6 5.7 5.8 Length (metres) 5.9 6.0 6.1 6.2 6.3 6.4 Jenny Fran [3] (d) Decide whether Jenny or Fran best satisfies each of the following questions. Give a reason for each of your decisions. (i) Who jumps longer on average? ..................................... because ....................................................................................... ...................................................................................................................................... [1] (ii) Who is the more consistent jumper? ..................................... because ....................................................................................... ...................................................................................................................................... [1] (iii) Who might produce the longer jump? ..................................... because ....................................................................................... ...................................................................................................................................... [1]14 © OCR 2016 Practice paper J560/04 15 Some boxes are to be loaded into a van. Each box measures exactly 40cm by 30cm by 50cm. Each box weighs 40kg, correct to the nearest kilogram. The loading space in the van measures exactly 110cm by 90cm by 180cm. The maximum total weight of the boxes that can be loaded into the van is 890kg, correct to the nearest 10 kilograms. Work out the maximum number of boxes that can be loaded into the van without exceeding the weight limit. Show clearly how you worked out your answer. ........................................................... [5]15 © OCR 2016 Practice paper J560/04 Turn over 16 ABD and CBD are triangles. 63° 58° 12.4 cm 8.2cm 5.6 cm A D C B x Not to scale BC = 5.6cm, CD = 8.2cm and AD = 12.4cm. Angle DAB = 63° and angle DBA = 58°. Calculate the angle marked x. .........................................................° [5]16 © OCR 2016 Practice paper J560/04 17 (a) The table shows values of x and y. x 2 4 5 y 12 48 75 Show that y is directly proportional to x2. [2] (b) b is inversely proportional to the square root of a. b is 12 when a is 9. Find a formula linking a and b. (b) ........................................................... [3]17 © OCR 2016 Practice paper J560/04 Turn over 18 Show that n n ( ) n n ( ) n 3 5 1 2 3 1 7 1 + + - = + - + . [3]18 © OCR 2016 Practice paper J560/04 19 Solve these simultaneous equations algebraically. y = x2 – 3x – 4 2x + y = 2 x = ....................... y = ....................... x = ....................... y = .......................[6] END OF QUESTION PAPER19 © OCR 2016 Practice paper J560/04 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE20 © OCR 2016 Practice paper J560/04 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. 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