OCR Oxford Cambridge and RSÄ Tuesday 7 June 2022 GCSE(921) Mathematics J560/05 Paper 5 (Higher Tier) — Morning

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INSTRUCTIONS • Use black ink. You can use an HB pencil, but only for graphs and diagrams. • Write your answer to each question in the space provided. If you need extra space, use the lined pag ... es at the end of this booklet. The question numbers must be clearly shown. • Answer all the questions. • Where appropriate, your answer should be supported with working. Marks might be given for using a correct method even if your answer is wrong. INFORMATION • The total mark for this paper is 100. • The marks for each question are shown in brackets [ ]. • This document has 24 pages. ADVICE • Read each question carefully before you start your answer. Tuesday 7 June 2022 – Morning GCSE (9–1) Mathematics J560/05 Paper 5 (Higher Tier) Time allowed: 1 hour 30 minutes You must have: • the Formulae Sheet for Higher Tier (inside this document) You can use: • geometrical instruments • tracing paper Do not use: • a calculator Oxford Cambridge and RSA OCR is an exempt Charity Turn over 2 © OCR 2022 Answer all the questions. 1 Two pupils are given data that shows the estimated number of computer tablet users worldwide from 2014 to 2018. (a) Li creates this pie chart to show the data. 2014 2015 2016 2017 2018 Number of computer tablet users (billions) Write down two reasons why Li’s pie chart is not suitable to represent the data. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ................................................................................................................................................... [2] 3 © OCR 2022 Turn over (b) Amaya creates this line graph to show the same data. Number of computer tablet users (billions) 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 2014 2015 2016 Year 2017 2018 Work out the percentage increase in the number of computer tablet users from 2014 to 2018. (b) ..................................................... % [4] 4 © OCR 2022 2 The scale diagram below shows the position of two castles, J and K. North K North J Scale: 1 cm represents 2 km The bearing of a tower from castle J is 072°. The bearing of the tower from castle K is 116°. Use construction to find the distance from castle J to the tower. Give your answer to the nearest 0.1 km. .................................................... km [4] 5 © OCR 2022 Turn over 3 Dinosaurs first appeared on Earth 2 4. 108 # years ago. Dinosaurs became extinct on Earth 7 107 # years ago. (a) Explain why it is appropriate to use standard form for these numbers. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [1] (b) Use the given information to work out how long dinosaurs existed on Earth. Give your answer in standard form. (b) .......................................................... [3] 6 © OCR 2022 4 (a) Complete this statement by writing the missing power in the box. 784 = 2 # 72 [1] (b) Use your answer to part (a) to find the value of 784. (b) .......................................................... [2] 7 © OCR 2022 Turn over 5 Recipes measure small quantities in teaspoons and tablespoons. 3 teaspoons is equivalent to 1 tablespoon. A cake recipe uses 4 3 of a teaspoon of salt and 1 tablespoon of baking powder. The ratio of salt to baking powder used in the recipe can be written in the form 1 : n. Find the value of n. n = .................................................... [3] 8 © OCR 2022 6 Morgan is playing a computer game. They can score 0, 1, 2 or 3 points on each turn. They record their scores for 100 turns. The table shows the relative frequencies of their scores. Score 0 1 2 3 Relative frequency 0.08 0.42 0.38 (a) Complete the table. [2] (b) Morgan says I scored more than 160 points in total in my 100 turns. Is Morgan correct? Show how you decide. ............................................................................................................................................. [4] 9 © OCR 2022 Turn over 7 (a) A car accelerates at 4.06 m/s2 for 10.1 seconds from an initial velocity of 2.93 m/s. Harper rounds each value to 1 significant figure. Harper uses the rounded values and the formula s ut at 2 1 = + 2 to estimate the distance travelled in the 10.1 seconds. Harper’s answer is 430 metres. Using Harper’s method, show that their answer is wrong. [4] (b) Rearrange this formula to make t the subject. s at 2 1 = 2 (b) .......................................................... [3] 10 © OCR 2022 8 A bag only contains red marbles, blue marbles and yellow marbles. • The probability of picking a red marble is 5 2 . • There are nine yellow marbles. • The probability of picking a blue marble is three times as likely as picking a yellow marble. Work out the total number of marbles in the bag. You must show your working. .......................................................... [5] 11 © OCR 2022 Turn over 9 The diagram shows the scale drawing of a sandpit, ABCD. It also shows the arc of all points in the sandpit that are 80 cm from corner A. A D B C Scale: 1cm represents 20 cm A game is played by throwing a ball into the sandpit. Points may be scored when the ball lands in the sandpit. • 1 point if the ball lands within 80 cm of corner A, and • 1 point if the ball is closer to side AB than side AD, and • 1 point if the ball is closer to corner A than corner B. By completing the construction, find and shade the regions where 2 points can be scored. Show all your construction lines. [6] 12 © OCR 2022 10 (a) Enlarge triangle A with scale factor 1.5 and centre of enlargement (-8, 0). -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x y 1 2 A 3 4 5 6 7 8 -6 -5 -8 -7 -4 -3 -2 -1 [3] 13 © OCR 2022 Turn over (b) Triangle A and triangle B are shown on the coordinate grid below. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x y 1 2 A B 3 4 5 6 7 8 -6 -5 -8 -7 -4 -3 -2 -1 Triangle A is mapped onto triangle B using a combination of two transformations: • a transformation T, followed by • a reflection in the x-axis. Describe fully transformation T. ................................................................................................................................................... ............................................................................................................................................. [4] 14 © OCR 2022 11 y is inversely proportional to x2. y = 9 when x = 2. Find the value of y when x = 10. y = .................................................... [3] 15 © OCR 2022 Turn over 12 An athlete goes for a training run. The graph shows their speed as they run. 4 0 400 1000 Time (secs) 1200 Speed (m/s) Not to scale (a) Write down the athlete’s acceleration between 400 seconds and 1000 seconds. (a) ................................................. m/s2 [1] (b) Work out the athlete’s average speed, in m/s, during the 1200 s [Show More]

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