OCR Oxford Cambridge and RSA Monday 13 June 2022 GCSE (9—1) Mathematics J560/06 Paper 6 (Higher Tier) — Morning

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Monday 13 June 2022 – Morning GCSE (9–1) Mathematics J560/06 Paper 6 (Higher Tier) Time allowed: 1 hour 30 minutes © OCR 2022 [601/4606/0] DC (PQ/SG) 300050/3 *8362186710* H You must ha... ve: • the Formulae Sheet for Higher Tier (inside this document) You can use: • a scientific or graphical calculator • geometrical instruments • tracing paper 2 © OCR 2022 Answer all the questions. 1 A student rolls two fair four-sided dice each numbered 1, 2, 3 and 4. They add the two scores together. (a) Complete the sample space diagram to show the possible outcomes from the dice. Second dice Total 1 2 3 4 1 2 First dice 2 3 4 8 [2] (b) Find the probability that the student gets an even total. (b) .......................................................... [1] (c) Find the probability that the student gets the same score on each dice. (c) .......................................................... [1] 2 The circumference of a circle is 23 cm. Show that the area of the circle is 42.1 cm2, correct to 3 significant figures. [4] 3 © OCR 2022 Turn over 3 Light from the Sun travels 1 kilometre in 3 3. 10 6 # - seconds. The distance from the Sun to the Earth is 1 5. 108 # kilometres. How long does it take light to travel from the Sun to the Earth? Give your answer in minutes and seconds. ............... minutes .............. seconds [4] 4 You are given that ma 10a a a 5 2 k 5 8 7 # = where k and m are integers. Find the value of k and the value of m. k = .................... and m = ..................... [4] 4 © OCR 2022 5 In each row of the table there are two triangles. State whether the two triangles are congruent or not. If they are congruent state a reason from SSS, SAS, ASA or RHS. Triangles Congruent (yes/no) Reason (SSS/SAS/ASA/RHS) Not to scale 8 cm 8cm 10cm 10 cm 11 cm 11 cm Not to scale 6 cm 7 cm Not to scale 9cm 9 cm 40° 50° 40° 6 cm 7 cm 50° [3] 5 © OCR 2022 Turn over 6 The mass of a stone is 680 g. The density of the stone is 1.6 g / cm3. (a) Work out the volume of the stone. (a) .................................................. cm3 [2] (b) Write 1.6 g / cm3 in kg / m3. (b) ............................................. kg / m3 [1] 7 (a) Multiply out and simplify. _ _ x x - + 4 5 i i (a) .......................................................... [2] (b) Factorise. x 25 2 - (b) .......................................................... [1] 6 © OCR 2022 8 1600 fish are released into a new lake which has no fish. The number of fish is expected to increase by 5% each year. (a) The table shows the expected number of fish in the lake at the end of 1 year and at the end of 2 years. Complete the table. Round your answers to the nearest integer. Years after release 0 1 2 3 4 Expected number of fish 1600 1680 1764 [3] (b) Use the table to draw a suitable graph to show the expected number of fish in the lake. 0 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 2050 1 2 Years after release Expected number of fish 3 4 [3] 7 © OCR 2022 Turn over (c) A maximum of 2000 fish can live in the lake. What effect would you expect this to have on the shape of your graph after 4 years? ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [2] 9 A garage is trying to sell a car. The price of the car is normally £18 000. In a sale, the price of the car is reduced by 30%. As a special offer, the sale price is then reduced by r %. The special offer price is £9450. Find the value of r. You must show your working. r = .......................................................... [5] 8 © OCR 2022 10 The diagram shows a triangular prism and a cube. The ends of the prism are right-angled triangles with base 16 cm and height 12 cm. The prism is 18 cm long. 12 cm 16 cm 18 cm The volume of the prism is equal to the volume of the cube. Find the surface area of the cube. Y ou must show your working. ................................................. cm2 [6] 9 © OCR 2022 Turn over 11 Amir, Beth and Charlie work in a cafe. Customers give spare change as tips. At the end of each week, Amir, Beth and Charlie share the total amount of tips between them in the ratio matching the number of hours they worked that week. This week: • Amir’s share of the tips was £25.40. • Beth worked twice as many hours as Amir. • Charlie worked 5 more hours than Amir. • The total hours worked by Amir, Beth and Charlie was 85 hours. Calculate the total amount of tips received this week. You must show your working. £ .......................................................... [6] 10 © OCR 2022 12 A student has a spinner with sectors numbered 1, 2, 3 and 4. 1 2 3 4 The table shows the probability of [Show More]

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