GCSE (9–1) Mathematics J560/06 Paper 6 (Higher Tier) - Practice Paper - Model Solutions

Sep 5, 2026

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Practice paper model solutions for GCSE (9–1) Mathematics (J560/06), focusing on problem-solving across fractions, ratio, right-triangle testing with the Pythagorean theorem, solving linear equations and inequalities, distance–time–speed calculations, percent increase in freezing, and interpreting data tables. Geometry and coordinate geometry tasks include sectors of circles, coordinate-grid triangle construction, and full descriptions of composite transformations, plus equation finding for lines through given points.

LanguageEnglish

CategoryExam

FormatPDF

Pages16

Reading Time40 min

AccessFree to download

Answer the questions

Algebra and inequalities

Geometry and measures

Coordinate geometry and transformations

Statistics and real-world calculations

MODEL SOLUTIONS GCSE (9–1) Mathematics J560/06 Paper 6 (Higher Tier) Practice Paper H Date – Morning/Afternoon Time allowed: 1 hour 30 minutes *0000000000* You may use: • A scienti􀀌c or graphical calculator • Geometrical instruments • Tracing paper *000000** 0 0 0 0 0 0 * | First name | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Last name | | | | | | | | | | | | | | | | | | | | | | | | | | Centre | | | | | | | Candidate | | | | | | number | | | | | | | number | | | | | INSTRUCTIONS • Use black ink. You may use an HB pencil for graphs and diagrams. • Complete the boxes above with 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 bar codes. INFORMATION • The total mark for this paper is 100. • The marks for each question are shown in brackets [ ] . • Use the π button on your calculator or take π to be 3 . 142 unless the question says otherwise. • This document consists of 16 pages. © OCR 2015 J560/06 Turn over [601/4606/0] 2 Answer all the questions 1 A bakery bakes small, medium and large pies. The ratio small : medium : large is 3 : 5 : 2 . (a) What fraction of the pies are large? (a) .................................. [1] (b) One day 460 medium pies are baked. Work out how many small pies are baked. (b) .................................. [2] 2 A triangle has sides of length 23 .8cm, 31 .2cm and 39 .6 cm. Is this a right-angled triangle? Show how you decide. a + b = c 23.8 + 31.2 = 1539.88 1539.88 = 39.2 39.2 = 39.6, so the triangle is not right-angled. Pythagorean Theorem .................................................................................................................................................... [4] © OCR 2015 J560/06 3 (a) Solve. 4x − 7 = 8 − 2x 3 4x-7 = 8-2x 6x-7 = 8 6x = 15 x = 2 .5 (a) x = ................................. [3] 2 .5 (b) Solve this inequality. 5x + 9 > 13 © OCR 2015 J560/06 Turn over 4 4 John is going to drive from Cambridge to Newcastle. Scale: 1cm represents 50miles Newcastle Cambridge (a) John needs to be in Newcastle at 11 am. He drives at an average speed of 60 miles per hour. What time does he need to leave Cambridge? time = distance speed = 4 X 50 60 = 10 3 = 3 hours X 60 = 20 minutes 11am-3hrs-20 mins = 7:40am (a) .................................. 7:40am [5] © OCR 2015 J560/06 5 (b) State one assumption you have made. Explain how this has affected your answer to part (a) . | | | --- | | | ............................................................................................................................................. [2] 5 When water freezes into ice its volume increases by 9% . What volume of water freezes to make 1962cm3 of ice? Assumed distance is a straight line, so distance is an underestimate and time taken will increase. 1962-1.09 = 1800cm © OCR 2015 J560/06 Turn over 6 6 The table shows data for the UK about its population and the total amount of money spent on healthcare in 2002, 2007 and 2012 . | Year | Population | Total spent on healthcare 􀀀£􀀁 | | --- | --- | --- | | 2002 | 5.94 × 107 | 8.14 × 1010 | | 2007 | 6.13 × 107 | 1.20 × 1011 | | 2012 | 6.37 × 107 | 1.45 × 1011 | (a) How much more was spent on healthcare in 2007 than in 2002? Give your answer in millions of pounds. (1.20 X 10 ) - (8.14 X 10 ) = £3.86 X 10 = 38,600 million

FAQs

What topics are covered in this GCSE Mathematics practice paper?

The paper includes fractions and ratios, right-triangle checks using the Pythagorean theorem, solving linear equations and inequalities, distance–speed–time problems, percentage change, data interpretation, and geometry on coordinate grids.

How is the right-angled triangle question decided?

Students compare the squared side lengths using the Pythagorean theorem and check whether the calculation matches the longest side; if it does not, the triangle is not right-angled.

What is required in the transformation question about triangle A to triangle B?

You must draw and label triangle B after applying the given rotation and reflection steps, and then describe transformation T fully for the second mapping approach.

Sep 5, 2026

Upload by Rowan