GCSE (9–1) Mathematics J560/06 Paper 6 (Higher Tier) Practice Paper – Set 3

Document Content and Description Below

GCSE (9–1) Mathematics J560/06 Paper 6 (Higher Tier) Practice Paper – Set 3 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 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 (ST/CGW) 143847/2 Last name First name Candidate number Centre number Oxford Cambridge and RSA GCSE (9–1) Mathematics J560/06 Paper 6 (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 6 *2 © OCR 2016 Practice paper J560/06 Answer all the questions 1 The graph below shows the cost of aluminium by weight. 0 0 500 1000 1500 Cost (£) Weight (tonnes) 2000 2500 3000 3500 2 4 6 (a) Write down the cost of 3 tonnes of aluminium. (a) £ ......................................................... [1] (b) (i) Work out the cost of 17 tonnes of aluminium. (b)(i) £ ......................................................... [3]3 © OCR 2016 Practice paper J560/06 Turn over (ii) What assumption have you made about the cost of aluminium in your calculations for part (b)(i)? ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [1] 2 The probability of each outcome of a computer game is shown in the table below. Outcome Win Lose Draw Probability 0.3 0.25 (a) Complete the table. [2] (b) Cynthia plays the game 30 times. (i) Calculate the number of times Cynthia should expect to win. (b)(i) ........................................................... [2] (ii) Cynthia wins the game 4 times. She says I should have won more times. Explain why she may be wrong. ........................................................................................................................................... ...................................................................................................................................... [1]4 © OCR 2016 Practice paper J560/06 3 The map shows two radio masts, Y and Z. North Y North Z (a) Mast X is on a bearing of 132° from Y and on a bearing of 252° from Z. Mark accurately the position of mast X on the map. [3] (b) The map scale is 2cm represents 25km. (i) The scale can be written in the form 1 : n. Find the value of n. (b)(i) ........................................................... [2] (ii) Work out the actual distance between Y and Z. (ii) ......................................................km [2]5 © OCR 2016 Practice paper J560/06 Turn over 4 Use the formula v r 2GM = to find the value of v when G = 6.67 × 10–11 M = 5.97 × 1024 and r = 6.4 × 106. v = ......................................................... [3]6 © OCR 2016 Practice paper J560/06 5 (a) Three schools provide this information. • 37 of the pupils at Harwood are girls. • 42% of the pupils at Crompton are girls. • The ratio of girls to boys at Astley is 4 : 5. Write the schools in the order of their proportion of girls, lowest to highest. Show how you reached your answer. (a) .......................................... ........................................... .......................................... [4] lowest7 © OCR 2016 Practice paper J560/06 Turn over (b) The pie charts below show the proportion of boys and girls at two other schools. Beechfield Kenwood Girls Girls Boys Boys Neil says The pie charts show that there are more girls at Kenwood than at Beechfield. Explain why Neil may be wrong. ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [1]8 © OCR 2016 Practice paper J560/06 6 Edeston village has a population of 3500 people. A new road is planned. In a survey, school pupils are asked if they are for or against the new road. Number of pupils For 36 Against 24 Hugo assumes responses from the whole village will be in the same proportion as those from the pupils. (a) Use Hugo’s assumption to calculate how many people in Edeston are against the new road. (a) ........................................................... [3] (b) Explain why the responses from the whole village may not be in the same proportion as the responses from the pupils. ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [1]9 © OCR 2016 Practice paper J560/06 Turn over 7 Show that the mean of 5 consecutive numbers is always equal to the median of the 5 numbers. [4]10 © OCR 2016 Practice paper J560/06 8 A mechanic tests the brakes and tyres of 60 cars. A car passes the test if both the brakes and the tyres are not faulty. • 18 cars pass the test. • 20 cars have faulty brakes. • 29 cars have faulty tyres. (a) Put this information into the Venn diagram below. Faulty brakes Faulty tyres ........... ........... ........... ........... E [3] (b) One of these cars is chosen at random. What is the probability that this car has faulty brakes, given that the car failed the test? (b) ........................................................... [2]11 © OCR 2016 Practice paper J560/06 Turn over 9 Simplify fully. (a) k k 3 2 # (a) ........................................................... [1] (b) 3 4 m m 5 # -2 1 (b) ........................................................... [2] (c) ( ) p p p 5 3 3 4 2 # - (c) ........................................................... [3]12 © OCR 2016 Practice paper J560/06 10 The graph below shows the velocity of a train during the first 30 seconds after it leaves a station. Not to scale 0 12 30 k Time (seconds) Velocity (m/s) (a) Show that the train travels a total distance of 24k metres during the 30 seconds. [3] A signal box is 410 metres from the station. (b) At the end of this 30 second period, the train passes the signal box. Find the value of k. Give your answer correct to 3 significant figures. (b) k = ..................................................... [3]13 © OCR 2016 Practice paper J560/06 Turn over (c) You may use this formula. s ut at 12 2 = + (i) A second train passes the station at a velocity of 13m/s. It accelerates at a constant rate after passing the station and 25 seconds later it passes the signal box. Find the acceleration. (c)(i) ...................................................m/s2 [3] (ii) A third train passes the station at 15m/s before accelerating at a constant rate of 0.4m/s2 until it passes the signal box. Find, to the nearest second, the time taken for the train to pass the signal box. (ii) .............................................seconds [5]14 © OCR 2016 Practice paper J560/06 11 Two functions, f and g, are represented by these function machines. Input × 3 + 6 Output Input Function f: Function g: + 2 × 8 Output (a) x is put into function f. The output from function f is then put into function g. Find a simplified expression for the output from function g. (a) ........................................................... [2] (b) A number is chosen. This number is put into both function f and function g. The output from both functions is the same. Work out the number that was chosen. (b) ........................................................... [3]15 © OCR 2016 Practice paper J560/06 Turn over 12 The design is a rectangle with a sector of a circle at each end, as shown below. 5 m Not to scale 2.5 m 140° 140° Show that the perimeter of the design is 19.4m, correct to 3 significant figures. [4]16 © OCR 2016 Practice paper J560/06 13 A white arrowhead is painted on a grey circle. A C B E Not to scale D 56° Points A, B, D and E are on the circumference of the circle, centre C. AD is a line of symmetry. Angle BAE is 56°. Calculate the percentage of the circle that is painted white. ....................................................... % [6]17 © OCR 2016 Practice paper J560/06 Turn over 14 Triangle ABC has sides x, x + 23 and 2x - 1. A B C Not to scale x 2x − 1 x + 23 (a) Verify that, for x = 33, triangle ABC is right-angled. [3] (b) Show that there is only one value of x which makes triangle ABC isosceles. [6]18 © OCR 2016 Practice paper J560/06 15 Javier invests £2400 at a rate of 3.2% per year compound interest. Calculate the total amount of interest he will have earned after 4 years. Give your answer correct to the nearest penny. £ ......................................................... [4] 16 (a) Show that 15 8 2 5 = . [2] (b) Write 8 27 # 3 in the form 3k, where k is a fraction in its simplest form. (b) ........................................................... [3]19 © OCR 2016 Practice paper J560/06 Turn over 17 In the diagram, P is the midpoint of BC. MP is parallel to AC. NP is parallel to AB. M A N P C B Not to scale Prove that triangle MBP is congruent to triangle NPC. [4]20 © OCR 2016 Practice paper J560/06 18 (a) The growth of a population of bacteria is given by the formula P = 30000 × 2.3t where P is the population t hours after 10am. Calculate the population at 4pm on the same day. (a) ........................................................... [2] (b) Another population of bacteria grows by k% each day. After 3 days, the population has doubled. Find the value of k. (b) k = ..................................................... [3] END OF QUESTION PAPER 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. For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE. [Show More]

Last updated: 1 year ago

Preview 1 out of 20 pages