Pre Public Examination March 2017 GCSE Mathematics (AQA style) Higher Tier Paper 3H. Question Mark. out of

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1 Question Mark out of Pre Public Examination March 2017 GCSE Mathematics (AQA style) Higher Tier Paper 3H Name Class TIME ALLOWED 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES all the questions. Read each question carefully. Make sure you know what you have to do before starting your answer. You are permitted to use a calculator in this paper. You may use the π button on your calculator or you may take the value of π to be Do all rough work in this book. INFORMATION FOR CANDIDATES The number of marks is given in brackets at the end of each question or part question on the Question Paper. You are reminded of the need for clear presentation in your answers. The total number of marks for this paper is Total 80 The PiXL Club Limited 2017 This resource is strictly for the use of member schools for as long as they remain members of The PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after membership ceases. Until such time it may be freely used within the member school. All opinions and contributions are those of the authors. The contents of this resource are not connected with nor endorsed by any other company, organisation or institution.

2 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED The PiXL Club Limited page 2

3 all questions in the spaces provided 1 Which of these numbers is the biggest? Circle your answer. [1 mark] The first term of a Fibonacci type sequence is 3. The second term of the same sequence is n. What is the fourth term in the sequence? Circle your answer. [1 mark] n + 3 2n + 3 3n 5n A pyramid has six faces. How many edges does it have? Circle your answer. [1 mark] Which of these ratios are always equivalent to 2 : 4? Circle both the correct answers. [1 mark] 2x : 4x x + 2 : x + 4 x x x : x : The PiXL Club Limited page 3

4 5 Mary sells hot drinks at a cafeteria. She records the numbers of hot drinks that she sells on each of the twelve days. She also records the temperature at midday on each of those days. She displays her data on the scatter diagram. The data for one of the days is missing. 150 S Number of hot drinks sold Temperature at midday ( C) 5 (a) On one day, the temperature at midday was 22 C, and Mary sold 40 hot drinks. Show this information on the scatter diagram. [1 mark] 5 (b) The diagram shows a negative correlation. Describe the relationship between the temperature at midday and the number of hot drinks Mary sells. [1 mark] The PiXL Club Limited page 4

5 5 (c) Use the diagram to estimate the number of hot drinks Mary could expect to sell on a day when the temperature at midday is 18 C. [2 marks] 5 (d) The point representing the data for one day is labelled S. Describe what you think happened on this day. [1 mark] The PiXL Club Limited page 5

6 6 Solve the equation 7x + 4 = 3x 10. [2 marks] 7 (a) Find the value of Write down all the numbers on your calculator display. [2 marks] 7 (b) Round your answer to 7 (a) to three significant figures. [1 mark] The PiXL Club Limited page 6

7 8 40 c b d a (a) Which of the following is a pair of alternate angles? Circle your answer. [1 mark] a and b a and c b and c b and d 8 (b) Find the size of the angle marked a. [3 marks] The PiXL Club Limited page 7

8 9 A solid is made using 1cm cubes. The front elevation, side elevation and plan view of the solid are each drawn on 1cm grids. front elevation side elevation plan view How many 1cm cubes are used to make the solid? Circle your answer. [1 mark] You may use the isometric grid below to help work out your answer. The PiXL Club Limited page 8 The PiXL Club Limited page 8

9 10 Jonathan runs a lucky dip stall. Lucky Dip Tickets cost 50p each If the number of the ticket ends with a 5, you win 1.50 If the number on the ticket is a multiple of 100, you win 20 There are 600 tickets, numbered from 1 to 600. Jonathan sells all the tickets. Does Jonathan make a profit? Tick a box. Yes. No. You must show how you obtain your answer. [3 marks] The PiXL Club Limited page 9

10 11 The lengths of 50 earthworms were measured. The results are given in the table. Length, x cm Midpoint Frequency 0 < x < x < x < x 40 1 Total = (a) Which class interval contains the median length of the earthworms? Circle your answer. [1 mark] 0 < x < x < x < x 40 The PiXL Club Limited page 10

11 11 (b) Calculate an estimate for the mean length of an earthworm. [3 marks] cm 11 (c) You are now told that one of the earthworms in the sample is 40cm long. How does this change the estimate you obtained in 11 (b)? Tick a box. It increases my estimate. It decreases my estimate. It does not change my estimate. Give a reason for your answer. You do not need to make any further calculations. [2 marks] The PiXL Club Limited page 11

12 12 I see this sign on the motorway while I am on holiday in Spain. Madrid 420 km I know that my car does an average of 56 miles on one gallon of fuel. When it is full, my car s fuel tank holds 10.5 gallons of fuel. The tank is two thirds full. The car s manual says I should never allow the amount of fuel in the tank to fall below 20% of the tank s capacity. Do I have enough fuel to reach Madrid? Tick a box. Yes, I have enough fuel. No, I need more fuel. You may use this conversion: 5 miles = 8 kilometres You must show how you obtain your answer. [4 marks] The PiXL Club Limited page 12

13 13 y P ( 0, 2 ) Q ( 6, 0 ) x Not drawn accurately R In the diagram, PQ is perpendicular to QR. P is at the point ( 0, 2 ). Q is at the point ( 6, 0 ). R lies on the y axis. 13 (a) Find the equation of the line passing through the points P and Q. [2 marks] 13 (b) Find the equation of the line passing through the points Q and R. [3 marks] The PiXL Club Limited page 13

14 14 Solve the simultaneous equations 2a 3b = 13 4a + 5b = 4. [3 marks] a = b = The PiXL Club Limited page 14

15 15 The Venn diagram shows information about the numbers of trees in a forest. ξ = trees in the forest. A = trees with red berries. B = trees that shed their leaves in winter. There are 750 trees in the forest. ξ A B (a) The ratio of the number of trees with red berries to the number of trees that shed their leaves in winter is 3 : 5. Complete the Venn diagram. [3 marks] 15 (b) A tree with red berries is chosen at random. What is the probability that it sheds its leaves in winter? [2 marks] The PiXL Club Limited page 15

16 16 Calculate the size of the angle marked y in this diagram. y 6cm Not drawn accurately 11cm [2 marks] 17 In a sale, all prices are reduced by 35%. What was the original price of a jacket that is reduced to 104 in the sale? [2 marks] The PiXL Club Limited page 16

17 18 Find all the integers that satisfy the inequality 2 < 3x [2 marks] 19 A function is defined as f(x) = x Find f 1 (x). [2 marks] The PiXL Club Limited page 17

18 20 D x Not drawn accurately O C 26 B A The diagram shows a circle, centre O. A, C and D are points on the circumference of the circle. The line AB is a tangent to the circle. Find the size of angle CDA, marked x on the diagram. Give reasons for each stage of your working out. [3 marks] The PiXL Club Limited page 18

19 21 (a) You are told that y is inversely proportional to x 2. Which of the following graphs represents the relationship between x and y? Circle the correct letter. [1 mark] y A y B x x y C y D x x 21 (b) You are now also told that y = 52 when x = 2. Find the value of y when x = 4. [3 marks] The PiXL Club Limited page 19

20 22 The area of this trapezium is 24cm 2. The lengths of three of its sides are given, in terms of x, on the diagram. x 3x Not drawn accurately 2x (a) Show that 3x 2 + 5x 16 = 0. [2 marks] 22 (b) Find the perimeter of the trapezium. Give your answer to three significant figures. [6 marks] cm The PiXL Club Limited page 20

21 23 You are told that 5 is a solution of the equation x x x Use the iterative formula x x 5 n n+ 1 = +, 2 2xn with x 1 = 2.5, to find the value of 5 to three decimal places. [3 marks] The PiXL Club Limited page 21

22 24 Alan wants to store his collection of DVDs. He measures the thickness of a DVD case to be 1.5cm, to the nearest millimetre. He sees a shelf in a shop that is 40cm long, to the nearest centimetre. What is the greatest number of DVD cases that Alan can be sure the shelf will hold? [3 marks] The PiXL Club Limited page 22

23 25 P 7cm Not drawn accurately Q 9cm 35 R PQR is a triangle. The length of PQ is 7cm. The length of QR is 9cm. The size of angle QRP is 35. Find the area of triangle PQR. [6 marks] cm 2 The PiXL Club Limited page 23

24 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED The PiXL Club Limited page 24