Question Mark out of Pre Paper 2H Practice June 2017 GCSE Mathematics (AQA style) Higher Tier Calculator Practice Paper 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 3.142. 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 80. It is expected that you will need a calculator to answer every question on this paper. In this respect, the topics it includes may not fully reflect the balance or mix of topics tested on a typical paper. 1 1 2 1 3 1 4 1 5 4 6 4 7 3 8 1 9 3 10 6 11 6 12 7 13 5 14 3 15 5 16 5 17 6 18 5 19 7 20 4 21 2 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.
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all questions in the spaces provided 1 What is the value of 5 300 when it is rounded to 2 decimal places? Circle your answer. [1 mark] 0.6 3.13 17.32 60. 2 A circle has radius 6.3cm. What is its circumference? Circle your answer. [1 mark] 19.8cm 39.6cm 124.7cm 498.8cm 3 How many seconds are there in a week? Circle your answer. [1 mark] 3 600 25 200 86 400 604 800 4 Find the value of 3.47 2.45 1.3. Circle your answer. [1 mark] 0.285 1.326 2.82 11.05195 The PiXL Club Limited page 3
5 (a) The number 2017 can be written in the form a 2 + b 2, where a and b are positive integers. Given that a = 9, find the value of b. [2 marks] 5 (b) The number 2017 can also be written in the form p 3 + 2q 3, where p and q are integers. Given that p = 11, find the value of q. [2 marks] The PiXL Club Limited page 4
6 Find the area of triangle ABC. Give your answer to 2 decimal places. A 7cm 11cm B C [4 marks] cm 2 The PiXL Club Limited page 5
7 Paint is sold in two sizes. Standard 400 ml 7.49 Large 1.5 l 27.99 Which size represents the better value for money? Tick a box. The Standard can is better value for money. The Large can is better value for money. You must show your working out. [3 marks] The PiXL Club Limited page 6
8 Use your calculator to find out which two of the following statements are correct. Put a tick in the box next to each correct statement. [1 mark] sin 23 = cos 67 tan 23 = tan ( 23 ) sin 41 = sin 221 cos 58 = cos ( 58 ) 9 The fuel consumption of a car is given by saying that it uses 6.7 litres for every 100 km that it travels. Change this figure into miles per gallon. 1 gallon = 4.546 litres. 1 mile = 1.6 km. [3 marks] mpg The PiXL Club Limited page 7
10 (a) Calculate the value of 3.7 10 2.6 10 15 4. Give your answer in standard form. [2 marks] The table shows the masses of gases in the Earth s atmosphere. Gas Mass (kg) Argon 7.81 10 16 Carbon dioxide 5.04 10 16 Neon 1.82 10 15 Nitrogen 3.08 10 18 Oxygen 7.53 10 17 10 (b) Keith said that the total mass of the Earth s atmosphere is 8.83 10 17, but he missed out one of the gases listed in the table when he made his calculation. State the name of the gas he omitted. Circle your answer. [1 mark] Argon Carbon dioxide Neon Nitrogen Oxygen 10 (c) What percentage of the Earth s atmosphere is made up of oxygen? [3 marks] % The PiXL Club Limited page 8
11 A ladder is 6 metres long. The instructions for using a ladder say that it must be placed so that the angle it makes with the ground is approximately 70. The ladder is placed so that its foot is 2 metres from the base of a wall. 6m This angle must be about 70 Not drawn accurately 2m 11 (a) Is the ladder safe to use in this position? Tick a box. The ladder is safe. The ladder is not safe. You must show your working out. [3 marks] The PiXL Club Limited page 9
11 (b) The ladder can be folded, as shown in the diagram. 3m 50 3m? The instructions say that it must be placed so that the angle at the top is 50. How far apart are the two points at which the ladder touches the floor? [3 marks] m The PiXL Club Limited page 10
12 (a) Which of these calculations decreases 285 by 3%? Circle your answer. [1 mark] 285 0.97 285 1.03 285 1.03 285 3 12 (b) 6000 is invested at 3.5% compound interest. (i) Show that, after two years, the value of the investment has increased to 6427.35. [2 marks] At the end of 2 years, the rate of interest is reduced to 2.5%. (ii) Compare the value of the investment at the end of 5 years with the value of 6000 which had been invested for 5 years at 3% simple interest. [4 marks] The PiXL Club Limited page 11
13 The equation x 3 + 4x 100 = 0 has a solution between 4 and 5. 13 (a) Show that the equation can be written in the form x 3 100 4x [2 marks] 13 (b) Work out an approximate solution to x 3 + 4x 100 = 0. Use the iteration x 3 n 1 100 4xn Start with x 1 5. Give your answer to 2 decimal places. [3 marks] The PiXL Club Limited page 12
14 In a sale, the price of a bicycle is reduced by 15%. Its new price is 408. What was its price before the reduction? [3 marks] The PiXL Club Limited page 13
15 The table summarises the length of time, t minutes, contestants in a crossword solving competition took to solve a crossword puzzle. None of the contestants took longer than an hour to solve the puzzle. Time taken (t minutes) Number of contestants 0 < t 15 5 15 < t 30 42 30 < t 45 37 45 < t 60 16 15 (a) Which class interval contains the median time taken to solve the crossword puzzle? Circle your answer. [1 mark] 0 < t 15 15 < t 30 30 < t 45 45 < t 60 15 (b) Work out an estimate of the mean length of time taken to solve the crossword puzzle. [4 marks] minutes The PiXL Club Limited page 14
16 An object will float in oil if its density is less than 0.7 g/cm 3. An object will float in water if its density is less than 1 g/cm 3. A spherical object has a radius of 0.38 metres. Its mass is 200 kg. Will the object float in oil or water? Tick a box. The object will float in oil and water. The object will float in water but not in oil. The object will not float in oil or water. You must show your working out. 1000 kg/m 3 = 1 g/cm 3. Volume of a sphere = 4 3 π r3. [5 marks] The PiXL Club Limited page 15
17 I have a rectangular lawn that is 7 m long and 4 m wide. I wish to surround it with a gravel path, as shown in the diagram. I have enough gravel to cover an area of 50 m 2. x m Lawn 4 m Not drawn accurately Path x m x m 7 m x m 17 (a) If the area of the path is to be 50 m 2, show that the width of the path in metres, x, satisfies the equation 2x 2 +11x 25 = 0 [3 marks] 17 (b) Find the width of the path. Give your answer to the nearest centimetre. [3 marks] The PiXL Club Limited page 16
18 Don runs 1500 metres in a time recorded as 5 minutes 42.4 seconds. The length of the course was accurate to the nearest metre. The time was measured was accurate to the nearest tenth of a second. By using bounds, find Don s average speed, giving your answer as accurately as you can based on the information you have been given. Justify the level of accuracy that you choose for your answer. [5 marks] m/s The PiXL Club Limited page 17
19 (a) Find the length of the side marked x cm in this triangle. 8.5cm 50 x cm 68 [3 marks] cm The PiXL Club Limited page 18
19 (b) Find the size of the largest angle in this triangle. 6cm 7 cm 11 cm [4 marks] The PiXL Club Limited page 19
20 Metal screws are sold by weight. The table gives information about size A and size B screws. Weight of a bag of screws Number of screws in a bag Length of one screw Size A 200 g 60 4 cm Size B 200 g 100 All size A screws are identical to each other. All size B screws are identical to each other. Size A screws are mathematically similar to size B screws. Find the length of a size B screw. [4 marks] cm The PiXL Club Limited page 20
21 A scientist surveys the population of rabbits in a forest. On 1 January, his survey indicates that there are 600 rabbits in the forest. He says that he can predict the population of rabbits, P, using the formula P = 600 2 0.15t where t is the number of months after 1 January. He says that by 31 December, the population will have grown to more than 2000. Is he correct? Tick a box. Yes, the population will be greater than 2000. No, the population will be less than 2000. You must show your working out. [2 marks] The PiXL Club Limited page 21
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