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1 For Edexcel Name GCSE Mathematics Paper 4H (Calculator) Higher Tier Time: 1 hour and 45 minutes Materials required Ruler, protractor, compasses, pen, pencil, eraser. Tracing paper may be used. Instructions and Information for Candidates Write your name in the box at the top of the page. Answer all the questions in the spaces provided in this question paper. The marks for each question and for each part of a question are shown in brackets. The total number of marks for this paper is 100. There are 22 questions in this paper. Calculators may be used. If your calculator does not have a π button, take the value of π to be unless the question instructs otherwise. Advice to Candidates Show all stages in any calculation. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Return at the end to those you have left out. Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college EH4H 09 Page 1

2 GCSE Mathematics Formulae: Higher Tier Volume of a prism = area of cross section length cross section length Volume of sphere = 4 3 πr3 Surface area of sphere = 4πr 2 Volume of cone = 1 3 πr2 h Curved surface area of cone = πrl r l h r In any triangle ABC b C a The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0, are given by x = b± b2 4ac 2a A c B Sine Rule a sin A = b sin B = c sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C EH4H 09 Page 2

3 Answer ALL TWENTY TWO questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1. Jenny buys 350 g of pick 'n' mix sweets for 2.17 Jill buys 500 g of pick 'n' mix sweets from the same shop. Work out how much Jill pays for her sweets. Q1 (Total 3 marks) 2. (a) Solve the inequality 5x + 12 > 2 (b) Represent your answer to part (a) on the number line below x (1) (Total 3 marks) Q2 EH4H 09 Page 3

4 3. Rob went out for a run. This travel graph shows part of his journey. Distance from home (km) Time in minutes 90 (a) Find Rob's average speed during the first 30 minutes of his journey. Give your answer in kilometres per hour. After running for 30 minutes, Rob stopped and rested for 10 minutes. He then jogged home at a speed of 8 km/h. km/h (b) Complete the travel graph. (3) (Total 5 marks) Q3 EH4H 09 Page 4

5 4. Diagram NOT B accurately drawn D 116 p 40 A q AB and CD are parallel lines. C (a) (i) Write down the size of the angle marked p. (ii) Give a reason for your answer. (b) Find the size of the angle marked q. (Total 4 marks) Q4 EH4H 09 Page 5

6 5. On the grid, draw the graph of 3x + 2y = 6 y O x 1 Q5 (Total 4 marks) EH4H 09 Page 6

7 6. Mark records the distance he travels and his average speed each time he goes cycling. The scatter graph shows information about 8 of his rides. Average speed (km/h) Distance (km) The table gives information for 2 more of Mark's rides. Distance (km) Average speed (km/h) (a) (b) On the scatter graph, plot the information from the table. What type of correlation does this scatter graph show? (1) (1) On another cycle ride, Mark's average speed is 25.6 km/h. (c) Use the graph to estimate the distance Mark cycled. km (Total 4 marks) Q6 EH4H 09 Page 7

8 7. The equation y 3 + 2y = 4 has a solution between 1 and 2. Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working. y = Q7 (Total 4 marks) EH4H 09 Page 8

9 8. Omar is using an elastic band to make quadrilaterals on a pin-board. The pin-board has 9 pins on a centimetre square grid. Here is a trapezium Omar made with an area of cm2. (a) Show one way in which Omar can make a trapezium with an area of 3 cm 2. (1) (b) Show one way in which Omar can make a square with an area of 2 cm 2. (1) (c) Show one way in which Omar can make a kite, with diagonals of different lengths, with an area of 2 cm 2. (1) (Total 3 marks) Q8 EH4H 09 Page 9

10 9. Solve each equation (a) 2y 5 = 13 y = (b) 4(z + 3) = 3(2z + 3) z = (3) (Total 5 marks) Q9 10. The table shows information about the area of 100 gardens. Area (A m 2 ) Frequency 0 A < A < A < A < A < A < (a) Complete the cumulative frequency table. Area (A m 2 ) Cumulative Frequency 0 A < A < 80 0 A < A < A < A < 240 (1) EH4H 09 Page 10

11 (b) On the grid, draw a cumulative frequency graph for your table. Cumulative Frequency O Area (A m 2 ) (c) Use your graph to estimate how many of these gardens have an area of less than 100 m 2. (1) (d) Use your graph to estimate the interquartile range of the areas of the gardens. m 2 (Total 6 marks) Q10 EH4H 09 Page 11

12 11. (a) Simplify 7p 3q + p 2q (b) Simplify (2a 2 ) 3 (c) Simplify fully x 2 3 x x 2 7 x 12 (3) (Total 7 marks) Q Tanya pays 420 rent each month for her flat. 18% of her rent pays the Council Tax. (a) Work out 18% of 420. Tanya's rent is 12% more than her rent last year. (b) Work out how much rent Tanya paid each month last year. (3) (Total 5 marks) Q12 EH4H 09 Page 12

13 13. A bag contains 20 plastic tiles for use in a game of scrabble. There are 18 tiles with a letter printed on them. 7 of these letters are vowels and the rest are consonants. There are also 2 blank tiles. One tile is picked at random from the bag. (a) Write down the probability that the tile (i) is blank, (ii) does not have a vowel on it. (3) Some tiles are removed from the bag. When a tile is now picked from the bag, the probability that it has a vowel on is 1 2. (b) (i) What is the smallest number of tiles that could have been removed from the bag? (ii) Explain your answer. (Total 5 marks) Q13 EH4H 09 Page 13

14 14. Diagram NOT accurately drawn 12 cm 28 cm The end of a solid cylinder is a circle with a diameter of 12 cm. The cylinder is 28 cm long. Work out the curved surface area of the cylinder. State the units of your answer. Q14 (Total 4 marks) 15. A picometre is m. Graphite is made up of layers that are m apart. (a) How many picometres are there in m. (b) Calculate the number of layers there are in a piece of graphite that is 1 cm thick. Give your answer in standard form correct to an appropriate degree of accuracy. (3) (Total 5 marks) Q15 EH4H 09 Page 14

15 16. The graph of y = f(x) is shown on the grids. (a) On this grid, sketch the graph of y = f(x) + 1 y O x 1 y = f(x) (b) On this grid, sketch the graph of y = f(2x) y O x 1 y = f(x) (Total 4 marks) Q16 EH4H 09 Page 15

16 17. Diagram NOT accurately drawn O N 34 P L M L, M and N are points on a circle, centre O. LN and OM intersect at P. Angle LNM = 34. Angle NPO = 90. (a) (i) Write down the size of angle LOM. (ii) Give a reason for your answer. (b) Hiro says that P is the midpoint of LN. Is he correct? Give a reason for your answer. (Total 4 marks) Q17 EH4H 09 Page 16

17 18. Lisa wants to find out the density of copper. She records the mass of a piece of copper as 23 grams and its volume as 2.6 cm 3. Both measurements are correct to 2 significant figures. Calculate the maximum possible density of copper. grams per cm 3 Q18 (Total 4 marks) 19. Solve 2 x x 1 = 1 Q19 (Total 5 marks) EH4H 09 Page 17

18 20. B Diagram NOT accurately drawn C A D 10 cm F G E 7 cm H 5 cm ABCDEFGH is a cuboid with sides of length 5 cm, 7 cm and 10 cm. Calculate the size of angle ACE. Give your answer correct to 1 decimal place. Q20 (Total 4 marks) EH4H 09 Page 18

19 21. The table shows the percentage pupil absence at a school over five terms. Year Term Autumn Spring Summer Autumn Spring Summer % Absence The first three-point moving average is 11.0% (a) Work out the second three-point moving average. % The figure for the Summer term 2008 is 9.5% The headteacher says that this shows that the school is continuing to rapidly reduce the level of absence. (b) Work out the third and fourth three-point moving averages and comment on the headteacher's claim. (3) (Total 5 marks) Q21 EH4H 09 Page 19

20 22. C D Diagram NOT accurately drawn B G E A 6 cm F ABCDEF is a regular hexagon of side 6 cm. The straight lines AC and BD intersect at G. (a) Find the exact length of AC in the form k 3. cm (3) (b) Show that triangle BCG is similar to triangle ABC. (c) Show that BG = 2 3. (Total 7 marks) Q22 TOTAL FOR PAPER: 100 MARKS END EH4H 09 Page 20

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