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2 International GCSE MATHEMATICS FORMULAE SHEET HIGHER TIER Pythagoras 1 Volume of cone = 3 r 2 h Theorem c Curved surface area of cone = b a a 2 + b 2 = c 2 hyp cross section adj r r opp length adj = hyp opp = hyp opp = adj or sin cos tan cos sin tan opp hyp adj hyp opp adj Volume of prism = area of cross section h Circumference of circle = 2 Area of circle = r 2 Volume of cylinder = r 2 h Curved surface area of cylinder = 2 rh l r r In any triangle ABC C A b a Sine rule: sin A 2 Cosine rule: a b c 2bc cos A length Area of triangle c b sin B Area of a trapezium = a h b a B c sin C ab sin C 1 (a+b)h 2 The Quadratic Equation 2 The solutions of ax + bx + c 0, where a 0, are given by x Volume of sphere = b+ 2 b 4ac 2a 1 2 r rl Surface area of sphere = 4 h r r 2 2 *P45841A0224*

3 Answer ALL TWENTY TWO questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Here are the ingredients needed to make 12 muffins. Sarah makes 60 muffins. (a) Work out how much sugar she uses. James makes some muffins. He uses 625 ml of milk. (b) How many muffins did he make? Ingredients to make 12 muffins 300g flour 150g sugar 250ml milk 100g butter 2 eggs... g (2)... (2) (Total for Question 1 is 4 marks) *P45841A0324* 3 Turn over

4 2 a c (a) Work out the value of 2a 2 + 6c There are 4 pens in a small box of pens. There are 10 pens in a large box of pens. Ami buys x small boxes of pens and y large boxes of pens. She buys a total of T pens. (b) Write down a formula for T in terms of x and y.... (2)... (3) (Total for Question 2 is 5 marks) 4 *P45841A0424*

5 3 The table shows information about the number of visits each of 40 adults made to the gym last week. Number of visits to the gym Frequency Work out the mean of the number of visits to the gym. 4 A = {2, 4, 6, 8, 10, 12, 14} B = {1, 3, 5, 7, 9, 11, 13} C = {3, 6, 9, 12} (a) List the members of the set (i) A C (ii) A C (b) Explain why A B = Ø... (Total for Question 3 is 3 marks) (2)... (1) (Total for Question 4 is 3 marks) *P45841A0524* 5 Turn over

6 5 On the grid, draw the graph of y = 3x 5 for values of x y O x (Total for Question 5 is 4 marks) 6 *P45841A0624*

7 6 (a) Show that = (b) Show that = (2) (3) (Total for Question 6 is 5 marks) *P45841A0724* 7 Turn over

8 7 (a) Factorise 3y 2 + 2y (b) Expand and simplify (x 9)(x + 2) (c) (i) Solve 6k + 5 < 20 (ii) n is an integer and 6n + 5 < 20 Write down the largest possible value of n (d) Simplify fully 28x y 4xy (1)... (2) (3)... (2) (Total for Question 7 is 8 marks) 8 *P45841A0824*

9 8 A C 53 Work out the length of AB. Give your answer correct to 1 decimal place cm B Diagram NOT accurately drawn... cm (Total for Question 8 is 3 marks) *P45841A0924* 9 Turn over

10 9 Bhavin, Max and Imran share 6000 rupees in the ratios 2 : 3 : 7 Imran then gives 3 of his share of the money to Bhavin. 5 What percentage of the 6000 rupees does Bhavin now have? Give your answer correct to the nearest whole number.... % (Total for Question 9 is 5 marks) 10 *P45841A01024*

11 10 The diagram shows a circle inside a rectangle. 2.5 cm 13.8 cm Work out the area of the shaded region. Give your answer correct to 3 significant figures. 7.6 cm Diagram NOT accurately drawn... cm 2 (Total for Question 10 is 3 marks) *P45841A01124* 11 Turn over

12 11 The frequency table shows information about the weights of 80 adults. Weight (w kg) Frequency 40 < w < w < w < w < w < w < w (a) Complete the cumulative frequency table. Weight (w kg) Cumulative frequency 40 < w < w < w < w < w < w < w 110 (1) 12 *P45841A01224*

13 (b) On the grid, draw a cumulative frequency graph for your table. (2) Cumulative frequency Weight (w kg) (c) Use your graph to find an estimate for the number of adults with weight more than 85 kg. (d) Use your graph to find an estimate for the interquartile range of the weights of the adults.... (2)... kg (2) (Total for Question 11 is 7 marks) *P45841A01324* 13 Turn over

14 12 Solve the simultaneous equations 4x + 5y = 13 3x 2y = 27 Show clear algebraic working. x =... y =... (Total for Question 12 is 4 marks) 14 *P45841A01424*

15 13 The straight line L Find an equation of the line that is parallel to L Give your answer in the form ax + by = c where a, b and c are integers.... (Total for Question 13 is 5 marks) *P45841A01524* 15 Turn over

16 14 A particle is moving along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds is s metres where s = 2t 3 12t 2 + 7t (a) Find an expression for the velocity, v m/s, of the particle at time t seconds. (b) Find the time at which the acceleration of the particle is instantaneously zero. v =... (2)... seconds (2) (Total for Question 14 is 4 marks) 16 *P45841A01624*

17 15 The diagram shows two mathematically similar vases, A and B. A Vase A has a surface area of 120 cm 2 Vase B has a surface area of 750 cm 2 and a volume of 1600 cm 3 Work out the volume of vase A. B Diagram NOT accurately drawn... cm 3 (Total for Question 15 is 3 marks) *P45841A01724* 17 Turn over

18 16 ABCDEFGH is a cuboid. The cuboid has C H length 17 cm width 5 cm height 8 cm D E 17 cm Work out the size of the angle that AH makes with the plane EFGH. Give your answer correct to 1 decimal place. G B A 8 cm F 5 cm Diagram NOT accurately drawn... (Total for Question 16 is 4 marks) 18 *P45841A01824*

19 17 The diagram shows a trapezium. x 1 x + 6 3x 4 All measurements on the diagram are in centimetres. The area of the trapezium is 119 cm 2 (i) Show that 2x 2 x 120 = 0 (ii) Find the value of x. Show your working clearly. Diagram NOT accurately drawn x =... (Total for Question 17 is 6 marks) *P45841A01924* 19 Turn over

20 18 Make t the subject of the formula m = t t (Total for Question 18 is 4 marks) 20 *P45841A02024*

21 19 A Diagram NOT accurately drawn A, B, C and D are points on a circle, centre O. Angle DAB = 75 Angle DBC = 27 Work out the size of angle ODC. C D O B... (Total for Question 19 is 4 marks) *P45841A02124* 21 Turn over

22 20 A metal cube has sides of length 4.5cm, correct to the nearest 0.5cm. The cube is melted down and the metal is used to make small spheres. Each sphere has a radius of 3mm, correct to the nearest millimetre. Work out the greatest number of spheres that could be made from the metal. Show your working clearly.... (Total for Question 20 is 5 marks) 22 *P45841A02224*

23 21 There are 9 counters in a bag. There is a number on each counter Kal takes at random 3 counters from the bag. He adds together the numbers on the 3 counters to get his Total. Work out the probability that his Total is 6... (Total for Question 21 is 5 marks) *P45841A02324* 23 Turn over

24 22 The diagram shows a pentagon. 12 cm 12 cm cm 8 cm 13 cm Work out the area of the pentagon. Give your answer correct to 3 significant figures. Diagram NOT accurately drawn... cm 2 (Total for Question 22 is 6 marks) TOTAL FOR PAPER IS 100 MARKS 24 *P45841A02424*

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