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2 GCSE Mathematics (Linear) 1380 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of a prism = area of cross section length cross section length 4 3 Volume of sphere = πr 3 Volume of cone = πr 2 h Surface area of sphere =4πr 2 Curved surface area of cone = πrl 1 3 r l h r In any triangle ABC C b A c a B The Quadratic Equation The solutions of ax 2 + bx + c =0 where a 0, are given by b± b ac x = 2a 2 ( 4 ) Sine Rule a = b = c sin A sin B sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *N34730A0224*

3 Answer ALL TWENTY SIX questions. Write your answers in the spaces provided. You must write down all stages in your working. You must NOT use a calculator. 1. The two-way table gives some information about how 100 children travelled to school one day. Walk Car Other Total Boy Girl 8 16 Total (a) Complete the two-way table. (3) One of the children is picked at random. (b) Write down the probability that this child walked to school that day. (1) Q1 2. (a) Simplify 4x + 3y 2x + 5y Compasses cost c pence each. Rulers cost r pence each. (b) Write down an expression for the total cost, in pence, of 2 compasses and 4 rulers. *N34730A0324*... pence Q2 3 Turn over

4 3. (a) Complete the table of values for y = 4x 3 x y (b) On the grid, draw the graph of y = 4x 3, for values of x from 2 to 3 y O x Q3 4 *N34730A0424*

5 4. P = 4k 10 P = 50 (a) Work out the value of k. y = 4n 3d n = 2 d = 5 (b) Work out the value of y. Q4 *N34730A0524* 5 Turn over

6 5. y O x (a) Rotate the shaded shape 90 clockwise about the point O. y P Q O x (b) Describe fully the single transformation that will map shape P onto shape Q.... Q5 6 *N34730A0624*

7 6. 4x + 1 Diagram NOT accurately drawn x x 2x + 12 The diagram shows a rectangle. All the measurements are in centimetres. (a) Explain why 4x + 1 = 2x (1) (b) Solve 4x + 1 = 2x + 12 x =... (c) Use your answer to part (b) to work out the perimeter of the rectangle.... cm Q6 (Total 5 marks) *N34730A0724* 7 Turn over

8 7. Use the information that to find the value of (a) = (1) (b) (1) (c) (1) Q7 (Total 3 marks) 8. 2x 2 = 72 (a) Find a value of x. (b) Express 72 as a product of its prime factors.... Q8 8 *N34730A0824*

9 9. Here are the plan and front elevation of a solid shape. Plan Front Elevation (a) On the grid below, draw the side elevation of the solid shape. (b) In the space below, draw a sketch of the solid shape. Q9 *N34730A0924* 9 Turn over

10 10. There are 40 litres of water in a barrel. The water flows out of the barrel at a rate of 125 millilitres per second. 1 litre = 1000 millilitres. Work out the time it takes for the barrel to empty completely.... seconds Q10 (Total 3 marks) 10 *N34730A01024*

11 11. The length of a line is 63 centimetres, correct to the nearest centimetre. (a) Write down the least possible length of the line. (b) Write down the greatest possible length of the line.... centimetres (1)... centimetres (1) Q11 (Total 2 marks) 12. A B C ABC is a triangle. Shade the region inside the triangle which is both and less than 4 centimetres from the point B closer to the line AC than the line AB. Q12 *N34730A01124* 11 Turn over

12 13. Fred is going to take a survey of the magazines read by students. He wants to design a questionnaire. (a) Design a suitable question that he could use to find out what types of magazine students read. Fred put the question below on his questionnaire. How many magazines have you read? A few A lot (b) Design a better question. You should include some response boxes. Q13 12 *N34730A01224*

13 14. Work out an estimate for the value of Q14 (Total 3 marks) 15. (a) Write in standard form. (1) (b) Write in standard form. (1) Q15 (Total 2 marks) 16. (a) Factorise fully 4x 2 6xy (b) Factorise x 2 + 5x 6 Q16 *N34730A01324* 13 Turn over

14 17. Lucy did a survey about the amounts of money spent by 120 men during their summer holidays. The cumulative frequency table gives some information about the amounts of money spent by the 120 men. Amount ( A) spent Cumulative frequency 0 A < A < A < A < A < A < A < (a) On the grid, draw a cumulative frequency diagram. (b) Use your cumulative frequency diagram to estimate the median.... A survey of the amounts of money spent by 200 women during their summer holidays gave a median of 205 (c) Compare the amounts of money spent by the women with the amounts of money spent by the men (1) 14 *N34730A01424*

15 120 Cumulative frequency O Amount spent ( ) Q17 (Total 5 marks) *N34730A01524* 15 Turn over

16 18. B Diagram NOT accurately drawn O C The diagram shows a circle centre O. A, B and C are points on the circumference. A DCO is a straight line. DA is a tangent to the circle. Angle ADO = 36 (a) Work out the size of angle AOD. 36 D... (b) (i) Work out the size of angle ABC.... (ii) Give a reason for your answer.... (3) Q18 (Total 5 marks) 16 *N34730A01624*

17 19. y O x The diagram shows graphs of y = 1 x and 2y + 3x = 12 (a) Use the diagram to solve the simultaneous equations y = 1 x y + 3x = 12 x =... y =... (1) (b) Find an equation of the straight line which is parallel to the line y = 1 x and passes through the point (0, 4). (Total 3 marks) Q19 *N34730A01724* 17 Turn over

18 20. (a) Solve the inequality 3t + 1 < t + 12 (b) t is a whole number. Write down the largest value of t that satisfies 3t + 1 < t + 12 (1) Q20 (Total 3 marks) 21. M is directly proportional to L 3. When L = 2, M = 160 Find the value of M when L = 3 Q21 18 *N34730A01824*

19 22. A call centre receives 64 telephone calls one morning. The table gives information about the lengths, in minutes, of these telephone calls. Length (x) minutes Frequency 0 < x < x < x < x < x 45 6 Draw a histogram for this information Length (minutes) Q22 *N34730A01924* 19 Turn over

20 23. In a game of chess, a player can either win, draw or lose. The probability that Vishi wins any game of chess is 0.5 The probability that Vishi draws any game of chess is 0.3 Vishi plays 2 games of chess. (a) Complete the probability tree diagram. 1st game 2nd game... Win Win... Draw Lose... Win 0.3 Draw... Draw... Lose Win Lose... Draw... (b) Work out the probability that Vishi will win both games. Lose Q23 20 *N34730A02024*

21 24. A Diagram NOT accurately drawn B D C ABC is an equilateral triangle. D lies on BC. AD is perpendicular to BC. (a) Prove that triangle ADC is congruent to triangle ADB. (3) (b) Hence, prove that BD = 1 2 AB. (Total 5 marks) Q24 *N34730A02124* 21 Turn over

22 = u v f u 1 1 = 2, v = (a) Find the value of f. (b) Rearrange = u v f (3) to make u the subject of the formula. Give your answer in its simplest form. Q25 (Total 5 marks) 22 *N34730A02224*

23 26. y = f(x) y O x The curve with equation y = f(x) is translated so that the point at (0, 0) is mapped onto the point (4, 0). (a) Find an equation of the translated curve. y 4 2 O x 2 4 The grid shows the graph of y = cos x for values of x from 0 to 540 (b) On the grid, sketch the graph of y = 3 cos (2x ) for values of x from 0 to 540 Q26 END TOTAL FOR PAPER: 100 MARKS *N34730A02324* 23

24 BLANK PAGE 24 *N34730A02424*

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