Questions Q1. x =... (Total for Question is 4 marks) Q2. Write down the value of (i) 7. (ii) 5 1. (iii) 9 ½. (Total for Question is 3 marks) Q3.

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1 Questions Q1. The equation x 3 6x = 72 has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working. Q2. Write down the value of (i) 7. (ii) 5 1. (iii) 9 ½ Q3. x = Rationalise the denominator Q (Total for Question is 2 marks) Rationalise the denominator of Give your answer in its simplest form.

2 Q5. Dan does an experiment to find the value of π. He measures the circumference and the diameter of a circle. He measures the circumference, C, as 170 mm to the nearest millimetre. He measures the diameter, d, as 54 mm to the nearest millimetre. Dan uses π = C d to find the value of π. Calculate the upper bound and the lower bound for Dan's value of π.. Q6. A solid sphere has Given that a mass of 1180 g measured to the nearest gram and a radius of 6.2 cm measured to the nearest millimetre. find the upper bound for the density of the sphere. Give your answer to 3 significant figures. Q7. k = 3e + 5 (a) Work out the value of k when e = g/cm (b) Solve 4y + 3 = 2y + 14 (c) Solve 3(x 5) = 21 3 < n < 4, n is an integer. (d) Write down all the possible values of n. y = x = (Total for Question is 8 marks)

3 Q8. (a) Expand and simplify (p + 9)(p 4) (b) Solve = 4w + 2 (c) Factorise x w = (d) Simplify (9x 8 y 3 ) ½ Q9. (3) (1) (Total for Question is 8 marks) Solve = x Q10. Solve the simultaneous equations 4x + y = 25 x 3y = 16 x =... y =...

4 Q11. Solve the simultaneous equations x 2 + y 2 = 9 x + y = 2 Give your answers correct to 2 decimal places. Q12. Solve 3x 2 4x 2 = 0 Give your solutions correct to 3 significant figures. x = y = or x = y = (Total for Question is 6 marks) Q13. Solve 2x 2 + 5x 3 = 0 Q14. Simplify fully

5 Q15. Simplify Q16. Make p the subject of the formula y = 3p 2 4 Q17. Make t the subject of the formula Q18. Make t the subject of the formula 2(d t) = 4t + 7 t =

6 Q19. Here are the first four terms of an arithmetic sequence (a) Find, in terms of n, an expression for the nth term of this arithmetic sequence. (b) Is 150 a term of this sequence? You must explain how you get your answer.... Q20. The first five terms of an arithmetic sequence are (a) Write down an expression, in terms of n, for the nth term of this sequence. An expression for the nth term of a different sequence is 20 5n (b) work out the 10th term of this sequence..... Q21. The diagram shows shape A. All the measurements are in centimetres. Diagram NOT accurately drawn (a) Find an expression in terms of x for the area, in cm 2, of shape A.

7 You must simplify your answer. Shape B is a rectangle. Shape B has the same area as shape A. Shape B has a length of (3x + 2) centimetres. (b) Find an expression in terms of x for the width, in centimetres, of shape B (4) Q22. * This shape is a solid prism. The cross section of the prism is a trapezium (1) (Total for Question is 5 marks) Show that the total surface area of the prism is 82x x 12

8 Q23. The diagram shows a trapezium. All the measurements are in centimetres. The area of the trapezium is 351 cm 2. (a) Show that 2x 2 + x 351 = 0 (b) Work out the value of x.... (3) Q24. A water trough is in the shape of a prism. (Total for Question is 5 marks) Hamish fills the trough completely. Water leaks from the bottom of the trough at a constant rate.

9 2 hours later, the level of the water has fallen by 20 cm. Water continues to leak from the trough at the same rate. How many more minutes will it take for the trough to empty completely? Q25. A piece of card is in the shape of a trapezium minutes (Total for Question is 6 marks) A hole is cut in the card. The hole is in the shape of a trapezium. Work out the area of the shaded region. Diagram NOT accurately drawn Q26. The diagram shows 3 sides of a regular polygon cm 2 Each interior angle of the regular polygon is 140. Work out the number of sides of the regular polygon. Diagram NOT accurately drawn

10 Q27. The interior angle of a regular polygon is 160. Diagram NOT accurately drawn (i) Write down the size of an exterior angle of the polygon. (ii) Work out the number of sides of the polygon Q28. The diagram shows a quadrilateral ABCD. accurately drawn AB = 16 cm. AD = 12 cm. Angle BCD = 40. Angle ADB = angle CBD = 90. Calculate the length of CD. Give your answer correct to 3 significant figures. Diagram NOT cm (Total for Question is 5 marks)

11 Q29. XYZ is a right-angled triangle. Calculate the length of XZ. Give your answer correct to 3 significant figures.. Q30. LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm. Calculate the size of the angle marked x. Give your answer correct to 1 decimal place. Diagram NOT accurately drawn Q31. Here are some cards. Each card has a letter on it. Rachel takes at random two of these cards.

12 Work out the probability that there are different letters on the two cards. Q32. The probability that Rebecca will win any game of snooker is p. She plays two games of snooker. (a) Complete, in terms of p, the probability tree diagram.. (b) Write down an expression, in terms of p, for the probability that Rebecca will win both games. (c) Write down an expression, in terms of p, for the probability that Rebecca will win exactly one of the games. (1)..... (Total for Question is 5 marks)

13 Q33. The table gives information about the heights, h metres, of trees in a wood. Height (h metres) Frequency 0 < h < h < h < h < h Draw a histogram to show this information. Q34. Bob asked each of 40 friends how many minutes they took to get to work. The table shows some information about his results. Time taken (m minutes) Frequency 0 < m < m < m < m < m 50 9 Work out an estimate for the mean time taken minutes

14 Q35. Faisel weighed 50 pumpkins. The grouped frequency table gives some information about the weights of the pumpkins. Weight (w kilograms) 0 < w < w < w < w 16 2 Work out an estimate for the mean weight. Frequency.