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 =...................... (Total for Question is 4 marks) Rationalise the denominator Q4....................... (Total for Question is 2 marks) Rationalise the denominator of Give your answer in its simplest form.
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.. (Total for Question is 4 marks) 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 = 2..................... g/cm 3 (Total for Question is 4 marks)....(2) (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 =..................... (2) x =..................... (2) (2)
(Total for Question is 8 marks)
Q8. (a) Expand and simplify (p + 9)(p 4) (2) (b) Solve = 4w + 2 (c) Factorise x 2 49. w =...................... (d) Simplify (9x 8 y 3 ) ½ Q9. (2) (3) (1) (Total for Question is 8 marks) Solve = x Q10. Solve the simultaneous equations 4x + y = 25 x 3y = 16 (Total for Question is 4 marks) x =... y =...
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
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 (Total for Question is 4 marks) t =......................
Q19. Here are the first four terms of an arithmetic sequence. 3 10 17 24 (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 (2) (2) (Total for Question is 4 marks) 2 6 10 14 18 (a) Write down an expression, in terms of n, for the nth term of this sequence. (2) An expression for the nth term of a different sequence is 20 5n (b) work out the 10th term of this sequence.....(2) Q21. The diagram shows shape A. All the measurements are in centimetres. (Total for Question is 4 marks) Diagram NOT accurately drawn
(a) Find an expression in terms of x for the area, in cm 2, of shape A. 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 2 + 32x 12
(Total for Question is 4 marks)
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. (2)... (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.
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
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)
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. 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. (Total for Question is 4 marks). (2) (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 (1)
exactly one of the games......(2) Q33. The table gives information about the heights, h metres, of trees in a wood. Height (h metres) (Total for Question is 5 marks) Frequency 0 < h 2 7 2 < h 4 14 4 < h 8 18 8 < h 16 24 16 < h 20 10 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 10 3 10 < m 20 8 20 < m 30 11 30 < m 40 9 40 < m 50 9
Work out an estimate for the mean time taken. Q35....................... minutes (Total for Question is 4 marks) Faisel weighed 50 pumpkins. The grouped frequency table gives some information about the weights of the pumpkins. Weight (w kilograms) 0 < w 4 11 4 < w 8 23 8 < w 12 14 12 < w 16 2 Work out an estimate for the mean weight. Frequency. (Total for Question is 4 marks)
Q36. The graph of y = f(x) is shown on each of the grids. (a) On this grid, sketch the graph of y = f(x 3) (b) On this grid, sketch the graph of y = 2f(x) (2) (2) (Total for Question is 4 marks)
Q37. The diagram shows a sketch of the graph of y = cos x (a) Write down the coordinates of the point A.. (1) (b) On the same diagram, draw a sketch of the graph of y = 2 cos x (1) (Total for Question is 2 marks) Q38. Diagram NOT accurately drawn ABC is a triangle. AB = 8.7 cm. Angle ABC = 49. Angle ACB = 64. Calculate the area of triangle ABC. Give your answer correct to 3 significant figures..................... cm 2 (Total for Question is 5 marks)
Q39. ABCD is a quadrilateral. Diagram NOT accurately drawn Work out the length of DC. Give your answer correct to 3 significant figures. Q40. * The diagram shows the triangle PQR....................... cm (Total for Question is 6 marks) PQ = x cm PR = 2x cm Angle QPR = 30 The area of triangle PQR = A cm 2 Show that x =
Q41. ABC is a triangle. D is a point on AB and E is a point on AC. DE is parallel to BC. AD = 4 cm, DB = 6 cm, DE = 5 cm, AE = 5.8 cm. Calculate the perimeter of the trapezium DBCE. Q42.... cm (Total for Question is 4 marks) A, B, C and D are points on the circumference of a circle with centre O. Angle ABC = 116 Find the size of the angle marked x. Give reasons for your answer.
(Total for Question is 4 marks)
Q43. ABC is a triangle. BC = 12.3 cm, Angle ABC = 73 The area of triangle ABC is 50 cm 2. Work out the length of AC. Give your answer correct to 3 significant figures..(total for Question is 6 marks) Q44. The diagram shows a large tin of pet food in the shape of a cylinder. The large tin has a radius of 6.5 cm and a height of 11.5 cm. A pet food company wants to make a new size of tin. The new tin will have a radius of 5.8 cm. It will have the same volume as the large tin. Calculate the height of the new tin. Give your answer correct to one decimal place.... cm
Q45. The diagram shows a solid made from a hemisphere and a cone. Diagram NOT accurately drawn The radius of the hemisphere is 4 cm. The radius of the base of the cone is 4 cm. Calculate the volume of the solid. Give your answer correct to 3 significant figures....cm 3