0570 Mathematics 2010 Solution Paper 1

1. The value of (7.1 × 10³)(6.0 × 10²) / (4 × 10⁴) is

• A. 1.05 × 10¹
• B. 10.5 × 10¹
• C. 10.5 × 10³
• D. 1.05 × 10^-2

2. Given that 123n − 46n = 44n then the value of n is

• A. 7
• B. 9
• C. 8
• D. 10

3. The number 0.0029087 correct to 3 significant figures is

• A. 0.00209
• B. 0.00290
• C. 0.003
• D. 0.00291

4. Anita, Nina and Tina shared 30,000 FCFA amongst themselves in the ratio 2 : 3 : 5. Therefore Nina’s share was

• A. 3,000 FCFA
• B. 6,000 FCFA
• C. 9,000 FCFA
• D. 15,000 FCFA

5. On a map of scale 1 : 20000 the distance, in cm, representing 5 km is

• A. 25 cm
• B. 4 cm
• C. 2500 cm
• D. 400 cm

6. Diana bought a TV set and resold it for 150,000 FCFA, thereby making a profit of 20%. The T.V. set cost her

• A. 31,200 FCFA
• B. 130,000 FCFA
• C. 124,800 FCFA
• D. 187,200 FCFA

7. In the diagram below it is given that PQ = 7 cm, angle PRN = 30° and N is the midpoint of PQ. The perimeter of ΔPQR is

• A. 21 cm
• B. 14 cm
• C. 10.5 cm
• D. 17.5 cm

8. The diagram below shows a cuboid of sides 8 cm, 5 cm and x cm. The volume of this cuboid is 240 cm³. The value of x in cm is

• A. 15
• B. 6
• C. 2
• D. 12

9. In the figure above, the area of the shaded sector in terms of π

• A. 3π
• B. 2π
• C. (9√3)/4
• D. 9π

10. In the Venn diagram above, the shaded area is defined by

• A. (P ∩ Q) ∪ R
• B. (P ∪ Q) ∩ R
• C. (P ∩ Q) ∩ R
• D. (P ∪ Q) ∪ R

11. The Venn diagram shows the number of people at a certain party. E represents those who eat eba, J those who are rice and W those who drank wine. The number of people who ate eba and drank wine is

• A. 41
• B. 30
• C. 12
• D. 10

12. Given that ξ = {1, 2, 3, …, 30}, M = {multiples of 3} and N = {even numbers}, then n(M ∩ N) is

• A. 5
• B. 6
• C. 10
• D. 15

13. The expression nx + 2n + 2x + 4 can be completely factorised as

• A. 2(n + x)(nx + 4)
• B. (x + 2)(n + 2)
• C. 2(n + x + 2)
• D. 2x(n + 4)

14. Given the equation 8/(x − 5) = 4, then the value of x is

• A. 7
• B. 13/4
• C. 5
• D. 9/4

15. The expression x² − 4x + 3 can be factorised as

• A. (x + 1)(x + 3)
• B. (x − 1)(x − 3)
• C. (x + 1)(x − 3)
• D. (x + 3)(x − 1)

16. The smallest whole number that satisfies the inequality 3x + 1 ≥ 7 is

• A. 2
• B. 1
• C. 3
• D. 4

17. Which of the shaded regions below satisfies all of the following inequalities? y ≥ 0, x ≥ 4 and 2x + y ≥ 23

• A
• B
• C
• D

18. The sum of the n terms of a sequence is given by Sₙ = 17n − 3n². The fourth term of the sequence is

• A. 6
• B. −10
• C. −4
• D. 10

19. Given that 3^(x+1) = 81, then x² =

• A. 9
• B. 27
• C. 16
• D. 64

20. The sets X and Y and the relation R between them is shown in the pappy graph below. The range of the relation R is

• A. X
• B. Y
• C. 4
• D. {2, −1, 0}

21. The function f is defined on R, the set of real numbers as f(x) = 1 − x², then f(−2) is

• A. −18
• B. 18
• C. 22
• D. −22

22. The function f and g are defined on R, the set of real numbers as f(x) = 2x − 1 and g(x) = (x² + 1). The composite function f(g(x)) is

• A. x² + 2x
• B. 4x² − 4x
• C. x²
• D. 2x² − 2x

23. Given that f(x) = (3x − 2)/4, then f⁻¹(x) is

• A. (x + 2)/4
• B. (4x + 2)/3
• C. (4x − 2)/3
• D. (4x − 2)

24. P is the point (1, 6) and Q is the point (5, 3). The length of PQ is

• A. √7
• B. √136
• C. 25
• D. 5

25. The equations of four lines are given as L₁: y + x − 6 = 0, L₂: x − 2y = 0, L₃: 3y − 2x = 7, L₄: 3x − 2y = 5. The pair of lines that are parallel is

• A. L₂ and L₃
• B. L₂ and L₁
• C. L₁ and L₄
• D. L₁ and L₂

26. A line has a slope of zero and passes through the point (−2, 5). The equation of the line is

• A. x = 2
• B. y = 5
• C. y = −5
• D. x = −2

27. The coordinates of the point at which the line 2y = x − 8 cuts the y-axis are

• A. (4, 0)
• B. (−4, 0)
• C. (0, 8)
• D. (0, −4)

28. Which of the following graphs represents a sketch of the graph y = (2x + 1)(x − 3)

• A
• B
• C
• D

29. The diagram above drawn to scale shows the speed-time graph of a cyclist. How long did the cyclist ride at uniform speed?

• A. 7
• B. 4
• C. 6
• D. 18

30. In the diagram below, PQ and MN are parallel and angle MTE = 60°. The value of p is

• A. 12°
• B. 36°
• C. 18°
• D. 24°

31. The exterior angle of a regular polygon is 18°. Then the number of sides of the polygon is

• A. 10
• B. 18
• C. 20
• D. 36

32. Given that PQ and YZ are parallel and that XP = 2 cm, while PY = 3 cm, the ratio of the area of ΔXPQ to the area of ΔXYZ is

• A. 2/7
• B. 2/5
• C. 25/4
• D. 4/25

33. In the diagram above, XYZ is a tangent to the circle. Given that PYZ = 63° and angle YPQ = 68°, then angle YPQ =

• A. 49°
• B. 53°
• C. 59°
• D. 63°

34. In the diagram T is a point 13 cm from O the centre of a circle of radius 5 cm. The length of a tangent drawn from T to the circle will be

• A. 10 cm
• B. 13 cm
• C. 12 cm
• D. 18 cm

35. The line MN is reflected in the line y = 2. The coordinates of N′, the image of N are

• A. (6, −7)
• B. (6, −3)
• C. (6, −5)
• D. (−6, −3)

36. In the right-angle triangle in the diagram above, tan PRQ is

• A. 3/4
• B. 3/5
• C. 4/3
• D. 5/3

37. In the diagram, the points P, M and S are such that the bearing of M from P is 035°, angle PMS = 90° and angle PSM = 30°. The bearing of S from P is

• A. 80°
• B. 55°
• C. 95°
• D. 72.5°

38. Given the following quadrilaterals: kites, rhombus, square and rectangle, in which of them do the diagonals not intersect at right angles

• A. kites
• B. Rhombus
• C. Square
• D. Rectangle

39. The number of lines of symmetry of a square is

• A. 4
• B. 2
• C. 3
• D. 1

40. In the diagram above, M is the midpoint of YZ in the triangle XYZ. Given that XY = a and XZ = b, then XM expressed in terms of a and b is

• A. a + b
• B. a − b
• C. ½ (a + b)
• D. ½ (a − b)

41. Given the vectors OP = 4i + j and OQ = i − 3j and that R is the mid point of PQ then the position vector of R is given by

• A. 3i − 4j
• B. 2½i − j
• C. 1½i − 2j
• D. 3i + 4j

42. Which of the following data is discrete?

• A. The heights of 12 year old girls
• B. The weights of form 5 boys
• C. The number of students in each class of a school
• D. The temperature at different times of the day

43. The average of two numbers is 3a. Given that one of the numbers is a − b, then the other number is

• A. 5a − b
• B. 5a + b
• C. 4a − b
• D. 3a + b

44. The pie chart shows best food items eaten by 480 students in a boarding school. The number of students who have garri as their best meal is

• A. 75
• B. 100
• C. 60
• D. 80

45. In the following frequency distribution table

Score: 2, 3, 4, 5, 6

Frequency: 1, 2, 3, 1, 1

The mean of the distribution, calculated to 1 d.p. is

• A. 1.5
• B. 3.9
• C. 3.1
• D. 3.4

46. The range of the following set of numbers is, 2, 3, 4, 7, 10, 10, 12, 13, 13, 14, 15, 19, 20

• A. 18
• B. 10
• C. 20
• D. 13

47. ξ = {students in Form 4}, G = {those doing Geography}, C = {those doing Chemistry}. A student is chosen at random. The probability that the student is studying only one subject is

• A. 1/2
• B. 12/16
• C. 13/24
• D. 8/13

48. The probability that a team will win a certain football match is 0.21 and the probability that the team will lose the match is 0.37. Then the probability that the team will draw the match is

• A. 0.22
• B. 0.60
• C. 0.79
• D. 0.42

49. Using the tree diagram, the probability of P followed by P is

• A.
• B.
• C.
• D.

50. (Diagram-based question)