2014 Nov/Dec WASSCE Further (Elective) Maths

Paper 1 (Objective Test)

40 marks

1 1/2 hours

Let us know if you want any clarifications or spot any errors or have any questions.

Read the answer key and detailed solutions on the answer page.

1. A binary operation * is defined on a set A = {a, b, c} by the following table

(table)

| * | a | b | c |

| a | c | a | b |

| b | a | b | c |

| c | b | c | a |

Find the inverse of the element c under *.

A. c

B. a

C. b

D. o

2. If \( \displaystyle \frac{8 – 3\sqrt{6}}{2\sqrt{3} + 3\sqrt{2}} = p\sqrt{3} + q\sqrt{2} \), evaluate (p + q).

A. -10/3

B. -4/3

C. 4/3

D. 10/3

3. If log_{3}x = 3, find log_{x}81.

A. 2

B. 4/3

C. 2/3

D. 1/2

4. Solve 9^{x} + 3^{x + 1} – 18 = 0.

A. 3

B. 2

C. 1

D. -1

5. Given that sin x = 4/5 and cos y = 4/5, evaluate cos(x – y).

A. 0

B. 12/25

C. 13/25

D. 24/25

6. If kx^{3} is a term in the binomial expansion of (1 + 3x)^{3}, find the value of k.

A. 9

B. 15

C. 27

D. 54

7. Given that \( f:x \to 25 – x^2 \) and \( g:x \to \sqrt x \), find the value of g o f(4).

A. 5

B. 3

C. 2

D. 0

8. Find the 26th term of the sequence, 1909, 1913, 1917, 1921, …

A. 2013

B. 2009

C. 2005

D. 2001

9. If (x + 1) is a factor of f(x) = x^{3} – 4x^{2} + x + 6, find the remaining factors.

A. (x + 2) and (x – 3)

B. (x + 2) and (x + 3)

C. (x – 2) and (x + 3)

D. (x – 2) and (x – 3)

10. The gradient of the curve y = Px^{2} + 5x – 2 at the point x = -2 is -4. Find the value of the constant P.

A. -3

B. -9/4

C. 9/4

D. 3

11. Given that g(x) = \( \frac{3 – 2x}{x}, x \neq 0 \) and \( x \in \mathbf{R} \), find the inverse of g.

A. \( \frac{3}{x – 2}, x \neq 2 \)

B. \( \frac{3}{2 – x}, x \neq 2 \)

C. \( \frac{3}{x + 2}, x \neq -2 \)

D. \( \frac{x}{x + 3}, x \neq -3 \)

12. Given that y = 12 – x + 1/x, find dy/dx.

A. \( 1 + \frac{1}{x^2} \)

B. \( -(1 + \frac{1}{x^2}) \)

C. \( \frac{1}{x^2 – 1} \)

D. \( \frac{12 – x}{x} \)

13. A fair die is thrown twice. Find the probability that the sum of the scores is less than 4.

A. 7/36

B. 5/36

C. 1/4

D. 1/12

14. The seventh term of an exponential sequence (GP) is 192. If the common ratio is 2, find the first term of the sequence.

A. 1/2

B. 2

C. 3

D. 4

15. If \( M = \) and \( N = \), find 2M + 3N.

A.

B.

C.

D.

16. If \( X = \) and \( Y = \), find XY.

A.

B.

C.

D.

17. Evaluate \( \int_1^2 \frac{x^3 – 1}{x^2} dx \).

A. 1

B. 2

C. 3

D. 5

18. Find the unit vector in the direction of the resultant of forces F_{1}(4i – 3j), F_{2}(i + 2j) and F_{3}(-2i + 5j).

A. \( \frac{\sqrt{3}}{2} i + \frac{\sqrt{3}}{3} j \)

B. \( \frac{\sqrt{3}}{3} i + \frac{\sqrt{3}}{2} j \)

C. \( \frac{3}{5} i + \frac{4}{5} j \)

D. \( \frac{3\sqrt{34}}{34} i + \frac{5\sqrt{34}}{34} j \)

The table shows the distribution of the scores of a group of students in a test. Use this information to answer questions 19 and 20.

(table)

| Scores | 1 | 2 | 3 | 4 | 5 | 6 |

| No. of students | 1 | 4 | 5 | 6 | x | 2 |

19. If the mean score is 4, what is x?

A. 3

B. 4

C. 6

D. 12

20. If a pie chart is drawn for the distribution, what would be the sectoral angle for those who scored 4?

A. 48 degrees

B. 72 degrees

C. 120 degrees

D. 144 degrees

21. The roots of a quadratic equation are \( (\sqrt{2} + 1) \) and \( (\sqrt{2} – 1) \). Find its equation.

A. \( x^2 – 12x + 2 = 0 \)

B. \( x^2 + 2\sqrt{2}x + 1 = 0 \)

C. \( x^2 + 24x + 5 = 0 \)

D. \( x^2 – 2\sqrt{2}x + 1 = 0 \)

22. If \( \overrightarrow{AB} = (9 \text{km}, 320^\circ) \), find \( \overrightarrow{BA} \).

A. (9km, 320 degrees)

B. (9km, 240 degrees)

C. (9km, 040 degrees)

D. (9km, 140 degrees)

23. If \( \alpha \) and \( \beta \) are the roots of 2x^{2} + 8x + 7 = 0, find the value of \( \alpha^2 + \beta^2 \).

A. 4

B. 8

C. 9

D. 16

24. Differentiate x^{2} + xy – 5 = 0 with respect to x.

A. \( \frac{-(2x + y)}{x} \)

B. \( \frac{2x – y}{x} \)

C. \( \frac{-x}{2x + y} \)

D. \( \frac{2x + y}{x} \)

25. The probability that Abu will fail Geography and Economics tests are 1/3 and 1/4, respectively. If the two events are independent, find the probability that he will pass one of the subjects.

A. 1/2

B. 5/12

C. 1/6

D. 1/12

26. Find the inter-quartile range of 8, 6, 9, 7, 8, 11, 9, 7, 8, 7.

A. 4.0

B. 3.5

C. 2.0

D. 1.5

27. Find the remainder when 3x^{3} + 5x^{2} – 11x + 4 is divided by (x + 3).

A. 4

B. 1

C. -1

D. -4

28. A ball is thrown vertically upwards with a velocity of 15ms^{-1}. Calculate the maximum height reached. [Take g = 10ms^{-1}]

A. 15.25 m

B. 13.25 m

C. 12.25 m

D. 11.25 m

29. An object moving with an initial velocity of u and acceleration a, covers a distance of 8 m and attains a velocity of 6.5 ms^{-1} after 2 seconds. Calculate its acceleration.

A. 2.0 ms^{-1}

B. 2.5 ms^{-1}

C. 3.0 ms^{-1}

D. 4.0 ms^{-1}

30. Express \( 40 \times 39 \times 38 \times 37 \) in factorial notation.

A. 40!

B. 40

C. 40

D. 36

31. Two bodies of masses 3kg and 5kg moving with velocities 2 ms^{-1} and V ms^{-1}, respectively in opposite directions collide. If they move together after collision with velocity 3.5 ms^{-1} in the direction of the 5kg mass, find the value of V.

A. 7.8

B. 6.8

C. 5.6

D. 4.6

32. Find the radius of the circle 3x^{2} + 3y^{2} – 4x + 5y + 3 = 0.

A. 1/2

B. 2/3

C. 1 1/2

D. \( \frac{\sqrt{5}}{6} \)

33. A force, F, moves a body of mass 12kg from rest until it reaches a velocity of 6 ms^{-1} after 5 seconds. Calculate the value of F.

A. 9.6 N

B. 10.0 N

C. 12.0 N

D. 14.4 N

34. Given that the resultant of two forces 14 N and 10 N is 24 N, find the angle between the forces.

A. 90 degrees

B. 60 degrees

C. 45 degrees

D. 0 degrees

35. In how many ways can the letters of the word “KALAZOO” be arranged?

A. 420 ways

B. 840 ways

C. 1260 ways

D. 2520 ways

36. Find [[$ \int (2x + 3)^5 dx $]]

A. 4(2x + 3)^{4} + c

B. 8(2x + 3)^{4} + c

C. \( \frac{1}{6} (2x + 3)^6 + c \)

D. \( \frac{1}{12} (2x + 3)^6 + c \)

37. A binary operation * is defined on the set of real numbers as p * q = pq + p + q. Find 1/2 * 1/3.

A. 2

B. 1

C. 2/3

D. 1/6

38. Solve (x – 3)(x + 2) < 0.

A. -2 < x < 3

B. -2 > x > 3

C. x > 3

D. x < -2

39. If \( y = x^4 – \frac{1}{x^3} + \frac{2}{x} \), find dy/dx.

A. \( \frac{1}{4} x^5 – \frac{3}{x^2} + 2 \)

B. \( x^3 – \frac{3}{x^4} + \frac{2}{x^2} \)

C. \( 4x^4 + \frac{3}{x^3} + \frac{2}{x^2} \)

D. \( 4x^3 + \frac{3}{x^4} – \frac{2}{x^2} \)

40. A body moves under the action of forces (3N, 030 degrees), (2N, 090 degrees) and (3N, 150 degrees). Calculate the magnitude of the resultant force.

A. 2N

B. 3N

C. 4N

D. 5N