Exam Questions Second Term SS 2 Further Mathematics

Further Mathematics SS 2 Second Term Examination Questions

Section A: Objective Questions (Fill in the Blanks)

1. Given that x = -3 and y = -7, evaluate (x² – y) / (y² – x)
   a) -1/11
   b) 1/23
   c) 4/13
   d) 12/17

2. Solve the equation x² – 2x – 8 = 0
   a) x = 0 or 12
   b) x = -2 or 4
   c) x = 2
   d) x = 2 or 4

3. The conjugate of 2 + √3 is:
   a) 2
   b) √3
   c) √3 + 2
   d) 2 – √3

4. If f(x) = 10x – 3, find f(2)
   a) 7
   b) 20
   c) 3
   d) 17

5. Find the 4th term of an arithmetic progression (AP) where the first term is 2 and the common difference is 0.5
   a) 0.5
   b) 2.5
   c) 3.5
   d) 4

6. Cot θ can be expressed as:
   a) 1/sin θ
   b) 1/cos θ
   c) 1/tan θ
   d) tan θ

7. Solve the inequality y + 9 > 5y – 7
   a) y > 4
   b) y > -4
   c) y < 4
   d) y < -4

8. Find the distance between the points P (1,6) and Q (5,3)
   a) 6
   b) 5
   c) 4
   d) 3

9. Find the sum of the first 12 terms of the arithmetic series 5 + 9 + 13 + …
   a) 612
   b) 702
   c) 119
   d) 324

10. Solve the simultaneous equations 3x – y = 23 and 2x + 5y = 4 for y
    a) -20
    b) -2
    c) 2
    d) 7

11. If 2ˣ = 4, find the value of x
    a) 5
    b) 10
    c) 12
    d) 9

12. Find the square root of 400
    a) 20
    b) 200
    c) 40
    d) 2000

13. If P = √(4 × 9 × 16), find the value of P
    a) 24
    b) 6
    c) 48
    d) 12

14. Express 27^(-2/3)
    a) 9
    b) 1/9
    c) 0.9
    d) 1

15. Simplify a⁶ × a⁻³
    a) a³
    b) a⁴
    c) a⁵
    d) a⁶

16. Find the 40th term of the arithmetic sequence 6, 11, 16, 21, …
    a) 201
    b) 200
    c) 75
    d) 150

17. Solve the equation (1/2)ˣ = 8 for x
    a) 3
    b) 6
    c) -3
    d) -6

18. Simplify log₁₀(√8) / log₁₀(108)
    a) 1/3
    b) 1/2
    c) log₁₀(√2)
    d) 1/3 log₁₀(√8)

19. Solve (x + 2)(x + 7) = 0
    a) x = 1 or 8
    b) x = -2 or 7
    c) x = -4 or 5
    d) x = -3 or 6

20. The nth term of a sequence is given by (-1)ⁿ⁻² × 2ⁿ⁻¹. Find the sum of the second term
    a) 3
    b) 4
    c) 2
    d) 10

21. Simplify log₅(8) / log₅(√8)
    a) -2
    b) -1/2
    c) 1/2
    d) 2

22. Simplify (3√2 – 1)(3√2 + 1)
    a) 17
    b) 18
    c) 1
    d) 6

23. If E = MN / (S + N) and E = 75, M = 120, N = 5000, find S
    a) 1000
    b) 200
    c) 3000
    d) 4000

24. Simplify log₃(7) + log₃(15) – log₃(5)
    a) log₃(19)
    b) log₃(5)
    c) 3
    d) 1

25. Find the common ratio of the geometric sequence 6, 12, 24, 48, …
    a) 6
    b) 12
    c) 2
    d) 48

26. Divide 4x³ – 6x² + 2x + 7 by 2x – 3, find the quotient
    a) 6x + 8
    b) 2x² + 6x + 8
    c) 2x² + 6x
    d) 2x + 8

27. Find the sum of the roots of the equation 2x² + 3x – 9 = 0
    a) -18
    b) -6
    c) 9/2
    d) -3/7

28. Find the distance between A(3,2) and B(4,6)
    a) 5
    b) 4
    c) 3
    d) 2

29. Find the common ratio of the geometric sequence 36, 12, 4, 4/3, …
    a) 3
    b) 1/3
    c) -3
    d) -1/3

30. Find the equation of a straight line that passes through the points P(2, -3) and Q(-4, 2)
    a) y = 5x + 3
    b) y = -5/6x – 3
    c) y = -5/6x + 2
    d) y = 5/6x – 3

Section B: Theory Questions

1. Determine if AB is parallel or perpendicular to PQ in the following cases:
   a) A(3,1), B(4,3), P(4,6), Q(5,8)
   b) A(5,1), B(3,2), P(2,4), Q(5,6)
   c) A(4,7), B(6,8), P(3,5), Q(5,6)

2. Find the distance between the following pairs of points:
   a) A(3,2) and B(4,6)
   b) C(-1,3) and D(2,-7)
   c) P(5,-8) and Q(-4,-2)
   d) S(-3,-2) and T(1,-4)

3. Find the equation of the straight line that passes through P(2,-3) and Q(-4,2).

4. Find the common ratio in the following exponential sequences:
   a) 6, 12, 24, 48, …
   b) 36, 12, 4, 4/3, …
   c) 4, -8, 16, -32, …
   d) 54, -18, 6, -2, …