Mathematics First Term Examination SS 1

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1. If P = { x: 1 ≤ x ≤ 6 } and Q = { x: 2 < x < 9 }, then P ∩ Q =
   a) {1, 2, 3, 4}
   b) {3, 4, 5, 6}
   c) {4, 2, 9, 8}
   d) {1, 2, 3, 5}
2. Simplify: -2/3 × 4 =
   a) -1/4
   b) 1/8
   c) -4
   d) -2/12
3. Simplify: -6 × 1/2 =
   a) r/2
   b) 2r
   c) 1/2r
   d) 2/r
4. What is the product of 27/5 × 3^-3 × (1/5)^-1?
   a) 5
   b) 3
   c) 1
   d) 1/25
5. Evaluate: 81^3/4 – 27^1/3 =
   a) 27
   b) 1
   c) 1/3
   d) 1/8
6. Without using tables, evaluate: (343)^1/3 × (0.14)^-1 × (25)^-1/2
   a) 12
   b) 10
   c) 8
   d) 7
7. If 23x + 101x = 130x, find the value of x:
   a) 7
   b) 6
   c) 5
   d) 4
8. Simplify: (0.2)^3 × 8 =
   a) 40
   b) 0.4
   c) 0.2
   d) 0.04
9. Simplify: 4(2n + 1) – 2n + 2 =
   a) 2n + 2
   b) 2n + 1
   c) 4
   d) 2
10. Express 0.0000407 correct to 2 significant figures:
    a) 0.0
    b) 0.00004
    c) 0.000041
    d) 0.0000407
11. If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
    a) x ∝ z
    b) x ∝ z^2
    c) x ∝ z
    d) x ∝ z^3
12. In the addition table modulo 5, (n × 4) + 3 = 0, solve for n:
    a) 1
    b) 2
    c) 3
    d) 4
13. The ages of Tunde and Ola are in the ratio 1:2. If the ratio of Ola’s age to Musa’s age is 4:5, what is the ratio of Tunde’s age to Musa’s age?
    a) 1:4
    b) 1:5
    c) 2:5
    d) 5:2
14. If M = { x: 3 ≤ x < 8 } and N = { x: 8 < x ≤ 12 }, which of the following is true?
    a) M ⊆ N
    b) N ⊆ M
    c) M ∪ N = { x: 3 ≤ x ≤ 12 }
    d) None of the above
15. If x = 5 and y = -6, evaluate xy:
    a) 0
    b) 5
    c) 8
    d) 9
16. Solve the equation x/3 + x/4 = 3:
    a) 2/3
    b) 3/4
    c) 5/6
    d) 7/5
17. A sum of 18,100 was shared among 5 boys and 4 girls with each boy taking 20 more than each girl. Find a boy’s share:
    a) 1,820
    b) 2,000
    c) 2,020
    d) 2,040
18. One of the factors of 7x² + 33x – 10 is:
    a) 7x + 5
    b) x – 2
    c) 7x – 2
    d) x – 5
19. Solve x/5 = 3x – 2:
    a) 2/3
    b) 3/4
    c) 5/6
    d) 3/5
20. Simplify 3x – (p – x) – (r – p):
    a) 2x – r
    b) 2x + r
    c) 4x – r
    d) 2x – 2p – r
21. An arc of a circle with radius 7.5 cm is 7.5 cm long. Find the angle which the arc subtends at the center of the circle (correct to the nearest degree):
    a) 290°
    b) 570°
    c) 650°
    d) 1150°
22. Which of the following is true about a parallelogram?
    a) Opposite angles are supplementary
    b) Opposite angles are complementary
    c) Opposite angles are equal
    d) Opposite angles are reflex angles
23. A bearing of 320° expressed as a compass bearing is:
    a) N50°W
    b) N40°W
    c) N50°E
    d) N40°E
24. In the diagram, XY is a straight line. ∠POX = ∠POQ and ∠ROY = ∠QOR. Find the value of ∠POQ + ∠ROY:
    a) 600°
    b) 900°
    c) 1000°
    d) 1200°
25. A stationary boat is observed from a height of 100m. If the horizontal distance between the observer and the boat is 80m, calculate the angle of depression of the boat (correct to two decimal places):
    a) 36.87°
    b) 39.70°
    c) 51.34°
    d) 53.13°
26. The average age of a group of 25 girls is 10 years. If one girl, aged 2 years and 4 months joins the group, find the new average age of the group (correct to one decimal place):
    a) 10.1 years
    b) 9.3 years
    c) 8.7 years
    d) 8.3 years
27. In the diagram, NQ ∥ TS, ∠RTS = 50° and ∠PRT = 100°. Find the value of ∠NPR:
    a) 110°
    b) 130°
    c) 140°
    d) 150°
28. Simplify the expression a² – b²:
    a) (a – b)(a + b)
    b) b² – a²
    c) a²b – ab²
    d) ab² – a²b
29. Find the 6th term of the sequence: 1/3, 1/9, 1/27, …
    a) 1/243
    b) 1/7
    c) 1/81
    d) 1/121
30. If the sum of angles in a triangle is 180°, the two angles in a triangle are 50° and 70°, what is the third angle?
    a) 40°
    b) 60°
    c) 50°
    d) 90°