Second Term Examination Volume 1
Class : SSS One
Subject : Mathematics
Duration : 2 Hours
Section A : Objective Questions
Instruction : Answer all questions in this section.
1. One of the factors of mn – ng – n² + mg is (m – n). The other factor is ___________. (a) (n – g) (b) (q – n) (c) (n + g) (d) (g – m) (e) (m – q)
2. The sum of the interior angles of a polygon is 1080°. How many sides has the polygon? (a) 6 (b) 8 (c) 9 (d) 10 (e) 12
3. If 7/2x – 4/3x = 13/12, then x = (a) – 12 (b) 0 (c) 2 (d) 3 (e) 12
4. Evaluate x³ – 2xy² + y³ given that x = – 2 and y = -3 (a) – 45 (b) – 23 (c) 1 (d) 17 (e) 23
5. If y = {5, 1, 4, 1, 2, 6, 1}, then n(y) = (a) 1 (b) 5 (c) 6 (d) 7 (e) 20
6. The angles of a pentagon are x°, 2x°, (x +30)°, (x – 10)°, (x + 40)°, x = ? (a) 30 (b) 50 (c) 60 (d) 80 (e) 108
7. Express 4/x – y/3 as a single fraction. (a) (4 – y)/3x (b) (4x – 3y)/3x (c) (4 – y)/(x – 3) (d) (3 – x)/3x (e) (12 – xy)/3x
8. A motorist drives at 100km/h. How many minutes will it take her to travel dkm? (a) 60d/100 (b) 6000/d (c) 100d/60 (d) d/6000 (e) 100/d
9. If sin A = 4/5, then tan A = ? (a) 2/5 (b) 3/5 (c) 3/4 (d) 1 (e) 4/3
10. If ε = {a, b, c, d, e} and x = {a, b, e}, then x’ = (a) (b) {a} (c) {a, b, c} (d) {c, d} (e) ε
11. A rope 24m long is divided into three pieces in the ratio 2:1:5. The length of the shortest piece, in M is ____________. (a) 3 (b) 6 (c) 8 (d) 16 (e) 16
12. What is the sum of the roots of the equation x² – 3x + 2 = 0 (a) – 3 (b) – 1 (c) 2 (d) 4 (e) 3
13. What is n(A), if A = {k! 2 ≤ x ≤ 9, x ∈ Z}? (a) 2 (b) 6 (c) 7 (d) 8 (e) 9
14. What is the other value of x in x² + 10x – 24 = 0, x = 12. (a) – 3 (b) – 2 (c) – 1 (d) 1 (e) 12
15. The height of a closed cylinder is equal to its radius, r. Express the total surface area of the cylinder in terms π and r. (a) πr² (b) 2πr² (c) 3πr² (d) 4πr² (e) 6πr²
16. Two bags of sugar at N x per bag are mixed with three bags of sugar at N y per bag. What is the cost of the mixture per bag? (a) (2x + 3y)/5 (b) (x + y)/2 (c) x/2 +y/3 (d) (x + y)/5 (e) (3x + 2y)/ 5
17. The mean of three number is 9. The mode is 11. The lowest of the three numbers is _________. (a) 3 (b) 5 (c) 8 (d) 9 (e) 11
18. Find the roots of the equation x² + 12x – 28 = 0. The greater of the two roots is ________. (a) – 14 (b) – 2 (c) 2 (d) 7 (e) 14
19. For what range of values of x is x² +2x – 2 increasing? (a) x > – 3 (b) x > – 2.7 (c) x > 1 (d) x < 0.7 (e) x < – 1
20. A rectangle is five times as long as it is wide. If it’s area is 180cm² then the length of the rectangle is _________. (a) 6cm (b) 12cm (c) 15cm (d) 30cm (e) 75cm
21. Evaluate 3y² – 5y – 6 when y = – 2. (a) – 8 (b) – 4 (c) 4 (d) 8 (e) 16
22. Expand (3 – x) (3 + x) (a) 3 – x + 3x² (b) 3 + x – 3x² (c) 3 – x – x² (d) 3 + x + 3x² (e) 9 – x²
23. If P = √ x – y, then in terms of p and y, x = _________. (a) √p – y (b) p² + y (c) √p² + y (d) p² – y² (e) (p – y)²
24. Calculate the value of (27/125) – 1/3 x (4/9) 1/2. (a) 12/125 (b) 2/5 (c) 3/5 (d) 7/10 (e) 10/9
25. Express 40cm as a percentage of 8m. (a) 5% (b) 8% (c) 20% (d) 10% (e) 32%
26. The sum of the roots of 2a² – 3a – 27 = 0 (a) 3/27 (b) – 3/27 (c) 2/27 (d) -2/ 27 (e) 3/2
27. Factorize : x² + 2a + ax + 2x. (a) (x +2a) (x + 1) (b) (x +2) (x + a) (c) (x +2a) (x – 1) (d) (x – 1) (x – a) (e) (x – 2a) (x – 1)
28. What is the additive Inverse of – 11/12? (a) 2/3 (b) 11/12 (c) – 12/11 (d) 12/11 (e) – 1/2
29. Find the simple interest on N600 for 3 years at 8% per annum. (a) N465.00 (b) N144.00 (c) N 744.00 (d) N14.40 (e) N46.50
30. Divide the sum of 1/8 and 1/9 by 17/12. (a) 17/12 (b) 1/6 (c) 12/7 (d) 7/12 (e) 12/73
31. A school boy spent 1/4 of his pocket money on book and 1/3 on dress. What fraction is remaining? (a) 7/12 (b) 5/12 (c) 3/12 (d) 1/3 (e) 1/4
32. If 23x + 101x = 130x, find the value of x. (a) 7 (b) 6 (c) 5 (d) 4 (e) 3
33. Express 0.00000407 in standard form. (a) 4.07 x 105 (b) 4.07 x 10-5 (c) 40.7 x 105 (d) 40.7 x 10– 5 (e) 4.07 x 10-6
34. Simplify : [4(2n+1) – 2n+2]/ [2n+1 – 2n]. (a) 2n+1 (b) 2n+2 (c) 4 (d) 2 (e) 2n
35. 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 = 1/Z (c) XZ = K (d) X = Z² (e) XZ = 1
36. A bearing of 320° expresses as a compass bearing is _________. (a) N50°W (b) N40°W (c) N50°E (d) N40°E (e) N20°E
37. A lecture ended by 6p.m, after 8 hours, what time did it start? (a) 2a.m (b) 2p.m (c) 10a.m (d) 4p.m (e) 12a.m
38. If the mean of 4, 6, y, 16 and 19 is 13. What is the value of y? (a) 24 (b) 20 (c) 15 (d) 8 (e) 13
39. The coefficient of x in the expansion of (x – 2) (x + 9) is _________. (a) 7 (b) 15 (c) 16 (d) 2 (e) – 15
40. The length, in cm of the sides of a right angled triangle are x, (x + 2) and (x+1), where x > 0. Find in cm, the length of its hypotenuse. (a) 4 (b) 5 (c) 13 (d) 17 (e) 7
41. A candidate scored 32 marks out of 80, find his percentage score. (a) 20% (b) 32% (c) 40% (d) 48% (e) 22%
42. Given that (2x – 1)(x + 5) = 2x² – mx – 5, what is the value of m? (a) 11 (b) 5 (c) – 9 (d) – 10 (e) – 12
43. Evaluate 110112 + 101112 in binary. (a) 1100112 (b) 1011012 (c) 1110112 (d) 101112 (e) 111012
44. When I divide 48 by the sum of 5 and a certain number, the result is 3. What is the number? (a) 11 (b) 16 (c) 119 (d) 139 (e) 53
45. Ada can travel 45 km in 3 hours using her bicycle. How many kilometer can she travel in 10 hours? (a) 120km (b) 150km (c) 155km (d) 160km (e) 56km
46. Five workers dig a piece of ground in 8 days. How long will it take 10 workers to do the same work? (a) 10 days (b) 8 days (c) 5 days (d) 4 days (e) 6 days
47. Convert 101110112 to decimal. (a) 187 (b) 178 (c) 718 (d) 127 (e) 817
48. A dealer bought a 1000 articles for N6000 and sold them at N9 each. Find his profit percent. (a) 90% (b) 70% (c) 60% (d) 50% (e) 30%
49. Find the area of a trapezium which has a height 20cm and it’s parallel sides are 7cm and 8cm long. (a) 140cm² (b) 150cm² (c) 160cm² (d) 560cm² (e) 120cm²
50. Which of these angles is complementary to 70°? (a) 20° (b) 30° (c) 90° (d) 110° (e) 290°
Section B : Theory
Instruction : Answer question one (1) and any other two (2) questions.
1a. If 5p-5 = 8 x 5 – 2, find p.
1b. Use the Venn Diagram to illustrate the information below:
ε = {1,2,3,4,5,6,7,8,9,10}, P = {2,4,5,7} Q = {1,2,5,6,8} and R = {1,2,4,6,9}
1c. The side of a rectangle shown below are given in cm.
i. Find the value of x and y
ii. Calculate area of the rectangle
iii. Calculate the perimeter of the figure.
2a. Make Q the subject of the formula when L = 4/3(M √PQ)
2b. Given that since sin = 8/17, evaluate (cos Q + sin Q)/ (cos Q – sinQ)
3a. Solve the quadratic equation using completing the square method: 2x² – 5x + 2 = 0
3b. PQRS is a trapezium in which PQ/ /SR, /PQ/ = 16cm, /QR/ = 12cm, /RS/ = 8cm and PQR = 30°. Calculate the area of PQRS
4a. Evaluate without calculator
³√(164.3 x 12.5²)/1.46²
4b. Find a quadratic whose root are p and q.
5a. Given that 231n – 143n = 44n, find the number base n
5b. The sum of the square of the first n-integers is given by :
∫n = [n(n + 1) (2n + 1) ] / 6, evaluate ∫25