Third Term Examination
Class : SSS 1
Subject : Mathematics
Duration : 2 Hours
Section A : Objective Questions
Instruction : Read the questions carefully and choose from the alternatives lettered a – d.
1. Evaluate (101.5)² – (100.5)² (a) 1 (b) 2.02 (c) 20.02 (d) 202
2. Express the product of 0.06 and 0..9 in standard form. (a) 5.4 × 10-³ (b) 5.4 × 10-² (c) 5.4 × 10-¹ (d) 5.4 × 10²
3. Simplify 36¹/² × 64-¹/² × 5° (a) 0 (b) 1/24 (c) 2/3 (d) 1¹/²
Use the following information to answer question 4 to 6.
The following frequency table shows the scores of 20 students in a mathematics test:
Score : 0 1 2 3 4 5
Frequency : 2 3 4 2 7 2
4. Find the mode of the scores. (a) 2 (b) 3 (c) 4 (d) 5
5. What is the mean score? (a) 1.75 (b) 2 (c) 2.5 (d) 2.75
6. The median score is _______. (a) 0 (b) 2.5 (c) 3 (d) 5
7. A ladder 9m long leans against a vertical wall, making angle of 64° with the horizontal ground. Calculate correct to one decimal place, how far the foot of the ladder is from the wall. (a) 40m (b) 5.8m (c) 7.1m (d) 8.1m
8. If sin x = 3/5, find tan x for 0° < x <90°. (a) 4/5 (b) 3/4 (c) 5/8 (d) 1/2
9. Simplify \³|(27)² (a) 4 1/2 (b) 6 (c) 9 (d) 18
10. Find the quadratic whose roots are x = – 2 or x = 7. (a) x² + 2x – 7 =0 (b) x² – 2x + 7 =0 (c) x² + 5x + 14 = 0 (d) x² – 5x – 14 = 0
11. Find the roots of the equation 2x² – 3x – 2 = 0. (a) x = 2 or – 1 1/2 (b) x = – 2 or 11 (c) x = 2 or – 2 (d) x = – 1/2 or 2.
12. Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures. (a) 213.18 (b) 213.00 (c) 213 (d) 210
13. A cone is made from a sector of a circle of radius 14cm and angle of 90°. What is the area of the curved surface of the cone? (take pie as 22/7) (a) 22cm² (b) 38.5cm² (c) 77cm² (d) 154cm²
14. If 3y² = 243, find the value of y. (a) 2 (b) 3 (c) 4 (d) 9
15. In the diagram below, O is the center of the circle. Calculate the length of the chord AB if /OA/ = 5cm, /OD/ = 3cm and <AOD = <BOD. (a) 4cm (b) 5cm (c) 8cm (d) 15cm
16. Calculate the surface area of a hollow cylinder which is closed at one end, if the base radius is 3.5cm and height 8cm. (take pie = 22/7) (a) 126.5cm² (b) 165cm² (c) 176cm² (d) 2145cm²
17. If A = {a, b, c}, B= {a, b, c, d} and C = {a, b, c, d, e, f}; find (AUB) n (AUC). (a) { } (b) {a, b} (c) {a, b, c, d} (d) {a, b, c}
18. Simplify: (9¹/²) / (27²/³) (a) 1/27 (b) 1 (c) 1/2 (d) 1/9
Use the following information to answer question 19 – 21.
For a Class of 30 students, the scores in a Mathematics test out of 10marks were as follows:
4, 5, 7, 2, 3, 6, 5, 5, 8, 9, 5, 4, 2, 3, 7, 9, 8, 7, 7, 7, 3, 4, 5, 5, 2, 3, 6, 7, 7, 2.
19. What is the mode of the scores? (a) 7 (b) 3 (c) 4 (d) 5
20. What is the median score? (a) 3 (b) 4 (c) 5 (d) 6
21. What is the range of the distribution? (a) 2 (b) 7 (c) 8 (d) 9.
22. If 3²* = 27, what is *? (a) 1 (b) 1.5 (c) 4.5 (d) 3.
23. Find the volume of a cone of radius 3.5cm and vertical height 12cm (take pie = 22/7). (a) 154cm³ (b) 3.4cm³ (c) 15.5cm³ (d) 21cm³
24. Simplify : (2 1/2 x 8 1/2) / 4 (a) 1 (b) 2 (c) 4 (d) 16
25. Which of the following is not a measure of dispersion? (a) variance (b) mean deviation (c) mode (d) standard deviation
26. The volume of a cylinder of radius 14cm is 210cm³. What is the curved surface area of the cylinder? (a) 15cm² (b) 30cm² (c) 616cm² (d) 1262cm²
27. A pyramid of volume 120cm³ has a rectangular base which measured 5cm by 6cm. Calculate the height of the pyramid. (a) 5cm (b) 9cm (c) 12cm (d) 15cm.
28. Evaluate (111 two)² and leave your answer in base 2. (a) 111001 two (b) 110001 two (c) 101001 two (d) 10010 two
29. What is the value of 9 in the number 3.0492? (a) thousand (b) thousandth (c) tenth (d) hundredth
30. Simplify 11011 two – 1101 two. (a) 1100 two. (b) 101000 two (c) 1110 two (d) 1011 two
31. The variance of a given distribution is 25. What is the standard deviation? (a) 12 (b) 75 (c) 25 (d) 5
32. The base diameter of a cone is 14cm and its volume is 462cm³. Find its height. (take pie 22/7) (a) 3.5cm (b) 5cm (c) 7cm (d) 9cm
33. Convert 101101 two to a number in base ten. (a) 61 (b) 46 (c) 45 (d) 44
34. Find the mean of the numbers : 1, 3,4, 8, 4 and 7. (a) 4 (b) 5 (c) 6 (d) 7
35. Find the total surface area of the container. (a) 35cm² (b) 154cm² (c) 220cm² (d) 514cm²
36. What is the volume of the container? (a) 770cm³ (b) 35cm³ (c) 154cm³ (d) 220cm³
37. In the figure shown, PQS is a straight line. What is the value of PRQ?
(a) 128° (b) 108° (c) 98° (d) 78°
38. Make f the subject of the formulae:
V = (U + ft) / t (a) (V – U)/ t (b) (U – V) / t (c) (Vt – U) / t (d) (V – t) / t
39. Use calculator to evaluate Cos 40° – Sin 30°. (a) – 0.2660 (b) – 0.0266 (c) 0.0266 (d) 0.2660
40. Calculate the value of x in the diagram below:
(a) 18° (b) 30° (c) 40° (d) 60°
Section B : Theory
Instruction : Answer question 1 and any other four questions.
1ai. The volume of a cylindrical tank 10m high is 385cm³. Find the diameter of the tank. (take pie as 22/7)
aii. If 124 base n = 232 base five. Find the value of n.
aiii. Convert 35 base ten to a number in base two.
bi. If Cos (x + 40)° = 0.0872 and x is acute, what is the value of x?
bii. Out of 30 candidates applying for a post, 17 have degree, 15 diploma and 4 neither degree nor diploma. How many of them have both?
2a. Find the volume of a right solid come of base radius 4cm and perpendicular height 6cm. (pie = 3.142).
2b. Given that Cos x = 0.7431, 0° < x < 90°, find the values of (i) 2Sin x (ii) Tan x/2
3. The table shows the monthly contributions and expenditure pattern of an employee in 1996.
Items Percentage
1. Pension. 5
2. Income Tax 25
3. Food 40
4. Transport 10
5. Rent 12.5
6. Others 7.5
(a.) Draw a Pie chart to illustrate the data.
(b.) If the employee’s gross monthly salary was #10, 800.00. Calculate the pension contribution of the employees.
4. In a triangle XYZ, |XY| = 5cm, |YZ| = 8cm and |XZ|= 6cm. P is a point of the side XY such that |XP| = 2cm and the line through P, parallel to YZ meets XZ at Q. Calculate |QZ|.
5. The table below shows the marks scored by a group of students in Examination.
Calculate, correct to 2 decimal places, the :
(a) Mean;
(b) Standard Deviation of the score.