Examination on General Mathematics
Class: JSS 3
Term: Second Term
Time: 1 Hour
Total Marks: 70

SECTION A: OBJECTIVES (40 Marks)
Instruction: Answer all questions.

1. ________ is the interest calculated on the principal and any accumulated interest. (a) Simple interest (b) Compound interest (c) Annual interest (d) Fixed interest
2. Which of the following describes the view of a solid from the top? (a) Front view (b) Side view (c) Plan (d) Elevation
3. If P = 2L + 2W, make L the subject of the formula. (a) L = P – 2W (b) L = P/2 – W (c) L = (P – W)/2 (d) L = 2P – 2W
4. The probability of an event is always a number between ________ and 1. (a) -1 (b) 0 (c) 0.5 (d) 100
5. All of these are characteristics of similar shapes except ________. (a) Corresponding angles are equal (b) Corresponding sides are proportional (c) They have the same size (d) They have the same shape
6. Which is NOT a type of angle that can be constructed using only a ruler and compass? (a) 60° (b) 75° (c) 80° (d) 90°
7. The ratio of the opposite side to the hypotenuse in a right-angled triangle is called the ________. (a) Cosine (b) Tangent (c) Sine (d) Secant
8. A cylinder has a radius of 7 cm and a height of 10 cm. Its volume is calculated using the formula V = ________. (a) 2πrh (b) πr²h (c) πr(r+h) (d) 2πr(r+h)
9. Which of these is not a common solid shape? (a) Cube (b) Circle (c) Cone (d) Cylinder
10. When a shape is enlarged, its corresponding angles ________. (a) Change proportionally (b) Remain the same (c) Double (d) Halve
11. The main reason for calculating compound interest is to understand how money grows over time with ________. (a) Fixed deposits (b) Reinvested interest (c) Simple calculations (d) Daily withdrawals
12. The correct step in bisecting a line segment is to draw arcs from both ends of the segment with a radius ________ half the segment length. (a) Equal to (b) Less than (c) Greater than (d) Exactly
13. If y = 3x + 5, find y when x = 2. (a) 7 (b) 8 (c) 11 (d) 13
14. A fair die is rolled. The probability of getting an even number is ________. (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
15. If two triangles are similar, their corresponding sides are in the same ________. (a) Sum (b) Difference (c) Ratio (d) Product
16. The scale factor for an enlargement describes the ratio of the new length to the ________. (a) Original length (b) Area (c) Volume (d) Perimeter
17. In trigonometry, SOH stands for Sine = Opposite / ________. (a) Adjacent (b) Hypotenuse (c) Opposite (d) Base
18. The curved surface area of a cone is given by the formula ________. (a) πrl (b) 2πrh (c) πr² (d) πr(r+l)
19. A cuboid has how many distinct views (front, side, top)? (a) 1 (b) 2 (c) 3 (d) 6
20. To construct an angle of 45°, one must first construct a 90° angle and then ________ it. (a) Double (b) Bisect (c) Triple (d) Square
21. ________ is a measure of the likelihood of an event occurring. (a) Statistics (b) Algebra (c) Probability (d) Geometry
22. The process of making a different variable the subject of a formula is known as change of subject of ________. (a) Equation (b) Term (c) Formula (d) Expression
23. If the scale factor of enlargement is 3, and the original length is 5 cm, the enlarged length will be ________ cm. (a) 5 (b) 8 (c) 15 (d) 25
24. Which of these defines the tangent ratio in a right-angled triangle? (a) Opposite/Hypotenuse (b) Adjacent/Hypotenuse (c) Opposite/Adjacent (d) Hypotenuse/Opposite
25. The total surface area of a closed cylinder with radius ‘r’ and height ‘h’ is ________. (a) 2πrh (b) 2πr² (c) 2πr(r + h) (d) πr²h
26. A coin is tossed once. The probability of getting a head is ________. (a) 0 (b) 1/2 (c) 1 (d) 2
27. When constructing a 60° angle, the compass arc intersects the original line segment at a point from which another arc is drawn with the ________ radius. (a) Double (b) Half (c) Same (d) Different
28. Two shapes are similar if they have the same shape but possibly different ________. (a) Colours (b) Sizes (c) Weights (d) Materials
29. The interest calculated only on the principal amount is called ________. (a) Compound interest (b) Simple interest (c) Annual interest (d) Monthly interest
30. If V = IR, make I the subject of the formula. (a) I = V + R (b) I = V – R (c) I = V/R (d) I = R/V
31. The front view of a cylinder is a ________. (a) Circle (b) Rectangle (c) Triangle (d) Square
32. If the probability of an event happening is 0.7, the probability of it not happening is ________. (a) 0 (b) 0.3 (c) 0.7 (d) 1
33. A scale factor of 1 means the enlarged shape is ________ to the original shape. (a) Larger (b) Smaller (c) Identical (d) Rotated
34. In a right-angled triangle, the side opposite the right angle is called the ________. (a) Adjacent (b) Opposite (c) Hypotenuse (d) Base
35. The volume of a cone is given by the formula V = (1/3)πr²h. If r = 3 cm and h = 7 cm, calculate the volume (use π = 22/7). (a) 21 cm³ (b) 66 cm³ (c) 198 cm³ (d) 462 cm³
36. Which of the following is an application of compound interest in daily life? (a) Calculating wages (b) Savings account growth (c) Measuring speed (d) Drawing plans
37. To copy a given angle, you essentially construct a ________ angle. (a) Perpendicular (b) Parallel (c) Congruent (d) Supplementary
38. If the area of a shape is enlarged by a scale factor of 2, the new area will be ________ times the original area. (a) 2 (b) 4 (c) 8 (d) 16
39. The top view of a cone is a ________. (a) Circle (b) Triangle (c) Rectangle (d) Square
40. If a = (v – u)/t, find a when v = 20, u = 5, t = 3. (a) 5 (b) 15 (c) 25 (d) 45

SECTION B: THEORY (30 Marks)
Instruction: Answer any THREE questions.

1. (a) Make ‘h’ the subject of the formula A = (1/2)h(a + b). (2 marks)
(b) A fair coin is tossed three times. What is the probability of getting exactly two heads? (3 marks)
(c) Describe the steps involved in bisecting an angle using a compass and a ruler. (3 marks)
(d) Two similar triangles have corresponding sides in the ratio 2:5. If the area of the smaller triangle is 12 cm², what is the area of the larger triangle? (2 marks)

2. (a) Calculate the compound interest on N50,000 for 2 years at 10% per annum, compounded annually. (3 marks)
(b) A ladder leans against a vertical wall. If the ladder is 13m long and its base is 5m from the wall, calculate the height the ladder reaches on the wall. (3 marks)
(c) Sketch the front view and plan (top view) of a cylinder. (2 marks)
(d) If the scale factor of enlargement for a solid is 4, what is the ratio of their volumes? (2 marks)

3. (a) A cylindrical tank has a radius of 7m and a height of 15m. Calculate its volume. (Use π = 22/7). (3 marks)
(b) Two dice are rolled simultaneously. What is the probability that the sum of the numbers shown is 7? (3 marks)
(c) If A = P(1 + R/100)^n, find A when P = 1000, R = 5, n = 2. (2 marks)
(d) State two characteristics of similar shapes. (2 marks)

4. (a) Construct an angle of 90 degrees at a point on a given straight line using a ruler and a pair of compasses. (3 marks)
(b) In a right-angled triangle, if the opposite side is 8 cm and the adjacent side is 6 cm, calculate the tangent of the angle. (2 marks)
(c) A cone has a radius of 5 cm and a slant height of 13 cm. Calculate its curved surface area. (Use π = 22/7). (3 marks)
(d) Define scale factor in the context of enlargement. (2 marks)

Objective Marking Scheme

Question 1 – ✅ (b) Compound interest
Question 2 – ✅ (c) Plan
Question 3 – ✅ (b) L = P/2 – W
Question 4 – ✅ (b) 0
Question 5 – ✅ (c) They have the same size
Question 6 – ✅ (c) 80°
Question 7 – ✅ (c) Sine
Question 8 – ✅ (b) πr²h
Question 9 – ✅ (b) Circle
Question 10 – ✅ (b) Remain the same
Question 11 – ✅ (b) Reinvested interest
Question 12 – ✅ (c) Greater than
Question 13 – ✅ (c) 11
Question 14 – ✅ (c) 1/2
Question 15 – ✅ (c) Ratio
Question 16 – ✅ (a) Original length
Question 17 – ✅ (b) Hypotenuse
Question 18 – ✅ (a) πrl
Question 19 – ✅ (c) 3
Question 20 – ✅ (b) Bisect
Question 21 – ✅ (c) Probability
Question 22 – ✅ (c) Formula
Question 23 – ✅ (c) 15
Question 24 – ✅ (c) Opposite/Adjacent
Question 25 – ✅ (c) 2πr(r + h)
Question 26 – ✅ (b) 1/2
Question 27 – ✅ (c) Same
Question 28 – ✅ (b) Sizes
Question 29 – ✅ (b) Simple interest
Question 30 – ✅ (c) I = V/R
Question 31 – ✅ (b) Rectangle
Question 32 – ✅ (b) 0.3
Question 33 – ✅ (c) Identical
Question 34 – ✅ (c) Hypotenuse
Question 35 – ✅ (b) 66 cm³
Question 36 – ✅ (b) Savings account growth
Question 37 – ✅ (c) Congruent
Question 38 – ✅ (b) 4
Question 39 – ✅ (a) Circle
Question 40 – ✅ (a) 5