Examination on General Mathematics
Class: JSS 2
Term: Third Term
Time: 1 Hour
Total Marks: 70

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

1. ________ is the direction pointing midway between North and East. (a) North-West (b) North-East (c) South-East (d) South-West
2. The longest side of a right-angled triangle is called the ________. (a) adjacent (b) opposite (c) hypotenuse (d) perpendicular
3. Which of the following is a unit for volume? (a) cm² (b) m (c) cm³ (d) km
4. The main reason for calculating probability is to determine the ________ of an event occurring. (a) certainty (b) impossibility (c) likelihood (d) frequency
5. All of these are Pythagorean triples except ________. (a) 3, 4, 5 (b) 5, 12, 13 (c) 6, 8, 10 (d) 2, 3, 4
6. The correct step in finding the square of a number using tables is to locate the number and read the value under the ________ column. (a) cube (b) square (c) square root (d) reciprocal
7. Approximating N1,234.56 to the nearest naira gives ________. (a) N1,234 (b) N1,235 (c) N1,230 (d) N1,200
8. Which is NOT a type of approximation? (a) Nearest whole number (b) Significant figures (c) Decimal places (d) Exact value
9. The number of times an item appears in a data set is known as its ________. (a) range (b) mode (c) median (d) frequency
10. The formula for the curved surface area of a cylinder is ________. (a) πrl (b) 2πrh (c) πr²h (d) 2πr(r+h)
11. Which of the following angles can be constructed using only a compass and a ruler? (a) 70° (b) 80° (c) 90° (d) 100°
12. The probability of an impossible event is ________. (a) 1 (b) 0.5 (c) 0 (d) -1
13. Which of these is not a side of a right-angled triangle? (a) Hypotenuse (b) Adjacent (c) Opposite (d) Diagonal
14. If two quantities increase or decrease together, they are in ________ proportion. (a) inverse (b) direct (c) simple (d) compound
15. The volume of a cone is ________ of the volume of a cylinder with the same base radius and height. (a) one-half (b) one-third (c) two-thirds (d) double
16. A bearing of N45°E is equivalent to a three-digit bearing of ________. (a) 045° (b) 135° (c) 225° (d) 315°
17. Which of the following instruments is used to draw an angle of 90 degrees accurately without calculation? (a) Protractor (b) Ruler (c) Compass (d) Set square
18. All of these are functions of ready reckoners except ________. (a) obtaining squares (b) obtaining square roots (c) obtaining reciprocals (d) obtaining logarithms
19. The probability of an event happening is always between ________. (a) 0 and 1 (b) -1 and 1 (c) 0 and 100 (d) -10 and 10
20. When presenting data in ordered form, it means arranging the data from the smallest to the largest or from the largest to the ________. (a) mean (b) mode (c) smallest (d) median
21. The total surface area of a closed cylinder is given by the formula ________. (a) 2πrh (b) πr²h (c) 2πr(r+h) (d) πrl + πr²
22. Which is NOT a standard angle that can be constructed with only a compass and ruler? (a) 30° (b) 45° (c) 60° (d) 75°
23. A scale drawing of 1:50,000 means 1 cm on the map represents ________ cm on the ground. (a) 500 (b) 5,000 (c) 50,000 (d) 500,000
24. A compound shape formed by a cone mounted on a cylinder requires calculating the volume of the cone and the volume of the ________ separately. (a) sphere (b) cube (c) cylinder (d) pyramid
25. In a right-angled triangle, if the two shorter sides are 6 cm and 8 cm, the hypotenuse is ________ cm. (a) 10 (b) 12 (c) 14 (d) 16
26. The main reason for using logarithm tables for multiplying directed numbers is to ________. (a) find squares (b) simplify calculations (c) get square roots (d) convert to fractions
27. The three-digit bearing of West is ________. (a) 090° (b) 180° (c) 270° (d) 360°
28. The formula for the curved surface area of a cone is ________. (a) πr²h (b) 2πrh (c) πrl (d) 2πr(r+h)
29. Rounding 0.00456 to two significant figures gives ________. (a) 0.0045 (b) 0.0046 (c) 0.005 (d) 0.004
30. To represent data on a pie chart, the total angle for all sectors is ________ degrees. (a) 90 (b) 180 (c) 270 (d) 360
31. All of these are common methods of data presentation except ________. (a) Bar chart (b) Pie chart (c) Line graph (d) Storytelling
32. Which is NOT a type of proportion? (a) Direct proportion (b) Inverse proportion (c) Linear proportion (d) Compound proportion
33. Bisection of an angle means dividing the angle into two ________ parts. (a) equal (b) unequal (c) perpendicular (d) parallel
34. The total surface area of a cone is the sum of its curved surface area and the area of its ________. (a) top (b) base (c) height (d) slant height
35. The probability of picking a prime number from numbers 1 to 10 is ________. (a) 1/2 (b) 3/10 (c) 2/5 (d) 1/5
36. The correct step in finding the square root of 64 using a table, you would look under the column for ________. (a) squares (b) cubes (c) square roots (d) reciprocals
37. Which of these is not a unit for area? (a) cm² (b) m² (c) km² (d) cm³
38. If 4 painters take 6 days to paint a house, then 8 painters will take 3 days to paint the same house. This is an example of ________ proportion. (a) direct (b) inverse (c) simple (d) compound
39. The population of a town is 123,456. Approximating this to the nearest thousand gives ________. (a) 123,000 (b) 124,000 (c) 120,000 (d) 100,000
40. A pie chart is used to display ________ data. (a) linear (b) categorical (c) numerical (d) continuous

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

Question 1
(a) Define a three-digit bearing. (2 marks)
(b) A right-angled triangle has sides 7 cm and 24 cm. Calculate the length of its hypotenuse. (3 marks)
(c) Explain the difference between direct and inverse proportion with a real-life example for each. (3 marks)
(d) State two tools required for the accurate construction of geometric angles. (2 marks)

Question 2
(a) Write down the formula for the volume of a cylinder and a cone. (2 marks)
(b) A cylindrical tank has a radius of 7 cm and a height of 10 cm. Calculate its curved surface area. (Use π = 22/7) (3 marks)
(c) The population of a city is 2,345,678. Approximate this population to the nearest hundred thousand. (3 marks)
(d) What is the probability of rolling an even number when a fair die is tossed once? (2 marks)

Question 3
(a) What is the purpose of a ready reckoner table in mathematics? (2 marks)
(b) The angles of a pie chart represent the proportion of different categories. If a category has 25% of the total data, calculate the angle it will occupy in the pie chart. (3 marks)
(c) Construct an angle of 60° using only a compass and a ruler. (3 marks)
(d) Identify the cardinal points and their corresponding three-digit bearings. (2 marks)

Question 4
(a) State the Pythagoras rule for a right-angled triangle. (2 marks)
(b) A school budget of N500,000 is to be shared between three departments: Science, Arts, and Commercial, in the ratio 2:3:5 respectively. Calculate the amount each department receives. (3 marks)
(c) A cone has a base radius of 5 cm and a slant height of 13 cm. Calculate its total surface area. (Use π = 3.14) (3 marks)
(d) List two ways data can be presented in an ordered form. (2 marks)

Objective Marking Scheme

Question 1 – ✅ (b) North-East
Question 2 – ✅ (c) hypotenuse
Question 3 – ✅ (c) cm³
Question 4 – ✅ (c) likelihood
Question 5 – ✅ (d) 2, 3, 4
Question 6 – ✅ (b) square
Question 7 – ✅ (b) N1,235
Question 8 – ✅ (d) Exact value
Question 9 – ✅ (d) frequency
Question 10 – ✅ (b) 2πrh
Question 11 – ✅ (c) 90°
Question 12 – ✅ (c) 0
Question 13 – ✅ (d) Diagonal
Question 14 – ✅ (b) direct
Question 15 – ✅ (b) one-third
Question 16 – ✅ (a) 045°
Question 17 – ✅ (c) Compass
Question 18 – ✅ (d) obtaining logarithms
Question 19 – ✅ (a) 0 and 1
Question 20 – ✅ (c) smallest
Question 21 – ✅ (c) 2πr(r+h)
Question 22 – ✅ (d) 75°
Question 23 – ✅ (c) 50,000
Question 24 – ✅ (c) cylinder
Question 25 – ✅ (a) 10
Question 26 – ✅ (b) simplify calculations
Question 27 – ✅ (c) 270°
Question 28 – ✅ (c) πrl
Question 29 – ✅ (b) 0.0046
Question 30 – ✅ (d) 360
Question 31 – ✅ (d) Storytelling
Question 32 – ✅ (c) Linear proportion
Question 33 – ✅ (a) equal
Question 34 – ✅ (b) base
Question 35 – ✅ (c) 2/5
Question 36 – ✅ (c) square roots
Question 37 – ✅ (d) cm³