Mathematics Exam Questions for SS3 First Term with Answers

You’re welcome to our school exams series where we provide you with termly examination questions in different subjects. In today’s post, we will focus on Mathematics exam questions. We will cover Mathematics exam questions for SS3 First term with answers. This means that we’ll be providing you with answers to the questions at the end. Also, you will get a few success tips on how to pass Mathematics examinations with flying colors. Remember to use the comments sections if you have questions, and don’t forget to join our Free Online Tutorial Classes on YouTube. (Subscribe to the Channel)

Introduction to Mathematics as a School Subject

Before we venture into Past Mathematics Exam Questions for SS3 First term, here’s a brief introduction to the subject:

Mathematics is one of the most important subjects in the school curriculum. It is the science that deals with numbers, shapes, quantities, and logical reasoning. Mathematics helps students develop problem-solving skills, critical thinking, and the ability to make sound decisions in everyday life.

From basic counting and arithmetic to advanced topics like algebra, geometry, and statistics, mathematics provides the foundation for many fields of study, including science, engineering, economics, and technology. It also trains the mind to think logically and systematically.

In schools, mathematics is taught not only to help students pass examinations but also to prepare them to apply mathematical concepts in real-life situations. A strong understanding of mathematics enables learners to analyze data, interpret information, and contribute meaningfully to society’s development.

Mathematics Exam Questions for SS3 First Term

Mathematics Exam Questions for SS3 First Term are divided into two sections:

• Section A
• Section B

The first section, namely, Section A is the objective test, and students are expected to attempt all questions in the section. Section B is the theory part, and students are expected to follow specific instruction and answer the required number of questions.

Note that what you have below are SS3 Mathematics First Term Exam Past Questions made available to assist students in their revision for 1st term examinations and also teachers in structuring standard examinations.

SECTION A: Objective Test

Instruction: Answer all questions in this section by choosing from the options lettered A—D. Each question carries equal marks.

1. Which of the following is a simplified form of √72?
A. 6√2          B. 3√8
C. 2√18        D. 9√1

2. The value of (16)^3⁄4 is equivalent to
A. 8            B. 16
C. 32          D. 4

3. Rationalize the denominator of ³⁄_√5. The result is
A. ^3√5⁄₅             B. ³⁄_5√5
C. ^3√5⁄₁₀        D. ⁹⁄₅

4. Which of the following numbers is irrational?
A. 22/7        B. 0.75
C. √2           D. 9

5. Using laws of logarithms, log_a(xy) equals
A. log_ax + log_ay
B. log_ax − log_ay
C. log_a(x)^y
D. y · log_ax

6. If log₁₀125 = k, then k equals
A. 2.0969…
B. 1.0969…
C. 3
D. 0.9030…

7. Solve for x: log₂x = 5. Then x =
A. 10        B. 32
C. 25        D. 16

8. The change of base formula for log_ba is
A. log a / log b
B. log b / log a
C. a · log b
D. b · log a

9. Which of the following is the inverse of the matrix A = [[2, 1], [1, 1]]?
A. [[1, -1], [-1, 2]] B. [[1, -1], [-1, 2]] ⁄ 1
C. 1⁄₁ [[1, -1], [-1, 2]] D. [[2, -1], [-1, 2]]

10. For the 2×2 matrix A = [[a, b], [c, d]], the determinant det(A) is
A. ad + bc
B. ad − bc
C. ab − cd
D. ac − bd

11. If A = [[1, 2], [0, 1]] and B = [[2, 0], [1, 3]], then AB equals
A. [[4, 6], [1, 3]] B. [[2, 6], [1, 3]] C. [[4, 6], [0, 3]] D. [[4, 6], [1, 6]]

12. A 2×3 matrix multiplied by a 3×2 matrix produces a matrix of order
A. 2×2        B. 3×3
C. 2×3        D. 3×2

13. The inverse of a 2×2 matrix [[a, b], [c, d]] exists when
A. a + d ≠ 0
B. ad − bc ≠ 0
C. a − d ≠ 0
D. ad + bc ≠ 0

14. For the quadratic f(x) = x² − 5x + 6, its roots are
A. 2 and 3
B. −2 and −3
C. 1 and 6
D. 3 and 5

15. The quadratic formula for ax² + bx + c = 0 is
A. x = [−b ± √(b² − 4ac)] ⁄ 2a
B. x = [−b ± √(b + 4ac)] ⁄ 2a
C. x = [b ± √(b² − 4ac)] ⁄ 2a
D. x = [−b ± √(b² + 4ac)] ⁄ 2a

16. Solve for x: 2x + 3 = 11. Then x =
A. 3         B. 4
C. 2         D. 5

17. If one root of x² − (k + 1)x + k = 0 is 1, then k equals
A. 0           B. 1
C. −1        D. 2

18. The system of equations x + y = 5 and x − y = 1 has solution
A. x = 2, y = 3
B. x = 3, y = 2
C. x = 4, y = 1
D. x = 1, y = 4

19. Using matrices, the system x + 2y = 5 and 3x − y = 4 can be written as AX = B with A equal to
A. [[1, 2], [3, −1]] B. [[1, 3], [2, −1]] C. [[1, 2], [−1, 3]] D. [[2, 1], [3, −1]]

20. The determinant of [[2, 3], [4, 5]] is
A. −2          B. 2
C. −10        D. 10

21. If the determinant of a 2×2 matrix is zero, the matrix is
A. invertible
B. singular
C. diagonalizable
D. orthogonal

22. The distance between points (2, 3) and (5, 7) is
A. 5          B. √20
C. √29      D. 4

23. The midpoint of the segment joining (−2, 4) and (6, −2) is
A. (2, 1)        B. (4, 2)
C. (2, −1)      D. (−4, 6)

24. The gradient (slope) of the line joining (1, 2) and (4, 8) is
A. 2        B. 3
C. 6        D. ³⁄₂

25. The equation of a line with gradient 2 passing through (1, 3) is
A. y = 2x + 1
B. y = 2x + 3
C. y = 2x − 1
D. y = x + 2

26. The equation of a circle with centre (0, 0) and radius 5 is
A. x² + y² = 25
B. x² + y² = 5
C. (x − 5)² + y² = 25
D. x² + (y − 5)² = 25

27. A point P(x, y) lies on the circle x² + y² = 25 when
A. x = 3, y = 4
B. x = 5, y = 5
C. x = 0, y = 6
D. x = 2, y = 2

28. Which of the following describes the amplitude of y = 3 sin x?
A. 1          B. 3
C. 0          D. 6

29. The period of y = sin(2x) is
A. 2π        B. π
C. ^π⁄₂         D. 4π

30. Solve 2 sin θ = 1 for 0° ≤ θ < 360°. Solutions include
A. θ = 30°, 150°
B. θ = 30°, 210°
C. θ = 150°, 330°
D. θ = 60°, 120°

31. If sin A = 3/5 and A is acute, then cos A equals
A. ⁴⁄₅        B. ⁵⁄₄
C. ³⁄₅        D. ²⁄₅

32. The identity cos²x + sin²x equals
A. 1          B. cos 2x
C. 0          D. sin 2x

33. Evaluate log₁₀1.
A. 0          B. 1
C. 10        D. −1

34. If log₂8 = m, then m equals
A. 2           B. 3
C. 8           D. ¹⁄₃

35. Expand: log_a(x²/y)
A. 2 log_ax − log_ay
B. 2 log_ax + log_ay
C. log_ax − 2 log_ay
D. log_a(2x) − log_ay

36. The compound interest on ₦1,000 at 10% per annum for 2 years (annual compounding) is nearest to
A. ₦100        B. ₦210
C. ₦200        D. ₦110

37. Simple interest on a sum of money for 3 years at 5% per annum on a principal of ₦2,000 is
A. ₦300        B. ₦200
C. ₦150        D. ₦100

38. A hire-purchase total of ₦12,000 is paid in three equal annual instalments. Each instalment is
A. ₦4,000       B. ₦3,000
C. ₦6,000       D. ₦2,000

39. The line y = 3x − 6 is parallel to which equation?
A. y = 3x + 2
B. y = −3x + 6
C. y = ¹⁄₃x − 6
D. y = 2x − 6

40. The line y = 3x − 6 is perpendicular to which equation?
A. y = ¹⁄₃x + 1
B. y = −¹⁄₃x + 2
C. y = −3x + 2
D. y = ¹⁄₂x − 3

41. The expansion of (x + 2)(x − 3) equals
A. x² − x − 6
B. x² − x + 6
C. x² − 6
D. x² + x − 6

42. If f(x) = 2x + 1, then f(3) equals
A. 7          B. 6
C. 5          D. 8

43. Solve for x: 3(x − 2) = 9. Then x =
A. 5         B. 6
C. 3         D. 4

44. The sum of the interior angles of a triangle is
A. 180°       B. 360°
C. 90°         D. 270°

45. In triangle ABC, if AB = AC, then the triangle is
A. isosceles
B. equilateral
C. scalene
D. right-angled

46. The area of a rectangle with length 8 cm and breadth 5 cm is
A. 40 cm²       B. 13 cm²
C. 20 cm²       D. 80 cm²

47. The value of 3² × 3³ equals
A. 3⁵       B. 3⁶
C. 3¹       D. 3⁹

48. The value of (x^a)(x^b) equals
A. x^ab         B. x^{a + b}
C. x^{a − b}      D. x^a + x^b

49. Simplify: (x³)²
A. x⁶       B. x⁵
C. x⁹       D. x¹

50. If matrix A = [[2, 0], [0, 2]], then A is
A. diagonal
B. symmetric only
C. skew-symmetric
D. singular

51. The sum of the first four terms of an arithmetic progression with first term 3 and common difference 2 is
A. 18      B. 20
C. 14      D. 24

52. The nth term of AP a, a + d, a + 2d, … is
A. a + nd
B. a + (n − 1)d
C. a + (n + 1)d
D. an + d

53. A function y = kx is called a
A. quadratic function
B. linear function
C. exponential function
D. constant function

54. Which of the following is an identity?
A. (x + y)² = x² + 2xy + y²
B. x² + y² = (x + y)²
C. x/y = y/x
D. x + x = 2

55. The matrix [[0, 1], [−1, 0]] is
A. skew-symmetric
B. symmetric
C. diagonal
D. singular

56. If tan θ = 1, one solution for θ in degrees between 0° and 180° is
A. 45°       B. 30°
C. 60°       D. 90°

57. The line through the origin with gradient m has equation
A. y = mx
B. y = x + m
C. y = m
D. mx + y = 1

58. Which expression equals (a − b)(a + b)?
A. a² − b²
B. a² + b²
C. a² − 2ab + b²
D. a² + 2ab + b²

59. If matrix A is [[1, 0], [0, 1]], then A is called
A. zero matrix
B. identity matrix
C. singular matrix
D. skew-symmetric matrix

60. The equation 2x² − 8 = 0 has roots
A. ±2        B. ±√2
C. ±4        D. ±²⁄_√2

SECTION B: Essay / Theory

INSTRUCTION – Answer only five (5) questions in this section. Write your answers clearly and show working where necessary.

1. (a) State and prove the laws of logarithms for multiplication and division.
(b) Hence solve the equation log₃(x + 2) − log₃x = 1 for x.

2. (a) Define a matrix and state the conditions for matrix multiplication.
(b) Given A = [[2, 1], [1, 3]] and B = [[1, 0], [2, 1]], compute AB and BA.

3. (a) Explain how to find the inverse of a 2×2 matrix and state the condition for its existence.
(b) Find the inverse of [[4, 3], [1, 2]] if it exists.

4. (a) Using coordinate geometry, derive the equation of the perpendicular bisector of the line segment joining P(2, 1) and Q(6, 5).
(b) Find its point of intersection with the x-axis.

5. (a) Prove the trigonometric identity sin²x + cos²x = 1.
(b) Solve the equation 2 cos²θ − 1 = 0 for 0° ≤ θ < 360°.

6. (a) Explain the difference between simple and compound interest.
(b) A principal of ₦5,000 is invested at 8% per annum compound interest, compounded annually. Calculate the amount after 3 years, showing your working.

7. (a) Solve the quadratic equation x² − 4x − 5 = 0 by completing the square.
(b) Verify your answers using the quadratic formula.

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Answers to Mathematics Exam Questions for SS3 First Term

Answers to Section A (Objective Test)

The following table gives the correct answers to the objective section of Mathematics exam questions for SS3 First term. If you are using a mobile device, hold the table and scroll to the right or left for a complete view.

So here you have the answers to the objective section of Mathematics Exam Questions for SS3 First term. Use the comments section to let me know if you have any questions you would want me to clarify or discuss further.

Answers to Section B (Theory)

How to Pass Mathematics Exam Questions for SS3 First Term

Passing your Mathematics exam questions for SS3 First term requires a combination of preparation, understanding, and strategy. Here are actionable tips to help you excel:

1. Know the syllabus.
Get the official WAEC topics for SS3 first term. Tick each topic as you cover it. Do not study beyond the term topics the week before the exam.

2. Make a simple study plan.
Divide topics across the weeks before the exam. Study one main topic a day. Spend 20–30 minutes revising what you learned the previous day.

3. Learn the rules, then practise.
Memorise key formulas and laws (surds, logarithms, matrices, trigonometric identities, coordinate geometry, compound interest). After you learn a rule, do at least 10 practice questions on it.

4. Use past questions smartly.
Do WAEC-style past questions on each topic. Time yourself. Mark your answers and study the solutions. Repeat the weak questions until you can do them without help.

5. Focus on exam technique.
Read each question carefully. Write down known formulas first. Show clear working. For MCQs, eliminate wrong choices quickly. For theory questions, plan short steps before writing the full solution.

6. Train your speed and accuracy.
Do timed drills: 10–20 objective questions in 15 minutes; one theory question in 20–25 minutes. Check for calculation mistakes. Slow, correct work first; then work on speed.

7. Learn to check answers.
For algebra and quadratics, substitute roots back into the equation. For geometry, re-check coordinates and slopes. For interest problems, re-calc with a simple method to confirm your result.

8. Keep a small formula sheet.
Write short formulas on one page you review daily: laws of logs, surd simplification, matrix inverse formula, compound interest formula, trig identities. Do not rely on the sheet in the exam — use it as memory aid while studying.

9. Common traps to avoid.

• Sign errors in algebra and when completing the square.
• Forgetting domain restrictions in log questions (x > 0) and surds.
• Mixing degrees and radians in trigonometry.
• Rushing matrix conformability rules — check orders first.

10. On exam day.
Arrive early. Read the whole paper fast. Do the objective section first if you are quick at MCQs. If you prefer theory, start with the part that scores most for you. Always show clear steps for any question that earns method marks.

It’s a wrap!

If you need more clarification on SS3 First Term Questions on Mathematics, you can use the comments box below. We’ll be there to answer you asap. Don’t forget to join our Free Online Tutorial Classes on YouTube. (Subscribe to the Channel)

Best wishes.