Mathematics for Exam Questions SS2 Third Term

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 SS2 Third 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 Facebook. (Like and Follow Page)

Introduction to Mathematics as a School Subject

Mathematics as a school subject is the study of numbers, shapes, patterns, and the relationships between them. It helps students to develop skills in reasoning, problem-solving, and logical thinking. Mathematics covers topics such as arithmetic, algebra, geometry, statistics, and calculus, depending on the level of study.

In school, Mathematics is not just about calculations — it trains the mind to think in an orderly and precise way. It is also a key subject because it is applied in science, technology, finance, engineering, and everyday decision-making. Mastering Mathematics builds confidence and prepares students for further studies and careers that require analytical skills.

Mathematics Exam Questions for SS2 Third Term

Mathematics Exam Questions for SS2 Third 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 SS2 Mathematics Third Term Exam Past Questions made available to assist students in their revision for 3rd term examinations and also teachers in structuring standard examinations.

SECTION A: Objectives

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

1. Two consecutive numbers are such that the sum of thrice the smaller and twice the larger is 17. What are the numbers?
A. 3, 5          B. 3, 4
C. 4, 7          D. 3, 2

2. What is the bearing of Yola from Jalingo if the bearing of Jalingo from Yola is 200°?
A. 160°           B. 340°
C. 020°           D. 220°

3. The percentage error made in estimating the depth of a classroom is 17.1%. If the classroom is actually 3.5m deep, what is the estimated depth of the classroom?
A. 2.9cm          B. 1.7cm
C. 2.7cm          D. 2.8cm

4. The point X is 38km due east of a point Y. The bearings of a flagpole from X and Y are N18°W and N40°E respectively. Calculate the distance of the flagpole from Y correct to 1dp.
A 38.1m          B. 38.3m
C. 39.6m         D. 37.2m

5. If log₃ x² = -8, what is x?
A. 1/3            B. 1/9
C. 1/27          D. 1/81

6. If |3x – 2| > 5, find the range of values for x.
A. 3/7           B. 4/3
C. 2/7           D. 7/3

7. Points A and C are respectively 15km North and 7km West of a point P. Calculate the distance of A point from B.
A. 25.5°         B. 26.5°
C. 29.2°         D. 28.7°

8. Which of the following is a measure of Central Tendency?
A. Range           B. Percentile
C. Quartile        D. Median

9. The bearing of a point X from a point Y is S35°W, what is the bearing of Y from X?
A. N55°E           B. 055°
C. N60°E           D. N35°E

10. What is the chance of choosing at random a three-digit number which is divisible by 77?
A. 1/12           B. 1/6
C. 1/13           D. 1/5

11. Given that 48, p, 3, q are consecutive terms of a G.P, find P × Q.
A. 9          B. 8
C. √2        D. 3

12. Solve |12x + 9| > 3
A. -6 > x > -3
B. -9 < x < -3
C. -6 > x > 3
D. 6 > x > 3

13. If the equation x² + mx + 11 = 0, find the value of m.
A. 7           B. 8
C. 9           D. 10

14. In how many ways can 3 prefects be chosen out of 8 prefects?
A. 6           B. 24
C. 56         D. 336

15. Find the Standard deviation of the numbers 3, 6, 2, 17 and 5.
A. 2.00         B. 2.16
C. 2.50         D. 2.56

16. The probability that Kofi and Ama hit a target in a Shooting Competition are 1/6 and 1/9 respectively. What is the probability that only one of them will hit the target?
A. 1/54           B. 13/54
C. 20/27         D. 41/54

17.

Find the median
A. 51         B. 50
C. 52         D. 70

18. A stick is 18cm long. Bisi estimates its length to be 20cm, Calculate the percentage error in the estimate.
A. 12.13%         B. 14.14%
C. 11.11%         D. 12.18%

19. A number is chosen at random from the set X = {p : 3 ≤ p ≤ 12}. Find the probability that the number chosen is a prime.
A. 1/4           B. 5/6
C. 2/5           D. 1/12

20. Three coins are tossed once, what is the probability of obtaining two tails and a head.
A. 1/4         B. 3/8
C. 1/8         D. 3/7

21. The sum of the 2nd and 5th terms of an AP is 42. If the difference between the 6th and 3rd terms is 12, find the 20th term.
A. 76             B. 92
C. 87             D. 59

22. In an examination Kofi scored X% in physics, 50% in chemistry and 70% in biology. If the mean score for the 3 subjects was 55%, find X.
A. 45           B. 46
C. 55           D. 60

23. The following are scores obtained by some students in a test:

Find the mode.
A. 8           B. 18
C. 20         D. 9

24. If sin θ = ½ and cos θ = √3/2 , what is the value of θ in the 2nd quadrant?
A. 120°         B. 150°
C. 110°         D. 170°

25. The 1st and last terms of an AP are 6.7 and 17.1 respectively. If there are 14 terms in the Sequence, find the common difference.
A 0.6          B. 0.9
C. 0.8         D. 0.9

26. If the roots of ax² + bx + c = 0 are real and equal, which condition must be true?
A. b² − 4ac < 0
B. b² − 4ac > 0
C. b² − 4ac = 0
D. b² + 4ac = 0

27. The sides of a Square are increased from 20cm to 21cm. Calculate the percentage increase in its area
A. 2.5%          B. 9.3%
C. 10.0%        D. 10.25%

28. Simplify (8y³ – 16y²) ÷ (2y³ – 2y² – 4y)
A. 2y/(2y + 2)
B. 4y/(y + 1)
C. y/(2y – 1)
D. (y + 1)/2

29. Two perfect dice are thrown together. Determine the probability of obtaining a total score of 8.
A. 3/36         B. 5/36
C. 7/6           D. 5/6

30. The probability of an event P is 3/4 while the probability of another event Q is 1/6. If the probability of both P and Q is ½. What is the probability of either P or Q.
A. 5/6             B. 7/12
C. 11/12         D. 9/11

31. The sum of the roots of a quadratic equation is 2½ and the product of its roots is 4. The equation is
A. 2x² − 5x + 8 = 0
B. 2x² − 5x – 8 = 0
C. 2x² − 8x + 5 = 0
D. 2x² − 5x + 8 = 0

32. Find the range of values of x which satisfies the inequality 12x² < x + 1.
A. −1/4 < x < 1/3
B. −1/3 < x < -1/4
C. −1/3 < x < 1/4
D. – ¼ < x < −1/3

33. Find the equation whose roots are ±A.
A. K² + A² = 0
B. K² – A = 0
C. K − A² = 0
D. K² − A² = 0

34. The bearing of A from B is X where 270° < x < 360°. Find the bearing of B from A.
A. x − 90°         B. x − 360°
C. x − 180°       D. x − 270°

35. A girl was facing S20°W. She turned 90° in the clockwise direction. What direction is she facing?
A N70°W         B. S80°N
C. N90°E          D. W90°S

36. A G.P has 8 terms. If the 3rd and 6th terms are 112 and 14 respectively, find the sum of the G.P.
A. 789 2/3        B. 892¹/₂
C. 15                D. 20¹/₂

37. Find x if the mean of the numbers 13, 2x, 0, 5x and 11 is 9.
A. 3          B. 0
C. 13        D. 11

38. The probability of a student passing any examination is 2/3. If the student takes 3 exams, what is the probability that he will not pass any of them?
A. 1/27         B. 2/3
C. 8/27         D. 7/27

39. If x = 30° and y = 60°, evaluate without using tables  (sin x + cos y)/(sin y + cos y).
A. 3          B. 2
C. 1          D. √3/3

40. What is the value of Sin45°Sin30° – Cos45°Cos30°
A. (√3 – √2)/4

B. (√2 – 1)/2

C. (√2 – √6)/4

D. (-√6 – √2)/4

41. If 27^x = 9^y, find the value of x/y.
A.  1/3         B. 2/3
C. 1½          D. 3

42. A man is four times as old as his son. The difference between their ages is 36 years. Find the sum of their ages.
A. 72           B. 60
C. 48           D. 40

43. What is the range of the distribution 3/4, 5/6, 7/12 and 2/3 ?
A. 1/4         B. 3/4
C. 2/3         D. 7/12

44. If the sum of the quadratic equation (x − p)(2x + 1) = 0 is 1, find the value of p.
A. -3/2          B. 3/2
C. 2/3            D. -2/3

45. If the sides of a triangle are (x + 4) cm, x cm and (x – 4) cm respectively, and the cosine of the largest angle is 1/5, find x.
A. 7           B. 24
C. 25         D. 7

46. P naira invested for 4 years at r% simple interest per annum yields 0.36P naira interest. Find the value of r.
A. 1 1/9           B. 1 4/9
C. 9                 D. 11

47. If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x.
A. 3          B. 6
C. 9          D. 12

48. What percentage of observation lie outside interquartile range of any distribution
A. 12½%           B. 25%
C. 50%               D. 62½%

49. m varies directly as n and inversely as the square of p, if m = 3, when n = 2 and p = 1. Find m term in terms of n and p.
A. m = 2n/3p
B. m = 3n²/2p²
C. m = n/2p
D. m = 3n/2p²

50. If the hypotenuse of a right-angled isosceles triangle is 2. What is the length of each of the other side?
A. 1/√2          B. √2
C. √2 – 1        D. 1

SECTION B: Essay

INSTRUCTION – Answer all five (5) questions in this section.

1. The data show the marks obtained by students in a biology test.

(a) Construct a frequency distribution table using the class intervals 0-9, 10-19, 20-29,…
(b) Draw a cumulative frequency curve for the distribution.
(c) Use the graph to estimate the:
i. Median
ii. Semi-interquartile range
iii. percentage of students who scored at least 66 marks, correct to the nearest whole number.

2. The table below shows the distribution of marks scored by some students in a test.

(a) If the mean mark is 3 6/23, find the value of m.
(b) find the
i. interquartile range
ii. probability of selecting a student who scored at least 4 marks in the test.

3. A. If the 6th term of an A.P is 37 and the sum of the first six terms is 147, find the
(i) first term
(ii) sum of the first fifteen terms.

B. Out of 120 customers in a shop, 45 bought both bags and shoes. If all the customers bought either bags or shoes and 11 more customers bought shoes than bags
i. find the number of customers who bought shoes.
ii. calculate the probability that a customer selected at random bought bags.

4(a) Without using mathematical tables or calculator, evaluate  leaving the answer in standard form.
(b) A transport company has a total of 20 vehicles made up of tricycles and taxicabs. Each tricycle carries 2 passengers while each taxicab carries 4 passengers. If a total of 66 passengers at a time were carried, how many tricycles does the company have?

5(a) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. Find the probability that the total is either a perfect square or an odd number.
(b) The bearing of Q from P is 150° and the bearing of P from R is 015°. If Q and R are 24km and 32km respectively from P,
i. represent this information in a diagram.
ii. calculate the distance between Q and R correct to 2 d.p.
iii. find the bearing of R from Q, correct to the nearest degree.

Read Also: Learn the Laws of Indices in Mathematics.

Answers to Mathematics Exam Questions for SS2 Third Term

Answers to Section A (Objective Test)

The following table gives the correct answers to the objective section of Mathematics exam questions for SS2 Third 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 SS2 Third 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)

1.

(a) The marks are arranged in a frequency distribution table with class intervals 0-9, 10-19, 20-29, …

(b) Plot the cumulative frequencies against the upper class boundaries and draw a smooth cumulative frequency curve (ogive).

(c) From the graph:

• Median: Approximately 53 marks.
• Semi-interquartile range: About 14 marks.
• Percentage scoring ≥ 66: ≈ 25%.

2.

(a) Mean mark = 3 6/23 = 75/23

Total students = (m+2) + (m−1) + (2m−3) + (m+5) + (3m−4) = 8m − 1

Total marks = 1(m+2) + 2(m−1) + 3(2m−3) + 4(m+5) + 5(3m−4) = 24m − 1

Mean = (24m − 1) / (8m − 1) = 75/23

Solving gives: m = 4

(b)(i) Data values:
Marks: 1 → 6 students, 2 → 3 students, 3 → 5 students, 4 → 9 students, 5 → 8 students.
Cumulative frequencies: 6, 9, 14, 23, 31.
Q1 is 8th value = 2, Q3 is 24th value = 5, so Interquartile range = 3.

(ii) Students scoring ≥ 4 = 9 + 8 = 17.
Total students = 31.
Probability = 17/31.

3.

A(i) Let first term be a, common difference be d.
6th term: a + 5d = 37.
Sum of first 6 terms: (6/2)[2a + 5d] = 147 → 2a + 5d = 49.
Solving gives: a = 12, d = 5.

(ii) S₁₅ = (15/2)[2(12) + 14(5)] = 615.

B(i) Let number buying bags = b, shoes = s.
b + s − 45 = 120, s = b + 11. Solving gives: s = 73.

(ii) Number buying bags = 62.
Probability = 62/120 = 31/60.

4.

(a) Evaluate: (2.7 × 10⁻³ × 3 × 10⁵) / (9 × 10²)
= (8.1 × 10²) / (9 × 10²) = 0.9 = 9 × 10⁻¹.

(b) Let number of tricycles = t, taxicabs = c.
t + c = 20, 2t + 4c = 66.
Solving gives: t = 7.

5.

(a) Sample space totals from {2, 3, 4} and {1, 3, 5} → 9 outcomes.

• Perfect squares: sums = 4, 9.
• Odd numbers: sums that are odd.

Favorable outcomes = 6, Probability = 6/9 = 2/3.

(b)(i) Diagram: Triangle PQR with PQ = 24 km at 150°, PR = 32 km at 015°.

(ii) Using cosine rule:
QR² = 24² + 32² − 2(24)(32)cos115°
QR ≈ 46.87 km.

(iii) Using sine rule:
sin(∠PQR) / PR = sin(115°) / QR
Bearing of R from Q ≈ 049°.

How to Pass Mathematics Exam Questions for SS2 Third Term

Passing your Mathematics exam questions for SS2 Third term requires a combination of preparation, understanding, and strategy. Here are actionable tips to help you excel:

How to Pass Mathematics Exam Questions for SS2 Third Term

1. Revise Your Class Notes Thoroughly
   Mathematics is built topic by topic. Go back to your notes and make sure you understand each concept before moving on to the next.
2. Practice Past Questions
   Work on past exam questions for your school, WAEC, and NECO SSCE levels. This will help you identify common question patterns.
3. Focus on Key Topics for Third Term
   For SS2 Third Term, you should pay special attention to topics like:
   • Statistics (mean, median, mode, standard deviation, ogives)
   • Probability
   • Bearing and distances
   • Simple and compound interest
   • Trigonometry
   • Algebraic equations and inequalities
   • Sequence and series (AP and GP)
4. Understand Formulas, Don’t Just Cram
   Memorising formulas is important, but knowing why and how to use them will help you solve unusual questions confidently.
5. Show All Your Working
   In Mathematics exams, marks are awarded for correct methods even if the final answer is wrong. Always show every calculation step.
6. Manage Your Time in the Exam Hall
   Don’t spend too long on one difficult question. Answer the easier ones first to secure marks before returning to the harder ones.
7. Check Your Units and Final Answers
   Always write the correct units (e.g., cm, m², %) and make sure your answers are clearly stated.
8. Avoid Common Mistakes
   • Misreading the question
   • Copying numbers wrongly
   • Forgetting to simplify fractions or leave answers in standard form
9. Practise Without a Calculator Sometimes
   Some questions may require mental or manual calculation. Build your speed and accuracy without depending too much on calculators.
10. Pray and Stay Calm
    Go into the exam hall with a clear mind. Read every question carefully before answering.

It’s a wrap!

If you need more clarification on SS2 Third Term Questions on Mathematics, you can use the comments box below. We’ll be there to answer you asap.

Best wishes.