Mathematics for Exam Questions SS1 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 SS1 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 SS1 Third Term

Mathematics Exam Questions for SS1 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 SS1 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 qual marks.

1. The angle which is one-quarter of its supplement is
A. 210°         B. 120°
C. 45°           D. 36°

2. In the diagram below, |PQ| = |PS| and |QR| = |RS|, <QPS = 40° and <QRS = 100°. Find <PQR.

A. 20°       B. 30°
C. 40°       D. 50°

3. The angle of elevation from the top of a tower from an observer on the ground is 60°. If the top of the tower is 100m away from the observer, how high is the tower?
A. 50m            B. 86.6m
C. 173.2m       D. 200m

4. One of the two parallel sides of a trapezium is one-half the length of the other. If the height of the trapezium is 7cm and its area 52.5cm², the length of the parallel sides are
A. 10cm, 20cm
B. 5cm, 10cm
C. 7.5cm, 15cm
D. 2.5cm, 5cm

5. In the triangle ABD, AC is the altitude from A to BD. If |AD| = 15cm, |AB| = 13cm and |CD| = 9cm, Find |BD|.

A. 12cm           B. 13cm
C. 14cm           D. 15cm

6. The angle of a sector of a circle of radius 4.2cm is 150°. If π = 22/7, the perimeter of the sector is
A. 11cm              B. 15.2cm
C. 16.8cm           D. 19.4cm

7. Evaluate 313₄ – 131₄ + 333₄
A. 1312₄           B. 1121₄
C. 211₄             D. 1311₄

8. Calculate the volume of a cone of radius 6cm and vertical height 7cm (take π = 22/7)
A. 21cm³        B. 26.4 cm³
C. 42 cm³       D. 264 cm³

9. The pie chart below shows the distribution of the expenditure of a household on various food items in a certain month. If ₦200 was spent on fruits, how much was spent on rice?

A. ₦400         B. ₦600
C. ₦800         D. ₦1,000

The diagram below illustrates the distribution of marks in a class test. Use the information in the diagram to answer questions 10 and 11.

10. The total number of students who sat for the test is
A. 35          B. 36
C. 40          D. 48

11. The percentage of students who scored less than 5 marks is
A. 75%        B. 67%
C. 50%        D. 33%

12. The angle which is one-third of its complement is
A. 22½°         B. 30°
C. 45°            D. 75°

13. A square tile measures 20cm by 20cm. How many such tiles will cover a floor measuring 5m by 4m?
A. 500          B. 400
C. 320          D. 250

14. A chord of length 9cm is drawn on a circle of radius 16cm. Find the angle subtended at the centre by the chord to the nearest whole number.
A. 28°            B. 30°
C. 33°            D. 35°

15. Find the smaller value of a for which a² – 3a + 2 = 0
A. –2          B. –1
C. 1            D. 0

16. Calculate the volume of a cone of 15cm diameter and 25cm height.
A. 1473.21cm²           B. 5892.86cm²
C. 17678.57cm²         D. 3345.54cm²

17. If 2p + m = 7 and 3p – 2m = 3, what is the difference between 7p and 10?
A. 1         B. 3
C. 7         D. 10

18. Each exterior angle of a regular polygon is 24°. How many sides has the polygon?
A. 15          B. 12
C. 10          D. 8

19. If cos θ = 4/5, then for 0° < θ  < 90°, tan θ is equal to
A.  5/4     B. 4/3
C. 3/4      D. 5/3

20. An arc of a circle of radius 5.6cm subtends an angle 45° at the centre of the circle. If π = 22/7, calculate the length of the arc.
A. 2.2cm          B. 4.4cm
C. 6.0cm          D. 8.8cm

21. Calculate the height, h, of a cylinder if the volume is 308cm³ and the radius is 7cm.
A. 1cm         B. 2cm
C. 3cm         D. 4cm

22. The roots of the equations 2y² – 3y – 2 = 0 are
A. –2 , 1           B. –2, ½
C. –2, 2            D. –½, 2

23. If the two adjacent angles on a straight line are (x – 60°) and (y + 30°), the value of x + y is.
A. 90         B. 150
C. 180       D. 210

24. If 301_{base a} = 193₁₀, find the value of a.
A. 5             B. 6
C. 7             D. 8

25. The sum of the prime numbers between 40 and 50 divided by the sum of the prime numbers between 1 and 6 is
A. 18.0         B. 13.1
C. 9.0           D. 8.4

26. If the size of each interior angle of a regular polygon with n sides is 160°, the value of n is
A. 12         B. 14
C. 16         D. 18

27. If cos θ = sin 50°, then is
A. 90°          B. 50°
C. 45°          D. 40°

28. If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, X = {2, 3, 6, 9} and Y = {1, 2, 4, 6, 10}, which of the following is equal to (X ∪ Y)’ ?
A. X’ ∪ Y’                  B. (X ∩ Y)’
C. X’ ∩ Y’                  D. X ∪ Y

29. A string of length 66cm is shaped into an arc of a circle of radius 28cm. Calculate the angle of the sector
A. 135°         B. 120°
C. 90°           D. 45°

30. Which of the following is not an exterior angle of a regular polygon?
A. 24°          B. 21°
C. 18°          D. 15°

31. If sin θ = x, the value of tan θ for 0° < θ  < 90° is
A. 1 – x
B.  x/[√(1 – x²)] C. x/(x – 1)
D. x/[√(x² – 1)]

32. Find the perimeter of the segment of a circle of radius 7cm if the chord subtends an angle of 120° at the centre.
A. 22.70 cm         B. 24.00 cm
C. 26.78 cm         D. 28.00 cm

A school registers 300 candidates for an examination. 180 of the candidates offer Economics and 70 offer Geography. 80 candidates offer neither Economics nor Geography. Use the information to answer questions 33 and 34.

33. The number of candidates offering both Economics and Geography is
A. 30           B. 40
C. 50           D. 60

34. The number of candidates offering at least one of Economics or Geography is
A. 200         B. 220
C. 230         D. 250

35. Given that a varies inversely as b, and b varies directly as the square of c, and a = 1 when c = 3, find the value a when c = ⅓.
A. 81            B. 27
C. 1/9           D. 1/27

36. The interior angles of a polygon add up to 1980°. How many sides has the polygon?
A. 10        B. 12
C. 13        D. 15

37. If  tan θ = 5/12, then the value of sin θ – cos θ is
A. 5/13           B. 7/13
C. 12/13         D. – 7/13

38. An observer standing on the top of a building 40m high views a stone on the ground level at an angle of depression of 38°.  The distance of the stone from the foot of the building in metres, is equal to
A. 40 sin 38°      B. 40 cos 38°
C. 40 cot 38°      D. 40 tan 38°

39. In the diagram below, AB||DE and DC||FE. If <ACD = 60° and <BAC = 35°, find the value of DEF.

A. 25°        B. 35°
C. 60°        D. 95°

40. One of the sides of a rectangle measures 5cm and the diagonal is 13cm long. Calculate the area of the rectangle
A. 65cm²          B. 60cm²
C. 32.5cm²       D. 30cm²

41. Find the length of a chord of a circle of radius 6cm if the chord subtends an angle of 80° at the centre.
A. 6.43 cm         B. 7.71 cm
C. 9.24 cm         D. 10.87 cm

42. The interior angles of a pentagon are 130°, 118°, 80°, 78° and x. Find the value of x.
A. 75°          B. 108°
C. 120°        D. 134°

43. Find the quadratic equation whose roots are y = 7 and y = –2.
A. y² + 2y – 7 = 0        B. y² – 2y + 7 = 0
C. y² – 5y – 14 =0        D. y² + 5y + 14 = 0

44. If PQ||ST in the figure below, find the value of x.

A. 165°           B. 95°
C. 85°             D. 50°

45. A sector of a circle of radius 14cm which subtends an angle of 120° at the centre is bent to form a cone. The base radius of the cone is
A. 3½cm         B. 4⅔cm
C. 9⅓cm         D. 14cm

46. Solve the equations simultaneously: 4u – v = 11; 5u + 2v = 4.
A. 6, 13          B. -2, -3
C. -2, 3           D. 2, -3

47. In a class there are 20 boys and 15 girls. What is the ratio of boys to girls is?
A. 4 : 3           B. 3 : 4
C. 4 : 5           D. none of these

48. A sector of a circle is bounded by two radii each of length 14cm and arc of length 12cm. The area of the sector is
A. 168cm²        B. 84cm²
C. 63cm²          D. 42cm²

49. Each interior angle of an eight-sided polygon is equal to
A. 140°        B. 135°
C. 130°        D. 120°

50. A chord of a circle of radius 14cm subtends an angle of 120° at the centre of the circle. Find the area of the segment bounded by the chord and the minor arc.
A. 100.52 cm²          B. 102.67 cm²
C. 103.64 cm²          D. 104.75 cm²

51. Factorize 3x² – 11x + 6
A. (3x – 2)(x – 3)
B. (2x – 2)(x – 3)
C. (3x – 2)(x + 3)
D. (3x + 2)(x – 3)

Use the diagram below to answer questions 52 and 53.

52. Calculate the area of the shape in the figure above.
A. 10.5cm²            B. 6.5cm²
C. 5.5cm²              D. 7.5cm²

53. Calculate the perimeter of the shape.
A. 22cm        B. 20cm
C. 18cm        D. 24cm

54. A trader sells an article for ₦54 at a profit of 8%. What is his percentage profit or loss if he sells the same article for ₦44?
A. 12% profit          B. 12% loss
C. 18.5% profit       D. 18.5 loss

55. Evaluate 81^-¼ x 36^½ x 10⁰
A. 0            B. 1
C. 2            D. 20

56. A parallelogram of area 425cm² has a height of 17cm. The length of the base is
A. 12.5cm          B. 20cm
C. 25cm             D. 50cm

57. Express 9.45 × 10^-3 in ordinary form:
A. 0.945         B. 0.00945
C. 9.45           D. 0.0945

58. In the figure below, find x if |QR| = 4.

A. 4√3
B. 4(1 + √3)
C. 2(3 – √3)
D. 6 + 2√3

59. A ladder of length 5m rests against a vertical wall and makes an angle of 30 with the wall. How far is the foot of the ladder from the wall?
A. 2½m      B. (5√3)/2m
C. 5m         D. 5√2m

60. The exterior angles of a quadrilateral are given as x, 2x + 5, x + 15 and 3x – 10. The value of x is
A. 50°          B. 50.86°
C. 60°          D. 61.43°

SECTION B: Essay

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

1. a. A sector of a circle of radius 4.2cm subtends an angle of 240° at the center. Calculate the
i.  perimeter of the sector
ii. area of the sector

1.b. If the sector is folded until the two edges coincide to form a cone, calculate the base radius of the cone.

2. The diagram below shows a vertical tower TF and an observer at point R.

If the distance between the foot F of the tower and the observer is 7cm, calculate
a. the height of the tower
b. the angle of elevation of the top T of the tower.

3. ABCD is a trapezium such that AD||BC, <BAD = 90°, < ADC = 45° and |BC| = 10cm. If the area of ∆BCD is 35cm2, calculate the area of ABCD.

4. The data below show the expenditure of a housewife for a particular day:

Display the information using
a.       Pie chart
b.      Bar chart

Read Also: Mathematics for Exam Questions SS2 Third Term

Answers to Mathematics Exam Questions for SS1 Third Term

Answers to Section A (Objective Test)

The following table gives the correct answers to the objective section of Mathematics exam questions for SS1 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 SS1 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. A sector of a circle of radius 4.2cm subtends an angle of 240° at the center.

i. Perimeter of the sector:
Arc length = (θ/360) × 2πr = (240/360) × 2 × (22/7) × 4.2 = (2/3) × 2 × (22/7) × 4.2 ≈ 25.28cm
Perimeter = Arc length + 2r = 25.28 + 2 × 4.2 = 33.68cm

ii. Area of the sector:
Area = (θ/360) × πr² = (240/360) × (22/7) × 4.2² = (2/3) × (22/7) × 17.64 ≈ 29.44cm²

1. b. If the sector is folded to form a cone:
Arc length becomes the circumference of the base of the cone.
C = 25.28cm, so r = C / 2π = 25.28 / (2 × 22/7) ≈ 4.02cm

2. The diagram below shows a vertical tower TF and an observer at point R.

Given: Distance from observer to foot of tower = 7cm

a. Height of the tower (TF):
Let the angle of elevation be 60° (common value).
tan(60°) = h / 7 → √3 = h / 7 → h = 7√3 ≈ 12.12cm

b. Angle of elevation:
If height of the tower is 12cm and base is 7cm:
tan(θ) = 12 / 7 → θ = arctan(12/7) ≈ 59.74°

3. ABCD is a trapezium with AD||BC, ∠BAD = 90°, ∠ADC = 45°, |BC| = 10cm.

Area of ∆BCD = 35cm²
In ∆ADC, ∠ADC = 45°, so triangle is isosceles right triangle.
Let DC = x → height h = x
Area of ∆BCD = ½ × base (DC = x) × height (from ∠BAD = 90°) = 35
½ × x × x = 35 → x² = 70 → x = √70 ≈ 8.37cm
So, height = 8.37cm, top base AD = 0, base BC = 10cm

Total area of trapezium ABCD:
Area = Area of triangle BCD + Area of triangle ABD (right triangle)
But AB = height = 8.37cm
Area = 35 + (½ × 10 × 8.37) = 35 + 41.85 = 76.85cm²

4. Expenditure of a housewife for a particular day:

Total Expenditure = ₦720

4.a. Pie Chart:
Each angle = (Amount / Total) × 360°

• Rice: (120/720) × 360 = 60°
• Yams: (100/720) × 360 = 50°
• Beans: (60/720) × 360 = 30°
• Vegetables: (140/720) × 360 = 70°
• Meat: (180/720) × 360 = 90°
• Sugar: (40/720) × 360 = 20°
• Palm-oil: (80/720) × 360 = 40°

(The pie chart the a circle divided into sectors with the above angles and labels)

4.b. Bar Chart:

Draw vertical bars with the following heights proportional to the amount:

• Rice: 120
• Yams: 100
• Beans: 60
• Vegetables: 140
• Meat: 180
• Sugar: 40
• Palm-oil: 80

(Label each bar with the item and amount)

How to Pass Mathematics Exam Questions for SS1 Third Term

Passing your Mathematics exam questions for SS1 Third term requires a combination of preparation, understanding, and strategy. Here are actionable tips to help you excel:

1. Know Your Syllabus

Start by knowing all the topics you are expected to cover in the third term. This includes geometry, algebra, trigonometry, statistics, and word problems. Focus on each topic and master its basic concepts.

2. Understand, Don’t Cram

Mathematics is not about cramming formulas or answers. It’s about understanding how and why the formulas work. Always seek to understand the logic behind every method you are taught.

3. Practice Regularly

Solve different types of questions from your textbook, past questions, and assignments. The more you practice, the better you understand how to apply the methods you’ve learned.

4. Memorize Important Formulas

While understanding is key, you also need to memorize some important formulas, especially in geometry and trigonometry. Write them out and revise them regularly.

5. Work on Your Weak Areas

Don’t ignore any topic you find difficult. Spend extra time on it and ask your teacher or a friend for help. Mastering your weak areas boosts your overall confidence.

6. Use Past Questions

Get past SS1 third term exam questions and try to solve them without looking at the answers. This helps you get used to the question patterns and time management during exams.

7. Avoid Distractions While Studying

Find a quiet place to study and stay away from your phone and social media while studying. Focused study time is more productive and helps you retain what you learn.

8. Believe in Yourself

Don’t be afraid of Mathematics. With the right mindset and consistent effort, you will succeed. Always believe that you can do it.

Conclusion: Passing Mathematics in SS1 Third Term is possible if you plan your study, practice well, and remain focused. Start early, stay consistent, and approach each question with confidence.

It’s a wrap!

If you need more clarification on SS1 Third Term Questions on Mathematics, you can use the comments box below. We’ll be there to answer you asap.

Best wishes.