2025 NECO examination questions and answers on mathematics

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2025 NECO examination questions and answers on mathematics

Contents
NECO Mathematics Objective Questions and Answers (1–20)2025 NECO examination questions and answers on mathematicsSection B: Theory QuestionsQuestion 1: StatisticsQuestion 2: Geometry (Circle Theorems)Question 3: Algebra2025 NECO examination questions and answers on mathematicsQuestion 4: MensurationQuestion 5: TrigonometryQuestion 6: Financial ArithmeticQuestion 7: Bearing and Scale DrawingQuestion 8: Sets and Venn DiagramsTheory Section: Solutions & Marking GuideQuestion 1: Statistics2025 NECO examination questions and answers on mathematicsQuestion 2: Geometry (Circle Theorems)Question 3: AlgebraQuestion 4: Mensuration2025 NECO examination questions and answers on mathematicsQuestion 5: TrigonometryQuestion 6: Financial ArithmeticQuestion 7: Bearings and Scale DrawingQuestion 8: Sets and Venn Diagram

NECO Mathematics Objective Questions and Answers (1–20)

Instructions: Choose the correct option from A–D. Only one option is correct.

  1. Evaluate: 12 ÷ 0.4
    A) 3
    B) 30
    C) 48
    D) 4.8
    Answer: B) 30

  2. Simplify: 5(x − 2) + 3(x + 4)
    A) 8x + 2
    B) 5x − 6
    C) 8x + 14
    D) 8x − 2
    Answer: D) 8x − 2

  3. Find the HCF of 60, 72 and 108
    A) 6
    B) 12
    C) 18
    D) 24
    Answer: B) 12

  4. If x = −3, evaluate: x² − 5x − 6
    A) 18
    B) 30
    C) 0
    D) 24
    Answer: B) 30

  5. Solve for x: 2x − 5 = 9
    A) 2
    B) 7
    C) −7
    D) 5
    Answer: B) 7

  6. Find the median of 7, 12, 5, 9, 3, 11, 10
    A) 7
    B) 9
    C) 10
    D) 11
    Answer: B) 9

  7. Express 0.45 as a fraction in its simplest form
    A) 9/10
    B) 45/100
    C) 9/20
    D) 45/90
    Answer: C) 9/20

  8. If a = 3 and b = −2, evaluate ab² + a²b
    A) −6
    B) 30
    C) −30
    D) 6
    Answer: C) −30

  9. A trader made a profit of 20% by selling a radio for ₦18,000. Find the cost price.
    A) ₦15,000
    B) ₦14,400
    C) ₦18,000
    D) ₦21,600
    Answer: A) ₦15,000

  10. Convert 135° to radians.
    A) 2.36 rad
    B) 2.25 rad
    C) 3.14 rad
    D) 2.36π rad
    Answer: A) 2.36 rad

  11. Find the area of a triangle with base 8 cm and height 5 cm.
    A) 40 cm²
    B) 20 cm²
    C) 13 cm²
    D) 30 cm²
    Answer: B) 20 cm²

  12. A bag contains 3 red, 2 white, and 5 blue balls. What is the probability of picking a red ball?
    A) 1/10
    B) 3/10
    C) 2/5
    D) 3/5
    Answer: B) 3/10

  13. Evaluate: log₁₀ 1000
    A) 2
    B) 3
    C) 1
    D) 0
    Answer: B) 3

  14. Solve: 3(2x − 1) = 2(3x + 4)
    A) −11
    B) 2
    C) −2
    D) 11
    Answer: C) −2

  15. Find the simple interest on ₦5,000 at 6% per annum for 3 years.
    A) ₦300
    B) ₦800
    C) ₦900
    D) ₦600
    Answer: C) ₦900

  16. Evaluate 2⁴ ÷ 2²
    A) 2
    B) 4
    C) 6
    D) 8
    Answer: B) 4

  17. Find the LCM of 18, 24, and 30.
    A) 60
    B) 90
    C) 120
    D) 180
    Answer: D) 360

  18. If the exterior angle of a regular polygon is 45°, how many sides has the polygon?
    A) 6
    B) 8
    C) 9
    D) 12
    Answer: D) 8

  19. If sin θ = 0.6, find cos θ given that θ is acute.
    A) 0.6
    B) 0.8
    C) 1
    D) 1.6
    Answer: B) 0.8

  20. Find the mode of the following data: 4, 6, 4, 7, 9, 4, 6
    A) 4
    B) 6
    C) 7
    D) 9
    Answer: A) 4

  1. A number is divisible by 6 if it is divisible by:
    A) 2 and 3
    B) 3 and 4
    C) 2 and 4
    D) 3 and 5
    Answer: A) 2 and 3

  2. What is the cube root of 512?
    A) 6
    B) 8
    C) 9
    D) 7
    Answer: B) 8

  3. Simplify: 35+47\frac{3}{5} + \frac{4}{7}
    A) 2935\frac{29}{35}
    B) 1235\frac{12}{35}
    C) 1735\frac{17}{35}
    D) 2135\frac{21}{35}
    Answer: A) 2935\frac{29}{35}

  4. If the circumference of a circle is 44 cm, find its radius. (π = 22/7)
    A) 7 cm
    B) 14 cm
    C) 21 cm
    D) 22 cm
    Answer: A) 7 cm

  5. What is the value of 81^(¼)?
    A) 2
    B) 3
    C) 4
    D) 9
    Answer: B) 3

  6. Solve: (x + 2)(x − 3) = 0
    A) x = −2 or 3
    B) x = 2 or −3
    C) x = −2 only
    D) x = 3 only
    Answer: A) x = −2 or 3

  7. Find the volume of a cube of side 5 cm.
    A) 25 cm³
    B) 75 cm³
    C) 100 cm³
    D) 125 cm³
    Answer: D) 125 cm³

  8. What is the next prime number after 29?
    A) 31
    B) 33
    C) 35
    D) 37
    Answer: A) 31

  9. Express 5.625 as a fraction.
    A) 458\frac{45}{8}
    B) 92\frac{9}{2}
    C) 112\frac{11}{2}
    D) 234\frac{23}{4}
    Answer: A) 458\frac{45}{8}

  10. Convert 6.25% to a decimal.
    A) 0.0625
    B) 0.625
    C) 6.25
    D) 0.00625
    Answer: A) 0.0625

  1. A train travels 180 km in 3 hours. What is its average speed?
    A) 30 km/h
    B) 60 km/h
    C) 90 km/h
    D) 120 km/h
    Answer: B) 60 km/h

  2. If the mean of 4, 8, x, 10, and 6 is 8, find x.
    A) 12
    B) 14
    C) 16
    D) 18
    Answer: A) 12

  3. A straight line cuts the y-axis at 3 and has a gradient of 2. What is its equation?
    A) y = 2x + 3
    B) y = 3x + 2
    C) y = −2x + 3
    D) y = 3x − 2
    Answer: A) y = 2x + 3

  4. Find the value of x in 2:5 = x:25
    A) 10
    B) 5
    C) 8
    D) 12
    Answer: A) 10

  5. In a class of 40 students, 28 are boys. What percentage are girls?
    A) 25%
    B) 30%
    C) 35%
    D) 40%
    Answer: B) 30%

  6. The 5th term of an AP is 17 and the common difference is 3. Find the first term.
    A) 5
    B) 2
    C) 3
    D) 7
    Answer: D) 5

  7. If x varies directly as y and x = 10 when y = 4, find x when y = 9.
    A) 20
    B) 22.5
    C) 18
    D) 24
    Answer: B) 22.5

  8. Solve: 2x−34=5\frac{2x – 3}{4} = 5
    A) 10
    B) 11
    C) 13
    D) 9
    Answer: B) 11

  9. Convert 2.5 km to meters.
    A) 2500 m
    B) 250 m
    C) 25,000 m
    D) 2.05 m
    Answer: A) 2500 m

  10. A man shared ₦24,000 among his three children in the ratio 3:2:1. How much did the second child get?
    A) ₦8,000
    B) ₦6,000
    C) ₦4,000
    D) ₦12,000
    Answer: B) ₦8,000

  1. Which of the following represents ¾ as a percentage?
    A) 75%
    B) 25%
    C) 50%
    D) 80%
    Answer: A) 75%

  2. Find the square root of 1.44.
    A) 0.12
    B) 1.2
    C) 12
    D) 2.4
    Answer: B) 1.2

  3. What is the next number in the sequence: 2, 4, 8, 16, …?
    A) 24
    B) 30
    C) 32
    D) 36
    Answer: C) 32

  4. A chord divides a circle into two parts called:
    A) Radius and diameter
    B) Arc and radius
    C) Sector and segment
    D) Segment and arc
    Answer: C) Sector and segment

  5. What is the probability of getting a tail in a fair coin toss?
    A) 1/3
    B) 1/2
    C) 1/4
    D) 3/4
    Answer: B) 1/2

  6. The interior angle of a regular polygon is 150°. How many sides does the polygon have?
    A) 12
    B) 10
    C) 9
    D) 8
    Answer: B) 12

  7. Simplify: (3x²y)(2xy²)
    A) 6x³y³
    B) 5x²y²
    C) 6x²y³
    D) 6x³y²
    Answer: A) 6x³y³

  8. The decimal equivalent of 3/8 is:
    A) 0.325
    B) 0.375
    C) 0.625
    D) 0.25
    Answer: B) 0.375

  9. If the area of a square is 49 cm², find its perimeter.
    A) 28 cm
    B) 14 cm
    C) 21 cm
    D) 16 cm
    Answer: A) 28 cm

  10. Which of these is irrational?
    A) 35\frac{3}{5}
    B) 2\sqrt{2}
    C) 0.75
    D) 1.25
    Answer: B) 2\sqrt{2}

2025 NECO examination questions and answers on mathematics

Section B: Theory Questions

Instruction: Answer five questions only. All questions carry equal marks. Show all necessary workings for full credit

Question 1: Statistics

The marks scored by 10 students in a test are:
12, 18, 15, 20, 25, 17, 20, 18, 15, 20.

a) Construct a frequency table for the data.
b) Find the:
    (i) Mode
    (ii) Median
    (iii) Mean

(Total: 10 marks)

Question 2: Geometry (Circle Theorems)

In the diagram, AB is a diameter of a circle. C is a point on the circle such that angle ACB = x.

a) State the value of angle ACB.
b) Prove that triangle ACB is a right-angled triangle.
c) If AB = 10 cm and AC = 6 cm, calculate the length of BC.

(Total: 10 marks)

Question 3: Algebra

a) Solve the quadratic equation:
    2x² − 3x − 5 = 0 using the quadratic formula.

b) Factorize completely:
    x² − 9x + 20

(Total: 10 marks)

2025 NECO examination questions and answers on mathematics

Question 4: Mensuration

A cylindrical tank has a radius of 3.5 m and height 10 m.

a) Calculate:
    (i) The volume of the tank
    (ii) The total surface area of the tank
(Take π = 22/7)

(Total: 10 marks)

Question 5: Trigonometry

In triangle XYZ, side YZ = 10 cm, angle Y = 30°, angle Z = 60°.

a) Calculate the length of side XY.
b) Find the area of triangle XYZ.
c) State the trigonometric ratios for angle Z.

(Total: 10 marks)

Question 6: Financial Arithmetic

a) A man borrowed ₦50,000 for 2 years at 6% per annum simple interest. Find the total interest and the amount due at the end of 2 years.
b) A trader bought an item for ₦12,000 and sold it at a profit of 25%. Calculate the selling price.
c) A mobile phone originally cost ₦75,000 but was discounted by 8%. What is the sale price?

(Total: 10 marks)

Question 7: Bearing and Scale Drawing

A ship sails from port A to port B on a bearing of 045°. It then sails from B to port C on a bearing of 135°. The distance AB = 80 km and BC = 100 km.

a) Using a scale of 1 cm to 10 km, draw the diagram.
b) Measure and state the distance AC.
c) Find the bearing of C from A.

(Total: 10 marks)

Question 8: Sets and Venn Diagrams

In a class of 50 students:

  • 30 offer Mathematics (M)

  • 25 offer English (E)

  • 10 offer both subjects

a) Represent the information on a Venn diagram.
b) Find the number of students who offer:
    (i) Only Mathematics
    (ii) Only English
    (iii) Neither subject
c) How many offer at least one subject?

(Total: 10 marks)

Theory Section: Solutions & Marking Guide

Question 1: Statistics

Given marks: 12, 18, 15, 20, 25, 17, 20, 18, 15, 20

a) Frequency Table:

Mark Frequency
12 1
15 2
17 1
18 2
20 3
25 1

b)
(i) Mode = 20 (occurs 3 times) → 1 mark
(ii) Median: Arrange data → 12, 15, 15, 17, 18, 18, 20, 20, 20, 25
Middle values = 18 and 18 → Median = (18 + 18)/2 = 18 → 2 marks
(iii) Mean = (Sum of marks) ÷ 10 = (12 + 15 + 15 + 17 + 18 + 18 + 20 + 20 + 20 + 25) ÷ 10
= 180 ÷ 10 = 18 → 2 marks

Total: 10 marks

2025 NECO examination questions and answers on mathematics

Question 2: Geometry (Circle Theorems)

a) Angle ACB = 90° (Angle in a semicircle) → 2 marks
b) Proof: Angle in a semicircle is always a right angle ⇒ triangle ACB is right-angled at C. → 2 marks
c) AB = 10 cm, AC = 6 cm
Using Pythagoras theorem:
BC² = AB² − AC² = 10² − 6² = 100 − 36 = 64
BC = √64 = 8 cm → 6 marks

Total: 10 marks

Question 3: Algebra

a) Solve: 2x² − 3x − 5 = 0
Use quadratic formula:
x = [-(-3) ± √((-3)² − 4×2×-5)] ÷ 2×2
x = [3 ± √(9 + 40)] ÷ 4 = [3 ± √49] ÷ 4
x = (3 ± 7)/4 ⇒ x = (3+7)/4 = 10/4 = 2.5 or x = (3–7)/4 = –1
So, x = 2.5 or –1 → 5 marks

b) Factorize: x² − 9x + 20
Find two numbers that multiply to 20 and sum to –9 → –5 and –4
= (x – 4)(x – 5) → 5 marks

Total: 10 marks

Question 4: Mensuration

Given: Radius (r) = 3.5 m, Height (h) = 10 m, π = 22/7

a)
(i) Volume = πr²h = (22/7) × 3.5² × 10 = (22/7) × 12.25 × 10 = 385 m³ → 4 marks

(ii) Surface Area = 2πr² + 2πrh
= 2×(22/7)×3.5² + 2×(22/7)×3.5×10
= 2×(22/7)×12.25 + 2×(22/7)×35
= 77 + 220 = 297 m² → 6 marks

Total: 10 marks

2025 NECO examination questions and answers on mathematics

Question 5: Trigonometry

Given: YZ = 10 cm, ∠Y = 30°, ∠Z = 60°, triangle XYZ

a) Using sine rule:
XY/sin Z = YZ/sin X
X = 180° − (30° + 60°) = 90°
XY/sin60 = 10/sin90
XY = 10 × sin60 = 10 × (√3/2) = 8.66 cm → 4 marks

b) Area = ½ × XY × YZ × sin∠Y
= ½ × 8.66 × 10 × sin30 = 43.3 × 0.5 = 21.65 cm² → 3 marks

c) Trig ratios for angle Z:

  • sin Z = opp/hyp = XY/YZ = 8.66/10

  • cos Z = adj/hyp

  • tan Z = opp/adj
    → 3 marks

Total: 10 marks

Question 6: Financial Arithmetic

a) SI = PRT/100 = (50000 × 6 × 2)/100 = 6000
Amount = 50000 + 6000 = ₦56,000 → 4 marks

b) Profit = 25% of 12000 = ₦3000
Selling Price = 12000 + 3000 = ₦15,000 → 3 marks

c) Discount = 8% of 75000 = ₦6000
Sale Price = 75000 – 6000 = ₦69,000 → 3 marks

Total: 10 marks

Question 7: Bearings and Scale Drawing

a) Draw port A, draw AB 045°, 8 cm long (scale 1 cm = 10 km)
From B, draw BC on 135°, 10 cm long. → 4 marks

b) Measure AC on diagram (e.g., 14.2 cm × 10 = 142 km) → 3 marks

c) Use protractor to measure bearing of C from A (e.g., 110°) → 3 marks

Total: 10 marks

Question 8: Sets and Venn Diagram

a) Venn diagram with two overlapping circles
M ∩ E = 10
Only M = 30 − 10 = 20
Only E = 25 − 10 = 15
Total = 20 + 15 + 10 = 45
Neither = 50 − 45 = 5 → 4 marks

b)
(i) Only Math = 20
(ii) Only English = 15
(iii) Neither = 5
(iv) At least one = 45 → 6 marks

Total: 10 marks

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