2025 NECO examination questions and answers on mathematics
NECO Mathematics Objective Questions and Answers (1–20)
Instructions: Choose the correct option from A–D. Only one option is correct.
-
Evaluate: 12 ÷ 0.4
A) 3
B) 30
C) 48
D) 4.8
Answer: B) 30 -
Simplify: 5(x − 2) + 3(x + 4)
A) 8x + 2
B) 5x − 6
C) 8x + 14
D) 8x − 2
Answer: D) 8x − 2 -
Find the HCF of 60, 72 and 108
A) 6
B) 12
C) 18
D) 24
Answer: B) 12 -
If x = −3, evaluate: x² − 5x − 6
A) 18
B) 30
C) 0
D) 24
Answer: B) 30 -
Solve for x: 2x − 5 = 9
A) 2
B) 7
C) −7
D) 5
Answer: B) 7 -
Find the median of 7, 12, 5, 9, 3, 11, 10
A) 7
B) 9
C) 10
D) 11
Answer: B) 9 -
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 -
If a = 3 and b = −2, evaluate ab² + a²b
A) −6
B) 30
C) −30
D) 6
Answer: C) −30 -
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 -
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 -
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 -
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 -
Evaluate: log₁₀ 1000
A) 2
B) 3
C) 1
D) 0
Answer: B) 3 -
Solve: 3(2x − 1) = 2(3x + 4)
A) −11
B) 2
C) −2
D) 11
Answer: C) −2 -
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 -
Evaluate 2⁴ ÷ 2²
A) 2
B) 4
C) 6
D) 8
Answer: B) 4 -
Find the LCM of 18, 24, and 30.
A) 60
B) 90
C) 120
D) 180
Answer: D) 360 -
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 -
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 -
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
-
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 -
What is the cube root of 512?
A) 6
B) 8
C) 9
D) 7
Answer: B) 8 -
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} -
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 -
What is the value of 81^(¼)?
A) 2
B) 3
C) 4
D) 9
Answer: B) 3 -
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 -
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 -
What is the next prime number after 29?
A) 31
B) 33
C) 35
D) 37
Answer: A) 31 -
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} -
Convert 6.25% to a decimal.
A) 0.0625
B) 0.625
C) 6.25
D) 0.00625
Answer: A) 0.0625
-
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 -
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 -
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 -
Find the value of x in 2:5 = x:25
A) 10
B) 5
C) 8
D) 12
Answer: A) 10 -
In a class of 40 students, 28 are boys. What percentage are girls?
A) 25%
B) 30%
C) 35%
D) 40%
Answer: B) 30% -
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 -
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 -
Solve: 2x−34=5\frac{2x – 3}{4} = 5
A) 10
B) 11
C) 13
D) 9
Answer: B) 11 -
Convert 2.5 km to meters.
A) 2500 m
B) 250 m
C) 25,000 m
D) 2.05 m
Answer: A) 2500 m -
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
-
Which of the following represents ¾ as a percentage?
A) 75%
B) 25%
C) 50%
D) 80%
Answer: A) 75% -
Find the square root of 1.44.
A) 0.12
B) 1.2
C) 12
D) 2.4
Answer: B) 1.2 -
What is the next number in the sequence: 2, 4, 8, 16, …?
A) 24
B) 30
C) 32
D) 36
Answer: C) 32 -
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 -
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 -
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 -
Simplify: (3x²y)(2xy²)
A) 6x³y³
B) 5x²y²
C) 6x²y³
D) 6x³y²
Answer: A) 6x³y³ -
The decimal equivalent of 3/8 is:
A) 0.325
B) 0.375
C) 0.625
D) 0.25
Answer: B) 0.375 -
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 -
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