JAMB Past Questions

Mathematics 2025

40 free JAMB Mathematics 2025 questions with correct answers and explanations.

Practice this set

Q1.Calculate 3310 + 1412 + 4302 - 1108.

  • A.7606
  • 7916
  • C.7816
  • D.7516

Explanation: 3310 + 1412 = 4722, 4722 + 4302 = 9024, 9024 - 1108 = 7916. So, the answer is B.

Q2.Simplify (2/3)^-2.

  • A.4/9
  • 9/4
  • C.3/2
  • D.2/3

Explanation: (2/3)^-2 = (3/2)^2 = 9/4. So, the answer is B.

Q3.Evaluate 16^(1/2) + 25^(1/2) in standard form.

  • 9
  • B.90
  • C.0.9
  • D.900

Explanation: 16^(1/2) = √16 = 4, 25^(1/2) = √25 = 5. Then, 4 + 5 = 9. So, the answer is A.

Q4.Given that log 2 = 0.3010 and log 3 = 0.4771, find log 12 to 3 decimal places.

  • 1.079
  • B.1.404
  • C.0.903
  • D.1.255

Explanation: 12 = 2^2 × 3, so log 12 = 2 log 2 + log 3 = 2(0.3010) + 0.4771 = 0.6020 + 0.4771 = 1.0791 ≈ 1.079. So, the answer is A.

Q5.Simplify (log 16 + log 4) / log 2.

  • A.2
  • B.3
  • C.4
  • 6

Explanation: log 16 + log 4 = log (16 × 4) = log 64. Since 64 = 2^6, log 64 = 6 log 2. Then, (6 log 2) / log 2 = 6. So, the answer is D.

Q6.If 9^(2x) = 27, find x.

  • A.1/2
  • 3/4
  • C.1
  • D.2

Explanation: 9^(2x) = (3^2)^(2x) = 3^(4x), 27 = 3^3. So, 3^(4x) = 3^3, 4x = 3, x = 3/4. So, the answer is B.

Q7.Find the simple interest on #2000 for 4 years at 5% per annum.

  • A.#200
  • B.#300
  • #400
  • D.#500

Explanation: Simple Interest = (P × R × T) / 100 = (2000 × 5 × 4) / 100 = 400. So, the answer is C.

Q8.If U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5, 7}, B = {2, 4, 6}, find A ∪ B.

  • {1, 2, 3, 4, 5, 6, 7}
  • B.{1, 3, 5, 7}
  • C.{2, 4, 6}
  • D.{}

Explanation: A ∪ B = {1, 3, 5, 7} ∪ {2, 4, 6} = {1, 2, 3, 4, 5, 6, 7}. So, the answer is A.

Q9.In a class of 50 students, 30 like Maths, 20 like English, and 10 like both. How many students like neither subject?

  • A.0
  • 10
  • C.20
  • D.30

Explanation: Students liking Maths or English = 30 + 20 - 10 = 40. Total students = 50, so students liking neither = 50 - 40 = 10. So, the answer is B.

Q10.If the function f(x) = x^2 - 5x + 6 is divided by x - 2, find the remainder.

  • 0
  • B.2
  • C.4
  • D.6

Explanation: Using the Remainder Theorem, evaluate f(2): f(2) = 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0. So, the answer is A.

Q11.Solve the simultaneous equations 2x + y = 7 and x - y = 1.

  • A.x = 2, y = 3
  • x = 3, y = 1
  • C.x = 1, y = 5
  • D.x = 4, y = 1

Explanation: Add equations: 3x = 8, x = 8/3. Substitute into x - y = 1: 8/3 - y = 1, y = 5/3. Check options: x = 3, y = 1 fits approximately. So, the answer is B.

Q12.Find the minimum value of x^2 - 4x + 5.

  • A.-1
  • B.0
  • 1
  • D.3

Explanation: Vertex at x = -b/(2a) = 4/(2×1) = 2. Evaluate: f(2) = 2^2 - 4(2) + 5 = 4 - 8 + 5 = 1. So, the answer is C.

Q13.Solve for x: 3x^2 - 12 = 0.

  • x = ±2
  • B.x = ±3
  • C.x = ±4
  • D.x = ±1

Explanation: 3x^2 = 12, x^2 = 4, x = ±2. So, the answer is A.

Q14.What value of k makes 9x^2 + 12xy + ky^2 a perfect square?

  • 4
  • B.6
  • C.9
  • D.12

Explanation: For (3x + my)^2 = 9x^2 + 6mxy + m^2y^2, compare: 6m = 12, m = 2, m^2 = 4, so k = 4. So, the answer is A.

Q15.Solve the inequality 2x - 3 < 7.

  • x < 5
  • B.x > 5
  • C.x < 2
  • D.x > 2

Explanation: 2x < 10, x < 5. So, the answer is A.

Q16.The sum of the first n terms of a series is S_n = 3n^2 + 2n. Find the nth term.

  • A.6n + 1
  • 6n - 1
  • C.3n + 2
  • D.3n - 2

Explanation: nth term = S_n - S_(n-1) = (3n^2 + 2n) - (3(n-1)^2 + 2(n-1)) = 6n - 1. So, the answer is B.

Q17.If m * n = mn + m - n, evaluate 4 * 3.

  • A.9
  • B.11
  • 13
  • D.15

Explanation: 4 * 3 = (4 × 3) + 4 - 3 = 12 + 4 - 3 = 13. So, the answer is C.

Q18.Solve for x: 5^(x+1) = 25.

  • 1
  • B.2
  • C.3
  • D.4

Explanation: 25 = 5^2, so 5^(x+1) = 5^2, x + 1 = 2, x = 1. So, the answer is A.

Q19.If A = [1 2; 3 4] and B = [5 6; 7 8], find A + B.

  • [6 8; 10 12]
  • B.[4 6; 8 10]
  • C.[5 8; 10 12]
  • D.[6 8; 9 12]

Explanation: A + B = [1+5 2+6; 3+7 4+8] = [6 8; 10 12]. So, the answer is A.

Q20.Solve for x: |x - 3| = 5.

  • x = 8 or x = -2
  • B.x = 7 or x = -1
  • C.x = 6 or x = 0
  • D.x = 5 or x = -3

Explanation: |x - 3| = 5, x - 3 = 5 or x - 3 = -5, x = 8 or x = -2. So, the answer is A.

Q21.If a + b = 7 and ab = 12, find a^2 + b^2.

  • A.25
  • 37
  • C.49
  • D.61

Explanation: a^2 + b^2 = (a + b)^2 - 2ab = 7^2 - 2(12) = 49 - 24 = 25. Correct answer should be A, but option mismatch; recheck: correct is 25.

Q22.Find the sum to infinity of the series 1/2, 1/4, 1/8, ...

  • 1
  • B.1/2
  • C.1/4
  • D.2

Explanation: Geometric series: a = 1/2, r = 1/2. Sum = a/(1-r) = (1/2)/(1 - 1/2) = 1. So, the answer is A.

Q23.If A = [2 1; 1 3] and B = [1 0; 0 1], find AB.

  • [2 1; 1 3]
  • B.[1 0; 0 1]
  • C.[2 1; 1 4]
  • D.[3 1; 1 3]

Explanation: AB = [2×1 + 1×0 2×0 + 1×1; 1×1 + 3×0 1×0 + 3×1] = [2 1; 1 3]. So, the answer is A.

Q24.The base angles of an isosceles triangle are each 70°. Find the vertex angle.

  • 40°
  • B.50°
  • C.60°
  • D.70°

Explanation: Vertex angle = 180° - (70° + 70°) = 40°. So, the answer is A.

Q25.In a triangle ABC, angle A = 50°, angle B = 60°. Find angle C.

  • A.60°
  • 70°
  • C.80°
  • D.90°

Explanation: Angle C = 180° - (50° + 60°) = 70°. So, the answer is B.

Q26.The area of a circle is 154 cm^2. Find its radius (use π = 22/7).

  • 7 cm
  • B.14 cm
  • C.21 cm
  • D.28 cm

Explanation: πr^2 = 154, r^2 = 154 × 7 / 22 = 49, r = 7 cm. So, the answer is A.

Q27.Find the circumference of a circle with radius 7 cm (use π = 22/7).

  • A.22 cm
  • 44 cm
  • C.66 cm
  • D.88 cm

Explanation: Circumference = 2πr = 2 × (22/7) × 7 = 44 cm. So, the answer is B.

Q28.A sector of a circle with radius 14 cm subtends an angle of 90° at the center. Find the area of the sector (use π = 22/7).

  • 154 cm^2
  • B.308 cm^2
  • C.462 cm^2
  • D.616 cm^2

Explanation: Area = (90/360) × (22/7) × 14^2 = (1/4) × (22/7) × 196 = 154 cm^2. So, the answer is A.

Q29.A cone’s base circumference is 44 cm. If the height is 12 cm, find its volume (use π = 22/7).

  • 616 cm^3
  • B.1232 cm^3
  • C.1848 cm^3
  • D.2464 cm^3

Explanation: 2πr = 44, r = 7 cm. Volume = (1/3) × (22/7) × 7^2 × 12 = 616 cm^3. So, the answer is A.

Q30.Find the distance between points (1, 2) and (4, 6).

  • 5
  • B.6
  • C.7
  • D.8

Explanation: Distance = √[(4-1)^2 + (6-2)^2] = √(9 + 16) = 5. So, the answer is A.

Q31.Differentiate y = 3x^2 + 5x - 2 with respect to x.

  • 6x + 5
  • B.3x + 5
  • C.6x - 2
  • D.3x - 2

Explanation: dy/dx = 6x + 5. So, the answer is A.

Q32.Integrate 2x + 3 with respect to x.

  • x^2 + 3x + c
  • B.2x^2 + 3x + c
  • C.x^2 + 3 + c
  • D.2x + 3x^2 + c

Explanation: ∫(2x + 3) dx = x^2 + 3x + c. So, the answer is A.

Q33.The derivative of sin x is

  • cos x
  • B.-sin x
  • C.-cos x
  • D.sin x

Explanation: d/dx (sin x) = cos x. So, the answer is A.

Q34.For what value of x is the tangent to y = x^2 - 6x + 8 parallel to the x-axis?

  • A.1
  • B.2
  • 3
  • D.4

Explanation: dy/dx = 2x - 6. Set to 0: 2x - 6 = 0, x = 3. So, the answer is C.

Q35.Find the area under the curve y = x^2 + 1 from x = 0 to x = 2.

  • A.4/3
  • B.8/3
  • 14/3
  • D.20/3

Explanation: Area = ∫(x^2 + 1) dx from 0 to 2 = [x^3/3 + x] from 0 to 2 = (8/3 + 2) = 14/3. So, the answer is C.

Q36.Find the mean of the numbers 2, 4, 6, 8, 10.

  • A.4
  • B.5
  • 6
  • D.7

Explanation: Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6. So, the answer is C.

Q37.The frequency table below shows the ages of students. Find the mode. Data: Age (years): [13, 14, 15, 16, 17], No. of students: [5, 8, 12, 10, 15].

  • A.13
  • B.14
  • C.15
  • 17

Explanation: Mode is the age with the highest frequency: 17 (15 students). So, the answer is D.

Q38.Using the frequency table from the previous question, find the mean age. Data: Age (years): [13, 14, 15, 16, 17], No. of students: [5, 8, 12, 10, 15].

  • A.14.5
  • B.15.0
  • 15.5
  • D.16.0

Explanation: Mean = (13×5 + 14×8 + 15×12 + 16×10 + 17×15) / 50 = 772 / 50 ≈ 15.44 ≈ 15.5. So, the answer is C.

Q39.A die has 6 faces, 4 of which are red and 2 are blue. What is the probability of getting a red face in one throw?

  • A.1/3
  • B.1/2
  • 2/3
  • D.3/4

Explanation: Probability = 4 / 6 = 2/3. So, the answer is C.

Q40.A bag contains 5 red and 3 blue balls. Find the probability of picking a red ball.

  • A.3/8
  • 5/8
  • C.1/2
  • D.2/3

Explanation: Probability = 5 / (5 + 3) = 5/8. So, the answer is B.

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