JAMB Mathematics 2025 past questions

Checked by the Skolra question team · Last updated 23 October 2026

Ten questions from the 2025 JAMB Mathematics paper, with answers and explanations. We hold 55 questions from this paper, and the Skolra app has all of them.

JAMB Mathematics 2025 questions and answers

1. 1.

   The average weight of 15 iron bars is 1000 kg. If the heaviest iron bar is removed, the average weight is reduced by 5 kg. Find the weight in kg of the heaviest iron bar.

   1. A
      930 kg
   2. B
      1005 kg
   3. C
      1075 kg
   4. D
      1070 kg
      Correct
   Show answerHide answer

   Answer: D

   In any average question, always convert the average back to a total first, because it is the totals that you can add and subtract.

   Step 1 - Total of all 15 bars:
   Total = number x average = 15 x 1000 = 15000 kg.

   Step 2 - Total of the 14 bars left:
   When the heaviest bar is removed, 14 bars remain and the average falls by 5 kg, so the new average = 1000 - 5 = 995 kg.
   Total = 14 x 995 = 13930 kg.

   Step 3 - The heaviest bar:
   Heaviest bar = 15000 - 13930 = 1070 kg.

   Check it: 13930 + 1070 = 15000, and 15000 ÷ 15 = 1000 kg, exactly as the question says. So 1070 kg is the correct weight.

2. 2.

   A car dealer bought a used car for ₦270,000 and spent ₦70,000 to refurbish it. He later sold the car for ₦490,000. What was the percentage profit?

   1. A
      30.61%
   2. B
      44.12%
      Correct
   3. C
      55.56%
   4. D
      81.48%
   Show answerHide answer

   Answer: B

   In any profit-and-loss question, the cost price is everything the trader spent before selling, not just the buying price. Here the dealer spent money twice.

   Step 1 - Total cost price:
   ₦270,000 + ₦70,000 = ₦340,000

   Step 2 - Profit:
   Selling price - Cost price = ₦490,000 - ₦340,000 = ₦150,000

   Step 3 - Percentage profit:
   Profit / Cost price x 100 = 150,000/340,000 x 100
   = 15/34 x 100 = 44.1176... = 44.12%

3. 3.

   Y is partly constant and partly varies as x. When x = 3, y = 7 and when x = 5, y = 11. Find the constants of variation.

   1. A
      k = -1 and m = -2
   2. B
      k = 1 and m = 2
      Correct
   3. C
      k = 13 and m = 2
   4. D
      k = 2 and m = 1
   Show answerHide answer

   Answer: B

   When a quantity is partly constant and partly varies as x, you write it as y = k + mx, where k is the constant part and m is the constant of variation.

   Now put in the two pairs of values given:
   When x = 3, y = 7: k + 3m = 7 ... (i)
   When x = 5, y = 11: k + 5m = 11 ... (ii)

   Subtract equation (i) from equation (ii): the k cancels and you are left with 2m = 4, so m = 2.
   Put m = 2 back into (i): k + 3(2) = 7, so k = 7 - 6 = 1.

   So the constants are k = 1 and m = 2, and the relation is y = 1 + 2x. Test it: x = 3 gives 1 + 6 = 7, and x = 5 gives 1 + 10 = 11. Both check out.

4. 4.

   Calculate the interior angle of a 5 - sided regular polygon

   1. A
      108°
      Correct
   2. B
      120°
   3. C
      144°
   4. D
      72°
   Show answerHide answer

   Answer: A

   A 5-sided polygon is a pentagon, so n = 5.

   Step 1 - Sum of the interior angles:
   Sum = (n - 2) × 180°
   = (5 - 2) × 180°
   = 3 × 180° = 540°

   Step 2 - Share it equally. The polygon is regular, so all five interior angles are equal:
   Each interior angle = 540° ÷ 5 = 108°

   Quick check using the exterior angle: the exterior angles of any polygon add up to 360°, so each exterior angle = 360° ÷ 5 = 72°. Interior and exterior angles are on a straight line, so interior = 180° - 72° = 108°. Same answer.

5. 5.

   If cos $\theta$ = $\frac{\text{x}}{\text{y}}$, find tan $\theta$ in terms of x and y 

   1. A
      $\frac{\sqrt{y^2 - x^2}}{y}$
   2. B
      $\frac{\sqrt{x^2 - y^2}}{x}$
   3. C
      $\frac{x}{\sqrt{y^2 - x^2}}$
   4. D
      $\frac{\sqrt{y^2 - x^2}}{x}$
      Correct
   Show answerHide answer

   Answer: D

   Start by drawing a right-angled triangle. Since cos θ = adjacent/hypotenuse, the statement cos θ = x/y tells you that the adjacent side is x and the hypotenuse is y.

   Now use Pythagoras' theorem to get the third side (the opposite):
   opposite² = y² − x²
   opposite = √(y² − x²)

   Then apply tan θ = opposite/adjacent:
   tan θ = √(y² − x²) ÷ x

   So √(y² − x²)/x is the correct expression. Test it with numbers: if x = 3 and y = 5, then cos θ = 0.6, so θ ≈ 53.13° and tan θ ≈ 1.33. And √(25 − 9)/3 = 4/3 = 1.33. It agrees.

6. 6.

   If the probability of death is q and the probability of survival is p, find the probability of one death and one survival in an accident involving two persons

   1. A
      2pq
      Correct
   2. B
      1 − p²
   3. C
      p² + q²
   4. D
      pq
   Show answerHide answer

   Answer: A

   Two people are involved, and each one either dies (probability q) or survives (probability p), with p + q = 1. We want exactly one death and exactly one survival.

   The important point is that this can happen in two different ways:
   • the first person dies and the second survives → q × p
   • the first person survives and the second dies → p × q

   These two cases cannot happen together, so we add them:
   qp + pq = 2pq.

   You can also get it straight from the binomial formula, ⁿC_r p^rq^n−r, with n = 2 and one survival: ²C₁ × p × q = 2pq.

7. 7.

   A binary operation * is defined on the set X = {1, 2, 3, 4, 5, 6} as a*b = ab + a + b. Compute 1 * 3 

   1. A
      4
   2. B
      7
      Correct
   3. C
      8
   4. D
      3
   Show answerHide answer

   Answer: B

   A binary operation is just a rule telling you what to do with the two numbers given. Here the rule is a * b = ab + a + b, so you must multiply the two numbers and add both of them.

   Take a = 1 and b = 3:
   ab = 1 × 3 = 3
   a + b = 1 + 3 = 4
   1 * 3 = 3 + 4 = 7

   So the value 7 is the correct answer.

8. 8.

   If I is a 2 × 2 identity matrix, find the determinant of the matrix.

   1. A
      1
      Correct
   2. B
      -1
   3. C
      0
   4. D
      2
   Show answerHide answer

   Answer: A

   First, write out what the identity matrix of order 2 actually looks like. It carries 1 along the leading diagonal and 0 everywhere else:
   I = (1  0)
       (0  1)

   For any 2 x 2 matrix (a b / c d), the determinant is ad - bc. So here:
   det(I) = (1 x 1) - (0 x 0)
   det(I) = 1 - 0 = 1

   That is why the answer is 1. In fact this is a standard result you should memorise: the determinant of an identity matrix is 1 no matter the order — 2 x 2, 3 x 3, and so on. That is exactly what makes I behave like the number 1 in matrix multiplication.

9. 9.

   The second and fifth terms of a G.P are 1 and $\frac{1}{8}$ respectively. Find the common ratio

   1. A
      $\frac{1}{2}$
      Correct
   2. B
      $\frac{1}{8}$
   3. C
      $\frac{1}{4}$
   4. D
      2
   Show answerHide answer

   Answer: A

   For a G.P. the nth term is T_n = ar^n-1, where a is the first term and r the common ratio.

   So:
   Second term: ar = 1
   Fifth term: ar⁴ = $\frac{1}{8}$

   Divide the fifth term by the second term so that a cancels:
   $\frac{ar^4}{ar} = \frac{1/8}{1}$
   $r^3 = \frac{1}{8}$
   $r = \sqrt[3]{\frac{1}{8}} = \frac{1}{2}$

   Check it: since ar = 1 and r = $\frac{1}{2}$, then a = 2, and the G.P. runs 2, 1, $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$. The second term is 1 and the fifth is $\frac{1}{8}$, exactly as given. So $\frac{1}{2}$ is the common ratio.

10. 10.

    Integrate y = 4x$^3$ + 2x + cos x.

    1. A
       x$^4$ + x$^2$ − sin x + c
    2. B
       12x$^2$ + 2 − sin x + c
    3. C
       4x$^4$ + 2x$^2$ + sin x + c
    4. D
       x$^4$ + x$^2$ + sin x + c
       Correct
    Show answerHide answer

    Answer: D

    Integrate the expression term by term, using the rule ∫xⁿ dx = xⁿ⁺¹/(n + 1) + c for the powers of x, and ∫cos x dx = sin x + c for the trigonometric part.

    ∫4x³ dx = 4 × x⁴/4 = x⁴
    ∫2x dx = 2 × x²/2 = x²
    ∫cos x dx = sin x

    Adding them and remembering the constant of integration gives x⁴ + x² + sin x + c. Always check your answer by differentiating it back: d/dx(x⁴ + x² + sin x + c) = 4x³ + 2x + cos x, which is exactly what you were given.

The questions come from past JAMB, WAEC and NECO papers. We use software to help write the answer options and explanations, and every answer is checked twice before it goes on the site. How we check

Spotted a wrong answer? Tell us from the app or on the contact page and we check it.

Practise all 55 questions we hold from the 2025 paper, on a timed CBT screen

Every question has the answer and an explanation, in the Skolra app.

Download for WindowsDownload for Mac

About the app · Skolra for Windows · Skolra for Mac