JAMB Mathematics 2016 past questions

Checked by the Skolra question team · Last updated 15 October 2026

Ten questions from the 2016 JAMB Mathematics paper, with answers and explanations. We hold 38 questions from this paper, and the Skolra app has all of them.

JAMB Mathematics 2016 questions and answers

1. 1.Evaluate $\int$(sinx - 5x²)dx
   1. A
      cosx - (5x³/3) + c
   2. B
      -cosx - 5x³ + c
   3. C
      -cosx - (5x³/3) + c
      Correct
   4. D
      cosx + (5x³/3) + c
   Show answerHide answer

   Answer: C

   Integrate term by term.

   ∫sinx dx = -cosx (the integral of sine is negative cosine, not positive cosine).

   ∫5x² dx = 5x³/3, using the power rule (increase the power by 1, then divide by the new power), so this term becomes -5x³/3 since it was being subtracted.

   Adding the constant of integration gives -cosx - (5x³/3) + c, which is correct.

   Writing +cosx instead of -cosx is a common sign slip on the sine integral. Forgetting to divide by the new power 3 gives -5x³ instead of -5x³/3. Getting both signs wrong (cosx and +5x³/3) combines both mistakes.

2. 2.Find $\frac{dy}{dx}$, if y = $\frac{2}{3}$ X³ - $\frac{4}{x}$
   1. A
      2x³ - 4/x²
   2. B
      2x² + 4/x²
      Correct
   3. C
      2x² - 4/x²
   4. D
      2x² + 4/x³
   Show answerHide answer

   Answer: B

   We are given y = (2/3)x³ - 4/x, and we need dy/dx.

   First rewrite the second term with a negative index: y = (2/3)x³ - 4x^-1.

   Differentiate each term using the power rule (bring the power down, then reduce the power by 1):

   For (2/3)x³: multiply the power 3 by the coefficient 2/3, giving 2x².
   For -4x^-1: multiply the power -1 by the coefficient -4, giving 4x^-2, which is the same as 4/x².

   Adding these gives dy/dx = 2x² + 4/x².

3. 3.If y = 2x³ + 6x² + 6x + 1, Find $\frac{dy}{dx}$
   1. A
      6x² + 12x + 6
      Correct
   2. B
      6x² + 12x + 1
   3. C
      2x² + 12x + 6
   4. D
      6x² + 6x + 6
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   Answer: A

   Differentiate each term of y = 2x³ + 6x² + 6x + 1 using the power rule (multiply by the power, then reduce the power by 1).

   2x³ becomes 3 × 2x² = 6x².
   6x² becomes 2 × 6x = 12x.
   6x becomes 6 (the power of x drops to 0).
   The constant 1 disappears completely, since the derivative of any constant is zero.

   Putting these together gives 6x² + 12x + 6, which is the correct derivative.

   A candidate who forgets to multiply 2x³'s coefficient by its power ends up with 2x² + 12x + 6 instead of 6x². Forgetting to multiply 6x²'s power gives 6x² + 6x + 6 instead of 12x. Wrongly carrying the constant term 1 forward instead of dropping it to zero gives 6x² + 12x + 1.

4. 4.An arc subtends an angle of 30^o at the centre of a circle radius 12cm. Calculate the length of the arc.
   1. A
      π cm
   2. B
      4π cm
   3. C
      2π cm
      Correct
   4. D
      6π cm
   Show answerHide answer

   Answer: C

   The formula for the length of an arc is (θ/360) × 2πr, where θ is the angle subtended at the centre and r is the radius.

   Here, θ = 30° and r = 12cm, so:
   Length = (30/360) × 2π × 12 = (1/12) × 24π = 2π cm.

   The option of π cm comes from mistakenly using the radius alone (πr) instead of the full circumference (2πr), leaving out the doubling.

   The option of 4π cm comes from wrongly using 60/360 instead of 30/360 for the fraction of the circle.

   The option of 6π cm comes from using the diameter (24cm) as if it were the radius before applying the fraction, which overstates the arc length.

   The correct working keeps the fraction 30/360 and the full circumference 2π × 12, giving 2π cm.

5. 5.

   If N = $\cfrac{P}{2}$$\cfrac{T_1 - T_2}{T_1}$. Find P when N = 12, T₁ = 27 and T₂ = 24.

   1. A
      P = 216
      Correct
   2. B
      P = 192
   3. C
      P = 108
   4. D
      P = 27
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   Answer: A

   We are given N = (P/2) × (T₁ − T₂)/T₁, with N = 12, T₁ = 27, T₂ = 24.

   First find T₁ − T₂ = 27 − 24 = 3.

   Substitute: 12 = (P/2) × (3/27) = (P/2) × (1/9) = P/18.

   So P = 12 × 18 = 216, which is the correct value.

   A common slip is to drop the ÷2 in the formula altogether, giving N = P × (3/27) = P/9, which wrongly produces 108. Another mistake is using T₂ in place of (T₁ − T₂), giving (P/2) × (24/27) = 12, which wrongly produces 27. Dividing the temperature difference by T₂ instead of T₁ gives (P/2) × (3/24) = 12, wrongly producing 192. Keeping both the ÷2 and using (T₁ − T₂)/T₁ correctly is what leads to 216.

6. 6.Find $\frac{dy}{dx}$. If y = 3x³ + 2x² + 3x + 1
   1. A
      9x² + 4x + 1
   2. B
      9x³ + 4x + 3
   3. C
      6x² + 4x + 3
   4. D
      9x² + 4x + 3
      Correct
   Show answerHide answer

   Answer: D

   To differentiate a polynomial, multiply each term by its power and then reduce that power by 1.

   3x³ becomes 3 × 3x² = 9x²
   2x² becomes 2 × 2x¹ = 4x
   3x becomes 3 (the power drops to zero)
   1 (a constant) differentiates to 0, so it disappears entirely.

   Putting these together gives 9x² + 4x + 3, which is the correct derivative.

   A candidate who forgets that a constant vanishes on differentiation and carries the +1 along ends up with 9x² + 4x + 1. Multiplying 3x³ by 2 instead of 3 gives the wrong lead term 6x² + 4x + 3. Forgetting to reduce the power of x³ down to x² gives the incorrect 9x³ + 4x + 3.

7. 7.Calculate the perimeter of a sector of a circle of raduis 12cm and angle 60^o.
   1. A
      12.6cm
   2. B
      49.1cm
   3. C
      36.6cm
      Correct
   4. D
      24.6cm
   Show answerHide answer

   Answer: C

   The perimeter of a sector is made up of the two straight radii plus the arc length, not the arc alone.

   Radii: 2 × 12cm = 24cm.

   Arc length = (θ/360°) × 2πr = (60/360) × 2 × 22/7 × 12 = (1/6) × 75.43cm ≈ 12.57cm.

   Perimeter = 24cm + 12.57cm ≈ 36.6cm.

   The option giving 12.6cm only counts the arc and forgets the two radii. The option giving 24.6cm mistakenly uses just one radius instead of two before adding the arc. The option giving 49.1cm comes from doubling the radius inside the arc formula (treating it like a diameter), which overstates the arc length.

8. 8.Factorize k² - 2kp + p².
   1. A
      (k - p)²
      Correct
   2. B
      (k - p)(k + p)
   3. C
      (k + p)²
   4. D
      (k - 2p)(k + p)
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   Answer: A

   k² - 2kp + p² matches the perfect-square pattern a² - 2ab + b² = (a - b)², with a = k and b = p.

   So k² - 2kp + p² = (k - p)², which expands back to k² - 2kp + p² — confirming the factorization.

   Picking (k + p)² is the mistake of ignoring the negative sign on the middle term (that expands to k² + 2kp + p²). Writing (k - p)(k + p) is the difference-of-squares pattern, which only applies when there is no middle term, giving k² - p². (k - 2p)(k + p) expands to k² - kp - 2p², which does not match the given expression at all.

9. 9.

   Calculate the perimeter of a sector of a circle of radius 9cm and angle 36^o.

   1. A
      29.31cm
   2. B
      5.66cm
   3. C
      23.66cm
      Correct
   4. D
      18.00cm
   Show answerHide answer

   Answer: C

   Perimeter of a sector = 2r + arc length, not just the arc, because the sector is bounded by the curved edge plus the two straight radii.

   Arc length = (θ/360°) × 2πr = (36/360) × 2 × 22/7 × 9 = 0.1 × 56.57cm = 5.66cm.

   Perimeter = 2r + arc length = (2 × 9) + 5.66 = 18 + 5.66 = 23.66cm.

   Giving only 18.00cm forgets the curved arc entirely and leaves just the two radii. Giving only 5.66cm makes the opposite mistake — reporting the arc length alone and forgetting the two straight sides. The 29.31cm figure comes from wrongly treating 36° as a fraction of 180° instead of the full 360° in a circle, which inflates the arc length.

10. 10.

    Evaluate $\cfrac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}$

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

    Answer: B

    Numerator: $27^{1/3}$ is the cube root of 27, which is 3. $8^{2/3}$ means (cube root of 8) squared = $2^2 = 4$. So the numerator is $3 - 4 = -1$.

    Denominator: $16^{2/4}$ simplifies to $16^{1/2}$, the square root of 16, which is 4. Multiplying by 2 gives $4 \times 2 = 8$.

    So the expression evaluates to $\dfrac{-1}{8}$, which is correct.

    A candidate who forgets the negative sign from $3-4$ lands on the positive fraction. Another common slip is treating the denominator as just the square root (4) without multiplying by 2, giving a fraction with denominator 2 instead of 8 — that produces the wrong distractors.

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

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