JAMB Mathematics 2019 past questions

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

Ten questions from the 2019 JAMB Mathematics paper, with answers and explanations. We hold 79 questions from this paper, and the Skolra app has all of them.

JAMB Mathematics 2019 questions and answers

1. 1.

   A factory worker earns ₦50,000 per month out of which he spends 15% on his children's education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?

   1. A
      ₦28,600
   2. B
      ₦41,000
   3. C
      ₦27,400
      Correct
   4. D
      ₦34,900
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   Answer: C

   Income: ₦50,000 per month.

   Education takes 15% of ₦50,000 = ₦7,500.

   Food takes a flat ₦13,600 (already stated in naira, not a percentage).

   Electricity takes 3% of ₦50,000 = ₦1,500.

   Total spent = ₦7,500 + ₦13,600 + ₦1,500 = ₦22,600.

   What is left for his personal purpose = ₦50,000 − ₦22,600 = ₦27,400.

2. 2.

   Evaluate $(\frac{6}{0.32} \div \frac{2}{0.084})^{-1}$ correct to 1 decimal place.

   1. A
      1.2
   2. B
      1.3
      Correct
   3. C
      1.4
   4. D
      0.8
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   Answer: B

   Step 1: Simplify inside the bracket.
   6 ÷ 0.32 = 18.75
   2 ÷ 0.084 = 23.8095 (approximately)

   Step 2: Divide the two results.
   18.75 ÷ 23.8095 = 0.7875

   Step 3: Apply the power of -1, which means find the reciprocal.
   1 ÷ 0.7875 = 1.269841...

   Correct to 1 decimal place, this rounds to 1.3.

3. 3.

   If 2x$^2$ + x - 3 divides x - 2, find the remainder.

   1. A
      3
   2. B
      13
   3. C
      7
      Correct
   4. D
      -3
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   Answer: C

   The Remainder Theorem says that when a polynomial f(x) is divided by (x - a), the remainder equals f(a). Here f(x) = 2x² + x - 3 is divided by (x - 2), so a = 2.

   Remainder = f(2) = 2(2)² + 2 - 3 = 2(4) + 2 - 3 = 8 + 2 - 3 = 7.

   A common mistake is to substitute x = -2 instead of x = 2, since the divisor is (x - 2) and some students wrongly flip the sign of the root. That gives 2(-2)² + (-2) - 3 = 8 - 2 - 3 = 3, which is not the value the theorem asks for.

   Another slip is mixing up the signs when combining the constant term, adding 3 instead of subtracting it, which wrongly gives 8 + 2 + 3 = 13.

4. 4.

   $\frac{d}{dx} [\log (4x^3 - 2x)]$ is equal to

   1. A
      $\frac{12x^2-2}{4x^3-2x}$
      Correct
   2. B
      12x^2-2
   3. C
      $\frac{12x^2+2}{4x^3-2x}$
   4. D
      $\frac{12x^2-2x}{4x^3-2x}$
   Show answerHide answer

   Answer: A

   To differentiate log(4x³ − 2x), we use the rule for differentiating a logarithm of a function: if y = log(u), then dy/dx = (1/u) × (du/dx).

   Here, u = 4x³ − 2x, so du/dx = 12x² − 2 (the power rule applied term by term: the derivative of 4x³ is 12x², and the derivative of −2x is −2).

   Putting this into the rule gives:
   dy/dx = (12x² − 2) / (4x³ − 2x)

5. 5.

   Find the value of x for $\frac{2 + 2x}{3} - 2 \geq \frac{4x - 6}{5}$

   1. A
      x ≤ -2
   2. B
      x ≤ -1
      Correct
   3. C
      x ≥ -1
   4. D
      x ≥ 2
   Show answerHide answer

   Answer: B

   Clear the fractions first. Multiply every term by 15, the LCM of 3 and 5:

   15 × (2 + 2x)/3 − 15 × 2 ≥ 15 × (4x − 6)/5

   which gives 5(2 + 2x) − 30 ≥ 3(4x − 6).

   Expand both sides: 10 + 10x − 30 ≥ 12x − 18, so 10x − 20 ≥ 12x − 18.

   Collect the x terms on one side and the numbers on the other: 10x − 12x ≥ −18 + 20, giving −2x ≥ 2.

   Now divide both sides by −2. Whenever you divide or multiply an inequality by a negative number, the inequality sign must flip. So −2x ≥ 2 becomes x ≤ −1.

6. 6.

   Rationalize $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}$

   1. A
      −5 − 2√6
      Correct
   2. B
      5 + 2√6
   3. C
      5 − 2√6
   4. D
      −5 + 2√6
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   Answer: A

   To rationalize (√2 + √3)/(√2 − √3), multiply the top and bottom by the conjugate of the denominator, which is (√2 + √3).

   The denominator becomes a difference of two squares: (√2 − √3)(√2 + √3) = 2 − 3 = −1.

   The numerator becomes a perfect square: (√2 + √3)² = 2 + 2√6 + 3 = 5 + 2√6.

   Dividing gives (5 + 2√6) ÷ (−1) = −5 − 2√6, which is the correct answer.

7. 7.

   The nth term of a sequence is given by 2$^{2n - 1}$. Find the sum of the first four terms.

   1. A
      85
   2. B
      42
   3. C
      340
   4. D
      170
      Correct
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   Answer: D

   The nth term is given by 2^{2n - 1}. Substitute n = 1, 2, 3, 4 in turn to get the first four terms.

   n = 1: 2^{2(1) - 1} = 2¹ = 2
   n = 2: 2^{2(2) - 1} = 2³ = 8
   n = 3: 2^{2(3) - 1} = 2⁵ = 32
   n = 4: 2^{2(4) - 1} = 2⁷ = 128

   Adding these: 2 + 8 + 32 + 128 = 170, which is the correct sum.

   Notice the terms form a geometric progression with first term 2 and common ratio 4, so you could also confirm it with the geometric sum formula: 2(4⁴ - 1)/(4 - 1) = 2(255)/3 = 170.

8. 8.

   If the volume of a frustrum is given as $V = \frac{\pi h}{3} (R^2 + Rr + r^2)$, find $\frac{\mathrm d V}{\mathrm d R}$.

   1. A
      $\dfrac{\pi h}{3}(R + r)$
   2. B
      $\dfrac{\pi h}{3}(2R + 2r)$
   3. C
      $\pi h(2R + r)$
   4. D
      $\dfrac{\pi h}{3}(2R + r)$
      Correct
   Show answerHide answer

   Answer: D

   We are given $V = \dfrac{\pi h}{3}(R^2 + Rr + r^2)$ and asked to differentiate with respect to $R$, treating $h$ and $r$ as constants.

   Differentiate term by term inside the bracket:
   R² becomes 2R (power rule);
   Rr becomes r (since $r$ is a constant multiplying $R$);
   r² is a constant, so it becomes 0.

   Adding these gives $2R + r$, and the constant factor $\dfrac{\pi h}{3}$ stays unchanged. So $\dfrac{dV}{dR} = \dfrac{\pi h}{3}(2R + r)$, which is correct.

9. 9.

   $\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}$

   1. A
      32/31
   2. B
      50/31
      Correct
   3. C
      60/31
   4. D
      31/50
   Show answerHide answer

   Answer: B

   First simplify the top of the big fraction: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

   Next simplify the bottom: 1/4 + 3/5 − 1/3. Using the LCD of 60: 15/60 + 36/60 − 20/60 = 31/60.

   Now divide the two results: 5/6 ÷ 31/60 = 5/6 × 60/31 = 300/186, which cancels down to 50/31. That is the correct value.

   A candidate who forgets to invert the division in the numerator (multiplying 2/3 by 4/5 instead of by its reciprocal) ends up with 8/15 on top, and dividing that by 31/60 gives 32/31 — a common slip.

   Another common mistake is turning the whole fraction upside down at the last step, giving 31/50 instead of 50/31.

10. 10.

    If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.

    1. A
       1/9
    2. B
       1/3
       Correct
    3. C
       -1/3
    4. D
       3
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    Answer: B

    Given: 3rd term (T3) = ar² = 9, and 7th term (T7) = ar⁶ = 1/9.

    Divide T7 by T3 to eliminate a:
    ar⁶ ÷ ar² = r⁴ = (1/9) ÷ 9 = 1/81.

    So r⁴ = 1/81 = (1/3)⁴, which gives r = 1/3.

    The distractor 3 comes from flipping the division (T3 ÷ T7 instead of T7 ÷ T3). The distractor -1/3 comes from taking the negative fourth root, which is not the ratio JAMB expects here. The distractor 1/9 is simply the value of T7 mistaken for the common ratio.

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