JAMB Mathematics 2021 past questions

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

Ten questions from the 2021 JAMB Mathematics paper, with answers and explanations. We hold 40 questions from this paper, and the Skolra app has all of them.

JAMB Mathematics 2021 questions and answers

1. 1.

   Three brothers in a business deal share the profit at the end of a contract. The first received $\frac{1}{3}$ of the profit and the second $\frac{2}{3}$ of the remainder. If the third received the remaining N12000.00 how much profit did they share?

   1. A
      ₦54,000.00
      Correct
   2. B
      ₦36,000.00
   3. C
      ₦18,000.00
   4. D
      ₦27,000.00
   Show answerHide answer

   Answer: A

   Let the total profit be P.

   The first brother took 1/3 of P, leaving a remainder of 2/3 P.

   The second brother took 2/3 of that remainder, which is 2/3 × 2/3P = 4/9 P.

   So the third brother's share is what is left: P − 1/3P − 4/9P = 2/9 P.

   Since the third brother received ₦12,000.00:
   2/9 P = 12000
   P = 12000 × 9/2 = ₦54,000.00.

2. 2.

   The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number

   1. A
      38
      Correct
   2. B
      20
   3. C
      40
   4. D
      22
   Show answerHide answer

   Answer: A

   The mean of the ten numbers is 16, so their total sum is 16 × 10 = 160.

   After the eleventh number joins the set, the new mean is 18, so the new total sum is 18 × 11 = 198.

   The eleventh number is simply the difference between the two totals: 198 − 160 = 38.

   A common mistake is multiplying the new mean by the old count of numbers (18 × 10 = 180) instead of the new count of eleven, which gives the wrong total and leads to 20. Another mistake is multiplying only the difference in means by the count, either the old count (giving 20) or the new count (giving 22) — this does not correctly account for the full sums involved. Always find the two full sums first, then subtract.

3. 3.

   If w varies inversely as $\frac{uv}{u + v}$ and w =8 when

   u = 2 and v= 6, find a relationship between u, v, w.

   1. A
      uvw = 12(u + v)
      Correct
   2. B
      w(u + v) = 12uv
   3. C
      uv = 12w(u + v)
   4. D
      uvw = 8(u + v)
   Show answerHide answer

   Answer: A

   Setting up the variation: Since w varies inversely as uv/(u+v), we write w = k ÷ [uv/(u+v)], which simplifies to w = k(u+v)/(uv), where k is the constant of variation.

   Finding k: When u = 2 and v = 6, uv/(u+v) = 12/8 = 1.5. Since w = 8, we have 8 = k/1.5, so k = 12.

   The relationship: Substituting k = 12 back gives w = 12(u+v)/(uv). Multiplying both sides by uv gives uvw = 12(u + v), which is correct.

   The option w(u+v) = 12uv is the trap for a candidate who mixed up direct and inverse variation — that equation actually describes w varying directly as uv/(u+v), the opposite of what the question states.

4. 4.

   If the binary operation $\ast$ is defined by m $\ast$ n = mn + m + n for any real number m and n, find the identity of the elements under this operation

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

   Answer: A

   An identity element e satisfies m * e = m for every real number m.

   Using the rule m * n = mn + m + n, put n = e:

   m * e = me + m + e

   Set this equal to m:

   me + m + e = m
   me + e = 0
   e(m + 1) = 0

   This must hold for every value of m, not just special ones, so the only value of e that works for all m is e = 0.

   Check it: m * 0 = m(0) + m + 0 = m. It works.

   The tempting wrong answers come from mixing this up with ordinary multiplication, where 1 is the identity — but under this new operation, testing e = 1 gives m * 1 = m + m + 1 = 2m + 1, which is not equal to m, so 1 fails. Similarly, e = -1 or e = 2 do not satisfy m * e = m for all m; they only work for isolated values of m, not generally.

5. 5.

   Factorize completely 81a$^4$ - 16b$^4$

   1. A
      (9a² - 4b²)(9a² + 4b²)
   2. B
      (3a - 2b)(3a + 2b)(9a² + 4b²)
      Correct
   3. C
      (3a - 2b)²(3a + 2b)²
   4. D
      (3a - 2b)(3a + 2b)(3a² + 4b²)
   Show answerHide answer

   Answer: B

   81a⁴ - 16b⁴ is a difference of two squares, since 81a⁴ = (9a²)² and 16b⁴ = (4b²)².

   So 81a⁴ - 16b⁴ = (9a² - 4b²)(9a² + 4b²).

   Stopping here gives an incomplete factorization, because 9a² - 4b² is still a difference of two squares: (3a)² - (2b)². Factorizing it further gives (3a - 2b)(3a + 2b).

   The remaining factor, 9a² + 4b², is a sum of squares, not a difference, so it cannot be broken down any further.

   Putting it all together, the complete factorization is (3a - 2b)(3a + 2b)(9a² + 4b²).

6. 6.

   What is the n-th term of the sequence 2, 6, 12, 20...?

   1. A
      2n²
   2. B
      n² - n
   3. C
      n² + n
      Correct
   4. D
      n² + 2n
   Show answerHide answer

   Answer: C

   The sequence is 2, 6, 12, 20, ...

   Look at the differences between consecutive terms: 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8. The differences themselves increase by 2 each time, which tells us this is a quadratic sequence, so the n-th term has the form Tn = n² + n (each term is the product of two consecutive integers: 2 = 1×2, 6 = 2×3, 12 = 3×4, 20 = 4×5).

   Checking n² + n:
   n = 1: 1 + 1 = 2
   n = 2: 4 + 2 = 6
   n = 3: 9 + 3 = 12
   n = 4: 16 + 4 = 20

   All four terms match, so n² + n is the correct formula.

7. 7.

   A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

   1. A
      28
   2. B
      25
      Correct
   3. C
      22
   4. D
      23
   Show answerHide answer

   Answer: B

   This is a three-set Venn diagram problem. Let Y, P and M represent the sets of women selling yam, plantain and maize respectively.

   We are given n(Y) = 10, n(P) = 14, n(M) = 12, n(P∩M) = 5, n(Y∩M) = 4, the "yam and plantain only" region = 2, and the triple overlap n(Y∩P∩M) = 3.

   Since "2 sell yam and plantain only" excludes those who also sell maize, the full yam-and-plantain overlap is n(Y∩P) = 2 + 3 = 5.

   Using the inclusion-exclusion principle:
   Total = n(Y) + n(P) + n(M) − n(Y∩P) − n(Y∩M) − n(P∩M) + n(Y∩P∩M)
   Total = 10 + 14 + 12 − 5 − 4 − 5 + 3
   Total = 36 − 14 + 3 = 25

8. 8.

   Determine the maximum value of y=3x$^2$ + 5x - 3

   1. A
      -25/12
   2. B
      -61/12
      Correct
   3. C
      -11/12
   4. D
      61/12
   Show answerHide answer

   Answer: B

   For y = 3x² + 5x - 3, compare with y = ax² + bx + c, so a = 3, b = 5, c = -3.

   Step 1: Find the x-value of the turning point using x = -b/(2a) = -5/6.

   Step 2: Substitute back, or use the shortcut y = c - b²/(4a):
   y = -3 - (25/12) = -36/12 - 25/12 = -61/12.

   So the turning-point value of the function is -61/12.

   The value -11/12 comes from wrongly adding b²/(4a) instead of subtracting it. The value -25/12 comes from forgetting to combine the -3 with the fraction properly. The value 61/12 is the correct magnitude but with the sign dropped — a common slip when candidates rush the subtraction.

9. 9.

   Simplify 2log $\frac{2}{5}$ - log$\frac{72}{125}$ + log 9

   1. A
      log 5/18
   2. B
      log 5/2
      Correct
   3. C
      log 25/4
   4. D
      log 2/5
   Show answerHide answer

   Answer: B

   Using the power law, 2log(2/5) = log(2/5)² = log(4/25). The expression becomes log(4/25) − log(72/125) + log 9.

   Using the quotient law on the first two terms: log(4/25) − log(72/125) = log[(4/25) ÷ (72/125)] = log[(4/25) × (125/72)] = log(5/18).

   Now add the last term using the product law: log(5/18) + log 9 = log(5/18 × 9) = log(45/18) = log(5/2). That is the simplified value.

10. 10.

    What is the rate of change of the volume Vof a hemisphere with respect to its radius r when r = 2?

    1. A
       8π cm³/cm
       Correct
    2. B
       8π/3 cm³/cm
    3. C
       16π cm³/cm
    4. D
       4π cm³/cm
    Show answerHide answer

    Answer: A

    The volume of a hemisphere of radius r is V = (2/3)πr³.

    The rate of change of V with respect to r is the derivative: dV/dr = 2πr² (the 3 from the power rule cancels the 3 in the denominator, leaving 2).

    At r = 2: dV/dr = 2π(2)² = 2π × 4 = 8π.

    Where the other options come from:

    16π comes from differentiating the full sphere formula V = (4/3)πr³ instead of the hemisphere formula, giving 4πr² = 16π at r = 2 — a candidate who forgets the shape is only half a sphere.

    4π comes from a squaring slip, treating the derivative as 2πr instead of 2πr² (2π × 2 = 4π).

    8π/3 comes from confusing the rate of change with the volume itself divided by r, i.e. (2/3)π(2)³ ÷ 2, rather than actually differentiating.

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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