JAMB Mathematics 1998

22 reviewed questions with answers and explanations.

Practice selection: full-paper coverage has not been confirmed.

Question 2

Evaluate [(1/0.03) ÷ (1/0.024)]⁻¹ to two decimal places.

  1. 3.76
  2. 1.25
  3. 0.94
  4. 0.75
Answer and explanation

B: 1.25

The ratio inside the brackets is 0.024/0.03 = 0.8. Raising it to−1 takes its reciprocal,1/0.8 = 1.25.

AI-reviewed · calculation checked

Question 10

The polynomial pm² + qm + 1 leaves remainder 2 on division by m − 1 and remainder 4 on division by m + 1. Find p and q.

  1. 2, −1
  2. −1, 2
  3. 3, −2
  4. −2, 3
Answer and explanation

A: 2, −1

The remainder theorem gives p + q + 1 = 2 and p − q + 1 = 4. Thus p + q = 1 and p − q = 3, yielding p = 2 and q = −1.

AI-reviewed · calculation checked

Question 11

Factorise r² − r(2p + q) + 2pq.

  1. (r − 2q)(2r − p)
  2. (r − q)(r + p)
  3. (r − q)(r − 2p)
  4. (2r − q)(r + p)
Answer and explanation

C: (r − q)(r − 2p)

The two terms q and 2p have sum 2p + q and product 2pq. Therefore the expression factors as(r − q)(r − 2p).

AI-reviewed · calculation checked

Question 12

Solve √x − √(x − 2) − 1 = 0 over the real numbers.

  1. 3/2
  2. 2/3
  3. 4/9
  4. 9/4
Answer and explanation

D: 9/4

Rearrange to√x = 1 + √(x − 2). Squaring gives 1 = 2√(x − 2), so x = 9/4. Substitution gives 3/2 − 1/2 − 1 = 0.

AI-reviewed · calculation checked

Question 15

Divide 2x³ + 11x² + 17x + 6 by 2x + 1.

  1. x² + 5x + 6
  2. 2x² + 5x + 6
  3. 2x² − 5x + 6
  4. x² − 5x + 6
Answer and explanation

A: x² + 5x + 6

Polynomial division gives x² + 5x + 6. Multiplication confirms(2x + 1)(x² + 5x + 6) = 2x³ + 11x² + 17x + 6.

AI-reviewed · calculation checked

Question 16

Resolve(11x + 2)/(6x² − x − 1) into partial fractions, excluding denominator zeros.

  1. 1/(3x − 1) + 3/(2x + 1)
  2. 3/(3x + 1) − 1/(2x − 1)
  3. 3/(3x − 1) − 1/(2x + 1)
  4. 1/(3x + 1) + 3/(2x − 1)
Answer and explanation

D: 1/(3x + 1) + 3/(2x − 1)

The denominator is(3x + 1)(2x − 1). Combining 1/(3x + 1) and 3/(2x − 1) gives numerator(2x − 1) + 3(3x + 1) = 11x + 2.

AI-reviewed · calculation checked

Question 17

For positive real x, solve 1/(3x) + 1/2 > 1/(4x).

  1. x > −1/6
  2. x > 0
  3. 0 < x < 4
  4. 0 < x < 1/6
Answer and explanation

B: x > 0

Subtracting the right side gives 1/(12x) + 1/2 > 0. Both terms are positive whenever x > 0, so every positive x satisfies the inequality.

AI-reviewed · calculation checked

Question 18

Enable JavaScript to verify this question's diagram before viewing its answer.

Which inequalities describe the shaded region, including the boundary lines?

  1. x ≥ 0, 3y + 2x ≥ 6
  2. x ≥ 0, y ≥ 3, 3x + 2y ≥ 6
  3. x ≥ 2, y ≥ 0, 3x + 2y ≤ 6
  4. x ≥ 0, y ≥ 0, 3x + 2y ≥ 6

Question 19

If p + 1,2p − 10 and 1 − 4p² are consecutive arithmetic-progression terms, find p.

  1. −4, 2
  2. −2, 4/11
  3. −11/4, 2
  4. 5, −3
Answer and explanation

C: −11/4, 2

Twice the middle term equals the sum of the outer terms:4p − 20 = p + 2 − 4p². Thus 4p² + 3p − 22 = 0, giving p = 2 or−11/4.

AI-reviewed · calculation checked

Question 20

The first three terms of a convergent geometric progression sum to half its nonzero infinite sum. Find its positive common ratio.

  1. 1/4
  2. 1/2
  3. 1/∛3
  4. 1/∛2
Answer and explanation

D: 1/∛2

For common ratio r, the first-three-term sum is(1 − r³) times the infinite sum. Hence 1 − r³ = 1/2, so r = ∛(1/2) = 1/∛2.

AI-reviewed · calculation checked

Question 27

PQST is a parallelogram with TS = 10 cm. T,S,R lie in that order on a straight line, SR = 8 cm, and triangle QRS has area 20 cm². Find trapezium PQRT’s area.

  1. 35 cm²
  2. 65 cm²
  3. 70 cm²
  4. 140 cm²
Answer and explanation

C: 70 cm²

Triangle QRS has height 2×20/8 = 5 cm above the baseline. The parallelogram shares that height and has area 10×5 = 50 cm². Adding the triangle gives 70 cm².

AI-reviewed · calculation checked

Question 31

Distinct points S and T lie on a circle of radius 8 cm centred at N. If ST = SN, find the area of triangle STN.

  1. 4√3 cm²
  2. 16√3 cm²
  3. 32 cm²
  4. 64 cm²
Answer and explanation

B: 16√3 cm²

Both SN and TN are radii of length 8 cm, and ST = SN. The triangle is equilateral, so its area is(√3/4)×8² = 16√3 cm².

AI-reviewed · calculation checked

Question 35

Q,T,R lie in that order on a straight line. PQ = 15, PT = 8, PR = 10 and angle PQT = 30°. Find sin(angle PTR).

  1. 8/15
  2. 2/3
  3. 3/4
  4. 15/16
Answer and explanation

D: 15/16

In triangle PQT, the sine rule gives sin(angle PTQ)/15 = sin 30°/8. The angles PTQ and PTR are supplementary, so they have the same sine,15/16.

AI-reviewed · calculation checked

Question 36

For 0° ≤ x ≤ 180°, at what x does 6sin(2x − 25)° attain its maximum?

  1. 12.5°
  2. 32.5°
  3. 57.5°
  4. 147.5°
Answer and explanation

C: 57.5°

Sine reaches 1 when its angle is 90° plus a full turn. In the given range,2x − 25 = 90 gives the only maximum, x = 57.5°.

AI-reviewed · calculation checked

Question 37

From a150 m mast, huts due east and west are seen at depression angles 60° and 45°. Find their separation on level ground.

  1. 150(1 + √3) m
  2. 50(3 + √3) m
  3. 150√3 m
  4. 50/√3 m
Answer and explanation

B: 50(3 + √3) m

The horizontal distances are 150/tan 60° = 50√3 m and 150/tan 45° = 150 m. They lie on opposite sides, so the separation is 50(3 + √3) m.

AI-reviewed · calculation checked

Question 38

For y = 243(4x + 5)⁻², find dy/dx at x = 1.

  1. −8/3
  2. 3/8
  3. 9/8
  4. −8/9
Answer and explanation

A: −8/3

The chain rule gives dy/dx = −1944(4x + 5)⁻³. At x = 1 this is−1944/9³ = −1944/729 = −8/3. The factor 4 comes from differentiating the inner expression.

AI-reviewed · calculation checked

Question 39

Differentiate x/cos x with respect to x, where cos x ≠ 0.

  1. 1 + x sec x tan x
  2. 1 + sec²x
  3. cos x + x tan x
  4. sec x + x sec x tan x
Answer and explanation

D: sec x + x sec x tan x

Write the function as x sec x. The product rule gives 1×sec x + x×sec x tan x, or sec x + x sec x tan x.

AI-reviewed · calculation checked

Question 41

Find the curve through(2,5) with derivative 6x − 5.

  1. 6x² − 5x + 5
  2. 6x² + 5x + 5
  3. 3x² − 5x − 5
  4. 3x² − 5x + 3
Answer and explanation

D: 3x² − 5x + 3

Integrating gives y = 3x² − 5x + C. At(2,5),5 = 12 − 10 + C, so C = 3 and y = 3x² − 5x + 3.

AI-reviewed · calculation checked

Question 43

Class intervals 5–9,10–14,15–19,20–24 have frequencies 17,32,25,24. Estimate the grouped mode to one decimal place using continuous class boundaries.

  1. 12.2
  2. 12.7
  3. 12.9
  4. 13.4
Answer and explanation

C: 12.9

The modal class is 10–14. Its lower boundary is 9.5 and width 5, so mode ≈ 9.5 + [(32 − 17)/(64 − 17 − 25)]×5 = 12.9.

AI-reviewed · calculation checked

Question 48

Marks 0 through 10 have frequencies 1,3,4,7,10,8,7,9,8,2,1 respectively. If the pass mark is 5, what percentage failed, to one decimal place?

  1. 59.4%
  2. 50.0%
  3. 41.7%
  4. 25.0%
Answer and explanation

C: 41.7%

The frequencies total 60 pupils. Marks below 5 account for 1 + 3 + 4 + 7 + 10 = 25 pupils, giving(25/60)×100 ≈ 41.7%.

AI-reviewed · calculation checked

Question 49

Only one team can win gold. If teams X and Y have winning probabilities 2/5 and 1/3, find the probability that either wins.

  1. 2/15
  2. 7/15
  3. 11/15
  4. 13/15
Answer and explanation

C: 11/15

The two winning outcomes are mutually exclusive because there is one gold winner. Add their probabilities:2/5 + 1/3 = 6/15 + 5/15 = 11/15.

AI-reviewed · calculation checked

Question 50

Choose x and y independently and uniformly from{1,2,3,4}. Find the probability that xy ≤ 6.

  1. 5/8
  2. 5/16
  3. 1/2
  4. 3/8
Answer and explanation

A: 5/8

There are 16 equally likely ordered pairs. For x = 1,2,3,4, the numbers of allowed y values are 4,3,2,1. Thus 10 pairs work, giving 10/16 = 5/8.

AI-reviewed · calculation checked

Plan your study weekAll Mathematics years