JAMB Mathematics 1995

22 reviewed questions with answers and explanations.

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Question 1

Calculate 3310₅ − 1442₅.

  1. 1313₅
  2. 2113₅
  3. 4302₅
  4. 1103₅
Answer and explanation

A: 1313₅

In base ten, 3310₅ = 455 and 1442₅ = 247. Their difference is 208, which is 1×125 + 3×25 + 1×5 + 3 = 1313₅.

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Question 2

Round 3.1415926 to five decimal places.

  1. 3.14160
  2. 3.14159
  3. 0.31415
  4. 3.14200
Answer and explanation

B: 3.14159

The first five decimal digits are 14159. The sixth digit is 2, so the fifth digit stays unchanged and the rounded value is 3.14159.

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Question 3

A notebook is 15 cm long but is measured as 16.8 cm. Find the percentage error to two significant figures.

  1. 12%
  2. 11%
  3. 10.71%
  4. 0.12%
Answer and explanation

A: 12%

The absolute error is 16.8 − 15 = 1.8 cm. Divide by the true length and multiply by 100: (1.8 ÷ 15)×100 = 12%.

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Question 5

Express 0.0014 × 0.011 in standard form.

  1. 1.54 × 10²
  2. 1.54 × 10⁻³
  3. 1.54 × 10⁴
  4. 1.54 × 10⁻⁵
Answer and explanation

D: 1.54 × 10⁻⁵

Multiplying gives 0.0000154. Moving the decimal point five places gives 1.54 × 10⁻⁵, with the coefficient between 1 and 10.

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Question 6

Evaluate (81^(3/4) − 27^(1/3))/(3 × 2³).

  1. 27
  2. 1
  3. 1/3
  4. 1/8
Answer and explanation

B: 1

Since 81 = 3⁴ and 27 = 3³, the numerator is 27 − 3 = 24. The denominator is 3×8 = 24, so the quotient is 1.

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Question 7

Evaluate 16^(3/2) + log₁₀(0.0001) + log₂(32).

  1. 0.065
  2. 0.650
  3. 6.500
  4. 65.00
Answer and explanation

D: 65.00

The three terms are 64, −4 and 5 respectively. Adding them gives 64 − 4 + 5 = 65, matching the value 65.00.

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Question 8

Simplify (√12 − √3)/(√12 + √3).

  1. 1/3
  2. 0
  3. 9/15
  4. 1
Answer and explanation

A: 1/3

Since √12 = 2√3, the numerator is √3 and the denominator is 3√3. Cancelling the common nonzero factor gives 1/3.

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Question 9

Four players belong to both an 11-player cricket team and a 14-player rugby team. How many belong to at least one team?

  1. 25
  2. 21
  3. 16
  4. 3
Answer and explanation

B: 21

Adding the team sizes counts each shared player twice. Subtract the four overlaps once: 11 + 14 − 4 = 21 players.

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Question 10

If S = {x : x² = 9 and x > 4}, what is S?

  1. 0
  2. {0}
  3. ∅
  4. {∅}
Answer and explanation

C: ∅

The real solutions of x² = 9 are −3 and 3. Neither is greater than 4, so there are no elements satisfying both conditions.

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Question 14

At which points does y = x² − 5x + 6 cross the x-axis?

  1. (−6, 0), (−1, 0)
  2. (−3, 0), (−2, 0)
  3. (−6, 0), (1, 0)
  4. (2, 0), (3, 0)
Answer and explanation

D: (2, 0), (3, 0)

Set y = 0 and factor x² − 5x + 6 as (x − 2)(x − 3). Hence x = 2 or x = 3, giving the two intercepts (2, 0) and (3, 0).

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Question 15

Factorise abx² + 6y − 3ax − 2byx completely.

  1. (ax − 2y)(bx − 3)
  2. (bx + 3)(2y − ax)
  3. (bx + 3)(ax − 2y)
  4. (ax − 2y)(ax − b)
Answer and explanation

A: (ax − 2y)(bx − 3)

Group the terms as ax(bx − 3) − 2y(bx − 3). Factoring the common binomial gives (ax − 2y)(bx − 3).

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Question 16

Solve (x − 3)(x − 4) ≤ 0.

  1. 3 ≤ x ≤ 4
  2. 3 < x < 4
  3. 3 ≤ x < 4
  4. 3 < x ≤ 4
Answer and explanation

A: 3 ≤ x ≤ 4

The roots are 3 and 4. Between them the two factors have opposite signs, and at the roots their product is zero. Therefore 3 ≤ x ≤ 4.

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Question 18

Simplify (x² − 1)/(x³ + 2x² − x − 2), for x ≠ −2, −1, 1.

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

A: 1/(x + 2)

The denominator factors as (x + 2)(x² − 1). Cancelling x² − 1 gives 1/(x + 2), while retaining the original excluded values.

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Question 21

Which binary rule is commutative for all integers a and b?

  1. a*b = a + 2b
  2. a*b = a + b − ab
  3. a*b = a² + b
  4. a*b = a(b + 1)/2
Answer and explanation

B: a*b = a + b − ab

Interchanging a and b leaves a + b − ab unchanged. The other listed expressions do not generally give the same value after that interchange.

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Question 33

A closed circular cylinder has diameter 14 cm and height 12 cm. Find its total surface area using π = 22/7.

  1. 836 cm²
  2. 528 cm²
  3. 308 cm²
  4. 154 cm²
Answer and explanation

A: 836 cm²

The radius is 7 cm. Including both circular ends, the area is 2πrh + 2πr² = 2×(22/7)×7×(12 + 7) = 836 cm².

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Question 34

Triangle PQR has PR = 10 cm, angle QPR = 30° and area 35 cm². Find PQ.

  1. 97 cm
  2. 10 cm
  3. 14 cm
  4. 17 cm
Answer and explanation

C: 14 cm

Using area = ½×PQ×PR×sin(angle P),35 = ½×PQ×10×½. Thus 35 = 2.5PQ and PQ = 14 cm. The 30° angle is included between PQ and PR.

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Question 36

In triangle QRS, QS = 12 m, angle RQS = 30° and angle QRS = 45°. Find RS.

  1. 18√2 m
  2. 12√2 m
  3. 6√2 m
  4. 3√2 m
Answer and explanation

C: 6√2 m

By the sine rule, RS/sin 30° = 12/sin 45°. Hence RS = 12×(1/2)/(√2/2) = 6√2 m. Each side is paired with its opposite angle.

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Question 38

Differentiate cosec x with respect to x, with angles in radians.

  1. tan x cosec x
  2. −cot x cosec x
  3. tan x sec x
  4. −cot x sec x
Answer and explanation

B: −cot x cosec x

Since cosec x = 1/sin x, differentiation gives −cos x/sin²x. This is −(cos x/sin x)(1/sin x) = −cot x cosec x.

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Question 40

Given dy/dx = 4x − 3 and y = 5 at x = 2, find y.

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

B: 2x² − 3x + 3

Integrating gives y = 2x² − 3x + C. Substituting x = 2 and y = 5 gives 5 = 8 − 6 + C, so C = 3.

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Question 42

Ages 13,14,15,16,17 have frequencies 3,10,30,42,15. What pie-chart angle represents the 15-year-olds?

  1. 27°
  2. 30°
  3. 54°
  4. 108°
Answer and explanation

D: 108°

The frequencies total 100 students. The 30 students aged 15 represent 30/100 of the circle, giving(30/100)×360° = 108°.

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Question 43

In a class pie chart, Economics occupies 150°, History 90° and French 90°; C.R.K. occupies the remainder. If30 students take French, how many take C.R.K.?

  1. 25
  2. 15
  3. 10
  4. 8
Answer and explanation

C: 10

C.R.K. occupies 360° − 150° − 90° − 90° = 30°. This is one-third of the French sector, so the number is 30÷3 = 10.

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Question 46

Find the population variance of the scores 1,2,3,4,5.

  1. 1.2
  2. 1.4
  3. 2.0
  4. 3.0
Answer and explanation

C: 2.0

The mean is 3. The squared deviations are 4,1,0,1,4, totalling 10. Dividing by the five scores gives population variance 2.0.

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