JAMB Mathematics 2003

17 reviewed questions with answers and explanations.

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Question 3

Multiply 213₄ by 23₄, giving the result in base four.

  1. 13211₄
  2. 10311₄
  3. 10321₄
  4. 12231₄
Answer and explanation

D: 12231₄

In decimal, 213₄ = 39 and 23₄ = 11, so their product is 429. Dividing repeatedly by four, or using place values, gives 12231₄.

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Question 7

Evaluate log_(√2)(4) + log_(1/2)(16) − log₄(32).

  1. −2.5
  2. 5.5
  3. −5.5
  4. 2.5
Answer and explanation

A: −2.5

The three logarithms are 4, −4 and 5/2 respectively: (√2)⁴ = 4, (1/2)⁻⁴ = 16 and 4^(5/2) = 32. Thus the expression equals −2.5.

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Question 8

Let U be the even integers strictly between 0 and 30, P the multiples of 6 in U and Q the multiples of 4 in U. Find the complement of P ∪ Q in U.

  1. {0,2,6,22,26}
  2. {2,4,14,18,26}
  3. {2,10,14,22,26}
  4. {0,10,14,22,26}
Answer and explanation

C: {2,10,14,22,26}

Remove from U every integer divisible by 6 or 4. The remaining even integers are 2, 10, 14, 22 and 26, which form the required complement.

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Question 10

Evaluate [(1/0.06) ÷ (1/0.042)]⁻¹, correct to two decimal places.

  1. 4.42
  2. 3.14
  3. 1.53
  4. 1.43
Answer and explanation

D: 1.43

Dividing the reciprocals gives 0.042/0.06 = 0.7. The exponent −1 takes the reciprocal, giving 1/0.7 = 1.428571… , or 1.43 to two decimal places.

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Question 12

Factorise completely 4abx − 2axy − 12b²x + 6bxy.

  1. 2x(3b − a)(2b − y)
  2. 2x(a − 3b)(b − 2y)
  3. 2x(2b − a)(3b − y)
  4. 2x(a − 3b)(2b − y)
Answer and explanation

D: 2x(a − 3b)(2b − y)

Factor out 2x to obtain 2x[2ab − ay − 6b² + 3by]. Grouping the bracket gives a(2b − y) − 3b(2b − y), yielding the stated factorisation.

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Question 14

The graphs of y = x² + 4 and a straight line PQ are used to solve x² − 3x + 2 = 0. Find the equation of PQ.

  1. y = 3x + 2
  2. y = 3x − 4
  3. y = 3x + 4
  4. y = 3x − 2
Answer and explanation

A: y = 3x + 2

At intersections with y = 3x + 2, equating the y values gives x² + 4 = 3x + 2. Rearrangement produces exactly x² − 3x + 2 = 0.

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Question 16

Solve 3x − 5y + 5 = 0 and 4x − 7y + 8 = 0 for x and y respectively.

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

C: 5, 4

The equations give 3x − 5y = −5 and 4x − 7y = −8. Multiplying by 4 and 3 respectively and subtracting gives y = 4; substitution then gives x = 5.

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Question 20

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Which inequalities describe triangle OPQ, including its boundary?

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

Question 21

Three consecutive terms of a geometric progression are n − 2, n and n + 3. Find its common ratio.

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

B: 3/2

Consecutive geometric terms satisfy n² = (n − 2)(n + 3) = n² + n − 6. Hence n = 6 and the terms are 4, 6 and 9, with ratio 3/2.

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Question 24

A point P lies on one chosen side of the line through distinct fixed points X and Y, with angle XPY = 90°. Which option most precisely describes its locus, excluding X and Y?

  1. The perpendicular bisector of XY
  2. A circle
  3. A semicircle
  4. An arc of a circle through X and Y
Answer and explanation

C: A semicircle

By the angle-in-a-semicircle theorem, P lies on the circle with diameter XY. Restricting P to one side of XY selects one semicircle; its endpoints are excluded because the angle is undefined there.

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Question 31

Find the locus of P(x,y) equidistant from Q(0,0) and R(2,1).

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

C: 4x + 2y = 5

Equating squared distances gives x² + y² = (x − 2)² + (y − 1)². Cancelling x² and y² leaves 4x + 2y = 5.

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Question 32

An arc subtends 30° at a point on the circumference of a circle of radius 21 cm. Find its length, using π = 22/7.

  1. 66 cm
  2. 44 cm
  3. 22 cm
  4. 11 cm
Answer and explanation

C: 22 cm

The corresponding angle at the centre is twice the circumference angle, giving 60°. Arc length is (60/360) × 2π × 21 = 7π = 22 cm.

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Question 34

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A circle has radius 7 cm. Angle XZY is 45°. Find the shaded minor segment cut off by chord XY, using π = 22/7.

  1. 14 cm²
  2. 38 cm²
  3. 77 cm²
  4. 84 cm²

Question 37

Differentiate y = 3sin(−4x).

  1. −12cos(−4x)
  2. 12sin(−4x)
  3. 12x cos(4x)
  4. −12x cos(−4x)
Answer and explanation

A: −12cos(−4x)

The derivative of sin u is cos u multiplied by du/dx. Here u = −4x, so dy/dx = 3cos(−4x) × (−4) = −12cos(−4x).

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Question 44

A pie chart has four sectors, three measuring 45°, 90° and 135°. If the smallest sector represents ₦28, how much does the largest represent?

  1. ₦48
  2. ₦96
  3. ₦42
  4. ₦84
Answer and explanation

D: ₦84

The fourth angle is 360° − 45° − 90° − 135° = 90°. The largest sector is 135°, three times the smallest 45° sector, so its value is 3 × ₦28 = ₦84.

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Question 48

Two fair six-sided dice are thrown independently. Find the probability that their sum is divisible by three.

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

B: 1/3

There are 36 equally likely ordered outcomes. Sums 3, 6, 9 and 12 have 2, 5, 4 and 1 outcomes respectively, giving 12 favourable outcomes and probability 12/36 = 1/3.

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Question 50

By how much is the mean of 30, 56, 31, 55, 43 and 44 less than their median? Give the answer to two decimal places.

  1. 0.50
  2. 0.75
  3. 0.17
  4. 0.33
Answer and explanation

D: 0.33

In order, the numbers are 30, 31, 43, 44, 55 and 56, so the median is (43 + 44)/2 = 43.5. The mean is 259/6 = 43.1666… . Their difference rounds to 0.33.

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