JAMB Mathematics 2002

22 reviewed questions with answers and explanations.

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Question 2

Simplify (√0.7 + √70)².

  1. 217.7
  2. 168.7
  3. 84.7
  4. 70.7
Answer and explanation

C: 84.7

Since √70 = 10√0.7, the bracket equals 11√0.7. Squaring gives 121 × 0.7 = 84.7. Both radicals are nonnegative real numbers.

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Question 3

Evaluate (0.21 × 0.072 × 0.0054)/(0.006 × 1.68 × 0.063), correct to four significant figures.

  1. 0.1286
  2. 0.1285
  3. 0.01286
  4. 0.01285
Answer and explanation

A: 0.1286

Multiplying the numerator and denominator gives a quotient of 0.128571428… . Its first four significant digits are 1, 2, 8 and 5; the next digit rounds this to 0.1286.

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Question 5

Simplify 52.4 − 5.7 − 3.45 − 1.75.

  1. 42.2
  2. 42.1
  3. 41.5
  4. 41.4
Answer and explanation

C: 41.5

The quantities being subtracted total 5.7 + 3.45 + 1.75 = 10.9. Subtracting this from 52.4 gives 41.5. Align decimal places when adding or subtracting.

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Question 7

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Two concentric circles have radii r and R, with r = 2R/5. Find the area shaded between the circles.

  1. 9πR²/25
  2. 5πR²/9
  3. 21πR²/25
  4. 21πR²/23

Question 10

XZ is a diameter of a circle of radius 15/2 cm. Point Y lies on the circle and XY = 12 cm. Find the area of triangle XYZ.

  1. 75 cm²
  2. 54 cm²
  3. 45 cm²
  4. 27 cm²
Answer and explanation

B: 54 cm²

The angle at Y is 90° because it subtends a diameter. XZ = 15 cm, so YZ = √(15² − 12²) = 9 cm. Area = ½ × 12 × 9 = 54 cm².

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Question 11

Find the midpoint of the segment joining the x- and y-intercepts of 2y = 4x − 8.

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

D: (1,−2)

Setting y = 0 gives the x-intercept (2,0). Setting x = 0 gives the y-intercept (0,−4). Averaging the coordinates gives midpoint (1,−2).

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Question 13

If tan θ = 4/3, calculate sin²θ − cos²θ.

  1. 7/25
  2. 9/25
  3. 16/25
  4. 24/25
Answer and explanation

A: 7/25

Using tan²θ = 16/9 and sin²θ + cos²θ = 1 gives sin²θ = 16/25 and cos²θ = 9/25. Their difference is 7/25.

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Question 15

Which option precisely identifies the complete locus of points P equidistant from distinct fixed points S and T?

  1. A perpendicular to ST
  2. A line parallel to ST
  3. The angle bisector of PS and ST
  4. The perpendicular bisector of ST
Answer and explanation

D: The perpendicular bisector of ST

The required points lie on the perpendicular through the midpoint of ST. This is the perpendicular bisector, whose every point has equal distances to S and T.

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Question 17

Triangle PQR has angle PQR = 50° and an exterior angle at R of 128°. Classify the triangle.

  1. A scalene triangle
  2. An isosceles triangle
  3. An equilateral triangle
  4. An obtuse-angled triangle
Answer and explanation

A: A scalene triangle

The interior angle at R is 180° − 128° = 52°. The third angle is 180° − 50° − 52° = 78°. All three angles differ, so all three sides differ and the triangle is scalene.

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Question 19

Find the locus of points equidistant from the parallel lines x = 1 and x = 7.

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

D: x = 4

The equidistant locus is the parallel line halfway between them. Its x-coordinate is (1 + 7)/2 = 4, so the equation is x = 4.

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Question 25

In a class of 80 students, 30 offer Music, 40 offer History and 20 offer neither. Find the probability that a randomly chosen student offers Music only.

  1. 0.13
  2. 0.25
  3. 0.38
  4. 0.50
Answer and explanation

B: 0.25

The union contains 80 − 20 = 60 students. Therefore the overlap is 30 + 40 − 60 = 10. Music only contains 30 − 10 = 20 students, giving 20/80 = 0.25.

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Question 30

Calculate the mean absolute deviation about the mean of 7, 3, 14, 9, 7 and 8.

  1. 2½
  2. 2⅓
  3. 2⅙
  4. 1⅙
Answer and explanation

B: 2⅓

The mean is 48/6 = 8. Absolute deviations are 1, 5, 6, 1, 1 and 0, totalling 14. Their average is 14/6 = 7/3 = 2⅓.

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Question 31

Find the maximum value of y = 1 − 2x − 3x².

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

B: 4/3

Completing the square gives y = 4/3 − 3(x + 1/3)². The squared term is nonnegative, so the largest possible value is 4/3, attained at x = −1/3.

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Question 32

The ninth term of an arithmetic progression is five times its fifth term. Find the relationship between first term a and common difference d.

  1. a + 2d = 0
  2. a + 3d = 0
  3. 3a + 5d = 0
  4. 2a + d = 0
Answer and explanation

B: a + 3d = 0

The condition is a + 8d = 5(a + 4d). Rearranging gives 4a + 12d = 0; dividing by four gives a + 3d = 0.

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Question 33

Time is inversely proportional to the number of workers. If 45 workers complete a job in 5 days, how long will 25 workers take?

  1. 5 days
  2. 9 days
  3. 12 days
  4. 15 days
Answer and explanation

B: 9 days

The job requires a constant 45 × 5 = 225 worker-days. With 25 workers, time is 225/25 = 9 days, assuming the stated inverse relationship.

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Question 37

The boundary of px + qy < 4 crosses the axes at (−4,0) and (0,2). Find p and q.

  1. p = 1, q = 2
  2. p = 2, q = 1
  3. p = −1, q = 2
  4. p = 2, q = −1
Answer and explanation

C: p = −1, q = 2

Points on the boundary satisfy px + qy = 4. At (−4,0), −4p = 4, giving p = −1. At (0,2), 2q = 4, giving q = 2.

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Question 38

Find the inverse function of f(x) = 3x + 4.

  1. (x + 4)/3
  2. (x + 3)/4
  3. (x − 5)/5
  4. (x − 4)/3
Answer and explanation

D: (x − 4)/3

Let y = 3x + 4. Solving for x gives x = (y − 4)/3. Interchanging the variable names gives f⁻¹(x) = (x − 4)/3.

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Question 39

Solve x³ − 5x² − x + 5 = 0.

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

D: 1, −1 or 5

Group the terms as x²(x − 5) − (x − 5) = (x − 5)(x² − 1). Factoring again gives (x − 5)(x − 1)(x + 1), so the roots are 5, 1 and −1.

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Question 43

Find the sum to infinity of 1 + 1/3 + 1/9 + 1/27 + … .

  1. 3/2
  2. 5/2
  3. 10/3
  4. 11/3
Answer and explanation

A: 3/2

This is a geometric series with first term 1 and common ratio 1/3. Since the ratio has magnitude below one, its sum is 1/(1 − 1/3) = 3/2.

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Question 46

Evaluate ∫sin(3x) dx.

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

B: −(1/3)cos(3x) + c

The derivative of cos(3x) is −3sin(3x). Multiplying by −1/3 cancels that factor, so an antiderivative is −(1/3)cos(3x) + c.

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Question 48

Given dy/dx = 2x − 3 and y = 3 when x = 0, find y.

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

B: x² − 3x + 3

Integrating the derivative gives y = x² − 3x + C. Substitution of x = 0 and y = 3 gives C = 3, hence y = x² − 3x + 3.

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Question 49

Differentiate y = sin²(5x) with respect to x.

  1. 2sin(5x)cos(5x)
  2. 5sin(5x)cos(5x)
  3. 10sin(5x)cos(5x)
  4. 15sin(5x)cos(5x)
Answer and explanation

C: 10sin(5x)cos(5x)

Apply the chain rule twice: the square contributes 2sin(5x), and differentiating sin(5x) contributes 5cos(5x). Their product is 10sin(5x)cos(5x).

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