JAMB Mathematics 1988 past questions and answers

Simplify
1½/(2 ÷ 1/4 of 32)

1. A.3/256
2. B.3/32
3. C.6
4. D.85

If x is the addition of prime numbers between 1 and 6; and y the H.C.F. of 6, 9, 15, find the product of x and y.

1. A.27
2. B.30
3. C.33
4. D.90

A 5.0g of salt was weighed by Tunde as 5.1g. What is the percentage error?

1. A.20
2. B.2
3. C.1
4. D.0.2

Find correct to one dec. place, 0.24633 ÷ 0.0306

1. A.0.8
2. B.1.8
3. C.8.0
4. D.8.1

Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later Kehinde sells ²/₃ of her share to Taiwo for N720.00 find the value of the store.

1. A.N1,080.00
2. B.N2,400.00
3. C.N3,000.00
4. D.N3,600.00

A basket contains green, black and blue balls in the ratio 5:2:1. If there are 10 blue balls, find the corresponding new ratio when 10 green and 10 black balls are removed from the basket.

1. A.1:1:1
2. B.4:2:1
3. C.5:1:1
4. D.4:1:1

A tax payer is allowed ¹/₈th of his income tax-free and pays 20% on the remainder. If he pays N490.00 tax, what is his income?

1. A.N560.00
2. B.N2,450.00
3. C.N2,800.00
4. D.N3,920.00

Evaluate (8^1/3 × 5^2/3)/10^2/3

1. A.2/5
2. B.5/3
3. C.∛5
4. D.∛2

If log₁₀2 = 0.3010 and log₁₀3 = 0.4771, evaluate without using logarithm tables, log₁₀4.5.

1. A.0.3010
2. B.0.4771
3. C.0.6532
4. D.0.9542

Find m such that (m + √3)(1 − √3)² = 6 − 2√3.

1. A.1
2. B.2
3. C.3
4. D.4

The thickness of an 800-page book is 18mm. Calculate the thickness of one leaf of the book giving your answers in metres and in standard form.

1. A.2.25 × 10⁻⁴m
2. B.4.50 × 10⁻⁴m
3. C.2.25 × 10⁻⁵m
4. D.4.50 × 10⁻⁵m

Simplify
(x + 2)/(x + 1) − (x − 2)/(x + 2)

1. A.3/(x + 1)
2. B.(3x + 2)/((x + 1)(x + 2))
3. C.(5x + 6)/((x + 1)(x + 2))
4. D.(2x² + 5x + 2)/((x + 1)(x + 2))

If 1/p = (a² + 2ab + b²)/(a − b) and 1/q = (a + b)/(a² − 2ab + b²) find p/q

1. A.(a + b)/(a − b)
2. B.1/(a² − b²)
3. C.(a − b)/(a + b)
4. D.a² − b²

If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3.

1. A.1/3
2. B.2/3
3. C.8/27
4. D.4/9

If a = −3, b = 2, c = 4, evaluate
(a³ − b³ − c^1/2)/(b − a − c)

1. A.37
2. B.−37/5
3. C.37/5
4. D.−37

If g(y) = (y − 3)/11 + 11/(y² − 9) what is g(y + 3)?

1. A.y/11 + 11/(y(y + 6))
2. B.y/11 + 11/(y(y + 3))
3. C.(y + 30)/11 + 11/(y(y + 3))
4. D.(y + 3)/11 + 11/(y(y − 6))

Factorize completely (x² + x)² − (2x + 2)²

1. A.(x + 1)(x + 2)(x − 2)
2. B.(x + 1)²(x − 2)²
3. C.(x + 1)²(x + 2)²
4. D.(x + 1)²(x + 2)(x − 2)

Simplify (x − y)/(x^1/3 − y^1/3)

1. A.x² + xy + y²
2. B.x^2/3 + x^1/3y^1/3 + y^2/3
3. C.x^2/3 − x^1/3y^1/3 − y^2/3
4. D.x² − xy + y²

Solve the following equation for x.
x² + (2/r²)x + 1/r⁴ = 0

1. A.r²
2. B.1/r²
3. C.−1/r²
4. D.1/r

List the integral values of x which satisfy the inequality −1 < 5 − 2x ≤ 7

1. A.−1, 0, 1, 2
2. B.0, 1, 2, 3.
3. C.−1, 0, 1, 2, 3.
4. D.−1, 0, 2, 3.

Given that 3x − 5y − 3 = 0
2y − 6x + 5 = 0
the value of (x, y) is

1. A.(−1/8, 19/24)
2. B.(8, 24/19)
3. C.(−8, 24/19)
4. D.(19/24, −1/8)

The solution of the quadratic equation px² + qx + b = 0 is

1. A.(−b ± √(b² − 4ac))/2a
2. B.(−b ± √(p² − 4pb))/2a
3. C.(−q ± √(q² − 4bp))/2p
4. D.(−q ± √(p² − 4bp))/2p

Simplify
1/(x² + 5x + 6) + 1/(x² + 3x + 2)

1. A.(x + 3)/((x + 1)(x + 2))
2. B.1/((x + 1)(x + 2)(x + 3))
3. C.2/((x + 1)(x + 3))
4. D.4/((x + 1)(x + 3))

Simplify (4a² − 49b²)/(2a² + 5ab − 7b²)

1. A.(a − b)/(2a + b)
2. B.(2a + 7b)/(a − b)
3. C.(2a − 7b)/(a + b)
4. D.(2a − 7b)/(a − b)

Use the graph of y = (x² + 3)/(x + 4) and y = 1 to answer this question. What is the solution of the equation x² − x − 1 = 0?

1. A.x = 1.6 and x = −0.6
2. B.x = −1.6 and x = 0.6
3. C.x = 1.6 and x = 0.6
4. D.x = −1.6 and x = −0.6.

The solution of x² − 2x − 1 = 0 are the points of intersection of two graphs. If one of the graphs is y = 2 + x − x², find the second graph.

1. A.y = 1 − x
2. B.y = 1 + x
3. C.y = x − 1
4. D.y = 3x + 3

If the sum of the 8th and 9th terms of an arithmetic progression is 72 and the 4th term is −6, find the common difference

1. A.4
2. B.8
3. C.6⅔
4. D.9⅓

If 7 and 189 are the first and fourth terms of a geometric progression respectively, find the sum of the first three terms of the progression.

1. A.182
2. B.91
3. C.63
4. D.28.

In the figure above, PQRS is a circle. If chords QR and RS are equal, calculate the value of x

1. A.80°
2. B.60°
3. C.45°
4. D.40°

In the figure above, PQ is parallel to ST and QR̂S = 40°. Find the value of x

1. A.55
2. B.60
3. C.65
4. D.75

For which of the following exterior angles is a regular polygon possible? i. 35° ii. 18° iii. 15°

1. A.i and ii
2. B.ii only
3. C.ii and iii
4. D.iii only

In the figure above, PS = 7cm and RY = 9cm. If the area of parallelogram PQRS is 56cm², find the area of trapezium PQTS.

1. A.56cm²
2. B.112cm²
3. C.120cm²
4. D.176cm²

A quadrant of a circle of radius 6cm is cut away from each corner of rectangle 25cm long and 18cm wide. Find the perimeter of the remaining figure.

1. A.38cm
2. B.(38 + 12π)cm
3. C.(86 − 12π)cm
4. D.(86 − 6π)cm

In the figure above, ST̂Q = SR̂P, PT = TQ = 6cm and QS = 5cm. Find SR.

1. A.47/5
2. B.5
3. C.32/5
4. D.22/5

Four interior angles of a pentagon are 90° − x°, 90° + x°, 110° − 2x°, 110° + 2x°, Find the fifth interior angle.

1. A.110°
2. B.120°
3. C.130°
4. D.140°.

In the figure above, PS = RS = QS and QŜR = 50°. Find QP̂R.

1. A.25°
2. B.40°
3. C.50°
4. D.65°

In the figure above, XR and YQ are tangents to the circle YZXP. If ZX̂R = 45° and YẐX = 55°, find ZŶQ

1. A.135°
2. B.125°
3. C.100°
4. D.90°

From a point 14√3 metres away from a tree, a man discovers that the angle of elevation of the tree is 30°. If the man measures this angle of elevation from a point 2 metres above the ground, how high is the tree?

1. A.12m
2. B.14m
3. C.14√3m
4. D.16m

Alero starts a 3km walk from P on a bearing 023°. She then walks 4km on a bearing 113° to Q. What is the bearing of Q from P?

1. A.26°52'
2. B.53°8'
3. C.76°8'
4. D.90°

If cot θ = x/y, find cosec θ

1. A.(1/y)(x² + y²)
2. B.√(x/y)
3. C.(1/y)√(x² + y²)
4. D.y/x

In triangle PQR, PQ = 1cm, QR = 2cm and PQ̂R = 120°. Find the longest side of the triangle.

1. A.√3cm
2. B.√7cm
3. C.3cm
4. D.7cm

If cos²θ + ¹/₈ = sin²θ, find tan θ.

1. A.3
2. B.3√7/7
3. C.3√7
4. D.√7

If a metal pipe 10cm long has an external diameter of 12cm and a thickness of 1cm, find the volume of the metal used in making the pipe.

1. A.120πcm³
2. B.110πcm³
3. C.60πcm³
4. D.50πcm³

In the figure above, a solid consists of a hemisphere surmounted by a right circular cone, with radius 3.0cm and height 6.0cm. Find the volume of the solid.

1. A.18πcm³
2. B.36πcm³
3. C.54πcm³
4. D.108πcm³

PQR is a triangle in which PQ = 10cm and QP̂R = 60°. S is a point equidistant from P and Q. Also, S is a point equidistant from PQ and PR. If U is the foot of the perpendicular from S on PR, find the length SU in cm to one decimal place.

1. A.2.7
2. B.2.9
3. C.3.1
4. D.3.3

In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 12°. How many students are offering Physics?

1. A.18
2. B.15
3. C.10
4. D.5

If x and y represent the mean and the median respectively of the following set of numbers; 11, 12, 13, 14, 15, 16, 17, 18, 19, 21. Find x/y correct to one decimal place.

1. A.1.6
2. B.1.2
3. C.1.1
4. D.1.0.

Score (x): 0, 1, 2, 3, 4, 5, 6
Frequency (f): 7, 11, 6, 7, 7, 5, 3
In the distribution above, the mode and median respectively are

1. A.1, 3
2. B.1, 2
3. C.3, 3
4. D.0, 2.

If two dice are thrown together, what is the probability of obtaining at least a score of 10?

1. A.1/6
2. B.1/12
3. C.5/6
4. D.11/12