JAMB Mathematics 2002 past questions and answers

Without using tables, evaluate (343)^1/3 × (0.14)⁻¹ × (25)^−1/2

1. A.10
2. B.12
3. C.8
4. D.7

In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 Mathematics. How many offer Biology but not Mathematics?

1. A.95
2. B.80
3. C.125
4. D.110

Simplify 52.4 − 5.7 − 3.45 − 1.75

1. A.41.4
2. B.41.5
3. C.42.1
4. D.42.2

Simplify (√0.7 + √70)²

1. A.84.7
2. B.70.7
3. C.217.7
4. D.168.7

Evaluate (0.21 × 0.072 × 0.00054)/(0.006 × 1.68 × 0.063), correct to four significant figures.

1. A.0.01286
2. B.0.01285
3. C.0.1286
4. D.0.1285

A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy?

1. A.60
2. B.50
3. C.45
4. D.36

If dy/dx = 2x − 3 and y = 3 when x = 0, find y in terms of x.

1. A.2x² − 3x
2. B.x² − 3x
3. C.x² − 3x − 3
4. D.x² − 3x + 3

Find the derivative of y = sin²(5x) with respect to x.

1. A.10 sin 5x cos 5x
2. B.5 sin 5x cos 5x
3. C.2 sin 5x cos 5x
4. D.15 sin 5x cos 5x

The slope of the tangent to the curve y = 3x² − 2x + 5 at the point (1, 6) is

1. A.4
2. B.1
3. C.6
4. D.5

Evaluate ∫sin 3x dx

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

A circle with a radius 5cm has its radius increasing at the rate of 0.2cms⁻¹. What will be the corresponding increase in the area?

1. A.2π
2. B.5π
3. C.π
4. D.4π

If y = x² − 1/x, find dy/dx

1. A.2x − 1/x²
2. B.2x + x²
3. C.2x − x²
4. D.2x + 1/x²

Use the graph above to find the values of p and q if px + qy ≤ 4.

1. A.p = 2, q = 1
2. B.p = 2, q = −1
3. C.p = 1, q = 2
4. D.p = −1, q = 2

Solve for x in the equation x³ − 5x² − x + 5 = 0

1. A.1, −1 or 5
2. B.1, 1 or −5
3. C.−1, 1 or −5
4. D.1, 1 or 5

The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?

1. A.15 days
2. B.12 days
3. C.5 days
4. D.9 days

If P = [2, 1; −3, 0] and I is a 2 × 2 unit matrix, evaluate P² − 2P + 4I

1. A.[9, 4; −12, 1]
2. B.[−3, 0; 0, −3]
3. C.[1, 0; 0, 1]
4. D.[1, 4; 4, 1]

Find the range of values of x for which (x + 2)/4 − (2x − 3)/3 < 4

1. A.x > −6
2. B.x > −3
3. C.x < 8
4. D.x < 4

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

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

If the 9th term of an A.P. is five times the 5th term, find the relationship between a and d.

1. A.2a + d = 0
2. B.3a + 5d = 0
3. C.a + 3d = 0
4. D.a + 2d = 0

The inverse of the function f(x) = 3x + 4 is

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

If −2 is the solution of the equation 2x + 1 − 3c = 2c + 3x − 7, find the value of c.

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

An operation * is defined on the set of integers p and q by p * q = pq + p + q. Find 2 * (3 * 4).

1. A.59
2. B.19
3. C.67
4. D.38

If N = [3, 5, −4; 6, −3, −5; −2, 2, 1], find |N|

1. A.17
2. B.23
3. C.65
4. D.91

The sum to infinity of the series 1 + 1/3 + 1/9 + 1/27 + … is

1. A.11/3
2. B.10/3
3. C.5/2
4. D.3/2

If x varies directly as √n and x = 9 when n = 9, find x when n = 17/9

1. A.4
2. B.27
3. C.√3
4. D.√17

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72°, find x.

1. A.36°
2. B.18°
3. C.72°
4. D.24°

A chord of a circle subtends an angle of 120° at the centre of a circle of diameter 4√3cm. Calculate the area of the major sector.

1. A.4πcm²
2. B.32πcm²
3. C.16πcm²
4. D.8πcm²

Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7

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

In the diagram above, XZ is the diameter of the circle XYZW, with centre O and radius 15/2cm. If XY = 12cm, find the area of the triangle XYZ.

1. A.54cm²
2. B.45cm²
3. C.27cm²
4. D.75cm²

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

1. A.16/25
2. B.24/25
3. C.7/25
4. D.9/25

In the diagram above are two concentric circles of radii r and R respectively with centre O. If r = (2/5)R, express the area of the shaded portion in terms of π and R.

1. A.(21/25)πR²
2. B.(9/25)πR²
3. C.(21/23)πR²
4. D.(5/9)πR²

A bucket is 12cm in diameter at the top, 8cm in diameter at the bottom and 4cm deep. Calculate its volume.

1. A.(304/3)πcm³
2. B.144πcm³
3. C.(128/3)πcm³
4. D.72πcm³

In the diagram above, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid.

1. A.180πcm³
2. B.162πcm³
3. C.216πcm³
4. D.198πcm³

The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

1. A.12
2. B.20
3. C.40
4. D.10

Find the coordinate of the midpoint of x and y intercepts of the line 2y = 4x − 8.

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

A hunter 1.6m tall, views a bird on top of a tree at an angle 45°. If the distance between the hunter and the tree is 10.4m, find the height of the tree.

1. A.9.0m
2. B.12.0m
3. C.8.8m
4. D.10.4m

A solid hemisphere has radius 7cm. Find the total surface area. [π = 22/7]

1. A.400cm²
2. B.462cm²
3. C.66cm²
4. D.308cm²

Find the value of α if the line 2y − αx + 4 = 0 is perpendicular to the line y + (1/4)x − 7 = 0

1. A.−4
2. B.4
3. C.8
4. D.−8

The triangle PQR above is

1. A.an obtuse-angled triangle
2. B.a scalene triangle
3. C.an isosceles triangle
4. D.an equilateral triangle

The locus of a point P which is equidistant from two given points S and T is

1. A.the perpendicular bisector of ST
2. B.the angle bisector of PS and ST
3. C.a perpendicular to ST
4. D.a line parallel to ST

Find the mean of the data: 7, −3, 4, −2, 5, −9, 4, 8, −6, 12

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

The venn diagram above shows the number of students offering Music and History in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?

1. A.0.38
2. B.0.13
3. C.0.50
4. D.0.25

The range of the data k+2, k−3, k+4, k−2, k, k−5, k+3, k−1 and k+6 is

1. A.10
2. B.11
3. C.6
4. D.8

The probability of a student passing any examination is 2/3. If the student takes three examinations, what is the probability that he will not pass any of them?

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

The acres for rice, pineapples, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector for cassava in a pie chart?

1. A.108°
2. B.180°
3. C.36°
4. D.60°

How many three-digit numbers can be formed from 32564 without any digit being repeated?

1. A.120
2. B.10
3. C.20
4. D.60

The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set

1. A.105
2. B.100
3. C.95
4. D.110

Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7 and 8

1. A.2⅙
2. B.2½
3. C.1⅙
4. D.2⅓

No. of days: 1, 2, 3, 4, 5, 6
No. of students: 20, x, 50, 40, 2x, 60
The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term?

1. A.210
2. B.40
3. C.120
4. D.160