JAMB Mathematics 2003 past questions and answers

Evaluate log_√24 + log_½16 − log₄32

1. A.−5.5
2. B.−2.5
3. C.2.5
4. D.5.5

Simplify 213₄ × 23₄

1. A.10311₄
2. B.10321₄
3. C.12231₄
4. D.13211₄

In a class of 40 students, 32 offer Mathematics, 24 offer Physics. How many offer both Mathemaics and Physics?

1. A.20
2. B.16
3. C.8
4. D.4

A woman buys 270 oranges for N1,800.00 and sells at 5 for N40.00. What is her profit?

1. A.N2,160.00
2. B.N1,620.00
3. C.630.00
4. D.N360.00

Simplify 1 − (2⅓ × 1¼) + 3/5

1. A.−1 1/15
2. B.−1 19/60
3. C.−2 7/15
4. D.−2 31/60

Simplify (√98 − √50)/√32

1. A.3
2. B.1
3. C.½
4. D.¼

A cinema hall contains a certain number of people. If 22½% are children, 47½% are men and 84 are women, find the number of men in the hall.

1. A.63
2. B.84
3. C.113
4. D.133

If 9^{2x − 1}/27^x+1 = 1, find the value of x.

1. A.8
2. B.5
3. C.3
4. D.2

The sum of four numbers is 1214₅. What is the average expressed in base five?

1. A.114
2. B.141
3. C.401
4. D.411

Given:
U = {Even numbers between 0 and 30}
P = {Multiples of 6 between 0 and 30}
Q = {Multiples of 4 between 0 and 30}
Find (P∪Q)^c

1. A.{2,10,14,22,26}
2. B.{0,10,14,22,26}
3. C.{2,4,14,18,26}
4. D.{0,2,6,22,26}

x varies directly as the product of u and v and inversely as their sum. If x = 3 when u = 3 and v = 1, what is the value of x if u = 3 and v = 3?

1. A.3
2. B.4
3. C.6
4. D.9

Find the range of the values of x satisfying the inequalities 5 + x ≤ 8 and 13 + x ≥ 7.

1. A.−3 ≤ x ≤ 3
2. B.3 ≤ x ≤ 6
3. C.−6 ≤ x ≤ 3
4. D.−6 ≤ x ≤ −3

If |−x 2; 4x 1| = |3 3x; 4 −5|, find the value of x. (Each is a 2 × 2 determinant written row by row.)

1. A.5
2. B.2
3. C.−2
4. D.−5

The graph of the function y = x² + 4 and a straight line PQ are drawn to solve the equation x² − 3x + 2 = 0. What is the equation PQ?

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

The length a person can jump is inversely proportional to his weight. If a 20kg person can jump 1.5m, find the constant proportionality.

1. A.60
2. B.30
3. C.20
4. D.15

Find the values of x and y respectively if 3x − 5y + 5 = 0 and 4x − 7y + 8 = 0

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

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

1. A.¼
2. B.½
3. C.2/3
4. D.3/2

Triangle OPQ above is the solution to the inequalities

1. A.x + 1 ≥ 0, y + x ≤ 0, y − x ≥ 0
2. B.y + x ≤ 0, y − x ≥ 0, x − 1 ≥ 0
3. C.x − 1 ≤ 0, y − x ≥ 0, y + x ≥ 0
4. D.x − 1 ≤ 0, y + x ≤ 0, y − x ≤ 0

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

1. A.2x(a − 3b)(2b − y)
2. B.2x(3b − a)(2b − y)
3. C.2x(a − 3b)(y − 2b)
4. D.2x(2b − a)(3b − y)

A matrix P has an inverse P⁻¹ = (1 −3; 0 1). Find P. (Matrices are written row by row.)

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

The sum of the first n terms of an arithmetic progression is 252. If the first term is −16 and the last term is 72, find the number of terms in the series.

1. A.6
2. B.7
3. C.8
4. D.9

An arc of a circle subtends an angle of 30° on the circumference of a circle of radius 21cm. Find the length of the arc. [π = 22/7]

1. A.11cm
2. B.22cm
3. C.44cm
4. D.66cm

Find the equation of the locus of a point P(x,y) which is euidistant from Q(0,0) and R(2,1).

1. A.4x + 2y = 5
2. B.4x − 2y = 5
3. C.2x + 2y = 5
4. D.2x + y = 5

In the diagram above, PQ is parallel to RS. What is the value of α + β + γ?

1. A.360°
2. B.200°
3. C.180°
4. D.90°

A trapezium has two parallel sides of length 5cm and 9cm. If the area is 21cm², find the distance between the parallel sides.

1. A.3cm
2. B.4cm
3. C.6cm
4. D.7cm

Which of the following is the graph of sinθ for −π/2 ≤ θ ≤ 3π/2?

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

In the diagram above, O is the centre of the circle, POM is a diameter and ∠MNQ = 42°. Calculate ∠QMP.

1. A.42°
2. B.48°
3. C.132°
4. D.138°

Find the value of p, if the line which passes through (−1, −p) and (−2p, 2) is parallel to the line 2y + 8x − 17 = 0

1. A.7/6
2. B.6/7
3. C.−2/7
4. D.−6/7

An aeroplane flies due north from airports P to Q and then flies due east to R. If Q is euidistant from P and R, find the bearing of P from R.

1. A.090°
2. B.135°
3. C.225°
4. D.270°

The locus of a point P which moves on one side only of a straight line XY so that ∠XPY = 90° is

1. A.a circle
2. B.a semicircle
3. C.an arc of a circle through X, Y
4. D.the perpendicular bisector of XY

If π/2 ≤ θ ≤ 2π, find the maximum value of f(θ) = 4/(6 + 2cosθ)

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

XYZ is a circle with center O and radius 7cm. Find the area of the shaded region. [π = 22/7]

1. A.84cm²
2. B.77cm²
3. C.38cm²
4. D.14cm²

A triangle has vertices P(−1,6), Q(−3,−4) and R(1,−4). Find the midpoints of PQ and QR respectively.

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

In the diagram above, PQR is a straight line and PS is a tangent to the circle QRS with |PS| = |SR| and ∠SPR = 40°. Find ∠PSQ.

1. A.40°
2. B.30°
3. C.20°
4. D.10°

Find the slope of the curve y = 2x² + 5x − 3 at (1,4).

1. A.4
2. B.6
3. C.7
4. D.9

Evaluate ∫₂³ (x² − 2x)dx

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

If y = 3 sin(−4x), dy/dx is

1. A.12x cos(4x)
2. B.−12x cos(−4x)
3. C.−12 cos(−4x)
4. D.12 sin(−4x)

Determine the maximum value of y = 3x² − x³.

1. A.0
2. B.2
3. C.4
4. D.6

By how much will the mean of 30, 56, 31, 55, 43 and 44 less than the median?

1. A.0.75
2. B.0.50
3. C.0.33
4. D.0.17

The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21 and 16 is

1. A.16
2. B.21
3. C.23
4. D.24

Value: 0, 1, 2, 3, 4
Frequency: 1, 2, 2, 1, 9
Find the mean of the distribution above.

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

On a pie chart, there are four sectors of which three angles are 45°, 90° and 135°. If the smallest sector represents N28.00, how much is the largest sector?

1. A.N96.00
2. B.N84.00
3. C.N48.00
4. D.N42.00

Two dice are thrown. What is the probability that the sum of the numbers is divisible by 3?

1. A.2/3
2. B.½
3. C.1/3
4. D.¼

If ⁿP₃ − 6(ⁿC₄) = 0, find the value of n.

1. A.5
2. B.6
3. C.7
4. D.8

Find the number of committees of three that can be formed consisting of two men and one woman from four men and three women.

1. A.3
2. B.6
3. C.18
4. D.24

The mean of the numbers 3, 6, 4, x and 7 is 5. Find the standard deviation.

1. A.√2
2. B.√3
3. C.2
4. D.3

A bag contains 5 black balls and 3 red balls. Two balls are picked randomly without replacement. What is the probability that a black and a red ball are picked?

1. A.15/28
2. B.13/28
3. C.5/14
4. D.3/14

The histogram above shows the ages of the victims of a pollution. How many people were involved in the pollution?

1. A.15
2. B.18
3. C.20
4. D.21

Number: 1, 2, 3, 4, 5, 6
Frequency: 12, 20, x, 21, x − 1, 28
The result of tossing a fair dice 120 times is summarized above. Find the value of x.

1. A.19
2. B.20
3. C.21
4. D.22