JAMB Mathematics 2005 past questions and answers

Find the value of m if 13_m + 24_m = 41_m.

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

If 321₄ is divided by 23₄ and leaves a remainder r, what is the value of r?

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

Simplify 3½ − (2⅓ × 1¼) + 3/5

1. A.2 11/60
2. B.2 1/60
3. C.1 11/60
4. D.1 1/60

A father decided to give 20% of his monthly income to his three children as their monthly allowance. The eldest child got 45% of the allowance and the youngest got 25%. How much was the father's monthly income if the second child got N3,000?

1. A.N33,000
2. B.N45,000
3. C.N50,000
4. D.N60,000

If the interest on N150.00 for 2½ years is N4.50, find the interest on N250.00 for 6 months at the same rate.

1. A.N1.50
2. B.N7.50
3. C.N15.00
4. D.N18.00

Evaluate (81^3/4 − 27^1/3)/(3 × 2³).

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

If log₁₀2 = 0.3010 and log₁₀3 = 0.4771, evaluate log₁₀4.5

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

Simplify (√12 − √3)/(√12 + √3)

1. A.0
2. B.1/3
3. C.3/5
4. D.1

If U = {x/x is a positive integer less than 10} and P = {x/ x is a prime factor of 30}, find the complement of P.

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

The Venn diagram above shows a class of 40 students with the games they play. How many of the students play two games only?

1. A.19
2. B.16
3. C.15
4. D.4

If m = 3, p = −3, q = 7 and r = 5/2, evaluate m(p + q + r).

1. A.19.50
2. B.19.15
3. C.18.95
4. D.18.05

Divide 6x² − 13x + 5 by 2x − 1

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

A polynomial in x whose zeros are −2, −1 and 3 is

1. A.x³ − 7x + 6
2. B.x³ + 7x − 6
3. C.x³ + 7x + 6
4. D.x³ − 7x − 6

The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 30 men to do a piece of work in 6 days, how many men are required to do the work in 4 days?

1. A.20
2. B.35
3. C.45
4. D.60

The weight W kg of a metal bar varies jointly as its length L metres and the square of its diameter d metres. If W = 140 when d = 4⅔ and L = 54, find d in terms of W and L.

1. A.√(42W/5L)
2. B.√(5L/42W)
3. C.42W/5L
4. D.5L/42W

Find the range of values of x for which 7x − 3 > 25 + 3x.

1. A.x > 7
2. B.x < 7
3. C.x > −7
4. D.x < −7

The diagram above is the graph of the function f(x). Determine the range of values of x for which f(x) ≤ 0.

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

If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference.

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

Find the sum of the first 20 terms of the series 8, 12, 16, ......., 96.

1. A.1400
2. B.1040
3. C.960
4. D.920

An operation * is defined on the set of real numbers by a * b = ab + 2(a + b + 1). Find the identity element.

1. A.2
2. B.1
3. C.−1
4. D.−2

If M and N are two matrices defined by M = (1 3 2; 4 5 −1; −3 2 0) and N = (1 −2 3; 4 −1 5; 2 −3 −1), evaluate 2M − 3N. (Matrices written row by row.)

1. A.(−1 12 5; 4 7 13; 0 −5 −3)
2. B.(−1 0 −5; −4 7 −17; 0 −5 3)
3. C.(−1 12 −5; −4 13 −17; −12 13 3)
4. D.(−1 12 −5; 4 13 13; −12 13 3)

If P = (1 3 2; 4 5 −1; −3 2 0), find the determinant of matrix P. (Matrix written row by row.)

1. A.75
2. B.57
3. C.−57
4. D.−75

In the diagram above, calculate the value of x.

1. A.60°
2. B.100°
3. C.120°
4. D.140°

Three straight lines EF, GH and LK intersect at O as shown above. If ∠KOF = 52° and ∠LOH = 85°, calculate the size of ∠EOG.

1. A.26°
2. B.43°
3. C.52°
4. D.85°

The sum of the interior angles of a regular polygon is 1800°. Calculate the size of one exterior angle of the polygon.

1. A.30°
2. B.24°
3. C.18°
4. D.12°

In the diagram above, O is the centre of the circle, ∠UOT = 70° and ∠RST = 100°. Calculate ∠RUO.

1. A.20°
2. B.25°
3. C.50°
4. D.80°

A chord of a circle subtends an angle of 60° at the centre of a circle of radius 14cm. Find the length of the chord.

1. A.7cm
2. B.14cm
3. C.21cm
4. D.28cm

A sector of a circle has an area of 55 cm². If the radius of the circle is 10 cm, calculate the angle of the sector. [π = 22/7]

1. A.45°
2. B.63°
3. C.75°
4. D.90°

Find the curved surface area of a cone with circular base diameter 10 cm and height 12 cm.

1. A.25πcm²
2. B.65πcm²
3. C.120πcm²
4. D.156πcm²

Two lines PQ and ST intersect at 75°. The locus of points equidistant from PQ and ST lies on the

1. A.perpendicular bisector of PQ
2. B.perpendicular bisector of ST
3. C.bisector of the angles between lines PQ and ST
4. D.bisector of the angles between lines PT and QS.

Find the equation of the perpendicular at point (4, 3) to the line y + 2x = 5.

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

Find the coordinates of the midpoint of the line joining (3, −4) and (−1, 10).

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

If sin θ = −½ for 0 < θ < 360°, the value of θ is

1. A.30° and 150°
2. B.150° and 210°
3. C.210° and 330°
4. D.150° and 330°

From the diagram above, find the bearing of R from S.

1. A.226°
2. B.224°
3. C.136°
4. D.134°

If y = (1 − 2x)³, find the value of dy/dx at x = −1.

1. A.57
2. B.27
3. C.−6
4. D.−54

Find the derivative of y = sin(2x³ + 3x − 4).

1. A.cos(2x³ + 3x − 4)
2. B.−cos(2x³ + 3x − 4)
3. C.(6x² + 3) cos(2x³ + 3x − 4)
4. D.−(6x² + 3) cos(2x³ + 3x − 4)

The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At what rate is the area of the disc increasing when its radius is 6cm?

1. A.36π cm²/sec.
2. B.18π cm²/sec.
3. C.6π cm²/sec.
4. D.3π cm²/sec.

Evaluate ∫₀^π/2 sin 2x dx.

1. A.1
2. B.0
3. C.−½
4. D.−1

Scores: 1, 2, 3, 4, 5, 6
No. of students: 1, 4, 5, 6, x, 2
The table above shows the scores of a group of students in a test. If the average score is 3.5, find the value of x.

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

The modal height and range of heights 1.35, 1.25, 1.35, 1.40, 1.35, 1.45, 1.50, 1.35, 1.50 and 1.20 are m and r respectively. Find m + 2r.

1. A.1.35
2. B.1.65
3. C.1.95
4. D.3.00

Find the value of t if the standard deviation of 2t, 3t, 4t, 5t and 6t is √2.

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

In how many ways can 6 coloured chalks be arranged if 2 are of the same colour?

1. A.60
2. B.120
3. C.240
4. D.360

How many possible ways are there of seating seven people P, Q, R, S, T, U and V at a circular table?

1. A.360
2. B.720
3. C.2520
4. D.5040

A box contains 5 blue balls, 3 red balls and 2 white balls. Two balls are selected from the box with replacement. Find the probability of obtaining two blue or two red balls.

1. A.17/50
2. B.3/25
3. C.1/50
4. D.3/250

What is the probability that an integer x, (1 ≤ x ≤ 20) chosen at random is divisible by both 2 and 3?

1. A.1/20
2. B.1/3
3. C.3/20
4. D.7/10