JAMB Mathematics 2013 past questions and answers

Convert 27₁₀ to another number in base three.

1. A.1100₃
2. B.1000₃
3. C.1001₃
4. D.1010₃

3 girls share a number of apples in the ratio 5:3:2. If the highest share is 40 apples, find the smallest share.

1. A.16
2. B.38
3. C.36
4. D.24

Evaluate (1.25 × 0.025)/0.05, correct to 1 decimal place.

1. A.6.3
2. B.0.5
3. C.0.6
4. D.6.2

Calculate the time taken for N3000 to earn N600 if invested at 8% simple interest.

1. A.3½ years
2. B.1½ years
3. C.2½ years
4. D.3 years

Simplify 3⁻⁵ⁿ/9¹⁻ⁿ × 27ⁿ⁺¹

1. A.3⁵
2. B.3
3. C.3²
4. D.3³

If log₁₀4 = 0.6021, evaluate log₁₀4^⅓

1. A.1.8063
2. B.0.2007
3. C.0.3011
4. D.0.9021

Simplify: √5(√147 − √12)/√15

1. A.1/9
2. B.9
3. C.5
4. D.1/5

P, Q and R are subsets of the universal set U. The venn diagram showing the relationship (P∩Q)∪R is

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

If P = {x: x is odd, −1 < x ≤ 20} and Q = {y: y is prime; −2 < y ≤ 25}, find P∩Q.

1. A.{3,5,7,11,13,17,19}
2. B.{2,3,5,7,11,1...}
3. C.{3,5,7,11,17,19}
4. D.{...6,11,13,17...}

If S = √(t² − 4t + 4), find t in terms of S.

1. A.S − 2
2. B.S² + 2
3. C.S² − 2
4. D.S + 2

If x − 4 is a factor of x² − x − k, then k is

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

The remainder when 6p³ − p² − 47p + 30 is divided by p − 3 is

1. A.63
2. B.18
3. C.21
4. D.42

P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 when q = 1, find the value of p when m = 6, u = 4 and q = 8/5.

1. A.10
2. B.288/5
3. C.128/5
4. D.15

If r varies inversely as the square root of s and t, how does s vary with r and t?

1. A.s varies directly as r² and t².
2. B.s varies directly as r and t.
3. C.s varies inversely as r and t².
4. D.s varies inversely as r² and t.

Evaluate 3(x + 2) > 6(x + 3)

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

If the sum of the first two terms of a G.P. is 3 and the sum of the second and the third terms is −6, find the sum of the first term and the common ratio.

1. A.−5
2. B.5
3. C.−2
4. D.−3

The nth term of the progression 4/2, 7/3, 10/4, 13/5, ... is

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

If a binary operation * is defined by x * y = x + 2y, find 2*(3*4)

1. A.14
2. B.26
3. C.24
4. D.16

If P = (5 3; 2 1) and Q = (4 2; 3 5), find 2P + Q. (Matrices written row by row.)

1. A.(7 7; 8 14)
2. B.(8 14; 7 7)
3. C.(7 7; 14 8)
4. D.(14 8; 7 7)

Find the inverse of (5 3; 6 4). (Matrices written row by row.)

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

In the diagram above, find the value of x.

1. A.45°
2. B.15°
3. C.30°
4. D.40°

Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8cm.

1. A.8√3 cm
2. B.4 cm
3. C.8 cm
4. D.8√2 cm

The locus of the points which is equidistant from the line PQ forms a

1. A.perpendicular line to PQ
2. B.circle centre P
3. C.circle centre Q
4. D.pair of parallel lines to PQ.

If the mid point of the line PQ is (2,3) and the point P is (−2,1), find the coordinate of the point Q.

1. A.(8,6)
2. B.(5,6)
3. C.(0,4)
4. D.(6,5)

Find the equation of the perpendicular bisector of the line joining P(2, −3) to Q(−5, 1)

1. A.8y + 14x + 13 = 0
2. B.8y − 14x + 13 = 0
3. C.8y − 14x − 13 = 0
4. D.8y + 14x − 13 = 0

In triangle PQR, q = 8 cm, r = 6cm and Cos P = 1/12. Calculate the value of p.

1. A.√108 cm
2. B.9cm
3. C.√92 cm
4. D.10 cm

If tan θ = 3/4, find the value of sin θ + cos θ.

1. A.1⅓
2. B.1⅔
3. C.1⅗
4. D.1⅖

The radius of a circle is increasing at the rate of 0.02 cms⁻¹. Find the rate at which the area is increasing when the radius of the circle is 7 cm.

1. A.0.35cm²s⁻¹
2. B.0.88cm²s⁻¹
3. C.0.75cm²s⁻¹
4. D.0.55cm²s⁻¹

Integrate ((1 + x)/x³) dx.

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

Find the mean of t + 2, 2t − 4, 3t + 2 and 2t.

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

The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.

1. A.14
2. B.2
3. C.6
4. D.8

If the variance of 3 + x, 6, 4, x, and 7 − x is 4 and the mean is 5, find the standard deviation.

1. A.3
2. B.√2
3. C.√3
4. D.2

Score: 3, 4, 5, 6, 7, 8, 9, 10
Frequency: 1, 0, 7, 5, 2, 3, 1, 1
The table above shows the scores of 20 students in Further Mathematics test. What is the range of the distribution?

1. A.3
2. B.10
3. C.7
4. D.6

In how many ways can a student select 2 subjects from 5 subjects?

1. A.5!/(2!3!)
2. B.5!/2!
3. C.5!/3!
4. D.5!/(2!2!)

In how many ways can three seats be occupied if 5 people are willing to sit?

1. A.5
2. B.120
3. C.60
4. D.20

A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor orange.

1. A.7/24
2. B.2/3
3. C.3/8
4. D.1/3