JAMB Mathematics 2008 past questions and answers

Add 1101₂, 10111₂ and 111₂

1. A.111011₂
2. B.110110₂
3. C.101011₂
4. D.101010₂

If 125_x = 20₁₀, find x.

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

Evaluate (3/8 ÷ 1/2 − 1/3)/(1/8 × 2/3 + 1/3)

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

Express 123456 to 3 significant figures

1. A.123 000
2. B.124 000
3. C.125 000
4. D.126 000

Calculate the simple interest on N7 500 for 8 years at 5% per annum

1. A.N3 000
2. B.N600
3. C.N300
4. D.N150

The cost of kerosene per litre increases from N60 to N85. What is the percentage rate of increase?

1. A.42%
2. B.41%
3. C.40%
4. D.25%

Simplify 16^−½ × 4^−½ × 27^1/3

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

If log_x^½ 64 = 3, find the value of x.

1. A.4
2. B.16
3. C.32
4. D.64

If (1 + √2)/(1 − √2) is expressed in the form x + y√2, find the values of x and y.

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

If X = {n² + 1 : n = 0, 2, 3} and Y = {n + 1 : n = 2, 3, 5}, find X∩Y.

1. A.{1, 3}
2. B.{5, 10}
3. C.Φ
4. D.{4, 6}

A bookseller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books, how many customers has he altogether?

1. A.30
2. B.40
3. C.50
4. D.60

Make Q the subject of the formula when L = (4/3)M√(PQ)

1. A.9L²/16M²P
2. B.3L/4M√P
3. C.√(3L)/4MP
4. D.3L²/16M²P

If 2x² − kx − 12 is divisible by x − 4, find the value of k.

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

Factorize completely (4x + 3y)² − (3x − 2y)²

1. A.(x + 5y)(7x + y)
2. B.(x + 5y)(7x − y)
3. C.(x − 5y)(7x + y)
4. D.(x − 5y)(7x − y)

If x − 3 is directly proportional to the square of y and x = 5 when y = 2, find x when y = 6.

1. A.30
2. B.21
3. C.16
4. D.12

If p varies inversely as the square of q and p = 8 when q = 4, find q when p = 32.

1. A.±16
2. B.±8
3. C.±4
4. D.±2

Find the range of values of x which satisfy the inequalities 4x − 7 ≤ 3x and 3x − 4 ≤ 4x.

1. A.−4 ≤ x ≤ 7
2. B.−7 ≤ x ≤ 4
3. C.x ≥ −7
4. D.−7 ≤ x ≤ 6

Solve the quadratic inequality x² − 5x + 6 ≥ 0

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

The shaded area that gives the solution set for the inequalities x + y ≤ 3, x − y ≤ 3, is

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

The fifth term of an A.P. is 24 and the eleventh term is 96. Find the first term.

1. A.12
2. B.4
3. C.−12
4. D.−24

A binary operation * defined on the set of positive integers is such that x * y = 2x − 3y + 2 for all positive integers x and y. The binary operation is

1. A.commutative and closed on the set of positive integers
2. B.neither commutative nor closed on the set of positive integers
3. C.commutative but not closed on the set of positive integers
4. D.not commutative but closed on the set of positive integers.

A binary operation on the set of real numbers excluding −1 is such that for all m, n ∈ R, m Δ n = m + n + mn. Find the identity element of the operation.

1. A.1
2. B.0
3. C.−½
4. D.−1

Find the values of x and y respectively if (1 0; −1 −1; 2 2) + (x 1; −1 0; y −2) = (−2 1; −2 −1; −3 0) (matrices written row by row)

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

If (−2 1; 2 3)(p q; r s) = (1 0; 0 1), what is the value of r? (Matrices written row by row.)

1. A.−3/8
2. B.3/8
3. C.5/8
4. D.1/4

In the diagram above, PQ//RS. The size of the angle marked x is

1. A.100°
2. B.80°
3. C.50°
4. D.30°

Find the exterior angle of a 12 sided regular polygon.

1. A.12°
2. B.24°
3. C.25°
4. D.30°

In the diagram above, ∠OPQ is

1. A.90°
2. B.53°
3. C.36°
4. D.26°

Find the area of the figure above. [π = 22/7]

1. A.12.5cm²
2. B.75.0cm²
3. C.78.5cm²
4. D.84.8cm²

Find the angle subtended at the centre of a circle by a chord which is equal in length to the radius of the circle.

1. A.30°
2. B.45°
3. C.60°
4. D.90°

Find the gradient of the line which is perpendicular to the line with the equation 3x + 2y + 1 = 0

1. A.3/2
2. B.2/3
3. C.−2/3
4. D.−3/2

Calculate the distance between points L(−1, −6) and M(−3, −5)

1. A.√5
2. B.2√3
3. C.√20
4. D.√53

If sin θ = 3/5, find tan θ.

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

A student sitting on a tower 68 metres high observes his principal's car at an angle of depression of 20°. How far is the car from the bottom of the tower to the nearest metre?

1. A.184m
2. B.185m
3. C.186m
4. D.187m

Find the derivative of y = (x⁷ − x⁵)/x⁴.

1. A.x(x² − 1)
2. B.3x(x² − 1)
3. C.3x² − 1
4. D.7x⁶ − 5x⁴

Differentiate sin x − x cos x.

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

Find the minimum value of the function y = x(1 + x)

1. A.−1/4
2. B.−1/2
3. C.1/4
4. D.1/2

Evaluate ∫₁² (6x² − 2x) dx.

1. A.16
2. B.13
3. C.12
4. D.11

Evaluate ∫_−π/2^π/2 cos x dx.

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

On a pie chart, there are six sectors of which four angles are 30°, 45°, 60°, 90° and the remaining two angles are in the ratio 2:1. Find the smaller angles of the remaining two angles.

1. A.15°
2. B.30°
3. C.45°
4. D.60°

The bar chart above shows the number of times the words a, and, in, it, the, to appear in a paragraph in a book. What is the ratio of the least frequent word to that of the most frequent word?

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

What is the mean of the data t, 2t − 1, t − 2, 2t − 1, 4t and 2t + 2?

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

Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0.

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

If x > 0, find the range of the numbers x − 3, 3x + 2, x − 1, 4x, 2x − 1, x − 2, 2x − 2, 3x and 3x + 1.

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

In how many ways can the letters of the word ACCEPTANCE be arranged?

1. A.10!/(2! 2! 3!)
2. B.10!/(2! 3!)
3. C.10!/(2! 2!)
4. D.10!

Find the number of ways of selecting 6 out of 10 subjects for an examination.

1. A.218
2. B.216
3. C.215
4. D.210

The probability of picking a letter T from the word OBSTRUCTION is

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

The result of rolling a fair die 150 times is summarized in the table below.
Number: 1, 2, 3, 4, 5, 6
Frequency: 12, 18, x, 30, 2x, 45
What is the probability of obtaining a 5?

1. A.3/10
2. B.1/5
3. C.1/6
4. D.1/10