JAMB Mathematics 2012 past questions and answers

Convert 72₆ to a number in base three.

1. A.2211
2. B.2121
3. C.1212
4. D.1122

Simplify (2⅔ × 1½)/4⅘

1. A.1¼
2. B.1 1/6
3. C.5/6
4. D.4/5

Evaluate 21/9 to 3 significant figures.

1. A.2.30
2. B.2.31
3. C.2.32
4. D.2.33

A man earns N3 500 per month out of which he spends 15% on his children's education. If he spends additional N1 950 on food, how much does he have left?

1. A.N525
2. B.N1 025
3. C.N1 950
4. D.N2 975

If log₃x² = −8, what is x?

1. A.1/3
2. B.1/9
3. C.1/27
4. D.1/81

Simplify (√6 + 2)² − (√6 − 2)²

1. A.2√6
2. B.4√6
3. C.8√6
4. D.16√6

If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P∩Q.

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

In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games how many play neither?

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

Make n the subject of the formula if w = v(2 + cn)/(1 − cn)

1. A.(1/c)((w − 2v)/(v + w))
2. B.(1/c)((w − 2v)/(v − w))
3. C.(1/c)((w + 2v)/(v − w))
4. D.(1/c)((w + 2v)/(v + w))

Find the remainder when 2x³ − 11x² + 8x − 1 is divided by x + 3.

1. A.−871
2. B.−781
3. C.−187
4. D.−178

Solve for x and y in the equations below.
x² − y² = 4
x + y = 2

1. A.x = 0, y = −2
2. B.x = 0, y = 2
3. C.x = 2, y = 0
4. D.x = −2, y = 0

If y varies directly as √n and y = 4 when n = 4, find y when n = 1 7/9.

1. A.√17
2. B.4/3
3. C.8/3
4. D.2/3

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3.

1. A.24
2. B.27
3. C.32
4. D.36

The value of y for which (1/5)y + 1/5 < (1/2)y + 2/5 is

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

Find the range of values of m which satisfy (m − 3)(m − 4) < 0.

1. A.2 < m < 5
2. B.−3 < m < 4
3. C.3 < m < 4
4. D.−4 < m < 3

The shaded region above is represented by the equation

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

The nth term of a sequence is n² − 6n − 4. Find the sum of the 3rd and 4th terms.

1. A.24
2. B.23
3. C.−24
4. D.−25

The sum to infinity of a geometric progression is −1/10 and the first term is −1/8. Find the common ratio of the progression.

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

The binary operation * is defined on the set of integers such that p * q = pq + p − q. Find 2*(3*4).

1. A.11
2. B.13
3. C.15
4. D.22

A binary operation on the set of real numbers is defined by m * n = mn/2 for all m, n ∈ R. If the identity element is 2, find the inverse of −5.

1. A.−4/5
2. B.−2/5
3. C.4
4. D.5

Given that I₃ is a unit matrix of order 3, find |I₃|.

1. A.−1
2. B.0
3. C.1
4. D.2

In the diagram above, QR//TU, ∠PQR = 80° and ∠PSU = 95°. Calculate ∠SUT.

1. A.15°
2. B.25°
3. C.30°
4. D.80°

The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.

1. A.24°
2. B.30°
3. C.33°
4. D.36°

In the diagram above, PQR is a circle centre O. If ∠QPR is x°, find ∠QRP.

1. A.x°
2. B.(90 − x)°
3. C.(90 + x)°
4. D.(180 − x)°

Find the area of the trapezium above.

1. A.91 cm²
2. B.78 cm²
3. C.60 cm²
4. D.19 cm²

A circular arc subtends angle 150° at the centre of a circle of radius 12 cm. Calculate the area of the sector of the arc.

1. A.30π cm²
2. B.60π cm²
3. C.120π cm²
4. D.150π cm²

Calculate the volume of a cuboid of length 0.76 cm, breadth 2.6 cm and height 0.82cm.

1. A.3.92 cm³
2. B.2.13 cm³
3. C.1.97 cm³
4. D.1.62 cm³

The locus of a point equidistant from the intersection of lines 3x − 7y + 7 = 0 and 4x − 6y + 1 = 0 is a

1. A.line parallel to 7x + 13y + 8 = 0
2. B.circle
3. C.semicircle
4. D.bisector of the line 7x + 13y + 8 = 0.

The gradient of the straight line joining the points P(5,−7) and Q(−2,−3) is

1. A.1/2
2. B.2/5
3. C.−4/7
4. D.−2/3

The distance between the point (4,3) and the intersection of y = 2x + 4 and y = 7 − x is

1. A.√13
2. B.3√2
3. C.√26
4. D.10√5

Find the equation of the line through the points (−2,1) and (−½,4).

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

If angle θ is 135°, evaluate cos θ.

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

A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.

1. A.52cm
2. B.43cm
3. C.40cm
4. D.15cm

Find dy/dx if y = cos x.

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

Evaluate ∫₁² (x² − 4x) dx

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

Evaluate ∫₀^π/4 sec²θ dθ

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

The bar chart above shows the distribution of marks in a class test. If the pass mark is 5, what percentage of the students failed the test?

1. A.10%
2. B.20%
3. C.50%
4. D.60%

The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.

1. A.126
2. B.180
3. C.216
4. D.224

Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5.

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

Find the range of 4,9,6,3,2,8,10 and 11.

1. A.11
2. B.9
3. C.8
4. D.4

Evaluate ⁿ⁺¹C_n−2 if n = 15.

1. A.3630
2. B.3360
3. C.1120
4. D.560

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

1. A.6720
2. B.6270
3. C.6207
4. D.6027

The probability that a student passes a Physics test is 2/3. If he takes three Physics tests, what is the probability that he passes two of the tests?

1. A.4/9
2. B.6/9
3. C.4/27
4. D.2/27

The probabilities that a man and his wife live for 80 years are 2/3 and 3/5 respectively. Find the probability that at least one of them will live up to 80 years.

1. A.2/15
2. B.3/15
3. C.7/15
4. D.13/15