JAMB Mathematics Past Questions 2012

10 questions from the JAMB 2012 Mathematics paper, with answers and explanations. Tap "Show answer" under each one when you are ready.

JAMB 2012Question 1 · Algebraic Processes

Make 'n' the subject of the formula if w =

\frac{v ( 2 + c n )}{1 - c n}

A. $\frac{1}{c}$ ( $\frac{w - 2 v}{v + w}$ )
B. $\frac{1}{c}$ ( $\frac{w - 2 v}{v - w}$ )
C. $\frac{1}{c}$ ( $\frac{w + 2 v}{v - w}$ )
D. $\frac{1}{c}$ ( $\frac{w + 2 v}{v + w}$ )

Show answer

Answer: A. $\frac{1}{c}$ ( $\frac{w - 2 v}{v + w}$ )

n = (1/c)(w-2v)/(v+w) after cross-multiplying and collecting terms.

JAMB 2012Question 2 · Algebraic Processes

Given that

I_{3}

is a unit matrix of order 3, find

∣ I_{3} ∣

A.-1
B.0
C.1
D.2

Show answer

Answer: C. 1

The determinant of any identity matrix is 1.

JAMB 2012Question 3 · Coordinate Geometry and Trigonometry

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

A. $\frac{1}{2}$
B. $\frac{2}{5}$
C.- $\frac{4}{7}$
D.- $\frac{2}{3}$

Show answer

Answer: C. - $\frac{4}{7}$

Gradient = (-3+7)/(-2-5) = 4/-7 = -4/7.

JAMB 2012Question 4 · Coordinate Geometry and Trigonometry

A man stands on a tree

150 cm

high and sees a boat at an angle of depression of

7 4^{\circ}

. Find the distance of the boat from the base of the tree.

A. $52 cm$
B. $43 cm$
C. $40 cm$
D. $15 cm$

Show answer

Answer: B. $43 cm$

Distance = 150/tan74° ≈ 43.

JAMB 2012Question 5 · Inequalities, Permutation, and Combination

The value of y for which

\frac{1}{5}

y +

\frac{1}{5}

\frac{1}{2}

y +

\frac{2}{5}

A.y > $\frac{2}{3}$
B.y < $\frac{2}{3}$
C.y > - $\frac{2}{3}$
D.y < - $\frac{2}{3}$

Show answer

Answer: C. y > - $\frac{2}{3}$

Multiplying through by 10 and simplifying gives y > -2/3.

JAMB 2012Question 6 · Number, Fractions, and Approximation

Convert

(112)_{6}

to base three.

A. $(2211)_{3}$
B. $(2121)_{3}$
C. $(1212)_{3}$
D. $(1122)_{3}$

Show answer

Answer: D. $(1122)_{3}$

$(112)_{6} = 4 4_{10}$ , and $4 4_{10} = (1122)_{3}$ .

JAMB 2012Question 7 · Number, Fractions, and Approximation

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?

A.N525
B.N1,025
C.N1,950
D.N2,975

Show answer

Answer: B. N1,025

3500 - 525 (15%) = 2975; 2975 - 1950 = 1025.

JAMB 2012Question 8 · Sequences, Series, and Variation

If y varies directly as

n

and y = 4 when n = 4, find y when n = 1

\frac{7}{9}

A. $17$
B. $\frac{4}{3}$
C. $\frac{8}{3}$
D. $\frac{2}{3}$

Show answer

Answer: C. $\frac{8}{3}$

y=2 $n$ ; at n= $\frac{16}{9}$ , y=2× $\frac{4}{3}$ =8/3.

JAMB 2012Question 9 · Sets and Binary Operations

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 \cap Q

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

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Answer: B. {2,3}

Prime factors of 30 = {2,3,5}; factors of 18 <10 = {1,2,3,6,9}; intersection = {2,3}.

JAMB 2012Question 10 · Statistics and Probability

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

A.126
B.180
C.216
D.224

Show answer

Answer: D. 224

Sum of 8 numbers - sum of 7 numbers = 896-672 = 224.

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