JAMB Mathematics Past Questions & Answers

171.

Find the value of x if $\frac{\sqrt{2}}{x + \sqrt{2}}$ = $\frac{1}{x - \sqrt{2}}$

3 $\sqrt{2}$ + 4

3 $\sqrt{2}$ - 4

3 - 2 $\sqrt{2}$

4 + 2 $\sqrt{2}$

View answer & explanation

Correct answer is A

$\frac{\sqrt{2}}{x + 2}$ = x - $\frac{1}{\sqrt{2}}$

x $\sqrt{2}$ (x - $\sqrt{2}$ ) = x + $\sqrt{2}$ (cross multiply)

x $\sqrt{2}$ - 2 = x + $\sqrt{2}$

= x $\sqrt{2}$ - x

= 2 + $\sqrt{2}$

x ( $\sqrt{2}$ - 1) = 2 + $\sqrt{2}$

= $\frac{2 + \sqrt{2}}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}$

x = $\frac{2 \sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}$

= 3 $\sqrt{2}$ + 4

172.

If x is positive real number, find the range of values for which $\frac{1}{3x}$ + $\frac{1}{2}$ x = $\frac{2 + 3x}{6x}$ > $\frac{1}{4x}$

x > - $\frac{1}{6}$

x > 0

0 < x < 6

0 < x < $\frac{1}{6}$

View answer & explanation

Correct answer is A

$\frac{1}{3x}$ + $\frac{1}{2}$ x = $\frac{2 + 3x}{6x}$ > $\frac{1}{4x}$

= 4(2 + 3x) > 6x = 12x $^2$ - 2x = 0

= 2x(6x - 1) > 0 = x(6x - 1) > 0

Case 1 (-, -) = x < 0, 6x - 1 > 0

= x < 0, x < $\frac{1}{6}$ (solution)

Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0

x > $\frac{1}{6}$

Combining solutions in cases (1) and (2)

= x > 0, x < $\frac{1}{6}$ = 0 < x < $\frac{1}{6}$

173.

The pie chart shows the income of a civil servant in month. If his monthly income is N6,000. Find his monthly basic salary.

N2,050

N2,600

N3,100

N3,450

View answer & explanation

Correct answer is A

360 $^o$ - (60 $^o$ + 60 $^o$ + 67 + 50 = 237 $^o$ )

360 $^o$ - 237 = 130 $^o$

B. Salary = $\frac{123}{360} X \frac{N6000}{1}$

= N2,050

174.

Find the simple interest rate percent annum at which N1000 accumulates to N1240 in 3 years.

10%

12%

View answer & explanation

Correct answer is B

I = $\frac{PRT}{100}$ = 1 = 1240 - 1000 = 240

R = $\frac{240 \times 100}{100 \times 3}$ = 8%

175.

A school boy lying on the ground 30m away from the foot of a water tank towel observes that the angle of elevation of the top of the tank is 60 $^o$ . Calculate the height of the tank.

60 $\sqrt{3m}$

30 $\sqrt{3m}$

20 $\sqrt{3m}$

10 $\sqrt{3m}$

View answer & explanation

Correct answer is B

h = 30 tan 60

= 30 $\sqrt{3}$

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