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WAEC Mathematics Past Questions & Answers - Page 144

716.

Solve the inequality 1 - 2x < - $\frac{1}{3}$

x < $\frac{2}{3}$

x < - $\frac{2}{3}$

x > $\frac{2}{3}$

x > - $\frac{2}{3}$

View answer & explanation

Correct answer is C

1 - 2x < - $\frac{1}{3}$ ; -2x < - $\frac{1}{3}$ - 1

-2x < - $\frac{1- 3}{3}$

-2x < - $\frac{4}{-6}$

3x -2x < -4; -8x < -4

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

717.

Find the quadratic equation whose roots are c and -c

x² - c² = 0

x² + 2cx = 0

x² + 2cx + c² = 0

x² - 2cx + c² = 0

View answer & explanation

Correct answer is A

Explanation

Roots; x and -c

sum of roots = c + (-c) = 0

product of roots = c x -c = -c²

Equation; x² - (sum of roots) x = product of roots = 0

x² - (0)x + (-c²) = 0

x² - c² = 0

718.

If p = $\frac{1}{2}$ and $\frac{1}{p - 1} = \frac{2}{p + x}$ , find the value of x

-2 $\frac{1}{2}$

-1 $\frac{1}{2}$

1 $\frac{1}{2}$

2 $\frac{1}{2}$

View answer & explanation

Correct answer is B

p = $\frac{1}{2}; \frac{1}{p - 1} = \frac{2}{p + x}$

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

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

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

-2 = $\frac{4}{1 + 2x} -2(1 + 2x) = 4$

1 + 2x = $\frac{4}{-2}$

1 + 2x = -2

2x = -2 - 1

2x = -3

x = - $\frac{3}{2}$

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

719.

XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120^o at the centre of the circle. Calculate the perimeter of the minor segment. [Take $\pi = \frac{22}{7}$ ]

14.67cm

22.67cm

29.33cm

37.33cm

View answer & explanation

Correct answer is B

perimeter of minor segment = Length of arc xy + chord xy

where lxy = $\frac{120}{360} \times 2x \times \frac{22}{7} \times 7$

= 14.67cm

perimeter of minor segment = 14.67 + 8 = 22.67cm

720.

What is the length of an edge of a cube whose total surface area is X cm² and whose total surface area is $\frac{X}{2}$ cm³?

View answer & explanation

Correct answer is A

Total surface area of cube = 6s²

6s² = x

s² = x = $\frac{x}{6}$ .....(1)

volume of a cube = s² = $\frac{x}{2}$

s² = $\frac{x}{2}$ ......(2)

put(1) into (2)

s( $\frac{x}{6}$ ) = $\frac{x}{2}$

s = $\frac{x}{2} \times \frac{6}{x}$

= 3cm