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WAEC Mathematics Past Questions & Answers - Page 93

461.

The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.

10 $sqrt{2}$

4 $sqrt{5}$

5 $sqrt{2}$

2 $sqrt{5}$

View answer & explanation

Correct answer is D

p(4, 3) Q(2 - 1)

distance = $\sqrt{(x_2 - x_1)^2 + (Y_2 - y_1)^2}$

= $\sqrt{(2 - 4)^2 + (-1 - 3)^2}$

= $\sqrt{(-2)^2 = (-4)^2}$

= $\sqrt{4 + 16}$

= $\sqrt{20}$

= $\sqrt{4 \times 5}$

= 2 $\sqrt{5}$

462.

Find the truth set of the equation x² = 3(2x + 9)

{x : x = 3, x = 9}

{x : x = -3, x = -9}

{x : x = 3, x = -9}

{x : x = -3, x = 9}

View answer & explanation

Correct answer is D

x² = 3(2x + 9)

x² = 6x + 27

x² - 6x - 27 = 0

x² - 9x + 3x - 27 = 0

x(x - 9) + 3(x - 9) = (x + 3)(x - 9) = 0

x + 3 = 0 or x - 9 = 0

x = -3 or x = 9

x = -3, x = 9

463.

If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0 $\geq$ x $\geq$ 6}, find x $\cap$ (Y' $\cup$ Z)

{0, 2, 6}

{1, 3}

{0, 6)

{9}

View answer & explanation

Correct answer is C

x = {0, 2, 4, 6}; y = {1, 2, 3, 4}; z = {1, 3}

u = {0, 1, 2, 3, 4, 5, 6}

y' = {0, 5, 6}

to find x $\cap$ (Y' $\cup$ Z)

first find y' $\cup$ z = {0, 1, 3, 5, 6}

then x $\cap$ (Y' $\cup$ Z) = {0, 6}

464.

Three quarters of a number added to two and a half of the number gives 13. Find the number

View answer & explanation

Correct answer is A

let the number be x

2 $\frac{1}{2}x + \frac{3}{4}x = 13$

$\frac{5}{2}x + \frac{3}{4}x = 13$

multiply through by 4

4( $\frac{5}{2}$ )x + 4( $\frac{3}{4}$ )x = 13 x 4

2(5x) + 3x = 52

10x + 3x = 52

13x = 52

x = $\frac{52}{13}$

x = 4