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WAEC Mathematics Past Questions & Answers - Page 75

371.

Simplify: ( $\frac{3}{4} - \frac{2}{3}$ ) x 1 $\frac{1}{5}$

$\frac{1}{60}$

$\frac{5}{72}$

$\frac{1}{10}$

1 $\frac{7}{10}$

View answer & explanation

Correct answer is C

( $\frac{3}{4} - \frac{2}{3}$ ) x 1 $\frac{1}{5}$

= ( $\frac{9 - 8}{12} \times \frac{6}{5}$ )

= $\frac{1}{12} \times \frac{6}{5}$

= $\frac{1}{10}$

372.

If 23_x + 101_x = 130_x, find the value of x

View answer & explanation

Correct answer is D

23_x + 101_x = 130_x

2 x X¹ + 3 x X^o + 1 x X² + 0 x X¹ + 1 x X^o

= 1 x X^o = 1 x X² + 3 x X¹ + 0 x X^o

= X² + 3x + 0

2x + 3 = x² + 0 + 1 + x² + 3x

2x - 3x + x² - x² = -3 - 1

- x = -4

x = 4

373.

In the diagram, $\bar{OX}$ bisects < YXZ and $\bar{OZ}$ bisects < YZX. If < XYZ = 68^o, calculate the value of < XOZ

68^o

72^o

112^o

124^o

View answer & explanation

Correct answer is D

In $\Delta$ XYZ, 2m + 2n + 68^o = 180^o

2(m + n) + 68^o = 180^o...(1)

in $\Delta$ XOZ, m + n + q = 180^o ...(2)

(m + n) = 180^o - q...(3)

substituting 180^o - q for (m + n) in (1) gives

2(180^o - q) + 68^o = 180^o

360^o - 2q = 180^o - 68^o

360^o - 2q = 112^o

360^o - 112^o = 2q

248^o = 2q

q = $\frac{248^o}{2}$

= 124^o

hence, < XOZ = 124^o

374.

In a circle radius rcm, a chord 16 $\sqrt{3}cm$ long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r

22cm

17cm

16cm

15cm

View answer & explanation

Correct answer is B

In the diagram

|AM| = |MB| - $\frac{|AB|}{2}$

= $\frac{16\sqrt{3}}{2}$ cm

= 8 $\sqrt{3}$ cm

in $\Delta$ AMO, r² = |AM|Z + |MO|²

r² = (8 $\sqrt{3}$ )²
+ 10²

= 64 x 3 + 100

= 192 + 100

= 292

r = $\sqrt{292}$

17.088cm

17cm

375.

A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

$\frac{9}{13}$

$\frac{11}{26}$

$\frac{4}{13}$

$\frac{1}{26}$

View answer & explanation

Correct answer is C

Two word mathematics is first rewritten as mathematics, since every letter of mathematics appears once in the english alphabet.

Hence the probability that letter selected is from the word mathematics is prob. (matheics) = $\frac{8}{26}$

= $\frac{4}{13}$