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WAEC Mathematics Past Questions & Answers - Page 74

366.

Simplify; $\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}$

3²ⁿ

3ⁿ

3^{n + 1}

Correct answer is B

$\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}$

= $\frac{3^{n - 1} \times 3^{3(n + 1)}}{3^{4n}}$

= 3 $^{n - 1 + 3n + 3 - 4n}$

= 3 $^{4n - 4n - 1 + 3}$

= 3²

= 9

367.

On a map, 1cm represent 5km. Find the area on the map that represents 100km².

2cm²

4cm²

8cm²

View answer & explanation

Correct answer is B

On a map, 1cm represents 5km. Then it follows that 1cm² represents 25km². Acm² represents 100km². By apparent cross-multiplication, 1cm² x 100km² = Acm²x 25km²

therefore A = $\frac{100}{25}$ = 4cm²

368.

Which of following is a valid conclusion from the premise. "Nigeria footballers are good footballers"?

Joseph plays football in Nigeria therefore he is a good footballer

Joseph is a good footballer therefore he is a Nigerian footballer

Joseph is a Nigerian footballer therefore he is a good footballer

Joseph plays good football therefore he is a Nigerian footballer

View answer & explanation

Correct answer is C

From the venn diagram, Nigeria footballers from a subset of good footballers.

369.

The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?

90cm

135cm

180cm

225cm

View answer & explanation

Correct answer is C

d $\alpha$ t²

d = t² k

where k is a constant. d = 45cm, when t = 3s; thus 45 = 3² x t

k = $\frac{45}{9}$ = 5

thus equation connecting d and t is d = 5t²

when t = 6s, d = 5 x 6²

= 5 x 36

= 180cm

370.

Simplify:( $\frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15}$ )²

75.00

15.00

8.66

3.87

View answer & explanation

Correct answer is B

Note that $\frac{10\sqrt{3}}{\sqrt{5}} = \frac{10\sqrt{3}}{\sqrt{5}} \times - \frac{\sqrt{5}}{\sqrt{5}}$

= $\frac{10\sqrt{15}}{\sqrt{5}} = 2\sqrt{15}$

hence, ( $\frac{10\sqrt{3}}{\sqrt{5}} - \sqrt{15}$ )² = ( $2\sqrt{15} - \sqrt{15}$ )²

= ( $2\sqrt{15} - \sqrt{15}$ )( $2\sqrt{15} - \sqrt{15}$ )

= 4 $\sqrt{15 \times 15} - 2\sqrt{15 \times 15} - 2\sqrt{15 x 15} + \sqrt{15 \times 15}$

= 4 x 15 - 2 x 15 - 2 x 15 + 15

= 60 - 30 - 30 + 15

= 15