WAEC Mathematics Past Questions & Answers - Page 82

406.

The volume of a cone of height 3cm is 38\(\frac{1}{2}\)cm3. Find the radius of its base. [Take \(\pi = \frac{22}{7}\)]

A.

3.0cm

B.

3.5cm

C.

4.0cm

D.

4.5cm

Correct answer is B

Using V = \(\frac{3}{1} \pi r^2h\),

so, 38\(\frac{1}{2} = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 3\)

\(\frac{77}{2} = \frac{22}{7} \times r^2\)

r2 = \(\frac{77 \times 7}{2 \times 22}\)

r2 = \(\frac{49}{4}\)

Hence, r = \(\sqrt{\frac{49}{4}}\)

= 3\(\frac{1}{2}\)

407.

Ada draws the graph of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?

A.

x2 - x - 3 = 0

B.

x2 - 3x - 1 = 0

C.

x2 - 3x - 3 = 0

D.

x2 + 3x - 1 = 0

Correct answer is B

Given; y = x2 - x - 2, y = 2x - 1

Using y = y, gives

x2 - x - 2 = 2x - 1

x2 - 3x - 2 + 1 = 0

therefore, x2 - 3x - 1 = 0

408.

Adding 42 to a given positive number gives the same result as squaring the number. Find the number

A.

14

B.

13

C.

7

D.

6

Correct answer is C

Let the given positive number be x

Then 4 + x = x2

0 = x2 - x - 42

or x2 - x - 42 = 0

x2 - 7x + 6x - 42 = 0

x(x - 7) + 6(x - 7) = 0

= (x + 6)(x - 7) = 0

x = -6 or x = 7

Hence, x = 7

409.

If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)

A.

1\(\frac{5}{16}\)

B.

1\(\frac{1}{16}\)

C.

\(\frac{5}{16}\)

D.

- 1\(\frac{37}{48}\)

Correct answer is D

If m = 4, n = 9, r = 16,

then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)

= \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\)

= \(\frac{64 - 256 + 81}{144}\)

= \(\frac{-111}{144}\)

= - 1\(\frac{37}{48}\)

410.

Find the equation whose roots are \(\frac{3}{4}\) and -4

A.

4x2 - 13x + 12 = 0

B.

4x2 - 13x - 12 = 0

C.

4x2 + 13x - 12 = 0

D.

4x2 + 13x + 12 = 0

Correct answer is C

Let x = \(\frac{3}{4}\) or x = -4

i.e. 4x = 3 or x = -4

(4x - 3)(x + 4) = 0

therefore, 4x2 + 13x - 12 = 0