WAEC Mathematics Past Questions & Answers - Page 233

1,161.

Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.

A.

\(\frac{m}{2}-3\le 10\)

B.

\(\frac{m}{2}-3\ge 10\)

C.

\(\frac{m-3}{2}\ge10\)

D.

\(\frac{m-3}{2}\le10\)

Correct answer is C

Total number of mangoes = m

Amina ate 3 mangoes \(\implies\) Remainder = m - 3

Shared equally with Uche \(\implies \frac{m - 3}{2}\)

\(\frac{m - 3}{2} \geq 10\)

1,162.

Water flows from a tap into cylindrical container at the rate 5πcm\(^3\) per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of 9 seconds.

A.

2cm

B.

5cm

C.

8cm

D.

15cm

Correct answer is B

Volume of water after 9 seconds = \(5\pi \times 9 = 45\pi cm^3\)

Volume of cylinder = \(\pi r^2 h\)

\(\therefore \pi r^2 h = 45\pi\)

\(\pi \times 3^2 \times h = 45\pi\)

\(\implies 9h = 45 \)

\(h = 5 cm\)

(where h = height of the water after 9 secs)

1,163.

The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.

A.

24cm

B.

36cm

C.

72cm

D.

144cm

Correct answer is B

Area = \(\frac{1}{2} \times base \times height\)

\(height : base = 1 : 3\)

\(\implies base = 3 \times height\)

Let height = h;

Area = \(\frac{1}{2} \times 3h \times h = 216\)

\(3h^2 = 216 \times 2 = 432\)

\(h^2 = \frac{432}{3} = 144\)

\(h = \sqrt{144} = 12.0 cm\)

\(\therefore base = 3 \times 12 = 36 cm\)

1,164.

A car travel at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed

A.

\(\frac{2x + 2y}{3}kmh^{-1}\)

B.

\(\frac{x + y}{3}kmh^{-1}\)

C.

\(\frac{x + 2y}{3}kmh^{-1}\)

D.

\(\frac{2x + y}{3}kmh^{-1}\)

Correct answer is C

Travelled x km/h for 1 hour \(\therefore\) traveled x km in the first hour.

Traveled y km/h for 2 hours \(\therefore\) traveled 2y km in the next 2 hours.

Average speed = \(\frac{x + 2y}{1 + 2}\)

= \(\frac{x + 2y}{3} kmh^{-1}\)

1,165.

Two numbers 24\(_{x}\) and 31\(_y\) are equal in value when converted to base ten. Find the equation connecting x and y

A.

2x = 3(y - 1)

B.

4x - y = 1

C.

3y + 2x = 3

D.

3y = 2 (x + 3)

Correct answer is A

24\(_x\) = 31\(_y\)

\(2 \times x^1 + 4 \times x^0 = 3 \times y^1 + 1 \times y^0\)

\(2x + 4 = 3y + 1 \implies 2x = 3y + 1 - 4\)

\(2x = 3y - 3 = 3(y - 1)\)