2023 Mathematics WAEC (WASSCE) Essay Past Questions (Paper 2)

Question 1

(a) A car travels a distance of 112 km at an average speed of 70 km/h. it then travels a further 60 km at an average speed of 50 km/h. Calculate, for the entire journey, the total time taken.

Solution

t = \(\frac{distance}{speed}\)

t₁ = \(\frac{112}{70} \\ = \scriptsize 1.6\)

t₂ = \(\frac{60}{50} \\ = \scriptsize 1.2\)

Total time = 1.6 + 1.2 = 2.8 hr

(b) If \(\frac{x}{y} \scriptsize = 2\) and \(\frac{y}{z} \scriptsize = 3\)

Find the value of \(\frac{x\:+\:y}{y\:+\:z}\)

Solution

⇒ \(\frac{x}{y} \scriptsize = 2\)

⇒ \(\frac{y}{z} \scriptsize = 3\)

⇒ x = 2y ………(i)

⇒ z = \(\frac{y}{3}\)………(ii)

Substitute (i) and (ii) into the equation

⇒ \(\frac{x\:+\:y}{y\:+\:z}\)

⇒ \(\frac{2y\:+\:y}{y\:+\: \frac{y}{3}}\)

⇒ \(\frac{3y}{\frac{4y}{3}}\)

⇒ \(\frac{3y}{1} \: \times \: \frac{3}{4y}\)

⇒ \(\frac{9y}{4y}\)

⇒ \(\frac{9\not{y}}{4\not{y}}\)

⇒ \(\frac{9}{4}\)

= \(\scriptsize 2 \frac{1}{4}\)