WAEC 2023 · Paper 2 · Q11✱✱

(a)
Using a scale of 2 cm to 2 units on both axes, indicate on a graph sheet the area bounded by the inequalities $4y - x \le 4$ , $3x - 2y \le 6$ and $x + 2 \ge 0$ .
Model answer
Draw the three boundary lines: $4y - x = 4$ through $(0, 1)$ and $(-4, 0)$ ; $3x - 2y = 6$ through $(2, 0)$ and $(0, -3)$ ; and the vertical line $x = -2$ . The region is the triangle with corners $(-2, 0.5)$ , $(-2, -6)$ and $(3.2, 1.8)$ . Test a point such as $(0, 0)$ : it satisfies all three, so the triangle containing the origin is the region.
(b)
A debt of ₦472,560.00 is repaid weekly, such that the mode of payment forms an Arithmetic Progression (A.P.). If the first payment is ₦6,508.00 and the debt is fully repaid after 48 weeks, calculate the amount left after the 20th week.

Plot the curves, move them, and read values off the graph.

Worked solution (try it first)

Draw the lines $4y - x = 4$ , $3x - 2y = 6$ and $x = -2$ .
The origin satisfies all three inequalities, so keep the side of each line that contains it.
The region is the triangle with vertices $\left(-2, \frac12\right)$ , $(-2, -6)$ and $(3.2, 1.8)$ .
See the workspace.

The 48 payments add up to the debt: $\dfrac{48}{2}(2a + 47d) = 472\,560$ , so $2a + 47d = 19\,690$ .
With $a = 6508$ : $13\,016 + 47d = 19\,690$ , so $47d = 6674$ and $d = 142$ .
Paid in the first 20 weeks: $S_{20} = \dfrac{20}{2}(2 \times 6508 + 19 \times 142)$
$= 10(13\,016 + 2698)$
$= 157\,140$ .
Amount left after the 20th week: $472\,560 - 157\,140 =$ ₦315 420.