WAEC 2018 · Paper 2 · Q2

(a)
The graph of $y = 2px^2 - p^2x - 14$ passes through the point $(3, 10)$ . Find the values of $p$ .
Separate values with commas, e.g. 3, −2
(b)
Two lines, $3y - 2x = 21$ and $4y + 5x = 5$ , intersect at the point $Q$ . Find the coordinates of $Q$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

The point $(3, 10)$ is on the graph, so $x = 3$ and $y = 10$ satisfy the equation: $10 = 2p(9) - p^2(3) - 14$ .
So $10 = 18p - 3p^2 - 14$ , which rearranges to $3p^2 - 18p + 24 = 0$ .
Divide by 3: $p^2 - 6p + 8 = 0$ .
Factorise: $(p - 2)(p - 4) = 0$ .
So $p = 2$ or $p = 4$ .

(b)

$Q$ is on both lines, so solve the equations simultaneously.
Arrange them with $x$ first: $-2x + 3y = 21$ (1) and $5x + 4y = 5$ (2).
Multiply (1) by 4 and (2) by 3 so the $y$ terms match: $-8x + 12y = 84$ and $15x + 12y = 15$ .
Take the first from the second: $23x = -69$ , so $x = -3$ .
From (1): $6 + 3y = 21$ , so $y = 5$ .
$Q$ is the point $(-3, 5)$ .

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