Mathematics 4024 · O Level · Algebraic manipulation

Algebraic manipulation — practice question

$p = \dfrac{8 - 5q}{q}$. In trapezium $A$, the two parallel sides are $x\text{ cm}$ and $(x-2)\text{ cm}$. In trapezium $B$, the two parallel sides are $x\text{ cm}$ and $(x+3)\text{ cm}$. Each trapezium has area $15\text{ cm}^2$.
(a(i))[1]

Find $p$ for $q = 2.6$.

(a(ii))[2]

Express $q$ as an expression involving $p$.

(b(i))[2]

Show that $H = \dfrac{15}{x - 1}$ and $h = \dfrac{30}{2x + 3}$.

(b(ii))[3]

Find an expression in terms of $x$ for the height difference, $H - h$, between trapezium $A$ and trapezium $B$, and show that it simplifies to $\dfrac{75}{(x - 1)(2x + 3)}$.

(b(iii)(a))[2]

The height difference is $1.5\text{ cm}$. Show that $2x^2 + x - 53 = 0$.

(b(iii)(b))[2]

Find $x$, correct to $2$ decimal places.

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