Mathematics 0580 · IGCSE · Algebraic manipulation

Algebraic manipulation — practice question

(a)[2]

Rearrange $s = k - t^2$ so that $t$ is the subject.

(b(i))[1]

Factorise $x^2 - 25$ fully.

(b(ii))[3]

Simplify the fraction $\frac{x^2 - 25}{x^2 - 2x - 35}$.

(c)[3]

Express $\frac{x - 8}{x} + \frac{3x}{x + 1}$ as a single fraction in simplest form.

(d)[3]

Find all integer values of $n$ for which $18 - 2n < 6n \leq 30 + n$ holds.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence $t=\pm\sqrt{k-s}$.

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