Mathematics 0580 · IGCSE · Algebraic manipulation

Algebraic manipulation — practice question

(a)[2]

Solve for $x$ in $4x + 15 = 9$.

(b)[1]

Factorise the expression $a^2 - 9$.

(c)[3]

Write the expression as one fraction, then simplify completely: $\frac{4a}{5} \div \frac{3ad}{10c}$.

(d)[2]

Given $5^n + 5^n + 5^n + 5^n + 5^n = 5^m$, determine $m$ in terms of $n$.

(e)[3]

Solve $4x^2 + 8x - 5 = 0$ by factorisation.

(f(i))[3]

Find the value of $x$ when $y = 108$.

(f(ii))[2]

Determine $n$.

(g)[3]

Expand and then simplify $(2x + 3)(x - 1)(x + 3)$.

(h)[2]

Find $\frac{dy}{dx}$ for $y = 3x^2 + 4x - 1$.

Worked solution & mark scheme

This 21-mark question has a full step-by-step worked solution and mark scheme. One marking point: $-\frac{3}{2}$ or $-1.5$

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