Mathematics 0580 · IGCSE · Algebraic manipulation

Algebraic manipulation — practice question

(a(i))[2]

Factorise the expression. $x^2 - x - 12$

(a(ii))[2]

Simplify the expression. $\frac{x^2 - 16}{x^2 - x - 12}$

(b)[3]

Simplify the expression. $(2x-3)^2 - (x+1)^2$

(c)[4]

Express as one fraction in simplest form. $\frac{2x+4}{x+1} - \frac{x}{x-3}$

(d)[3]

Expand and simplify the product. $(x-3)(x-5)(2x+1)$

(e)[6]

Solve these simultaneous equations. $x-3y=13$ $2x^2-9y=116$

Worked solution & mark scheme

This 20-mark question has a full step-by-step worked solution and mark scheme. One marking point: Factors the quadratic by using $ab=-12$, $a+b=-1$

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