GCSE / IGCSE Maths – Algebra

(a) Expand and simplify $(2x – 3)(x + 5)$.(b) Expand $(x + 4)^2$.(c) Factorise fully $9x^2 – 16$.(d) Factorise $3x^2 + 7x – 6$.

Solve(a) $3(2x – 1) = 4x + 7$(b) $\dfrac{x + 2}{3} – \dfrac{x – 1}{4} = 2$

Here are the first four terms of a sequence: $5,\ 9,\ 13,\ 17$.(a) Write down an expression for the $n$th term.(b) Is 203 a term of the sequence? Justify your answer.(c) The first three terms of a geometric sequence are $3,\ 6,\ 12$. Write down the $n$th term.

Solve the simultaneous equations$3x + 2y = 12$$5x – 2y = 4$

(a) Solve the inequality $5x – 3 > 2x + 9$.(b) Write down the integer values of $x$ that satisfy $-4 < 2x \leq 6$.

(a) Solve $2x^2 – 5x – 3 = 0$ by factorising.(b) Solve $2x^2 – 3x – 7 = 0$, giving your answers correct to 3 significant figures.

The functions $f$ and $g$ are defined by $f(x) = 3x – 2$ and $g(x) = x^2 + 1$.(a) Find $fg(2)$.(b) Find an expression for $gf(x)$, simplifying your answer.(c) Find $f^{-1}(x)$.

Make $x$ the subject of $y = \dfrac{2x + 3}{x – 1}$.

The $n$th term of a quadratic sequence is given by the first four terms $2,\ 7,\ 16,\ 29$. Find an expression for the $n$th term.

(a) Write $2x^2 + 12x + 5$ in the form $a(x + b)^2 + c$.(b) Hence write down the coordinates of the turning point of the graph of $y = 2x^2 + 12x + 5$.

Solve the simultaneous equations$x^2 + y^2 = 25$$y = x + 1$

(a) Show that the equation $x^3 – 5x – 2 = 0$ has a solution between $x = 2$ and $x = 3$.(b) Show that the equation can be rearranged to $x = \sqrt[3]{5x + 2}$.(c) Starting with $x_0 = 2$, use the iteration $x_{n+1} = \sqrt[3]{5x_n + 2}$ to find $x_1$, $x_2$ and $x_3$ to 4 decimal places.(d) Solve the inequality $x^2 – 2x – 15 < 0$.