CCEA GCSE Further Mathematics Unit 1 Pure Mathematics overview quiz quiz

Simplify fully $\dfrac{x^2 - 16}{x^2 + 3x - 4}$.

Express $\sqrt{50} + \sqrt{18}$ in the form $k\sqrt{2}$.

Evaluate $8^{\frac{2}{3}}$.

Write $x^2 + 10x + 7$ in completed-square form.

For what value of $k$ does $x^2 + kx + 16 = 0$ have equal roots (taking the positive value)?

The polynomial $f(x) = x^3 - 7x + 6$. Which is a factor?

Given $f(x) = 2x + 3$ and $g(x) = x^2$, find $fg(x)$.

Find the inverse of $f(x) = 4x - 8$.

Solve $4^x = 64$.

Write $\log 8 + \log 5 - \log 4$ as a single logarithm.

Find the product $\begin{pmatrix} 1 & 2 \\ 3 & 0 \end{pmatrix}\begin{pmatrix} 2 \\ 1 \end{pmatrix}$.

Which matrix represents a reflection in the $x$-axis?

In triangle $ABC$, $b = 8$, $c = 5$ and angle $A = 60^\circ$. Find $a^2$ using the cosine rule.

Solve $\sin x = \dfrac{\sqrt{3}}{2}$ for $0^\circ \le x \le 180^\circ$.

Find the gradient of the tangent to $y = x^2 - 5x$ at $x = 4$.

Evaluate $\displaystyle\int_1^3 2x\,dx$.