Surds, indices and polynomials quiz: O-Level Additional Mathematics (SEAB 4049) quiz

Simplify $a^5 \times a^{-2}$.

What is the value of $16^{3/4}$?

What does $a^0$ equal for any non-zero $a$?

Solve $2^{x} = 32$.

Simplify $\sqrt{50}$ to the form $a\sqrt{b}$ with $b$ as small as possible.

Simplify $3\sqrt{2} + \sqrt{8}$.

Rationalise the denominator of $\dfrac{1}{2 + \sqrt{3}}$.

Expand $(\sqrt{5} + 2)(\sqrt{5} - 2)$.

By the remainder theorem, what is the remainder when $P(x) = x^3 + x - 5$ is divided by $(x - 2)$?

For which value of $x$ does the factor theorem confirm that $(x - a)$ is a factor of $P(x)$?

Given that $(x - 1)$ is a factor of $x^3 - 6x^2 + 11x - 6$, the full factorisation is:

Solve $x^3 - 4x = 0$.

Simplify $\left(\dfrac{8}{27}\right)^{-1/3}$.

Which of these is the conjugate used to rationalise $\dfrac{6}{\sqrt{7} - 1}$?

If $5^{2x} = 5^{x + 3}$, what is $x$?