Algebra: surds, indices and polynomials quiz: N(A)-Level Additional Mathematics (SEAB 4051) quiz

Using the laws of indices, simplify $a^4 \times a^3$.

What is the value of $5^0$?

Write $a^{-3}$ as a positive-index expression.

Evaluate $16^{3/4}$.

Solve $3^{x} = 81$.

Simplify $\sqrt{72}$ to the form $k\sqrt{2}$.

Simplify $\sqrt{48} + \sqrt{27}$.

Rationalise $\dfrac{4}{\sqrt{2}}$.

What is the conjugate of $5 - \sqrt{3}$, used to rationalise a denominator?

By the remainder theorem, the remainder when $f(x)$ is divided by $(x - a)$ is:

Find the remainder when $f(x) = x^3 - 2x^2 + 4x - 1$ is divided by $(x - 2)$.

The factor theorem says $(x - a)$ is a factor of $f(x)$ when:

Show $(x - 1)$ is a factor of $f(x) = x^3 + 2x^2 - 5x + 2$ by evaluating:

Simplify $(x^2)^3$.

Simplify $\dfrac{6\sqrt{5}}{\sqrt{5}}$.