Rewiting expressions involving sums or differences of surds into the form $a \sqrt{b}$.

Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) + (a_2 + b_2 \sqrt{c})$.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) - (a_2 + b_2 \sqrt{c})$.

Simplifying surds from $a\sqrt{b^2c}$ to $ab\sqrt{c}$, where $a$, $b$ and $c$ are positive integers.

Simplifying surds from $\sqrt{a^2b}$ to $a\sqrt{b}$, where $a$ and $b$ are positive integers.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Rewriting expressions from $\sqrt[m]{x^n}$ to $x^\frac{n}{m}$.

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Two BODMAS questions. Part of HELM Book 1.1.

A BODMAS fraction question. Part of HELM Book 1.1.

Factorise a quadratic. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2

Two BODMAS questions. Part of HELM Book 1.1.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions.