Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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

Single term expressions various degrees of difficulty simplifying

Simplifying single term expressions involving indices.

Simplifying single term expressions involving more than one letter.

Simplifying coefficients and establishing the standardized order of writing expressions.

A set of questions practicing finding equivalent fractions with an emphasis on simplifying.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

Simplifying a fraction with many factors up to cubed primes in common.

Simplifying a fraction with a common factor up to a square.

Cancelling down a single prime factor to simplify a fraction. 

Simplifying first is essential in terms of managing expressions that might need factorising.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

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).

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).

Solving equations involving algebraic fractions which simplify into quadratics

Solving quadratics which need simplifying first.

Questions on combining and simplifying algebraic fractions

Simplifying first is essential in terms of managing expressions that might need factorising.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

simplifying pL1^a/n+kL2^bL1^c/m

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Calculate an answer involving a fractional index.

Simplifying expressions from $(z^m)^n$ to $z^{mn}$. 

Simplifying expressions from $y^m\div y^n$ to $y^{m-n}$.