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. 

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. 

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. 

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Differentiate a polynomial expression involving coefficients and, negative and fractional indices. 

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

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. 

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

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

Calculate an answer involving a fractional index.

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

Multiple choice. Students need to select the correct simplification for a given expression. 

This question has four versions. Skills required are: using Pythagorean identities, converting to sine or cosine. Some also require fraction division.

Multlipying and subtracting mixed numbers. It is expected that a calculator is used to perform this question.

Multiply two algebraic fractions (unfortunately their appearance doesn't really change) and cancel. 

Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

Fractions already have a common denominator. Addition and subtraction 50:50 split. Students shouldn't have to worry about reducing fractions by design.

A whole number divided by a very simple algebraic fraction. No cancelling is required by design.

A very simple algebraic fraction multiplied by a whole number. No cancelling is required by design. 

A simple algebraic fraction dividing by another. Cancelling is recommended.

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