Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.

Questions testing understanding of numerators and denominators of numerical fractions, and reduction to lowest terms.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Questions testing understanding of numerators and denominators of numerical fractions.

Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.

Given five fractions, identify the odd fraction out. The denominators are mainly two or three digits long.

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

Adding several rational functions.

Simple ratio question with custom marking and partial credit possible

The marking checks for some common errors and awards partial credit and appropriate feedback. The errors that give different levels of partial credit include: forgetting to add one to the denominator, forgetting to change to a percentage.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$  for a polynomial $g(x)$. Find $g(x)$.

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$  for a polynomial $g(x)$. Find $g(x)$.

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$  for a polynomial $g(x)$. Find $g(x)$.

Differentiate $\displaystyle \ln((ax+b)^{m})$

Questions testing understanding of numerators and denominators of numerical fractions.

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$  for a polynomial $g(x)$. Find $g(x)$.

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

Questions about how the answer to a multiplication or a division is affected if you adjust the numbers involved. E.g. if you double the denominator, what happens to the answer.

Differentiate $\displaystyle \ln((ax+b)^{m})$