This is a set of questions designed to help you praction adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

A question testing the application of the Sine Rule when given two sides and an angle.  In this question the triangle is obtuse and the first angle to be found is obtuse.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

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This question allows you to practice working out a fraction of an amount.

It is designed for you to complete without a calculator.

Working with powers

Working with powers

Working with powers

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

A sneak peek at a really clever integration of GeoGebra with Numbas.

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.

Practice of dividing by a decimal.  This should be solvable without using a calculator.

Four questions, of increasing complexity, involving addition of decimals.  These should all be solvable without using a calculator.

Four questions, of increasing complexity, invoving multiplication.  These should all be solvable without using a calculator.

Four questions, of increasing complexity, involving long division.  These should be solvable without using a calculator.

Practice of multiplying fractions (without a calculator).

Basic calculation exercise using distance in km, expected mph and desired arrival time (with the conversion factor for km to miles given).

Based on a generic test QTS question.

Converting a fraction to a percentage by cancelling (without a calculator).

These are worded questions on percentages.  They can be done without a calculator.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Questions on linear programming techniques, with interactive graphics.

Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

Three questions on using the Student $t$ distribution to perform hypothesis tests.

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