Practice dividing polynomials using the long division method.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Practice of conversion between SI units of mass, volume & length.

Find roots and the area under a parabola

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Template question. Seven statements given and student should determine if they are true or false.  It is possible that 1,2,3,4,5 or 6 out of the 7 statements will be true and these are all equally likely.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each .

Multiplication of $2 \times 2$ matrices.

The simplest case. Divisor is single digit. There is no remainder. 

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Student sketches 1/x, by plotting several points and then selecting the graph from a list

Student sketches 1/x, by plotting several points and then selecting the graph from a list

Summation Notation

rebelmaths

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

15 questions based on module so far. 

Testing the understanding of the formal definition of $A\subseteq B$.

Example of a universal statement over the integers and its negation

Calculations are presented and students are asked to choose which angle/length the calculation corresponds to.

This question explores an understanding of an energy balance over a process stream.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Given a number evaluate simple power, negative power, to one half.

Simple Linear Equation.

$ \dfrac{n}{a} \pm b = c$

Testing addition, multiplication and division involving negative numbers.

Understanding order of operations on a calculator and using power and root keys.

Footballer expects to score in a/b matches.

Find a% of b using a calculator. Suggested method to use decimal equivalent.

Solve $p - t < \text{or}> q$