Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Given three vectors with integer components, find the corresponding magnitude and direction.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

Given the graph of the line determine the equation of the line.

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

No description given

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Given the graph of the line determine the equation of the line.

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

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.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.