Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. 

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a negative gradient.

Multiplication of $2 \times 2$ matrices.

Identifying positive, negative and no correlations.

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

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

A quick implementation of certainty-based marking: the student's score depends on how they rated their certainty in their answer before submission.

Because Numbas doesn't allow negative marking at the moment, scores are shifted upwards, so a high certainty incorrect answer scores 0, and a high certainty correct answer scores full credit.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

A "match choices with answers" part where the student either gets all the marks or none. Any incorrect choice is penalised with a huge negative mark, so they end up with the minimum mark of 0.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Multiplication of $2 \times 2$ matrices.

Find $\displaystyle\int \frac{ax^3-ax+b}{1-x^2}\;dx$. Input constant of integration as $C$.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

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

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Given an equation with an unknown, determine if the unknown is positive or negative.

First part is the product of two numbers; second part is the product of three.

Basic solving of linear equations

Multiplication of $2 \times 2$ matrices.

Using the chain rule with polynomials and negative powers

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ direction but the positive $y$. 

testing sin, cos, tan of angles that are negative or greater than 2pi radians that result in nice exact values. 

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.