Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Use the simplex method to solve a linear program.

Uses the $\chi^2$ test to see if there is any significant difference in preferences.

DIAGNOSYS is a knowledge-based test of mathematics background knowledge for first-year university students, created by John Appleby at Newcastle University.

The questions have been translated directly into Numbas, with as few changes as possible.

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The student is asked to find the square root of an integer of the form $\pm n^2$. If the root is not real, they should enter "nan".

A custom marking algorithm extends the built-in one to deal with "nan".

There's some custom javascript to set the expected answer correctly. In the future this will be possible in the marking algorithm - see https://github.com/numbas/Numbas/issues/856

DIAGNOSYS is a knowledge-based test of mathematics background knowledge for first-year university students, created by John Appleby at Newcastle University.

The questions have been translated directly into Numbas, with as few changes as possible.

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Fractions already have a common denominator. Addition and subtraction 50:50 split. Students shouldn't have to worry about reducing fractions by design.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

Graphing exponentials with a base between 0 and 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

More work on differentiation with trigonometric functions

More work on differentiation with trigonometric functions

More work on differentiation with trigonometric functions

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(x)+c$

Graphing $y=a\log_{b}(\pm x+d)+c$

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Recall of common units, along with understanding multiplication.

The student has to write the general solution of a 2nd order PDE. They can choose the names of their arbitrary functions of $x$ and $y$.

The marking algorithm finds the names of the functions of $x$ and $y$ in the student's answer, and replaces them with $\sin(x)$ and $\cos(y)$ (these could be changed) so that the expression can be evaluated.

A normal curve is shown, with the mean and +/- 1, 2 and 3 standard deviations marked. An area of the curve is shaded and students are asked to estimate the shaded area using the heuristic rule. There are 6 possible areas: (-infty, mu-2sd), (mu-2sd, mu-1sd), (mu-1sd,mu), (mu, mu+1sd), (mu+1sd, mu+2sd), (mu+2sd, infty). The mean and standard deviation are randomised.

Student is presented with a clock showing a random time (in 15 minute increments) with an idication of whether it is morning or afternoon, along with a scheduled meeting time (in 24 hour mode). Question asks them to calculate difference between times and whether they are early or late.