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This is a diagnostic test - we use it to determine where extra mathematical help is needed for the class as a whole and where you get to see specific areas where you may need to work on your mathematical skills. The diagnostic test DOES NOT count in any way towards your first year grade.

This question demonstrates sending commands to geogebra and getting geogebra values and using them as part of a marking algorithm.

This question is a simple example to show how to input value from numbas to geogebra applet, and get a value back from geogebra to numbas for marking.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

Three equilateral triangles are divided equally into 3, 4 and 5 parts respectively. Calculate the distance between two marked points.

Based on a puzzle by Catriona Shearer, shared on Twitter.

The student must calculate the number of digits a given decimal number would have when written in a different base. Alternative answers catch some common mal-rules and give appropriate feedback.

Based on table 2 from "diagnosing student errors in e-assessment questions" by Philip Walker, D. Rhys Gwynllyw and Karen L. Henderson.

The student must enter a number in scientific notation, with separate boxes for significand and exponent. They only get the marks if both elements are correct.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

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.

$x_n=\frac{an^2+b}{cn^2+d}$. 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.

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

Asking users to interpret a minitab output to give the coefficients of a multiple regression together with a prediction based on the subsequent equation.

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$. 

Trying out something: get the student to enter a set for each of "regular singular points" and "essential singular points".

Find and classify singular points of a second-order ordinary differential equation.  One equation is chosen from a selection of 10.

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

Dealing with functions in Numbas.