Converting between metres (m) and centimetres (cm). 

Converting between kilo, base, milli and micro. Grams, litres and metres.

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Counting the number of significant figures. 

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.

Example showing how to mark a "choose one from a list" part where the student has to pick the range a given number lies in.

This questions assesses the ability to conduct an ANOVA and interpret the results.

Adaptive marking: an error in calculating F can be carried over to the calculation of the p-value as well as the test conclusion.

This question assesses learners' basic knowledge of a one-way ANOVA and ability to interpret typical software output.

Practice factorising different types of quadratics. Repeat as many times as you want. 

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Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

Calculating the derivative of a function of the form $\frac{(x-a)^2}{bx} + c$, finding its stationary points and determining their nature.

In the first part, the student is asked to enter dimensions of a box in a spreadsheet.

The values are extracted as a list of numbers by changing the interpreted_answer note in the first part's marking algorithm, and the calculated volume is used as the answer to the second part, through adaptive marking.

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Given price, marginal cost and fixed cost, find the quantity that maximises profits.

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This question assesses learners' ability to conduct a two sample t-test. 

This question assesses the learner's ability to compute a confidence interval for a difference of two means, given two samples.

Randomized variables: sample raw data and confidence level. 

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

Most of the standard prefixes (not hecto, deca though), abbreviations, powers of 10, converting between prefixes for distance, capacity, mass.

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Calculate the Pearson correlation coefficient on paired data and comment on the significance.

rebelmaths

This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \cos(2\pi f_m t))\cos(2\pi f_c t)$, where $V_{DC}$ is a DC offset, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.

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