Reducing fractions to their lowest form by cancelling common factors in the numerator and denominator. There are 4 questions. 

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$.

There is a video included explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.

Find a regression equation.

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

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

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

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

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

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

Spearman rank correlation calculated. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

Elementary examples of multiplication and powers of complex numbers. Four parts.

Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

Product of one of 2, 3, 5, 9, or 10 by a number up to 10. With hints to learn calculation rather than memorisation.

This is supposed to demonstrate allowing one of two different free variables in the student's answer, but only marked as correct if the same free variable is used in all gaps. The custom marking algorithm should extend to any number of gaps, and one could add more alternative answers to allow for more free variable names. It doesn't allow just any free variable name.

Demonstration of the written number extension, which converts whole numbers to words.

No description given

In this question, the correct answers can't be evaluated by substituting numbers for each of the variables.

Numbas can now infer the types of variables in the answers to mathematical expression parts, so questions like this can be marked.

The student is asked to enter an approximation to $\sqrt{n}$, where $n$ is not a square number, to 20 decimal places.

This question is a demonstration of the high precision arithmetic in Numbas v4.

The student is asked to give the Avogadro constant in scientific form, calculate the mass of a number of moles of carbon, in grams, and then calculate the number of molecules in that mass.

This is a demonstration of the high-precision decimal arithmetic in Numbas v4.0.

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.