This question explores an understanding of an energy balance over a process stream.

6 questions which introduce the user to the Numbas system.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Calculate relative frequencies in a variety of scenarios.

An exam using an experimental theme to use KaTeX to render maths instead of MathJax

Find the first four non-zero terms in the Maclaurin series for $e^{ax}$.

Find the first three non-zero terms in the Maclaurin series for $\cos(x)$.

Find the first three non-zero terms in the Maclaurin series for $\sin(x)$.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

No description given

No description given

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Using the unit circle definition of sin, cos and tan, to calculate the exact value of trig functions evaluated at angles that depend on 0, 30, 45, 60 or 90 degrees.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

25 questions on solving quadratic equations

25 questions on solving quadratic equations

Binomial series for Natural exponent

Find the first 3 terms of Binomial series having a Natural exponent

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

The student will be given 2 integers between -9 and +9 to add together.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Putting algebraic fractions into their simplest forms

Choosing whether given random variables are qualitative or quantitative.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

A collection of questions (frequently updated) to demonstrate the usage of the Logic extension.

Current questions:

• Make syllogisms (either valid, invalid or valid under an additional assumption);
• Write statements in Polish and reverse Polish notation, find the truth table, determine satisfiability;
• Test whether a collection of statements $\Gamma$ models a statement $\phi$;
• Write the Disjunctive and Conjunctive Normal Forms for a statement.

Needs the Logic Extension!

Questions on presenting data in charts or tables.

Questions on the subtleties and pitfalls of methods of data collection.