Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Simplify n1.v^k1.(n2.v^k2), where n1, n2 are positive integers, v is a random letter variable, and k1 and k2 are nonzero integers.

The answer should be expressed as n.v^k

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2

Asks students to compute (base)^index without a calculator for two simple questions. Part of HELM Book 1.2

Find reciprocal. Find a modulus. Find a factorial. Part of HELM Book 1.1

Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.

Note that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.

Part of HELM Book 1.3

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Recovering original function given some information such as derivative and value at some point.

More work on differentiation with trigonometric functions

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

The student is shown a table with rows for each class in a school, and two columns of numbers: books, and children. They have to work out the column totals, and the number of books per child, and enter them in the table.

The student is shown a diagram with measurements of rooms in a house. They have to enter the measurements in a spreadsheet, then the area of each room, and finally the total area of the house.

Demonstrates how to construct a spreadsheet value from scratch, without uploading an .xlsx file.

Given a data sheet with distances between cities and costs for different forms of transport, and some information about modes of transport used, fill in a form for a journey.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

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.

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.

Students are given a number with two decimal places and are asked to multiply it by either 10, 100 or 1000.

Students have to match four receptacles of varying sizes with the following fractions of a litre: 1 whole, 1/10, 1/100 and 1/1000.

RLC series with phasor

This question shows how to display a plot generated in matplotlib from code written by the student.

Asks the student to calculate the sum of the triangular numbers (up to some randomised number). 

Steps guide the student through each step in the calculation.