Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

Practice with adding, subtracting and dividing basic algebraic fractions

The student is shown a diagram with a line between two points. They must make the line cross the axes at $x=1$ and $y=2$. They can drag the points around, or type a gradient in to move the points accordingly.

The student is shown a diagram containing a line between two points. They're given a gradient and $y$-intercept.

They must manipulate the line or the points so that the line has the given gradient and $y$-intercept.

Simple multiplication including multiples of 10, with answer that can be multiples of up to 1000.

Solving 2nd order differential equation for pendulum, with and without damping.

The student is shown a diagram containing a line between two points. They're given a gradient and $y$-intercept.

They must manipulate the line or the points so that the line has the given gradient and $y$-intercept.

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students need to add two fractions with different denominators, then subtract the answer from 1. There are 9 different versions of this question.

A simple test for practicing division with remainder. Numbers are randomised, and ranges for divisor and quotient can be specified.

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.

No description given

Real life problems with differentiation

Finding the stationary points of a cubic with two turning points

Using the chain rule within product rule problems

More work on differentiation with trigonometric functions

More work on differentiation with trigonometric functions

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients

This question tests a student's ability to add two fractions with the same denominator.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Calculating with vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.

Simple scalar multiplication of a general vector with the important scalars 0, 1, -1. Just the variable name is randomised.

Matrix addition, with the added test of whether they understand that only matrices of the same size can be added.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

Use matrix multiplication to get an equation for \(k\) which is then to be solved.

Calculating with vectors in \(\mathbb{R}^4\), including resolving brackets. The fixed vector size is so that a test is fair to all students.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.