Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.

A custom marking algorithm on the spreadsheet part changes it to interpret quantities in cells, so they can be compared to the expected answer.

In real use, you'd probably want more sophisticated logic, to give better feedback or to allow partial marks for different units, like the "quantity with units" part type does.

Find the unit vectors in the direction of four 3-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

Find the centroid of a shape made up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

Draws a triangle based on 3 side lengths.

Simple Hertz contact without friction.

This question tests students knowledge of basic matrix arithmetic.

This question contains information on how Numbas works, from the beginning of an exam to the end.

Note: it was written for students who access Numbas exams through the Numbas LTI provider. Some of the information does not apply to standalone exams, or those delivered through a generic SCORM player.

HELM Book 1.1.5 exercises

Calculating the derivative of a function of the form $ax^n \ln(bx)$ using the product rule.

Do not use this: adaptive marking is the best way to access the student's answer to another part.

Shows how to retrieve the student's answer to another part from a custom marking script.

You can use LaTeX in marking comments, but remember to escape backslashes!

series of R and L and C

find Z (mag and Phase)

step find Xl

given Voltage and loads calculated all the line currents

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

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Practice using the log rules to add and subtract logarithms

Solve equations involving logs and exponential functions, by using inverse operations.

Calculating several linear combinations of three 3-dimensional vectors. 

Calculating several linear combinations of three 2-dimensional vectors. 

This easy question is intended to be used by administrators to test the integration of Numbas with a learning environment.

Calculate the magnitude of a 3-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j + v_3 \mathbf k$.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

Calculate the magnitude of a 2-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j$.

Calculate the magnitude of a 2-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v1\\v2}$.

Given the position vectors of three 2-dimensional points $A$, $B$ and $C$, find the coordinates of a fourth point $D$ such that $ABCD$ forms a parallelogram. 

Find the unit vectors in the direction of four 2-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

Equilibrium of a rigid body.  Find tension to raise a pole.

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.