Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land$.

For example $\neg q \to \neg p$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

A question to test understanding of set cardinality and intersections when limited information is known about the size of certain sets.

An application of quadratic functions based on the Golden Gate Bridge in San Francisco, USA. Student is given an equation representing the suspension cable of the bridge and asked to find the width between the towers and the minimum height of the cable above the roadway. Requires and understanding of the quadratic function and where and how to apply correct formulae.

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

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

Convert numbers greater than 1 into standard form/scientific notation.

This is a copy of a question from the Numbas demos project, with references to the editor removed.

The student is shown a plot of a mystery function. They can enter values of $x$ check, within the bounds of the plot.

They're asked to give the formula for the function, and then asked for its value at a very large value of $x$.

A plot of the student's function updates automatically as they type. Adaptive marking is used for the final part to award credit if the student gives the right value for their incorrect function.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

No description given

This question tests if a students understands when matrices are conformable

Information on inputting powers

GIve a random linear program and ask the students to convert it to canonical form.

Putting algebraic fractions into their simplest forms

Simplifying indices

Simplifying indices

Simplifying indices

Simplifying indices

Basic solving of linear equations

Solving linear equations.

No description given

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

GIve a random linear program and ask the students to convert it to canonical form.

This question is a variation on another version which asks the student to find the height of a bridge arch and width of the river given a formula for the arch of the bridge (also available in the Numbas database)

Introduction to Laplace Transforms

An application of quadratic functions based on the Gladesville Bridge in Sydney, Australia. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

An application of quadratic functions based on the Gateshead Bridge in the UK city of Newcastle. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.