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.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Given a number evaluate simple power, negative power, to one half.

Interpreting a p-value given the hypothesis.  Common misconceptions. 

This exercise will help you rearrange a linear equation to find the value of a given variable

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

Given a linear or a quadratic function and asked whether it is continuous. Part of HELM Book 2.4.

This shows how to take an expression given by the student and plot the implicit curve of points where it equals zero.

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.

given Voltage and loads calculated all the line currents

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.

(a) Read subscript notation to identify an element in a 3x3 matrix; (b) chose the correct subscripted name from a list for a given element in a 3x3 matrix.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Finding the arc length of a sector of a circle when given the radius of the circle and angle of the sector.

Calculating the amount of money in a savings account after a given amount of time, and calculating how long it will take for the amount of savings to exceed a given value. 

A random dataset given by a linear function with noise (gradient and y-intercept of the linear function are randomised as is distribution of x values).

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given a height in centimetres and another height in metres, and are asked to write the ratio of the two heights in simplest form. There are 16 versions of this question.

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given the number of bagels baked, in a number of hours, and need to calculate the number baked per half-hour. There are 6 different versions of this question.

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students are given a proportion of staff who either have or haven't completed their reports. They are asked to find the complement, as a percentage. There are 6 different versions of this question. 

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Students are always given the same map of Western Australia and asked to select the one incorrect statement from four statements. The statements are randomly selected from four incorrect statements and twelve correct statements in total. 

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Student must calculate distance swum in km given number of laps of 50m pool, days of week and weeks in term. These variables are randomly selected.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students calculate the cost of the halogen globes given electricity cost, number of globes, number of years, replacement cost and lifespan of globes. Some of these variables are randomly selected. There are more than 10 different versions of this question.

Taken from question 37 of the book Problem Solving in GCSE Mathematics by Daniel Griller.

Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.

A Eukleides diagram shows the setup visually.

Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .

Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .

(a) Equation given, and five coordinates. Student should select those coordinates which lie on the line. (b) Gradient and a point on line is given. Student is to calculate coordinates of other points on the line.