$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Find eigenvalues and eigenvectors of a $2 \times 2$ matrix.

Find the determinants of three $2 \times 2$ invertible matrices.

Find the inverses of three $2 \times 2$ invertible matrices.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Multiplication of $2 \times 2$ matrices.

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A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Multiplication of $2 \times 2$ matrices.

Linear combinations of $2 \times 2$ matrices. Three examples.

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

Multiplication of $2 \times 2$ matrices.

Ratio, working hours

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$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Is this number divisible by 5? Half the time the number is, half the time it isn't. Steps give the divisibility test and a way to determine the number of fives.

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

Paired t-test to see if there is a difference between times taken to complete a task.

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

Inverse and division of complex numbers.  Four parts.

Add, subtract, multiply and divide numerical fractions.

Adapted from 'Algebraic fractions: operations involving algebraic fractions' by Ben Brawn.

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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