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

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

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 $d\times a+f \neq 0$.

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

Multiplication of $2 \times 2$ matrices.

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

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

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

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

Multiplication of $2 \times 2$ matrices.

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

Add, subtract, multiply and divide numerical fractions.

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

An investment of €x invested today will give a return of €y in n years time Calculate the net present value (NPV) of the investment given that the discount rate is 3.5% per annum.

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An investment of x invested today will give a return of €y in n1 years time and a further €z n2 years from today. Calculate the net present value (NPV) of the investment given that the discount rate is perc% per annum.

rebelmaths

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

rebelmaths

Ratio, working hours

rebelmaths

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 $d\times a+f \neq 0$.

This task is part of a set of three assessment tasks for 7.RP.2.

7.RP.2 Robot Races asks students to "explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation" and to "compute unit rates associated with ratios of fractions." Students also need to compare the speeds of the robots.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

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

Use the Impulse-Momentum principle to find the change in speed of an object after a constant force is applied for a given period of time.

Ball projected vertically within water of a swimming pool. Find the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.

Add, subtract, multiply and divide numerical fractions.

Add, subtract, multiply and divide numerical fractions.

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

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

Multiplication of $2 \times 2$ matrices.

Ball projected vertically within water of a swimming pool. Finding the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.

Multiplication of $2 \times 2$ matrices.

Basic calculation exercise using distance in km, expected mph and desired arrival time (with the conversion factor for km to miles given).

Based on a generic test QTS question.

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