Algebra and Graphs

The total mass of 4 small boxes and 6 large boxes is $30\,\text{kg}$.

Show that $2x + 3y = 15$.

The total mass of 6 small boxes and 1 large box is $13\,\text{kg}$.

Use this information to write down an equation in terms of $x$ and $y$.

______

Solve the simultaneous equations to find the mass of a small box and the mass of a large box.
You must show all your working.

Small box = ______ $\text{kg}$
Large box = ______ $\text{kg}$

Rearrange $5y + 3x = 10$ to make $y$ the subject.

$y$ = ______

Line $P$ is perpendicular to line $L$.
Line $P$ passes through the point $(6, 7)$.

Find the equation of line $P$.

______

Describe the motion of the cyclist between $t = 40$ and $t = 100$.

______

The acceleration of the cyclist between $t = 0$ and $t = 40$ is $0.25\,\text{m/s}^2$.

Show that $v = 10$.

The total distance travelled by the cyclist between $t = 0$ and $t = T$ is $1.4\,\text{km}$.

Find the value of $T$.

$T$ = ______

Write $x^2 + 4x - 12$ in the form $(x + a)^2 + b$.

______

Use your answer to part (a) to find the coordinates of the turning point of the graph of $y = x^2 + 4x - 12$.

( ______ , ______ )

Sketch the graph of $y = x^2 + 4x - 12$ indicating the values where the graph crosses the axes.

Solve.

$x$ = ______

Solve the simultaneous equations.
You must show all your working.

$x$ = ______
$y$ = ______

The car travels a total distance of $1.01\,\text{km}$ in the 90 seconds.

Calculate the value of $V$.

$V$ = ______

Calculate the deceleration of the car in the last 20 seconds.

______ $\text{m/s}^2$