For $0\le t\le 9$, find the total amount of time when the rate of growth of Plant $B$ was greater than the rate of growth of Plant $A$.

Calculate the area of cloth, in cm², needed to make Haruka’s bag.

Write down the $y$-intercept of the graph of $y=f\left(x\right)$.

Write down the number of possible solutions to the equation $f(x)=5$.

Sketch the graph of $y=f\left(x\right)$ for −3 ≤ $x$ ≤ 3 and −4 ≤ $y$ ≤ 12.

Let $l$ be the tangent to the curve $y=x{\text{e}}^{2x}$ at the point (1, ${\text{e}}^2$).

Find the coordinates of the point where $l$ meets the $x$-axis.

Find $\frac{\text{d}y}{\text{d}x}$ in terms of $x$ and $y$.

Differentiate from first principles the function $f\left(x\right)=3x^3-x$.

In the context of the population model, interpret the meaning of $\frac{dP}{dt}$.

Write down the $x$-coordinates of these two points;

Find the equation of the line DC. Write your answer in the form ax + by + d = 0 where a , b and d are integers.

Express this volume in $\text{c}{\text{m}}^3$.

Write down, in terms of $r$ and $h$, an equation for the volume of this water container.

Find $\frac{\text{d}A}{\text{d}r}$.

Using your answer to part (e), find the value of $r$ which minimizes $A$.

Determine the equation of the tangent to $C$ at the point $\left(\frac{2}{\text{e}},\text{ e}\right)$

Find the rate of change of the ball’s height above the ground when $t=\frac{1}{3}$. Give your answer in the form $p\mathrm{\pi }\sqrt{q} {\mathrm{ms}}^{-1}$ where $p\in \mathrm{\mathbb{Q}}$ and $q\in {\mathrm{\mathbb{Z}}}^{+}$.

Use your answer to part (f) to show that the width of Nanako’s bag is 12 cm.

Write down and simplify an expression in x and y for the area of cloth, A, used to make Nanako’s bag.

Find the gradient of the line DC.

Write down the $y$-intercept of the graph.

Show that $a=8$.

Find $f^{\prime }(x)$.

Determine the range of $f\left(x\right)$ for $p$ ≤ $x$ ≤ $q$.

The equation $f(x)=m$, where $m\in \mathbb{R}$, has four solutions. Find the possible values of $m$.

Show that $A=\pi r^2+\frac{1000000}{r}$.

Find the value of this minimum area.

Use your answers to parts (c) and (d) to show that

$A=3x^2+\frac{10368}{x}$.

Write down a formula for $A$, the surface area to be coated.

Find the least number of cans of water-resistant material that will coat the area in part (g).

Find $f(2)$.

Write down the intervals where the gradient of the graph of $y=f(x)$ is positive.

Write down the range of $f(x)$.

Calculate the volume, in cm³, of the bag.

Use this value to write down, and simplify, the equation in x and y for the volume of Nanako’s bag.

Find $\frac{\text{d}A}{\text{d}x}$.