Sketch the graph of y = f (x), for −4 ≤ x ≤ 3 and −50 ≤ y ≤ 100.

(i)   the gradient of this line in terms of $c$;

(ii)  the $y$-intercept of this line in terms of $A$.

Find the equation of the regression line for $\ln k$ on $\frac{1}{T}$.

Find the equation of the line through $\text{B}$ and $\text{D}$. Give your answer in the form $ax+by+d=0$, where $a, b$ and $d$ are integers.

Determine the number of lines parallel to $L$ that are tangent to $f\left(x\right)$. Justify your answer.

Find the gradient of the line through $\text{A}$ and $\text{C}$.

Find the equation of the line that the road follows.

Town $\text{C}$ is due north of town $\text{A}$ and the road passes through town $\text{C}$.

Find the $y$-coordinate of town $\text{C}$.

Write down the gradient of the line through $\text{B}$ and $\text{D}$.

Use your graphic display calculator to find the zero of f (x).

Karl decides to donate this interest to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = t EUR.

Calculate the value of t.

Find the coordinates of point $\text{C}$.

Find the gradient of $L_1$.

Find the value of $k$.

Find the gradient of $L$.

Use your graphic display calculator to find the coordinates of the local minimum point.

Find the $x$-coordinate of point A.

Find the distance between points $\text{M}$ and $\text{N}$.

Write down, in the form $y=mx+c$, the equation of $L_2$.

Find the equation of $L_2$. Give your answer in the form $ax+by+d=0$, where $a, b, d\in \mathrm{\mathbb{Z}}$.

Write down the amount of interest he earned after 5 years.

Find the equation of the line passing through these two points.

Calculate the amount of money he has in the account after 5 years.

Find the equation of $L$ in the form $y=mx+c$.

Given that the length of $\text{AM}$ is $\sqrt{45}$, find the area of triangle $\text{ANC}$.

Write down the $x$-coordinate of point $\text{D}$.