Write $7.14 \times 10^{-4}$ as a decimal, correct to 3 significant figures.

Simplify $(5^{3} \cdot 5^{-6}) \div 5^{-2}$. Give your answer as a single power of 5.

Solve $10^{2x} = 7.5$ for $x$. Give your answer to 3 significant figures.

A quantity is quoted as $a = 2.45\text{ m}$ to 2 decimal places. State the lower and upper bounds for $a$.

Write $f(x)$ in the form $a(x - 2)^{2} - 5$.

Find $a$, $b$ and $c$.

Using your GDC, estimate the $x$-intercepts to 3 significant figures.

State the strip width $h$.

Use the trapezium rule to estimate the area $A$. Give your answer to 3 significant figures.

From the shape of the graph, state whether this estimate is an overestimate or an underestimate and justify your answer.

Write a geometric model for the volume $V_n$ (mL) after $n$ months.

Find the volume after 24 months.

A second tank starts at 850 mL and increases by $k$ per month. After 24 months it reaches the same volume as in part (b). Find $k$ to 2 decimal places.

Find $P(A \cup B)$.

Find $P(A' \cap B)$.

Find $P(A \mid B)$.

Are $A$ and $B$ independent? Justify your answer.

Find $P(X > 70)$.

Find the 90th percentile of $X$.

A random sample of 25 values of $X$ has mean $\bar{X}$. Find $P(\bar{X} > 65)$.

Find $k$ and $r$.

Use your model to predict $M$ when $x = 5$.

State one limitation of using this model for much larger $x$.

Find the arc length $AB$ in terms of $r$ and $\theta$.

Show that the area of sector OAB is $\frac12 r^2 \theta$.

Show that the area of triangle OAB is $\frac12 r^2 \sin \theta$.

Hence, for $r = 6.0\text{ cm}$ and $\theta = 1.2\text{ rad}$, find the area of the segment cut off by chord $AB$.

Describe the direction and strength of the association between $x$ and $y$.

Which point, A or B, is more likely to have high leverage on a regression line of $y$ on $x$? Explain.

By eye, sketch a line of best fit on your answer paper and write a plausible equation $\hat{y} = a x + b$.

Using your line, estimate $y$ when $x = 40$. Comment on the reliability of this prediction.

Find $f'(x)$.

Find the $x$-coordinates of the stationary points and classify each as a local maximum or a local minimum.

Find the equation of the tangent to $y = f(x)$ at $x = 2$.

Compute $\int_0^2 g(x),dx$.

Find the total (geometric) area between the curve $y = g(x)$ and the $x$-axis on $[0, 2]$.

Compute the expected frequencies.

Calculate the test statistic $\chi^2$.

State the degrees of freedom and conclude the test at $\alpha = 0.05$. (Critical value for $df = 2$ is 5.991.)