Mathematics Advanced

Which of the following best represents the graph of

What is

A. $\frac{1}{2}\sqrt{x+5}+C$ B. C. D.

The graph of $y=f(x)$ is shown.

Which of the following is the graph of $y=-f(-x)$?

A–D. Candidate graphs are shown.

A ten-sided die has faces numbered 1 to 10.

The die is constructed so that the probability of obtaining the number 1 is greater than the probability of obtaining any of the other numbers. The numbers 2 to 10 are equally likely to occur.

When the die is rolled 153 times, a 1 is obtained 72 times.

By using the relative frequency of rolling a 1, which of the following is the best estimate for the probability of rolling a 10?
A. $\frac{1}{17}$
B. $\frac{1}{11}$
C. $\frac{1}{10}$
D. $\frac{1}{9}$

The minimum daily temperature, in degrees, of a town each year follows a normal distribution with its mean equal to its standard deviation. The minimum daily temperature was recorded over one year.

What percentage of the recorded minimum daily temperatures was above zero degrees?
A. $16\%$
B. $50\%$
C. $68\%$
D. $84\%$

The diagram shows the graph of $y=f'(x)$.

Given $f(1)=6$, which interval includes the best estimate for $f(1.1)$?
A. $[6.2,6.4)$
B. $[6.0,6.2)$
C. $[5.8,6.0)$
D. $[5.6,5.8)$

The graph of $y=f(x)$, with all its stationary points, is shown.

How many stationary points does the graph of $y=f(e^x)$ have?
A. $0$
B. $1$
C. $2$
D. $3$

The graph of a quadratic function represented by the equation $h=t^2-8t+12$ is shown.

The graph shows $h=12$ when $t=0$.

What is the other value of $t$ for which $h=12$?

[Visual: A graph of the parabola $h=t^2-8t+12$, with $h$ on the vertical axis and $t$ on the horizontal axis. The graph crosses the $$-axis at and , and the -axis at .]

The graph of a quadratic function represented by the equation $h=t^2-8t+12$ is shown.

Find the values of $t$ and $h$ at the turning point of the graph.

[Visual: A graph of the parabola $h=t^2-8t+12$, with $h$ on the vertical axis and $t$ on the horizontal axis. The graph crosses the $$-axis at and , and the -axis at .]

In a research study, participants were asked to record the number of minutes they spent watching television and the number of minutes they spent exercising each day over a period of 3 months. The averages for each participant were recorded and graphed.

Describe the bivariate dataset in terms of its form and direction.

Form: ............................................

Direction: ......................................

A sound wave can be modelled using a function $P(t)=k\sin(at)$, where $P$ is air pressure in Pascals, $t$ is time in milliseconds (ms), and $k$ and $a$ are constants.

Hence, find the values of $t$, where $0<t<10$, for which functions $P_1(t)$ and $$ are BOTH decreasing.

A sound wave can be modelled using a function $P(t)=k\sin(at)$, where $P$ is air pressure in Pascals, $t$ is time in milliseconds (ms) and $k$ and $a$ are constants.

The graph of $P_1(t)$ from part (a) is shown.

On the diagram, sketch the graph of

for $0\leq t\leq10$.

A sound wave can be modelled using a function $P(t)=k\sin(at)$, where $P$ is air pressure in Pascals, $t$ is time in milliseconds (ms) and $k$ and $a$ are constants.

Write the equation for a sound wave $P_1(t)$ that has an amplitude of 2 Pascals and a period of 5 ms.

Consider the function

Find the stationary points of the function and determine their nature.

Consider the function

Use your answer from part (a) to complete the graph.