DP Mathematics: Applications and Interpretation Questionbank

maximum value of $h$.

Find the period of the function.

Find the height of $\text{C}$ above the ground when $t=2$.

At any given instant, find the probability that point $\text{C}$ is visible from Tim’s window.

minimum value of $h$.

Find the time, in seconds, that point $\text{C}$ is above a height of $100 \text{m}$, during each complete rotation.

The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.

At any given instant, find the probability that Tim can see point $\text{C}$ from his window. Justify your answer.

Find the time, in seconds, it takes for the blade $\text{[BC]}$ to make one complete rotation under these conditions.

Write down the amplitude of the function.

Calculate the angle, in degrees, that the blade $\text{[BC]}$ turns through in one second.

Sketch the function $h\left(t\right)$ for $0\le t\le 5$, clearly labelling the coordinates of the maximum and minimum points.

Calculate the angle, in degrees, that the blade $\text{[BC]}$ turns through in one second.

The wind speed increases and the blades rotate faster, but still at a constant rate.

Given that point $\text{C}$ is now higher than $110 \text{m}$ for $1$ second during each complete rotation, find the time for one complete rotation.

Find the period of the function.

maximum value of $h$.

minimum value of $h$.

Find the height of $\text{C}$ above the ground when $t=2$.

Find the time, in seconds, it takes for the blade $\text{[BC]}$ to make one complete rotation under these conditions.

Write down the amplitude of the function.

Sketch the function $h\left(t\right)$ for $0\le t\le 5$, clearly labelling the coordinates of the maximum and minimum points.

Find the time, in seconds, that point $\text{C}$ is above a height of $100 \text{m}$, during each complete rotation.

Find the value of $t$ when the ball hits the ground.

Write down three equations that express the information given above.

Find the value of $b$.

Write down the height of the ball above the ground at the instant it is hit by the bat.

Find the value of $a$.

Given $0<M<8$, find the range for $N$.

Find the number of each type of ticket sold.

Find the average number of earthquakes in a year with a magnitude of at least $7.2$.

Find the value of $a$.

Find the value of $b$.

Calculate the pH of the coffee.

Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.

Write down the value of $d$.

Write down three simultaneous equations for $a, b$ and $c$.

Hence, or otherwise, find the values of $a, b$ and $c$.

Use the model to determine the total length of time, in years, for which a graduate is expected to be in debt after graduating from university.

the equation of the principal axis.

Hence or otherwise find the equation of this model in the form:

$f\left(t\right)=a \cos \left(bt\right)+d$

the amplitude.

the period.

Comment on the appropriateness of modelling this scenario with a geometric sequence.

State one criticism of this interpretation.

Using the values in the table and your answer to part (b), sketch the graph of $y=d\left(s\right)$ for 0 ≤ $s$ ≤ 10 and −10 ≤ $d$ ≤ 60, clearly showing the vertex.

Hence, identify why Model A may not be appropriate at lower speeds.

Use Model B to calculate an estimate for the braking distance at a speed of $20\text{m}{\text{s}}^{-1}$.

Calculate the percentage error in the estimate in part (e).

Write down a second equation to represent Model A, when the speed is $10\text{m}{\text{s}}^{-1}$.

Find the values of $p$ and $q$.

Find the coordinates of the vertex of the graph of $y=d\left(s\right)$.

It is found that once a driver realizes the need to stop their vehicle, 1.6 seconds will elapse, on average, before the brakes are engaged. During this reaction time, the vehicle will continue to travel at its original speed.

A truck approaches an intersection with speed $s\text{m}{\text{s}}^{-1}$. The driver notices the intersection’s traffic lights are red and they must stop the vehicle within a distance of $330\text{m}$.

Using model B and taking reaction time into account, calculate the maximum possible speed of the truck if it is to stop before the intersection.

Find the new value of the parameter identified in part (e)(i).

$a$.

$b$.

$d$.

Calculate the number of revolutions of the Ferris wheel per ride.

Identify which parameter will change.

Write down one reason, with reference to the context, to support this decision.

Find the value of $k$.

when the height of the object is zero.

the maximum height of the object.

Write down two more equations for $a$, $b$ and $c$.

Show that $4a+2b+c=34$.

Solve this system of three equations to find the value of $a$, $b$ and $c$.

Give two reasons why the prediction in part (b)(ii) might be lower than 14.

the number of new people infected on day 6.

the day when the total number of people infected will be greater than 1000.

Use an exponential regression to find the value of $a$ and of $b$, correct to 4 decimal places.

Hence predict the total number of people infected by this disease after several months.

$k$.

Use the logistic model to find the day when the rate of increase of people infected is greatest.

Explain why the number of degrees of freedom is 2.

Perform a ${\chi }^2$ goodness of fit test at the 5% significance level. You should clearly state your hypotheses, the p-value, and your conclusion.

Use your answer to part (a) to show that the model predicts 16.7 people will be infected on the first day.

$L$.

$c$.