DP Mathematics: Applications and Interpretation Questionbank

Write down three equations that express the information given above.

Find the number of each type of ticket sold.

The rate, $A$, of a chemical reaction at a fixed temperature is related to the concentration of two compounds, $B$ and $C$, by the equation

$A=k{B}^x{C}^y$, where $x$, $y$, $k\in \mathbb{R}$.

A scientist measures the three variables three times during the reaction and obtains the following values.

Find $x$, $y$ and $k$.

Boxes of mixed fruit are on sale at a local supermarket.

Box A contains 2 bananas, 3 kiwifruit and 4 melons, and costs $6.58.

Box B contains 5 bananas, 2 kiwifruit and 8 melons and costs $12.32.

Box C contains 5 bananas and 4 kiwifruit and costs $3.00.

Find the cost of each type of fruit.

Find the value of $a$ for which the system of equations does not have a unique solution.

Find the solution of the system of equations when $a=2$.

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

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.

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

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

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

Find the value of this minimum area.

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

Write down an equation, in terms of $u_1$ and $d$, for the amount of the drug that she receives on the seventh day.

Write down an equation, in terms of $u_1$ and $d$, for the amount of the drug that she receives on the eleventh day.

Write down the value of $d$ and the value of $u_1$.

Calculate the total amount of the drug, in mg, that she receives.

Find the amount of antibiotic, in mg, that Ted receives on the fifth day.

The daily amount of antibiotic Ted receives will first be less than 0.06 mg on the $k$ th day. Find the value of $k$.

Hence find the total amount of antibiotic, in mg, that Ted receives during the first $k$ days.

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

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

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

Use your graphic display calculator to find the equation of the tangent to the graph of y = f (x) at the point (–2, 38.75).

Give your answer in the form y = mx + c.