DP Mathematics: Applications and Interpretation Questionbank

Find ${\int }_0^5\frac{1000}{2+t}\text{d}t$.

State in context what this value represents.

Determine ${\int }_0^{365}P\left(t\right) \text{d}t$ and state what it represents.

Find an expression for $P$ in terms of $t$.

Find the value of $t$ at which the ball hits the ground.

Find an expression for the height $h$ of the ball at time $t$.

Find the range of $h$.

Use the expression found in (f) to calculate a value for $A$.

Hence write down the domain of $h$.

Determine whether the graph of $l$ against $\theta$ is increasing or decreasing at $\theta =50°$.

Sieun observes that when the angle is $40°$, the ball will travel a horizontal distance of $205.5 \text{m}$.

Find an expression for the function $l\left(\theta \right)$.

The company regularly increases the number of cars it produces.

Describe how their profit changes if they increase production to over $30$ cars per month and up to $50$ cars per month. Justify your answer.

Find an expression for $P$ in terms of $x$.

Find $\frac{dy}{dx}$.

Hence find the cross-sectional area of the tunnel.

Write down the integral which can be used to find the cross-sectional area of the tunnel.

Write down the integral which can be used to find the cross-sectional area of the tunnel.

Hence find the cross-sectional area of the tunnel.

Write down the value of $c$.

Hence form two equations in terms of $a$ and $b$.

Hence find the equation of the quadratic curve.

Find the area of the shaded region in Irina’s design.

Find the area of the unshaded region in the painting.

One year after the company was founded, the profit was $4$ thousand dollars.

Find an expression for $P\left(t\right)$, when $t\ge 0$.

Find the exact area of the shaded region in the painting.

Calculate the area of the shaded region in diagram 1.

Calculate the area of this region.

Write down an integral for the area of the shaded region in diagram 2.

Hence, determine the area enclosed between $y=6-x$ and $y=1.5x^2-2.5x+3$.

The goat is tied in the field for $8$ hours.

Find the total volume of grass eaten by the goat during this time.

The three points A(0, 0) , B(3, 10) and C($a$, 0) define the vertices of a triangle.

Find the value of $a$, the $x$-coordinate of C, such that the area of the triangle is equal to the area of region R.

Write down an integral for the area of region R.

Find the area enclosed by $y=f\left(x\right)$, the $x$-axis and the line $x=0.5$.

Find the area of the shaded region on the diagram.

Find the area of region R.

Find the value of $\underset{4}{\overset{\mathrm{\infty }}{\int }}\frac{1}{x^3}\text{d}x$.

Illustrate graphically the inequality .

Hence write down a lower bound for $\sum _{n=4}^{\mathrm{\infty }}\frac{1}{n^3}$.

Find an upper bound for $\sum _{n=4}^{\mathrm{\infty }}\frac{1}{n^3}$.

Find the value of $p$.

Write down the coordinates of A.

Write down the rate of change of $f$ at A.

Find the coordinates of B.

Find the the rate of change of $f$ at B.

Let $R$ be the region enclosed by the graph of $f$ , the $x$-axis, the line $x=b$ and the line $x=a$. The region $R$ is rotated 360° about the $x$-axis. Find the volume of the solid formed.

Write down the coordinates of the vertex of the graph of g.

On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.

Find the area of the region enclosed by the graphs of f and g.

Find $\int \left(6x^2-3x\right)\text{d}x$.

Find the area of the region enclosed by the graph of $f$, the x-axis and the lines x = 1 and x = 2 .

Find the x-intercept of the graph of $f$.

The region enclosed by the graph of $f$, the y-axis and the x-axis is rotated 360° about the x-axis.

Find the volume of the solid formed.

Find the value of $p$.

The following diagram shows part of the graph of $f$.

The region enclosed by the graph of $f$, the $x$-axis and the lines $x=-p$ and $x=p$ is rotated 360° about the $x$-axis. Find the volume of the solid formed.

Find $\int {\left(f\left(x\right)\right)}^2\text{d}x$.

Part of the graph of f is shown in the following diagram.

The shaded region R is enclosed by the graph of f, the x-axis, and the lines x = 1 and x = 9 . Find the volume of the solid formed when R is revolved 360° about the x-axis.

Find the volume of the container.

Find the value of $p$ and of $q$.

During the interval $p$ < $t$ < $q$, he volume of water in the container increases by $k$ m³. Find the value of $k$.

When $t$ = 0, the volume of water in the container is 2.3 m³. It is known that the container is never completely full of water during the 4 hour period.

Find the minimum volume of empty space in the container during the 4 hour period.

Use the model to find the volume of the barrel.

The empty barrel is being filled with water. The volume $V{\text{m}}^3$ of water in the barrel after $t$ minutes is given by $V=0.8(1-{\text{e}}^{-0.1t})$. How long will it take for the barrel to be half-full?

Find the $x$-intercept of the graph of $f$.

The region enclosed by the graph of $f$, the $x$-axis and the $y$-axis is rotated 360º about the $x$-axis. Find the volume of the solid formed.

Find the probability that this person is not allergic to nuts.

Find the probability that both people chosen are not allergic to nuts.

Copy and complete the tree diagram.

Find the probability that this adult is allergic to nuts and the liquid turns blue.

Find the probability that the liquid turns blue.

Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.

Estimate the number of employees, from this 38, who are allergic to nuts.

Two girls are selected at random.

Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.

Write down the value of a.

Write down the value of b.

Use the tree diagram to find the probability that an employee encountered traffic and was late for work.

Write down the null hypothesis, H₀ , for this test.

State the number of degrees of freedom.

the expected frequency of female students who chose to take the Chinese class.

State whether or not H₀ should be rejected. Justify your statement.

Find the probability that the student does not take the Spanish class.

Find the probability that neither of the two students take the Spanish class.

Find the probability that at least one of the two students is female.

Find the probability that both spins are yellow.

Find the probability that at least one of the spins is yellow.

Write down the probability that the second spin is yellow, given that the first spin is blue.

Express this volume in $\text{c}{\text{m}}^3$.