DP Mathematics: Applications and Interpretation Questionbank

Show that $\text{AC}=\tan \theta$.

Find the value of $\theta$ when the area of the shaded region is equal to the area of sector $\text{OADB}$.

Find the expression $\frac{dV}{d\theta }$.

Solve algebraically $\frac{dV}{d\theta }=0$ to find the value of $\theta$ that will maximize the volume, $V$.

Show that $r=\frac{6}{2+\theta }$.

Find an expression for $V$ in terms of $\theta$.

Find AM.

Find the area of the shaded region.

Find an expression for the shaded area in terms of $\alpha$, $\theta$ and $r$.

Show that $\alpha =4\arcsin \frac{1}{4}$.

Hence find the value of $r$ given that the shaded area is equal to 4.

A sector of a circle with radius $r$ cm , where $r$ > 0, is shown on the following diagram.
The sector has an angle of 1 radian at the centre.

Let the area of the sector be $A$ cm² and the perimeter be $P$ cm. Given that $A=P$, find the value of $r$.

Find an expression for the volume of water $V({\text{m}}^3)$ in the trough in terms of $\theta$.

Calculate $\frac{\text{d}\theta }{\text{d}t}$ when $\theta =\frac{\pi }{3}$.

Show that $\text{AC}=7\text{ cm}$.

The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the triangle.

Find the exact perimeter of this shape.

The following diagram shows the chord [AB] in a circle of radius 8 cm, where $\text{AB}=12\text{ cm}$.

Find the area of the shaded segment.

Find the length of arc ABC.

Find the perimeter of sector OABC.

Find the area of sector OABC.

Write down the exact value of $\theta$ in radians.

Find the value of $r$.

Find AB.

Find the area of triangle OBC in terms of $r$ and θ.

Boat A is situated 10km away from boat B, and each boat has a marine radio transmitter on board. The range of the transmitter on boat A is 7km, and the range of the transmitter on boat B is 5km. The region in which both transmitters can be detected is represented by the shaded region in the following diagram. Find the area of this region.

Find the volume of this log.

Use the cosine rule to find the two possible values for AC.

Find 50° in radians.

Find the difference between the areas of the two possible triangles ABC.