IB Mathematics Applications & Interpretation Topic…

Let $y=\cos^6(3x)$ .

Consider the function $h(x)=4-3\sin(3x)\cos^5(3x)$ , defined for $0\le x\le \frac{\pi}{6}$ .

The region $R$ is bounded by the graph of $h$ , the $x$ -axis, the $y$ -axis, and the line $x=\frac{\pi}{6}$ .

the derivative $\frac{dy}{dx}$ .

Using your result from the previous part, find .

Let $y=\sin^5(2x)$ .

Consider the function $g (x) = 3 -$ , defined for .

A tank in the shape of a cone with height 4 metres and base radius 2 metres is filled with water. The height of the water is $h(t)$ (in metres) at time $t$ minutes and satisfies the differential equation $\frac{dh}{dt}=-0.01\sqrt{h}$ , where has units .

A particle moves in a plane such that its position vector (in metres) at time $t$ seconds, for $t \ge 0$ , is given by $r = (\begin{array}{c} t^{2} \end{array}$ .

A circular mirror of radius $8\text{ cm}$ is centred at $O$ . The vertices $A$ , $B$ and of an equilateral triangular frame lie on the mirror, so the three regions between the frame and the mirror are shaded. Let represent the mass of silver coating, in grams, applied to the mirror after minutes. The application rate is given by .

a definite integral that represents the area of $R$ .

the precise area of $R$ .

the derivative $\frac{dy}{dx}$ .

Using your result from the previous part, find $\int \sin^4(2x)\cos(2x)\,dx$ .

a definite integral that represents the area of $S$ .

the precise area of $S$ .

Solve the differential equation to find $h(t)$ .

Given that $h(0)=4$ , find the time $T$ when the tank is empty ( $h=0$ ).

Find the rate of change of the volume of water when $h=1$ .

Find the velocity vector, $\mathbf{v}$ , of the particle in terms of $t$ .

Find the position vector of the particle at the instant its speed is at a minimum.

the magnitude of angle $A\hat{O}B$ .

the area of one shaded segment.

the length of minor arc $AB$ .

the total area of the shaded regions.

Find the time $t$ when the rate of coating is at its maximum.

IB Mathematics Applications & Interpretation AHL 5.9—differentiating Standard Functions and Derivative Rules Questionbank

IB Mathematics Applications & Interpretation AHL 5.9—differentiating Standard Functions and Derivative Rules Questionbank

IB Mathematics Applications & Interpretation AHL 5.9—differentiating Standard Functions and Derivative Rules Questionbank

IB Mathematics Applications & Interpretation AHL 5.9—differentiating Standard Functions and Derivative Rules Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 5.9—differentiating Standard Functions and Derivative Rules Questionbank