IB Maths AI SL 3.4 Arc length and sector area Question Bank

Practise IB Mathematics SL/HL 3.4 by applying arc length and sector area methods to exam-style questions.

[Maximum number: 5]

The Scheveningen Ferris wheel's lowest point is 8 m above sea level, and its highest point is 45 m above sea level.

Figure for Question SL 3.4—Arc length and sector area question 1 — IB Maths AI SL

(a)

Show that the radius of the Ferris wheel is 18.5 m .

[ 1 ]

$\frac{45-8}{2} \quad A1$ $18.5(\mathrm{~m})$ AG
Note: Use of 18.5 in the calculation is reverse engineering, and falls short of the demand of the command term "Show that'. In such cases, award A0.

(b)

Calculate the circumference of the Ferris wheel.

There are pods, equally spaced around the wheel, that carry passengers.

[ 1 ]

$\quad(2 \pi \times 18.5=) 116(116.2389 \ldots, 37 \pi)(\mathrm{m})$ .

(c)

When the wheel rotates $10^{\circ}$ , find the distance that a pod travels along the circumference.

The height in metres, above sea level, of a particular pod is modelled by the function:

h(t)=a \sin (b t)+d, \text { for } a, b>0

where t is the time, measured in minutes.
The wheel takes 15 minutes to complete 1 revolution.

[ 3 ]

recognition the distance is the arc length

\begin{aligned} & \frac{10^{\circ}}{360^{\circ}} \times 2 \pi \times 18.5 \text { OR } \frac{116.2389 \ldots}{36} \\ & =3.23\left(3.228859 \ldots, \frac{37 \pi}{36}\right)(\mathrm{m}) \end{aligned}

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SL 3.4—Arc length and sector area question 1

Question (a)

Question (b)

Question (c)