National 5 Prelim Revision Topics Worksheet - Elgin Academy Page 4

• Use Pythagoras in a circle (the tunnel/oil tanker problem!)

e.g. 22 The diagram shows the base of a compact disc stand which has the shape of part of a

circle.

Find the width of the stand.

• Arcs and Sectors (working forwards and back)

e.g. 23 The beam from a lighthouse reaches to a distance of 8km and spreads to an angle

of 35º. Calculate the area covered by the beam.

e.g. 24 A pendulum is 45 cm long. When the pendulum swings it travels through the arc of

a circle, covering a distance of 27.5 cm.

Find the angle through which the pendulum

travels.

Surds

• Simplify surds (non-calculator)

e.g. 25 Write each as a surd in its simplest form: a) √ 12

b) √ 75

c) √ 72

• Carry out calculations with Surds

e.g. 26 Calculate: a) √ 18 + √ 8

b) √ 80 − √ 45

c) √ 12 × √ 2

d) Calculate the value of x giving your answer as a surd in its simplest form.

√ 42

√ 10

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