0580/31 Oct/Nov 2023, Question 2: Scale Drawings

Part (ai) · 1 mark

Given the diameter is 168 mm, state the radius.

1. 1Radius = 168 ÷ 2 = 84 mm

Answer84

Part (aii) · 1 mark

Draw a chord on the circle shown.

1. 1Rule a straight line joining any two points on the circumference

AnswerAny chord

Part (bi) · 2 marks

Using 1 cm to 6 km, mark ship C, 45 km from B on a bearing of 124°.

1. 1On the drawing, 45 km = 45 ÷ 6 = 7.5 cm
2. 2From the North line at B measure a bearing of 124° clockwise and mark C 7.5 cm from B

AnswerAccurate position marked

Part (bii) · 2 marks

Work out how far ship C actually is from ship A.

1. 1Measure AC on the drawing: about 9.5 cm
2. 2Actual distance = 9.5 × 6 = 57 km

Answer57 (accept 55.2 to 57.6)

Part (ci) · 1 mark

Prove that each interior angle of a regular octagon equals 135°.

1. 1Exterior angle = 360 ÷ 8 = 45°
2. 2Interior angle = 180 − 360/8 = 135°

Answer180 − 360/8 or ((8 − 2) × 180)/8

Part (cii) · 1 mark

Explain why two regular octagons plus a square fit together at one point with no gaps.

1. 1Angles at the point: 135 + 135 + 90 = 360
2. 2They add to 360°, so there are no gaps

Answer135 + 135 + 90 = 360

Part (d) · 2 marks

With DF a diameter and angle EFD = 49°, calculate angle EDF.

1. 1Angle DEF = 90° (angle in a semicircle)
2. 2Angle EDF = 180 − 90 − 49 = 41°

Answer41

More past-paper questions on scale drawings

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