Scale drawing — KCSE Mathematics

KCSE Mathematics · 84 practice questions · 3 syllabus objectives

19 easy33 medium32 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Choose and use an appropriate scale and draw sketches from given information

State the bearing of one point from another and locate a point using bearing and distance

Determine angles of elevation and depression and solve problems involving bearings and scale drawing

Sample Questions

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1
easySHORT ANSWER4 marks

From point A, a tourist walks to point B on a bearing of 045° for 8 km. (a) State the compass direction of point B from point A. (b) If the tourist then walks to point C on a bearing of 135° for 4 km, state the bearing of point A from point C. (4 marks)

View Marking Scheme
Part (a) — 2 marks
Compass direction of B from A is North-East (1 mk)
B is at a bearing of 045° from A (1 mk)
Part (b) — 2 marks
Back bearing = 135° + 180° (1 mk)
Bearing of A from C = 315° (1 mk)
2
easySHORT ANSWER4 marks

A lighthouse is located at point X. A ship sails from point X on a bearing of 120° for 5 km to point Y. (a) State the bearing of point X from point Y. (b) If the ship then sails to point Z on a bearing of 210° for 3 km, state the bearing of point Y from point Z. (4 marks)

View Marking Scheme
Part (a) — 2 marks
Back bearing = 120° + 180° (1 mk)
Bearing of X from Y = 300° (1 mk)
Part (b) — 2 marks
Back bearing = 210° + 180° (1 mk)
Bearing of Y from Z = 030° (1 mk)
3
easySHORT ANSWER2 marks

A scale drawing of a football field uses a scale of 1:500. If the actual width of the field is 80 m, state the width of the field on the drawing in centimetres. (2 marks)

View Marking Scheme
Part (a) — 2 marks
Width on drawing = 80 m × (1/500) = 0.16 m (1 mk)
Convert to cm: 0.16 m = 16 cm (1 mk)
4

A map has a scale of 1:1000. If two towns are 5 cm apart on the map, calculate the actual distance between the towns in kilometres. (2 marks)

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