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Scale drawing — KCSE Mathematics

KCSE Mathematics · 84 practice questions · 3 syllabus objectives · 3 revision lessons

19 easy33 medium32 hard

Last updated · Aligned to the KNEC KCSE syllabus

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

Revision Notes

Concise lesson notes for Scale drawing, written to the KCSE Mathematics marking standard. Read the first lesson free below.

Understanding Scale Drawings

Scale drawings are essential in representing real objects in a manageable size. To create an accurate scale drawing, follow these steps:

  1. Choose a Scale: Select a scale that simplifies the drawing while maintaining proportionality. For example, a scale of 1:100 means 1 cm on the drawing represents 100 cm in reality.
  2. Gather Information: Collect all necessary measurements and dimensions of the object or area to be drawn.
  3. Calculate Dimensions: Convert the actual measurements to the scale using the chosen ratio. For instance, if a room is 400 cm long, it will be 4 cm on a 1:100 scale drawing.
  4. Draw the Sketch: Use a ruler and pencil to sketch the drawing accurately, ensuring all proportions are maintained.

Remember to label your drawing with the scale used for clarity. This helps anyone viewing the drawing understand the relationship between the drawing and the actual size of the object.

Key points to remember

  • Choose a scale that simplifies while maintaining accuracy.
  • Convert actual measurements using the selected scale.
  • Ensure all proportions are accurately represented in the drawing.
  • Label the drawing with the scale for clarity.

Worked example

A rectangular garden measures 300 cm by 200 cm. Draw it to a scale of 1:50.

  • Length on drawing: 300 cm ÷ 50 = 6 cm.
  • Width on drawing: 200 cm ÷ 50 = 4 cm.
  • Sketch a rectangle measuring 6 cm by 4 cm.

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More lessons in this topic

Lesson 2: Understanding Bearings in Scale Drawings

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

In navigation and geometry, bearings are used to describe the direction of one point from another. Bearings are measured in degrees from the North direction (0°) in a clockwise manner.

To state the bearing of one point from another, follow these steps:

  1. Identify the North direction on your scale drawing.
  2. Measure the angle clockwise from North to the line connecting the two points.

For example, if point A is located at a bearing of 045° from point B, it means that from point B, you would rotate 45° clockwise to point A.

To locate a point using a bearing and distance:

  • Start at the reference point.
  • Measure the bearing from the North.
  • Use a protractor to draw the angle.
  • Measure the distance with a ruler and mark the endpoint.

Example: If point B is at (2, 3) and point A is at a bearing of 060° and distance of 5 cm:

  1. From point B, measure 60° clockwise from North.
  2. Measure 5 cm along this bearing to locate point A.
  • Bearings are measured clockwise from North starting at 0°.
  • State the bearing as an angle (e.g., 045°).
  • To locate a point, draw the angle from the reference point.
  • Use a ruler to measure the specified distance accurately.
  • Ensure to mark the endpoint clearly on your drawing.

Q: State the bearing of point C from point D if point C is at 120°. A: The bearing of point C from point D is 120°.

Lesson 3: Understanding Angles of Elevation and Depression

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

In scale drawing, angles of elevation and depression are crucial for visualizing problems involving heights and distances. Angles of elevation are formed when you look up at an object, while angles of depression occur when you look down. To determine these angles, you often use trigonometric ratios such as tangent, sine, and cosine.

To solve problems involving bearings, remember that bearings are measured clockwise from the north direction. A bearing is expressed in degrees, ranging from 0° to 360°.

Steps to solve problems:

  1. Identify the position of the observer and the object.
  2. Draw a scale diagram to visualize the situation.
  3. Use trigonometric ratios to calculate unknown angles or distances.
  4. Apply the correct bearing format for directions.

For example, if an observer is 50 meters from a tree and the angle of elevation to the top of the tree is 30°, you can find the height of the tree using:

  • Height = Distance × tan(angle)
  • Height = 50 m × tan(30°) = 50 m × (1/√3) ≈ 28.87 m.
  • Angles of elevation are viewed upwards; depression is viewed downwards.
  • Bearings are measured clockwise from north.
  • Use trigonometric ratios to find unknown angles and distances.
  • Scale drawings help visualize problems effectively.
  • Always express bearings in degrees between 0° and 360°.

A ship sails 60 km on a bearing of 045°. Determine the angle of elevation if the lighthouse is 20 m high.

  • Draw a scale diagram.
  • Use tan(angle) = opposite/adjacent.
  • Angle = tan^(-1)(20/60) ≈ 18.43°.

Sample Questions

Read 3 questions and answers free. Sign up to access all 84 questions with full KNEC-style marking schemes and a personalised study plan.

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)

Answer & 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)

Answer & 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)

Answer & 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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Frequently asked questions

What does the KCSE Mathematics topic "Scale drawing" cover?

Scales, bearings, locating points; angles of elevation and depression; simple surveying

How many practice questions are available for Scale drawing?

HighMarks has 84 Scale drawing practice questions for KCSE Mathematics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Mathematics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Scale drawing for the KCSE exam?

Start with the revision notes on this page to refresh the core concepts, then work through the practice questions in increasing difficulty. Sign up for HighMarks to get a personalised study plan that adapts to the topics you keep getting wrong, plus mock exams, subject-wide practice, and detailed performance tracking. See pricing.

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