CSEC MATHEMATICS · MODULE 1 · LESSON A12

Speed, Margin of Error, Scales and Scale Drawings

Distance, speed and time; average speed; limits of accuracy; maps, scale factors and scale drawings including area scale.

Fundamentals of Secondary Level MathematicsM1 4.10M1 4.11M1 4.12M1 4.13≈ 35 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON A12 · EXPLAINER

Speed, Margin of Error, Scales and Scale Drawings

A 5:30 a.m. flight, a map of Tobago, a measurement “to the nearest cm” — three real-world skills in one lesson.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Speed triangle

D = S × T; S = D ÷ T; T = D ÷ S. Keep units consistent (km with km/h, m with m/s).

Unit change

km/h → m/s: ÷ 3.6. m/s → km/h: × 3.6.

Average speed

Total distance ÷ total time — not the mean of the speeds.

Time

Decimal hours → minutes: × 60 (1.25 h = 1 h 15 min).

Limits of accuracy

Nearest unit: ± half the unit. Lower limit ≤ x < upper limit.

Max / min

Max area = max × max; min area = min × min. Quotients: max ÷ min for the maximum.

Scale

1 : n means 1 cm on paper = n cm in real life. 100 000 cm = 1 km.

Scale on areas

Square the linear factor (k²); cube it for volumes (k³).

EXAM TIPS & COMMON MISTAKES

  • “Average speed” — add distances, add times, then divide. Never average the speeds.
  • Write the limits as an inequality: 7.5 ≤ L < 8.5. The upper limit is not actually reached.
  • Convert the scale to the SAME units as the answer wanted before you multiply (cm → km uses ÷ 100 000).
  • Area scale: if lengths ×0.2 km, areas ×0.04 km², NOT ×0.2.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

CSEC Paper 01 style · SO 4.10

1. A car travels 120 km in 1.5 hours. Its average speed is

Answer: C. 120 ÷ 1.5 = 80.
CSEC Paper 01 style · SO 4.10

2. A car travels 60 km at 40 km/h and then 60 km at 60 km/h. Its average speed for the whole journey is

Answer: D. Time = 1.5 + 1 = 2.5 h; 120 ÷ 2.5 = 48.
CSEC Paper 01 style · SO 4.10

3. A speed of 72 km/h expressed in metres per second is

Answer: A. 72 ÷ 3.6 = 20.
CSEC Paper 01 style · SO 4.10

4. How long will a journey of 150 km take at 60 km/h?

Answer: B. 150 ÷ 60 = 2.5 h.
CSEC Paper 01 style · SO 4.11

5. A length is 8 cm, measured to the nearest centimetre. Its upper limit is

Answer: C. Half a unit above: 8.5 cm.
CSEC Paper 01 style · SO 4.11

6. The side of a square is 8 cm, measured to the nearest cm. The maximum possible perimeter is

Answer: D. 4 × 8.5 = 34 cm.
CSEC Paper 01 style · SO 4.12

7. On a map with scale 1 : 50 000, a road is 3.2 cm long. The actual length of the road is

Answer: A. 3.2 × 50 000 = 160 000 cm = 1.6 km.
Adapted from CSEC P2 January 2026, Question 6 (map scale item)

8. On a map drawn to a scale of 1 : 20 000, a lake has an area of 12 cm². Its actual area, in km², is

Answer: A. 1 cm² represents 0.04 km², so 12 × 0.04 = 0.48.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (17 marks in total). Show all your working — method marks count. Your answers are saved on this device.

CSEC Paper 02 style · Module 1 (Speed)

Question 1 [8 marks]

A bus leaves Town A at 0730 and travels 90 km to Town B in 1 hour 30 minutes. It then travels 60 km to Town C at an average speed of 40 km/h.

(a) Calculate the average speed of the bus from A to B. [2]

MARK SCHEME — (a) (max 2)

(b) How long does the bus take to travel from B to C? [2]

MARK SCHEME — (b) (max 2)

(c) At what time does the bus arrive at C? [1]

MARK SCHEME — (c) (max 1)

(d) Calculate the average speed for the whole journey from A to C. [3]

MARK SCHEME — (d) (max 3)

CSEC Paper 02 style · Module 1 (Scale and accuracy)

Question 2 [9 marks]

A map is drawn to a scale of 1 : 25 000.

(a) How many kilometres does 1 cm on the map represent? [2]

MARK SCHEME — (a) (max 2)

(b) The distance between two towns on the map is 6.4 cm. Calculate the actual distance. [2]

MARK SCHEME — (b) (max 2)

(c) A lake has an actual area of 0.5 km². Calculate its area on the map in cm². [3]

MARK SCHEME — (c) (max 3)

(d) The distance 6.4 cm was measured to the nearest 0.1 cm. State the lower and upper limits of the actual distance. [2]

MARK SCHEME — (d) (max 2)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.