📖 Theory notes

Every note is built the same way: I can…, a quick recall, 🔑 key ideas, ✨ tips, ⚠️ common mistakes, ✏️ worked examples and 🧠 Remember in 3 lines.

🎯 Learn, then practise from two books

Each LO starts with 📘 a learning sheet (worked examples one step at a time), then 📗 Collins practice (Book 1 exercises) and, where Book 2 covers the topic, 📙 Pearson practice (Book 2 exercises, including starred questions).

🧪 LO tests · 30 minutes each

When the practice feels easy, take the timed test for that LO. Tests run in Quiz mode, submit themselves at 00:00 and can be taken once. Your report shows each LO as a pie chart.

About this chapter

A graph turns a rule or a journey into a picture you can read at a glance. In this chapter you use three kinds: conversion graphs (one unit into another), distance–time graphs (how far, and how fast) and speed–time graphs (speeding up, slowing down and distance). This chapter uses 📗 Collins Book 1 only.

LO	📗 Collins Book 1	📙 Pearson Book 2
LO 1	14.1 Conversion graphs	—
LO 2	14.2 Travel graphs	—
LO 3	14.3 Speed–time graphs	—

Learning objectives

LO 1 · 14.1 Conversion graphsI can read and draw straight-line conversion graphs (units, currencies, charges), using the scales carefully, and find a rule from two points.

LO 2 · 14.2 Distance–time (travel) graphsI can read distance–time graphs, describe a journey from them, work out average speeds (including in km/h from minutes) and draw a travel graph from a description.

LO 3 · 14.3 Speed–time graphsI can read speed–time graphs, recognise constant speed, acceleration and deceleration, and use the gradient (acceleration) and the area (distance travelled).

Check what you already know

You need	Quick check	Answer
Speed formula	120 km in 2 hours	60 km/h
Minutes to hours	45 minutes	0.75 hours
Reading a scale	5 small squares = 10, one square =	2
Area of a triangle	base 6, height 4	12

14.1 Conversion graphs

LO 1I can… read and draw straight-line conversion graphs (units, currencies, charges), using the scales carefully, and find a rule from two points.

🔁 Quick recall before you start
1 inch is about 2.5 cm. About how many cm is 4 inches? (10 cm.)

📗 Collins: 14.1 conversion graphs: units (litres–gallons, kg–lb, cm–inches, °C–°F), currencies and charges (electricity, hire, conferences, sales tax).
📙 Pearson Book 2: no matching unit (Book 2 assumes these graph skills).

🔑 Key idea · Reading a conversion graph
Find the value on one axis, go straight to the line, then straight across (or down) to the other axis and read the scale. Dashed lines show the route.

✏️ Worked example · Litres and gallons (Collins Example 1)

Up from 5 gallons, across: about 23 litres.
Across from 15 litres, down: about 3¼ gallons.

🔑 Key idea · Two kinds of line
Through (0, 0): a pure conversion (kg–lb, £–$). Doubling one doubles the other.
Starting higher up: a fixed charge plus a rate (electricity: $10 + 7 cents per unit), or °F = 1.8 × °C + 32.

✏️ Worked example · Finding the rule from two points (Collins 14A Q8)

850 units → $57.50 and 320 units → $31.
Rate = 26.50 ÷ 530 = $0.05 per unit; fixed charge = 31 − 320 × 0.05 = $15.
700 units: 15 + 35 = $50.

⚠️ Common mistake · The scale
Count what ONE small square is worth before you read anything: if 5 squares make 10, each square is 2.

✨ Tip · Off the graph?
For a pure conversion (through 0) scale up: 48 lb = 4 × 12 lb, so read 12 lb and multiply by 4. This does NOT work for a line with a fixed charge.

🧠 Remember in 3 lines

Check the scale first.
Up to the line, across to the answer.
Through 0 → you can scale; fixed charge → you cannot.

Memory hook: Up, across, read.

14.2 Distance–time (travel) graphs

LO 2I can… read distance–time graphs, describe a journey from them, work out average speeds (including in km/h from minutes) and draw a travel graph from a description.

🔁 Quick recall before you start
A car travels 30 km in 30 minutes. What is its speed in km/h? (60 km/h.)

📗 Collins: 14.2 travel graphs: reading a journey, stops, return journeys, average speeds, races and overtaking, drawing graphs from descriptions.
📙 Pearson Book 2: no matching unit (Book 2 assumes these graph skills).

🔑 Key idea · What the shape means
Sloping up = moving away. Steeper = faster. Horizontal = stopped. Sloping down = coming back.

🔑 Key idea · Average speed
average speed = total distance ÷ total time. For km/h with times in minutes, scale up to 60 minutes: 16 km in 20 minutes → × 3 → 48 km/h.

Time	Multiply the distance by	Example
30 min	2	40 km → 80 km/h
20 min	3	16 km → 48 km/h
15 min	4	25 km → 100 km/h
10 min	6	19 km → 114 km/h
45 min	÷ 0.75	9 km → 12 km/h

✏️ Worked example · Murcia to Cartagena (Collins Example 3)

A–B 48 km/h, B–C 114 km/h (steepest), C–D 45 km/h, D–E stopped, E–F 50 km/h back.

✏️ Worked example · Overtaking (Collins 14B Q6)

Walker 6 km/h from 0900; cyclist 15 km/h from 1030.
At 1030 the walker is 9 km ahead; the gap closes at 9 km/h → 1 hour → overtakes at 1130.
On the graph: where the two lines cross.

⚠️ Common mistake · Stops count for average speed
Whole-journey average speed includes the time spent stopped: 240 km in 5 hours (with a 1-hour break) is 48 km/h, not 60 km/h.

✨ Tip · Units
m/s × 3.6 = km/h; km/h ÷ 3.6 = m/s.

🧠 Remember in 3 lines

Steeper = faster; flat = stopped; down = coming back.
Speed = distance ÷ time (scale minutes to 60).
Crossing lines = meeting or overtaking.

Memory hook: Steep is speedy, flat is stopped.

14.3 Speed–time graphs

LO 3I can… read speed–time graphs, recognise constant speed, acceleration and deceleration, and use the gradient (acceleration) and the area (distance travelled).

🔁 Quick recall before you start
What does a horizontal line mean on a DISTANCE–time graph? (Stopped.) Watch out: on a speed–time graph it means something else.

📗 Collins: 14.3 speed–time graphs: constant speed, accelerating and decelerating cars, trains and boats, and two cars on the same graph.
📙 Pearson Book 2: no matching unit (Book 2 assumes these graph skills).

🔑 Key idea · What the shape means
Here the height is the SPEED. Horizontal = constant speed. Sloping up = accelerating (speeding up). Sloping down = decelerating (slowing down). On the time axis = stopped.

Feature	Distance–time graph	Speed–time graph
Horizontal line	stopped	constant speed
Gradient	speed	acceleration
Area under the line	—	distance travelled

✏️ Worked example · Car (Collins 14C Q1)

Maximum speed 20 m/s at 40 s.
Acceleration = 20 ÷ 40 = 0.5 m/s²; speed after 10 s = 5 m/s.
Distance = area of the triangle = ½ × 60 × 20 = 600 m.

✏️ Worked example · Two cars (Collins 14C Q5)

Red car: 15 m/s for 30 s → 15 × 30 = 450 m.
Blue car: 0 → 20 m/s in 15 s, then 20 m/s. It matches 15 m/s after 11.25 s.
Blue distance 15–30 s: 20 × 15 = 300 m.

⚠️ Common mistake · Two different graphs
Always read the label on the vertical axis. A line going down on a speed–time graph means slowing down, NOT going back.

✨ Tip · Area in pieces
Split the shape under the graph into triangles, rectangles and trapezia and add the areas. Units: (m/s) × s = m.

🧠 Remember in 3 lines

Height = speed; flat = constant speed.
Gradient = acceleration.
Area = distance.

Memory hook: Slope speeds you up, area adds up the metres.