How to use this lesson
1. Complete the warm-up questions from memory
2. Study the worked examples carefully
3. Try the practice problems: Green → Amber → Red
4. Check your answers and complete the mastery checklist
2. Study the worked examples carefully
3. Try the practice problems: Green → Amber → Red
4. Check your answers and complete the mastery checklist
🔥
Warm-Up (Retrieval Practice)💡 Quick Check
Answer from memory — no notes!Q1 What does a horizontal (flat) line on a distance-time graph mean?
Q2 What does the gradient (steepness) tell you on a distance-time graph?
Q3 What does the area under a speed-time graph tell you?
Q4 🔄 RECALL Factorise: 12x + 18
Q4 Factorise: 12x + 18
Lesson Progress
✓ Warm-up — complete
→ Worked examples & key concepts
· Tiered practice (Green → Amber → Red)
· Mistake Detective & Examiner Lens
· Mastery checklist
💡
Big Idea: Graphs Tell a Story💡 The Core Concept
Real-life graphs describe movement. Think of them as a story in picture form — you can tell whether something is moving, stopped, speeding up, or coming back just by looking at the shape of the line.
📏 Distance–Time Graph
⚡ Speed–Time Graph
🧠 The Golden Rules (memorise these!)
Distance-time graph: Gradient (steepness) = speed. Flat line = stopped.Speed-time graph: Area under the line = distance. Flat line = constant speed.
📖
Core DefinitionsGradient
How steep the line is. On a D-T graph, steeper = faster.
Stationary
Not moving. Shows as a flat (horizontal) line on a D-T graph.
Constant speed
Moving at the same speed — a straight line (not curved).
Area under graph
On a S-T graph, the area of the shape underneath = distance travelled.
📐
Part 1 — Distance–Time Graphs🔑 Key Facts
- Gradient = speed (steeper line = faster speed)
- Horizontal line = stationary (the object has stopped)
- Straight line = constant speed (same speed throughout)
- Line going down = returning towards the starting point
Worked Example 01Finding Speed (Constant Speed)
A line goes from (0, 0) to (5, 20) on a distance-time graph. Find the speed.
The line goes up 20 m in 5 seconds — that's the gradient
Calculate gradient (rise ÷ run)
Change in distance = 20 m
Change in time = 5 s
Speed = 20 ÷ 5
Change in time = 5 s
Speed = 20 ÷ 5
✓ Answer
✓ Speed = 4 m/s
Worked Example 02Stationary Section
The graph is horizontal (flat) between 4 s and 8 s. What does this mean?
Between 4 s and 8 s the distance doesn't change — the object has stopped
Think about it
The distance stays the same for 4 seconds.
If you're not getting further away or closer, you must be standing still.
If you're not getting further away or closer, you must be standing still.
✓ Answer
✓ The object is stationary. Speed = 0 m/s
Worked Example 03Return Journey
The line slopes downward from 30 m to 10 m. What is happening?
What does a downward line mean?
The distance from the starting point is getting smaller.
That means the object is going back the way it came.
That means the object is going back the way it came.
✓ Answer
✓ The object is moving back towards the start
📐
Part 2 — Speed–Time Graphs🔑 Key Facts
- Area under graph = distance travelled
- Break the area into rectangles and triangles
- Flat line on speed-time = constant speed (not stopped!)
⚠️ Don't mix them up!
Flat line on a distance-time graph = STOPPED.Flat line on a speed-time graph = CONSTANT SPEED (still moving!).
This is the most common confusion in the exam.
Worked Example 04Rectangle Area (Constant Speed)
Speed = 6 m/s for 5 seconds. Find the distance.
Constant speed = rectangle shape. Distance = speed × time.
Rectangle area = length × width
Distance = speed × time
Distance = 6 × 5
Distance = 6 × 5
✓ Answer
✓ Distance = 30 m
Worked Example 05Triangle Area (Speeding Up)
Speed increases steadily from 0 to 10 m/s over 4 seconds. Find the distance.
Speeding up from zero = triangle shape. Distance = ½ × base × height.
Triangle area = ½ × base × height
Base = 4 s
Height = 10 m/s
Distance = ½ × 4 × 10
Height = 10 m/s
Distance = ½ × 4 × 10
✓ Answer
✓ Distance = 20 m
Worked Example 06Multi-Section (Triangle + Rectangle)NEW
A speed-time graph shows: 0–4 s speed increases from 0 to 8 m/s, then 4–8 s constant speed 8 m/s. Find the total distance.
Split the graph into simple shapes, calculate each area, then add them together
Step 1: Triangle (speeding up section)
Area = ½ × 4 × 8 = 16 m
Step 2: Rectangle (constant speed section)
Area = 8 × 4 = 32 m
Step 3: Add them up
Total distance = 16 + 32
✓ Answer
✓ Total distance = 48 m
📌 Always break the graph into simple shapes (triangles and rectangles) first.
💬
Interpretation Skills📘 Exam Language
When describing graphs, the examiner expects specific words. Use "stationary" (not "stopped"), "constant speed" (not "same speed"), and "steeper" to compare speeds. Always include units (m, s, m/s).
✅
Process Checklists✅ Distance–Time
✓
Calculate gradient (rise ÷ run)✓
Spot stationary sections (flat)✓
Spot return journeys (going down)✓
Include correct units✅ Speed–Time
✓
Identify shape (rectangle or triangle)✓
Calculate area correctly✓
Add multiple sections if needed✓
Include units in final answer🧮
Arithmetic Support StripRectangle = length × width
Triangle = ½ × base × height
Distance = speed × time
Speed = distance ÷ time
Always check units (m, s, m/s)
✏️
Practice Questions💪 Three-Tier Practice
Attempt first, then tap to check.🟢 Green — Core Skills
🟢 Green · TYPE YOUR ANSWER
Speed = distance ÷ time. Find speed: 20m in 4s
✍️ Type Your Answer
Speed = 8 m/s, Time = 5 s. Find distance.
Distance = Speed × Time = 8 × 5 = 40 m
✓ 40 m
Problem 1
Find speed from (0, 0) to (3, 12) on a distance-time graph.
Gradient = rise ÷ run
Change in distance = 12 m
Change in time = 3 s
Speed = 12 ÷ 3
Change in distance = 12 m
Change in time = 3 s
Speed = 12 ÷ 3
✓ Answer: 4 m/s
👆 Tap to reveal
Problem 2
Describe a horizontal section on a distance-time graph.
Horizontal = flat line
Distance is not changing
No movement happening
Distance is not changing
No movement happening
✓ The object is stationary (speed = 0 m/s)
👆 Tap to reveal
Problem 3
Find distance for constant speed 5 m/s over 6 s (speed-time graph).
This is a rectangle
Distance = speed × time
Distance = 5 × 6
Distance = speed × time
Distance = 5 × 6
✓ Answer: 30 m
👆 Tap to reveal
🟠 Amber — Multi-Step
🟡 Amber · TYPE YOUR ANSWER
Area of triangle: base 6s, height 10 m/s
Problem 4
Calculate distance for a triangle with base 6 s and height 12 m/s.
Triangle area = ½ × base × height
= ½ × 6 × 12
= ½ × 72
= ½ × 6 × 12
= ½ × 72
✓ Answer: 36 m
👆 Tap to reveal
Problem 5
Constant speed 7 m/s for 5 s. Find distance.
Rectangle area
Distance = 7 × 5
Distance = 7 × 5
✓ Answer: 35 m
👆 Tap to reveal
Problem 6
Speed-time: triangle (0–3 s to 9 m/s) then rectangle (3–6 s at 9 m/s). Find total distance.
Triangle: ½ × 3 × 9 = 13.5 m
Rectangle: 9 × 3 = 27 m
Total: 13.5 + 27
Rectangle: 9 × 3 = 27 m
Total: 13.5 + 27
✓ Answer: 40.5 m
👆 Tap to reveal
Problem 5b
A car travels 45 km in 30 minutes. What is the speed in km/h?
30 minutes = 0.5 hours
Speed = Distance ÷ Time
Speed = 45 ÷ 0.5
Speed = Distance ÷ Time
Speed = 45 ÷ 0.5
✓ Answer: 90 km/h
👆 Tap to reveal
Problem 5c
A speed-time graph shows constant speed of 4 m/s for 8 s, then deceleration to 0 m/s over 4 s. Find total distance.
Rectangle: 4 × 8 = 32 m
Triangle: ½ × 4 × 4 = 8 m
Total = 32 + 8
Triangle: ½ × 4 × 4 = 8 m
Total = 32 + 8
✓ Answer: 40 m
👆 Tap to reveal
🔴 Red — Exam Style
🔴 Red · TYPE YOUR ANSWER
Gradient of line from (0,0) to (5, 30) on distance-time graph
Problem 7 · 3 marks
A speed-time graph shows acceleration from 0 to 12 m/s over 6 s, then constant speed for 4 s. Find total distance.
Section 1 (triangle):
½ × 6 × 12 = 36 m
Section 2 (rectangle):
12 × 4 = 48 m
Total = 36 + 48
½ × 6 × 12 = 36 m
Section 2 (rectangle):
12 × 4 = 48 m
Total = 36 + 48
✓ Answer: 84 m
👆 Tap to reveal
Problem 8 · 3 marks
Describe fully: 0–5 s travels 20 m, 5–10 s stays at 20 m, 10–15 s returns to 0 m.
0–5 s: Moving away at constant speed
Speed = 20 ÷ 5 = 4 m/s
5–10 s: Stationary (flat line at 20 m)
Speed = 0 m/s
10–15 s: Returning at constant speed
Speed = 20 ÷ 5 = 4 m/s
Speed = 20 ÷ 5 = 4 m/s
5–10 s: Stationary (flat line at 20 m)
Speed = 0 m/s
10–15 s: Returning at constant speed
Speed = 20 ÷ 5 = 4 m/s
✓ Travels away at 4 m/s, stops for 5 s, then returns at 4 m/s
👆 Tap to reveal
Problem 8b · 3 marks
A distance-time graph shows: 0–4 s travels 16 m, 4–7 s stationary, 7–10 s travels a further 12 m. Find the average speed for the whole journey.
Total distance = 16 + 12 = 28 m
Total time = 10 s
Average speed = 28 ÷ 10
Total time = 10 s
Average speed = 28 ÷ 10
✓ Answer: 2.8 m/s
👆 Tap to reveal
Problem 8c · 4 marks
Speed-time graph: accelerates from 0 to 10 m/s in 5 s, constant for 3 s, then decelerates to 0 in 2 s. Find total distance.
Triangle 1: ½ × 5 × 10 = 25 m
Rectangle: 10 × 3 = 30 m
Triangle 2: ½ × 2 × 10 = 10 m
Total = 25 + 30 + 10
Rectangle: 10 × 3 = 30 m
Triangle 2: ½ × 2 × 10 = 10 m
Total = 25 + 30 + 10
✓ Answer: 65 m
👆 Tap to reveal
0 / 13
Problems revealed
Tap problems to reveal working and answers
🔍
Mistake Detective⚠️ These mistakes cost marks
Study each one — then look for them in your own work.❌ Wrong
Using gradient to find distance on a speed-time graph
Distance = AREA under graph, not gradient
✅ Correct
Break into shapes → calculate AREA
❌ Wrong
"The flat part means speed is constant"
Only true on speed-time graphs! On distance-time, flat = stationary
✅ Correct
Distance-time flat = STATIONARY
Speed-time flat = CONSTANT SPEED
Speed-time flat = CONSTANT SPEED
🎓
Examiner Lens🎓 To Gain Full Marks
- State the formula before calculating (e.g. "Area = ½ × base × height")
- Show shape breakdown for multi-section graphs
- Add areas clearly with working shown
- Include correct units (m, s, m/s)
- Use correct terminology: "stationary", "constant speed", "steeper"
🏆
Mastery Checklist🏆 Unit 8 Mastery
✓
I understand gradient on distance-time graphs
✓
I can calculate area under speed-time graphs
✓
I can break graphs into simple shapes
✓
I describe motion accurately with correct terminology
✓
I include units in all my answers
Nice work — you’ve completed Unit 8!
2 units remaining. Consistent practice is what turns Grade 3 into Grade 4/5. Keep going.
Ready for Unit 9?
If you can do these 3 things confidently, you're ready to move on:
👨👩👧 For Parents
Your child has completed Unit 8 of a structured GCSE Foundation Maths revision programme covering Algebra and Graphs — key topics on every Foundation paper.
✔ AQA, Edexcel & OCR aligned
✔ 170+ practice questions
✔ Step-by-step explanations
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Unit 9: Linear Graph Applications →
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