Graphs in Practical Sitautions (Copy)

Graphs in Practical Situations Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Travel Graphs, Conversion Graphs, Gradient as Rate of Change

1. Use and Interpret Graphs in Practical Situations

Types of Graphs:

• Distance–Time Graphs
  • Show how distance changes over time (used for journeys)
• Speed–Time Graphs (not tested in detail at CORE level)
• Conversion Graphs
  • Show relationship between two different units or currencies
  • Usually straight line passing through origin

Distance–Time Graph Key Points:

Conversion Graph Key Points:

• Straight line graph through origin (0, 0)
• Gradient = conversion rate
• To convert, read values along x- and y-axis
• Can also use unit rate = y/x

2. Draw Graphs from Given Data

• Plot data points carefully using correct scales
• Label axes with units
• Use a ruler for straight lines, smooth curve if required
• For conversion graphs: line must go through origin (0,0)

3. Interpret the Gradient as Rate of Change

• Gradient (slope) = change in y ÷ change in x

In Distance–Time Graphs:

• Gradient = speed
  • Speed = Distance ÷ Time
  • Units: e.g., km/h or m/s

In Conversion Graphs:

• Gradient = conversion rate
  • e.g., £1 = $1.25 → gradient = 1.25

4. Practical Example Summaries

Example A – Travel Graph

A graph shows a car traveling 40 km in 2 hours.

• Gradient = 40 ÷ 2 = 20 km/h
• If horizontal for 1 hour after that → the car stopped
• If line returns to origin → return journey

Example B – Currency Conversion

If 10 USD = 7.5 GBP, then

• Conversion rate = 7.5 ÷ 10 = 0.75
• 1 USD = 0.75 GBP → Gradient = 0.75

Tips for Exams

• Always label axes clearly
• Check if graph should be a line or a curve
• Use graph to read values (e.g., how long journey took, how far traveled)
• When asked for rate, use gradient = rise/run
• Include units in final answers (e.g., km/h, $ per kg)

This topic links maths with real-life applications like travel, currency exchange, and time-distance relationships.