Real-life graphs use the coordinate plane to represent practical situations. GCSE Maths requires you to interpret and extract information from distance-time, speed-time, conversion, and other practical graphs.
Distance-Time Graphs
Key Points
- Gradient = speed. Steeper = faster.
- Horizontal line = stationary (not moving).
- Negative gradient = returning to start.
Reading Information
- Distance at a given time: read from the y-axis.
- Speed: calculate the gradient of a section.
- Total distance: sum of all sections (outward + return).
Speed-Time Graphs
Key Points
- Gradient = acceleration. Positive = speeding up. Negative = slowing down.
- Horizontal line = constant speed.
- Area under the graph = distance travelled.
Calculating Distance
Use areas of triangles and rectangles under the graph.
Conversion Graphs
Straight-line graphs for converting between units (e.g., miles ↔ km, £ ↔ $).
Cost Graphs
Step functions or linear graphs showing cost against quantity/time.
Worked Example: Example 1
A distance-time graph shows 20 km in 2 hours, then stationary for 1 hour, then return in 1 hour.
Outward speed = km/h. Return speed = km/h.
Worked Example: Example 2
A speed-time graph shows acceleration from 0 to 30 m/s in 10 seconds, then constant speed for 20 seconds.
Distance = m.
Practice Problems
- A car travels 60 km in 45 minutes. Calculate speed in km/h.
- Find the area under a speed-time graph with a triangle (base 8s, height 20 m/s) and rectangle (20 m/s for 12s).
Want to check your answers and get step-by-step solutions?
Key Takeaways
Distance-time: gradient = speed; flat = stationary.
Speed-time: gradient = acceleration; area under = distance.
Read carefully: check axes, units, and scales.