🔢 Fast Lanes & Smooth Conversions: Mastering Practical Graphs!

**Graphs tell stories!** Whether you are planning a journey, converting currencies, or tracking how quickly water drains from a tank, practical graphs turn real-life situations into clear visual data. Understanding these graphs is vital for O Level exams because they frequently test your ability to read, interpret, and create them.

Reading & Interpreting Practical Graphs

In a travel graph, the

x

-axis usually shows **time** while the

y

-axis shows **distance**. A steeper line means a **higher speed**, and a horizontal segment indicates the object is **stationary**. For conversion graphs (e.g..01 currency to dollars), the straight line passes through the origin because

0

units convert to

0

dollars. Rate-of-change graphs display how fast one quantity changes with respect to another; the gradient at any point gives the **instantaneous rate**.

Gradient $=$ rate of change.
Horizontal line $\Rightarrow$ no change in the dependent variable.
Intercept at origin in conversion graphs shows direct proportionality.

Worked Example: Cycling Trip Graph

Problem: A cyclist starts at home, 0 km from school, at 07:00. He reaches a checkpoint 5 km away at 07:20, rests for 10 minutes, then arrives at school (10 km total) at 07:50. Draw the travel graph and determine: (a) his speed during each leg, (b) total travel time excluding rest.

Step 1:
$\text{Speed}_1 = \frac{5\text{ km}}{20\text{ min}} = \frac{5}{\tfrac{1}{3}} = 15\text{ km h}^{-1}$
Step 2: During the rest, the line is horizontal so
$\text{Speed} = 0$
.
Step 3:
$\text{Speed}_2 = \frac{5\text{ km}}{20\text{ min}} = 15\text{ km h}^{-1}$
Step 4: Excluding the 10-minute rest, total travel time
$= 20\text{ min} + 20\text{ min} = 40\text{ min}$

Practical graphs are everywhere—from fuel gauges to currency charts. **Practise sketching and interpreting them daily** so you can swiftly spot gradients, intercepts, and rates of change in your O Level exam!