Graphs

1) Hook — The Story of Rohan’s Daily Cycle Journey

Imagine Rohan, a Class 10 student from Pune, who cycles to school every day. He notes down the time taken and distance covered each day. One day, he decides to plot these details on a graph to see how his speed changes. This simple graph helps Rohan plan his journey better and reach school on time. Graphs are not just lines on paper; they tell stories about our daily lives, from travel to business and even cricket scores!

2) Core Concepts — Understanding Graphs

A graph is a visual representation of data. It helps us understand relationships between two variables easily.

Types of Graphs commonly studied in IGCSE Class 10 Mathematics:

• Line Graphs: Show continuous data, like distance vs time.
• Bar Graphs: Compare quantities, like sales of mangoes in different months.
• Pie Charts: Show proportions, like percentage of students choosing different subjects.

Focus for this lesson: Line Graphs and Coordinate Geometry

Plotting Points on Cartesian Plane

The Cartesian plane has two perpendicular number lines:

• X-axis (horizontal)
• Y-axis (vertical)

Each point is represented as an ordered pair (x, y), where x is the horizontal distance from the origin and y is the vertical distance.

Plotting a Line Graph from Data

Suppose Rohan records his cycling distance (in km) over 5 days:

Plotting these points on graph paper with Day on X-axis and Distance on Y-axis gives a line graph showing Rohan’s cycling progress.

3) Key Formulas/Rules

4) Did You Know?

The concept of the Cartesian plane was developed by René Descartes, a French mathematician, in the 17th century. It revolutionized geometry by linking algebra and geometry, making it possible to describe shapes with equations. Today, GPS navigation systems in India use coordinate geometry to help you find the shortest route!

5) Exam Tips — Score High with Graphs

• Always label axes clearly with units (e.g., km, hours).
• Use a ruler to draw straight lines and plot points accurately.
• Check coordinates twice before plotting to avoid errors.
• Remember the slope formula and apply it carefully; division by zero means a vertical line.
• Practice drawing graphs from tables as these are common in board exams.
• Watch for scales: Sometimes axes use different scales; read instructions carefully.
• Common mistake: Mixing up x and y coordinates — always write as (x, y).
• Board exam pattern: Questions may ask you to find distance, midpoint, slope, or write the equation of a line from given points.