Real-Life Graphs - Year 11 PDF Download

CIE IGCSE Maths: Extended

Revision Notes

Syllabus Edition

First teaching 2023

First exams 2025

Conversion Graphs

Conversion Graphs

• A conversion graph illustrates the relationship between two quantities in a linear manner.
• It enables the conversion between units or quantities by interpreting values from the graph at various points on the line.
• Conversion graphs are commonly utilized for various purposes such as:

• Converting between different temperature units like degrees Celsius (°C) and degrees Fahrenheit (°F).
• Converting currencies, for instance, Dollars ($) to Yen (¥).
• Converting volume units like Litres to Gallons.
• Calculating charges based on usage, such as a taxi driver charging per kilometre driven.

Converting Units and Calculating Charges

• Converting between units of temperature such as degrees Celsius (°C) and degrees Fahrenheit (°F)
• Converting between different currencies like Dollars ($) and Yen (¥)
• Converting between units of volume such as Litres and Gallons
• Calculating charges based on usage, for instance, a taxi driver charging per kilometre driven

Using Conversion Graphs

• When utilizing a conversion graph for temperature, like the one below:

Converting Fahrenheit to Celsius

• To convert 100 °F into °C, follow these steps:
• Identify the axis you are converting from (in this case, °F on the y-axis)
• Draw a line from the value you want to convert (e.g., 100 °F) to the graphed line
• Intersect the graphed line and read off the result (100 °F is approximately equal to 37.8 °C)

Converting Graphs - Understanding Temperature Conversions

• When graphing temperature conversions, like from Fahrenheit to Celsius, it's essential to draw a horizontal line from the given Fahrenheit value, such as 100 °F.
• Using a ruler, extend this line to where it intersects with the corresponding temperature scale, and then determine the Celsius equivalent. For instance, 100 °F is approximately equal to 37.8 °C.

Reading Values from a Graph

• Prior to extracting a value from a graph, always identify the scale in use. Each square on the graph might represent different units, including 1, 2, or 5, on either axis.
• Remember, the scales on the x and y axes may not necessarily be identical.
• Interpret the graph provided below, illustrating the charges imposed by a plumber based on the hours worked on a specific task.

Draw a vertical line from the x-axis at 3 hours and then read the corresponding value on the y-axis.

Understanding Conversion Graphs

Conversion graphs are graphical representations that help us understand the relationship between two variables. Let's delve into the key concepts:

• The Cost-Time Relationship:
• Conversion graphs illustrate how cost varies with time for a particular job.
• For example, if a job costs $320, and on the graph, this corresponds to approximately 4.5 hours, we can interpret that the job took 4.5 hours to complete.
• Interpreting the Graph:
• To find the price charged for 0 hours (the y-intercept), we look at where the line graph meets the y-axis.
• For instance, if the graph indicates that the price for 0 hours is approximately $45, we understand this as the base cost.
• Utilizing Conversion Graphs:
• When faced with a specific cost, draw a horizontal line from that cost on the y-axis to determine the corresponding time on the x-axis.
• By following this method, we can extract valuable information about costs and time relationships from conversion graphs.

Practice and Application

• Engage in Self-Assessment:
• Test your understanding by working through various scenarios using conversion graphs.
• Challenge yourself to interpret different points on the graph to reinforce your comprehension.
• Exploration and Further Learning:
• Continue your educational journey by exploring additional topics related to conversion graphs.
• Download comprehensive notes on conversion graphs to deepen your knowledge in this area.