Tutorial
In Course: GCSE Mathematics: Higher Tier (9-1)

GCSE Maths: Advanced Graph Skills

Learn to use graphs to find approximate solutions to equations, estimate the gradient of a curve at a point, and estimate the area under a curve using the trapezium rule.

A close-up photograph of a student's desk with a hand-drawn graph on paper, a pencil drawing a tangent line to a curve, and a ruler lying nearby. The light is focused and highlights the tools and the precision required for the task.

Management & Tools

Deck Contents

27 Cards
Lesson#1
Welcome to this deck on advanced graph skills. You'll learn how to use graphs to solve equations, how to find the gradient of a curve at a specific point, and how to estimate the area under a curve. These are powerful techniques used in many areas of maths and science.
Lesson#2
Let's start with solving equations. You can find approximate solutions to an equation by looking at where two related graphs cross over, or intersect.
Quiz#3
The intersection points of the graphs y equals f of x and y equals g of x represent the solutions to what equation?

f of x equals g of x

Quiz#4
Which coordinate of an intersection point gives the solution to an equation like f of x equals g of x?

the x-coordinate

Lesson#5
For example, to solve the equation x squared equals 2x plus 1, you would draw the graph of y equals x squared, and the graph of y equals 2x plus 1. The x-values where they cross are your solutions.
Lesson#6
Sometimes, you need to rearrange an equation first to see which two graphs you need to draw. For example, to solve x cubed minus 4 equals 2x, you could rearrange it to x cubed equals 2x plus 4. Then you just need to draw the line y equals 2x plus 4 on the same axes as the graph of y equals x cubed.

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