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GCSEMathsEdexcelHigherRevision Notes2. AlgebraEstimating Gradients & Areas under GraphsFinding Areas under Graphs

Finding Areas under Graphs (Edexcel GCSE Maths)

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Finding Areas under Graphs

How do I estimate the area under a graph?

  • To find an estimate for the area:

    • Split area into vertical strips

    • Draw straight lines between the tops of the strips

    • Find area of strips (trapeziums) using Area = ½(a + b)h

    • Add the areas

How do I know if my answer is an underestimate or an overestimate?

  • A common exam question is to ask if your estimate of the area is an underestimate or an overestimate

  • To answer this, simply look at the straight lines joining the tops of your strips

    • If the straight lines are below the curve, it is an underestimate

    • If the straight lines are above the curve, it is an overestimate

  • In your exam, the lines will all be below or all be above the curve- though it may be difficult to tell which for some strips

Examiner Tips and Tricks

  • This is particularly useful when working with speed-time and distance-time graphs if they are curves and not straight lines.

Worked Example

The graph below shows y equals cube root of x for 0 less or equal than x less or equal than 1

Graph showing a concave curve from the origin, increasing from y=0 at x=0 to y=1 at x=1, on a grid with labelled axes. This is the graph of the cube root of x.

Find an estimate for the area between the curve, the x axis and the line x equals 1. Use four strips of equal width.

Split the area into four strips using the width of 0.25 for each one

Find the y coordinate at the end of each strip by reading the value from the graph or substituting the x coordinate into y equals cube root of x

EAG-REWRITTEN-Example-5-3-20-Diagram-2, downloadable IGCSE & GCSE Maths revision notes

Find the area of each strip by using the formula for the area of a trapezium

1 half open parentheses 0 plus 0.63 close parentheses open parentheses 0.25 close parentheses plus 1 half open parentheses 0.63 plus 0.79 close parentheses open parentheses 0.25 close parentheses plus 1 half open parentheses 0.79 plus 0.91 close parentheses open parentheses 0.25 close parentheses plus 1 half open parentheses 0.91 plus 1 close parentheses open parentheses 0.25 close parentheses equals 0.7075

Area almost equal to 0.708

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    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.