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Pie Charts

FoundationHigherAQAEdexcelOCR

Get to grips with pie charts using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on drawing and interpreting pie charts, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Each angle is the category's fraction of the total times 360°.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A pie chart shows proportions as sectors of a circle. The whole circle represents the total, and each sector's angle is proportional to its share.

Since a full circle is \(360^\circ\), each item is worth \(\frac{360}{\text{total}}\) degrees. Multiplying that by each frequency gives the angle for each sector.

Working out the degrees-per-item first is the reliable method, and the angles should always sum to \(360^\circ\). That check catches arithmetic errors before you draw anything.

Revision notes

Calculating the angles

Divide \(360\) by the total frequency to find the degrees per item, then multiply by each frequency.

For a total of \(40\), each item is \(9^\circ\). A frequency of \(12\) therefore gives a sector of \(108^\circ\).

Checking and drawing

The angles must add to \(360^\circ\). Draw them with a protractor, working round from a single radius.

Label each sector or provide a key, and keep the sectors in the order given in the table.

Interpreting a pie chart

To find a frequency from an angle, divide the angle by the degrees per item.

Without the total, a pie chart shows only proportions, so two pie charts cannot be compared directly unless their totals are known.

Key points

  • A pie chart shows proportions of a total.
  • The whole circle is \(360^\circ\).
  • Degrees per item is \(\frac{360}{\text{total}}\).
  • Multiply by each frequency for its angle.
  • The angles must sum to \(360^\circ\).
  • Label every sector or provide a key.

Worked examples

Example 1

A total of \(60\) is shown in a pie chart. Find the angle for one item.

Working

\[360 \div 60\]divide 360 by the total
\[= 6^\circ \text{ per item}\]state the degrees per item

Example 2

Using that, find the angle for a frequency of \(15\).

Working

\[15 \times 6\]multiply the frequency by the degrees per item
\[= 90^\circ\]state the sector angle

Example 3

A sector is \(72^\circ\) in a pie chart with total \(30\). Find the frequency.

Working

\[360 \div 30 = 12^\circ \text{ per item}\]find the degrees per item
\[72 \div 12\]divide the angle by the degrees per item
\[= 6\]state the frequency

Common mistakes

  • Forgetting to check the angles sum to 360.

    This check catches arithmetic errors before you draw.

  • Comparing two pie charts without knowing the totals.

    A pie chart shows proportions, so equal sectors can represent different frequencies.

  • Rounding the degrees per item too early.

    Keep full accuracy and round only the final angles.

  • Not labelling the sectors.

    Each sector needs a label or the chart needs a key.

Exam tips

  • Work out the degrees per item first.
  • Check your angles total 360 before drawing.
  • Use a protractor and work round from one radius.
  • Label every sector clearly.

Key terms

Pie chart
A circular chart showing proportions as sectors.
Sector
A slice of the pie chart.
Proportion
A share of the whole.
Degrees per item
360 divided by the total frequency.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.