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Distance Charts

FoundationChallengeAQAEdexcelOCR

Get to grips with distance charts using these Foundation GCSE Maths practice questions. The worksheet focuses on reading distance charts, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Read across the row and down the column to find a distance.

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Topic overview

A distance chart is a triangular table showing the distances between several places. Each cell gives the distance between the place in its row and the place in its column.

Only half the table is needed, because the distance from A to B is the same as from B to A. Filling in both halves would simply repeat the same information.

Reading one takes care. Follow the row across and the column down until they meet, and check you have used the right pair of places. Questions often combine several readings, such as finding the total distance for a journey through two or three towns.

Revision notes

Reading a distance chart

Find one place in the rows and the other in the columns, then read where they meet.

The triangular layout means each pair appears only once, so you may need to look for the pair the other way round.

Journeys with several stages

Read each leg separately, then add them.

A journey from A to B to C uses the A–B distance and the B–C distance, added together. The direct A–C distance is usually shorter.

Comparing routes

Work out the total for each possible route and compare.

Questions often ask which route is shorter, so both totals must be calculated and the conclusion stated.

Key points

  • Each cell gives the distance between a row and a column place.
  • Only half the table is needed.
  • The distance from A to B equals B to A.
  • Read across the row and down the column.
  • Add the legs for a multi-stage journey.
  • Compare totals when choosing between routes.

Worked examples

Example 1

A chart shows London to Bristol as \(190\)km and Bristol to Cardiff as \(70\)km. Find the total for London to Cardiff via Bristol.

Working

\[190 + 70\]add the two legs
\[= 260\text{km}\]state the total distance

Example 2

Why does a distance chart only need half its cells filled?

Working

\[\text{A to B equals B to A}\]distances are the same both ways
\[\text{So the other half would repeat}\]explain the reason

Example 3

Route A is \(85 + 60\)km and route B is \(130\)km. Which is shorter?

Working

\[85 + 60 = 145\text{km}\]find the total for route A
\[130 < 145\]compare with route B
\[\text{Route B is shorter}\]state the conclusion

Common mistakes

  • Reading the wrong cell.

    Follow the row and column carefully and check both place names.

  • Adding the direct distance as well as the legs.

    A journey via another town uses only the legs travelled.

  • Assuming a direct route is always given.

    Some pairs may only be reachable via another place.

  • Not stating which route is shorter.

    Comparison questions need a conclusion, not just two totals.

Exam tips

  • Trace the row and column with a finger or ruler.
  • Check you have the right pair of places before reading.
  • Add legs separately for multi-stage journeys.
  • State a clear conclusion when comparing routes.

Key terms

Distance chart
A triangular table of distances between places.
Leg
One stage of a multi-part journey.
Route
The path taken between two places.
Direct distance
The distance between two places without stopping.

Related topics

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