Read values and trends from a line graph of data over time, work out rises and falls, and say what a pattern does and does not tell you. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page.
Objectives
Read and compare values on a line graph and a time series.
Work out a rise, a fall and a mean rate of change.
Describe a trend and a repeating pattern without over claiming.
Key points
Read a value from a line graph after checking the scale on both axes.
Work out a rise or fall by subtracting the earlier reading from the later one.
Find a mean rate of change by dividing the total change by the time taken.
Describe a trend and a repeating pattern, and treat a prediction as an estimate.
Worked examples
Example 1
Monthly rainfall in millimetres is: January 40, February 55, March 35, April 50. By how much did the rainfall fall between February and March?
2 marks
A fall is the earlier reading minus the later reading
February is 55 and March is 35, so 55 - 35
55 - 35 = 20, so the rainfall fell by 20 mm
Answer: 20
Common slips
Slip: Add the two readings A fall is a difference, not a total.
Slip: 40 - 35 The question names February and March.
Slip: 55 - 35 = 25 Check the subtraction: 55 - 35 is 20.
Example 2
The temperatures at 9 am, 10 am, 11 am and 12 noon are 12, 14, 18 and 21 degrees. What is the mean rise per hour?
2 marks
Total rise: 21 - 12 = 9 degrees
Time taken: 9 am to 12 noon is 3 hours
Mean rise per hour: 9 ÷ 3 = 3 degrees
Answer: 3
Common slips
Slip: Total rise: 21 + 12 = 33 degrees A rise is the later reading minus the earlier reading.
Slip: Time taken: 4 hours because there are 4 readings Count the hours between the first and last reading.
Slip: Mean rise per hour: 9 ÷ 4 = 2.25 degrees Divide by the number of hours, not the number of readings.
Example 3
Quarterly sales in thousands of pounds in year 1 are 20, 35, 25, 30 and in year 2 are 24, 39, 29, 34. Each quarter keeps rising by the same amount each year. Predict the sales in the second quarter of year 3. What is the answer?
3 marks
Compare the same quarter in two years: 24 - 20 = 4
Quarter 2 in year 2 was 39
Add the yearly rise: 39 + 4 = 43
Answer: 43
Common slips
Slip: Compare neighbouring quarters: 35 - 20 = 15 The pattern repeats by quarter, so compare like with like.
Slip: Quarter 2 in year 2 was 35 Year 2 quarter 2 is the second value in the second list.
Slip: Add the yearly rise: 35 + 4 = 39 Start from the latest year, which is year 2.
Questions and answers
GCSE Maths line graphs and time series questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
a shop's sales (in £100) each month are January 34, February 41, March 29, April 38, May 45. What were the lowest sales?
Show answer
Answer: 29
Look for the smallest value in the list.
The smallest value is 29.
M1 — Look for the smallest value in the list.
A1 — Answer 29
Question 2 Easy2 marks
a shop's sales (in £100) each month are January 52, February 47, March 49, April 44, May 51. What were the lowest sales?
Show answer
Answer: 44
Look for the smallest value in the list.
The smallest value is 44.
M1 — Look for the smallest value in the list.
A1 — Answer 44
Question 3 Medium2 marks
The temperatures at 9 am, 10 am, 11 am, 12 pm and 1 pm are 10, 12, 17, 19, 20 degrees. What is the biggest rise between two neighbouring times?
Show answer
Answer: 5
Work out each rise: 2, 5, 2, 1.
The biggest is 5.
M1 — Work out each rise: 2, 5, 2, 1.
A1 — Answer 5
Question 4 Medium2 marks
The height of a plant (cm) at the end of each week for 5 weeks is 8, 11, 15, 17, 20. What was the mean growth per week?
Show answer
Answer: 3
Total growth: 20 - 8 = 12.
Divide by 4 weeks: 12 ÷ 4 = 3.
M1 — Total growth: 20 - 8 = 12.
A1 — Answer 3
Question 5 Hard2 marks
Quarterly sales (in £1000) for year 1 are 30, 45, 35, 40 and for year 2 are 35, 50, 40, 45. Each quarter has gone up by the same amount as the year before. Predict the sales in the second quarter of year 3. What is the answer?
Show answer
Answer: 55
Each quarter rose by 5 from year 1 to year 2.
Quarter 2 in year 2 was 50.
50 + 5 = 55.
M1 — Each quarter rose by 5 from year 1 to year 2.
A1 — Answer 55
Question 6 Hard2 marks
Quarterly sales (in £1000) for year 1 are 12, 20, 16, 24 and for year 2 are 15, 23, 19, 27. Each quarter has gone up by the same amount as the year before. Predict the sales in the second quarter of year 3. What is the answer?
Show answer
Answer: 26
Each quarter rose by 3 from year 1 to year 2.
Quarter 2 in year 2 was 23.
23 + 3 = 26.
M1 — Each quarter rose by 3 from year 1 to year 2.
A1 — Answer 26
Question 7 Exam-style3 marks
A plant is 8 cm tall in week 1 and 20 cm tall in week 5. Work out the mean growth each week.
Show answer
Answer: 3
Total growth: 20 - 8 = 12 cm.
Weeks between: 5 - 1 = 4.
12 ÷ 4 = 3 cm each week.
M1 — 20 - 8 = 12
M1 — Divides by 4 weeks
A1 — 3
Common mistakes
Most lost marks on this topic are one slip.
Adding two readings to find a rise
A rise is the later reading minus the earlier reading
Dividing a change by the number of readings
Divide by the time between the first and last reading
Reading the scale as steps of 1 when the grid goes up in 5s
Work out what each small square is worth before reading
Spot the slip
A line graph shows temperature at 9 am as 12 degrees and at 11 am as 18 degrees. Ben says the temperature rose by 30. What went wrong?
He added the two readings instead of subtracting
He should have divided 18 by 12
The rise must be 12
Show the slip
He added the two readings instead of subtracting 18 - 12 = 6, so the rise is 6 degrees.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.