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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Real-Life Graphs Questions and Answers

Real-Life Graphs questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

Practise real-life graphs in Unit 4 →Real-Life Graphs revision notes

What this topic covers

Real-Life Graphs worked examples

Worked example 1: Speed from a travel graph

A distance–time graph shows a journey of 45 km in 50 minutes at constant speed. Find the speed in km/h.

Solution

  1. 50 minutes \(=\tfrac{50}{60}\) hours.
  2. Speed \(=45\div\tfrac{5}{6}=54\) km/h.

Answer: 54 km/h

Tip: On a distance–time graph, speed is the gradient.

Worked example 2: Gradient from a tangent

A tangent drawn to a curve at \(x=3\) passes through \((2,\ 5)\) and \((4,\ 13)\). Estimate the gradient of the curve at \(x=3\).

Solution

  1. Gradient of tangent \(=\dfrac{13-5}{4-2}\).
  2. \(=4\).

Answer: 4

Tip: Use two points far apart on the tangent for accuracy.

Worked example 3: Average rate of change

Find the average rate of change of \(y=x^2+1\) between \(x=1\) and \(x=4\).

Solution

  1. \(y(1)=2\), \(y(4)=17\).
  2. Rate \(=\dfrac{17-2}{4-1}=5\).

Answer: 5

Tip: This is the gradient of the chord between the two points.

Real-Life Graphs exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

A distance–time graph shows that a cyclist travels 18 km in 45 minutes at a constant speed. Work out the speed of the cyclist in km/h.

Show the answer and mark scheme
  • M1 18 ÷ 0.75 or 18 ÷ 45 × 60
  • A1 24 cao

Answer: 24 km/h

Question 2 · medium · 3 marks

A speed–time graph is made of straight lines. A cyclist accelerates at a constant rate from rest to 12 m/s in 6 seconds and then travels at 12 m/s for a further 10 seconds. Work out the total distance travelled in these 16 seconds.

Show the answer and mark scheme
  • M1 ½ × 6 × 12 (= 36) or 12 × 10 (= 120)
  • M1 their 36 + their 120
  • A1 156 m

Answer: 156 m

Question 3 · hard · 3 marks

A speed–time graph is made of straight line segments joining the points (0, 0), (10, 15), (40, 15) and (55, 0), where time is in seconds and speed is in m/s. Work out the total distance travelled.

Show the answer and mark scheme
  • M1 area of at least one section, e.g. ½ × 10 × 15 = 75, 30 × 15 = 450 or ½ × 15 × 15 = 112.5
  • M1 complete method for the total area, e.g. ½ × (30 + 55) × 15
  • A1 637.5 m

Answer: 637.5 m

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise real-life graphs for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test real-life graphs?

Either Higher tier paper, 1H or 2H, can test real-life graphs: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more real-life graphs questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions