Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.9
Real-Life Graphs questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
A conversion graph is a straight line through \((0, 0)\) and \((50, 80)\). It changes miles (across) to kilometres (up).
Use it to change
(a) \(25\) miles to kilometres
(b) \(120\) kilometres to miles.
Answer: (a) \(40\) km (b) \(75\) miles
Sam's walk is shown on a distance-time graph made of straight lines joining \((0, 0)\), \((20, 1.5)\), \((35, 1.5)\) and \((60, 0)\). Time is in minutes and distance from home in kilometres.
(a) For how long did Sam stop?
(b) Work out Sam's speed on the way home in km/h.
Answer: (a) \(15\) minutes (b) \(3.6\) km/h
The graph of a taxi fare against distance is a straight line from \((0, 3)\) to \((10, 21)\), where the distance is in km and the fare is in dollars.
(a) Write down the fixed charge.
(b) Work out the charge per kilometre.
Answer: (a) \(\$3\) (b) \(\$1.80\)
A cyclist's journey is shown by straight lines joining \((0, 0)\), \((30, 12)\), \((45, 12)\) and \((75, 30)\), with time in minutes and distance in kilometres.
Work out the cyclist's average speed for the whole journey, in km/h.
Answer: \(24\) km/h
A distance–time graph shows that a car travels 120 km between 09 00 and 10 30. Work out its average speed.
Answer: \(80\) km/h
A conversion graph between miles and kilometres is a straight line through \((0, 0)\) and \((5, 8)\), with miles on the horizontal axis.
(a) Change 35 miles into kilometres.
(b) Change 100 km into miles.
Answer: (a) \(56\) km (b) \(62.5\) miles
Extended content, for Papers 2 and 4. Core students can skip these.
A car speeds up at a constant rate from rest to \(20\) m/s in \(8\) seconds.
Work out its acceleration.
Answer: \(2.5\) m/s²
A speed-time graph is made of straight lines joining \((0, 0)\), \((10, 15)\), \((40, 15)\) and \((50, 0)\), with time in seconds and speed in m/s.
Work out the total distance travelled.
Answer: \(600\) m
A speed-time graph is made of straight lines joining \((0, 4)\), \((6, 16)\) and \((16, 16)\), with time in seconds and speed in m/s.
(a) Work out the acceleration in the first \(6\) seconds.
(b) Work out the distance travelled in the \(16\) seconds.
Answer: (a) \(2\) m/s² (b) \(220\) m
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Real-Life Graphs is on both tiers (syllabus 2.9), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision