IGCSE Math RevisionQuestion 1
A car travels \(180\) km in \(2\) hours \(15\) minutes.
Work out its average speed in km/h.
Show the worked answer
- \(2\) hours \(15\) minutes \(= 2.25\) hours.
- Speed \(= 180 \div 2.25 = 80\) km/h.
Answer: \(80\) km/h
Cambridge IGCSE Maths (0580) · Topic 1: Number · 1.12
Cambridge IGCSE Maths 0580 Rates and Compound Measures Questions
Rates and Compound Measures 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.
- 10 questions
- 9 Core
- 1 Extended
- 3 non-calculator
- Free, no sign-in
What the syllabus asks
- 1.12 Rates Core Extended
Common measures of rate, and other rates such as density, pressure and population density; Average speed.
Extended also: Convert between units, including units of rate.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Rates and Compound Measures questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
A metal block has a mass of \(540\) g and a volume of \(200\) cm³.
Work out its density.
Show the worked answer
- Density \(= \frac{\text{mass}}{\text{volume}} = \frac{540}{200} = 2.7\) g/cm³.
Answer: \(2.7\) g/cm³
Question 3
A tap fills a tank at a rate of 4.5 litres per minute. How long does it take to fill 72 litres?
Show the answer and mark scheme
- M1 72 ÷ 4.5
- A1 16 minutes
Answer: \(16\) minutes
Question 4
A tap fills a tank at \(12\) litres per minute. The tank holds \(450\) litres.
How long does it take to fill the empty tank? Give your answer in minutes and seconds.
Show the worked answer
- \(450 \div 12 = 37.5\) minutes.
- \(0.5\) minutes \(= 30\) seconds.
Answer: \(37\) minutes \(30\) seconds
Question 5
A force of \(600\) newtons acts on an area of \(0.25\) m².
Work out the pressure in N/m². (Pressure \(= \frac{\text{force}}{\text{area}}\).)
Show the worked answer
- Pressure \(= 600 \div 0.25 = 2400\) N/m².
Answer: \(2400\) N/m²
Question 6
A region has a population of \(2.4\) million people and an area of \(1600\) km².
Work out the population density.
Show the worked answer
- Population density \(= \frac{\text{population}}{\text{area}} = \frac{2\,400\,000}{1600} = 1500\) people per km².
Answer: \(1500\) people per km²
Question 7
A cyclist rides at an average speed of 18 km/h for 40 minutes. How far does she ride?
Show the answer and mark scheme
- M1 18 × 40/60 oe
- A1 12 km
Answer: \(12\) km
Question 8
A force of 360 newtons acts on an area of \(0.25\text{ m}^2\). Work out the pressure, using pressure \(=\) force \(\div\) area.
Show the answer and mark scheme
- M1 360 ÷ 0.25
- A1 1440 N/m²
Answer: \(1440\text{ N/m}^2\)
Question 9
Asha drives \(60\) km at \(40\) km/h and then \(90\) km at \(60\) km/h.
Work out her average speed for the whole journey.
Show the worked answer
- Time for the first part: \(60 \div 40 = 1.5\) h. Second part: \(90 \div 60 = 1.5\) h.
- Total distance \(150\) km in \(3\) h.
- Average speed \(= 150 \div 3 = 50\) km/h (not the mean of \(40\) and \(60\)).
Answer: \(50\) km/h
Rates and Compound Measures questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 10
A train travels at \(72\) km/h.
(a) Change \(72\) km/h to metres per second.
(b) How long does the train take to travel \(350\) m?
Show the worked answer
- (a) \(72\) km/h \(= 72\,000\) m in \(3600\) s, so \(72\,000 \div 3600 = 20\) m/s.
- (b) Time \(= 350 \div 20 = 17.5\) seconds.
Answer: (a) \(20\) m/s (b) \(17.5\) s
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).
Keep going
- Number practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Number revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test rates and compound measures?
Rates and Compound Measures is on both tiers (syllabus 1.12), 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.
Are these Cambridge past-paper questions?
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.
Where can I practise more rates and compound measures questions?
In the 0580 practice for topic 1 (Number), 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.