Use the three compound-measure formulae, keep units consistent, and handle times given in hours and minutes. It is on Foundation and Higher, aimed at grade 5. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Three formula triangles, one idea: speed=timedistance, density=volumemass, pressure=areaforce. Cover the one you want. Units must match: km/h with km and hours; g/cm³ with grams and cm³, never g/m³ for a metal cuboid.
A two-part journey is not the average of the two speeds unless the times (or distances) are equal. Total distance over total time is the only average speed that is honest. Compound shapes: find the volume first, then density =m/V.
The three formulae are rearrangements of the same triangle: s=td, d=vm, p=AF. Convert hours and minutes before you divide. Density of a metal cuboid is g/cm³ (or kg/m³), never g/m³.
Objectives
Find a speed in km/h.
Find a density in g/cm³.
Find a pressure, and a distance from speed and time.
Key points
Use speed = distance ÷ time and rearrange it for distance or time.
Use density = mass ÷ volume and pressure = force ÷ area, and rearrange them.
Convert minutes to a decimal number of hours (45 minutes =0.75 h) and back.
Work out average speed for a journey in stages using total distance ÷ total time.
Worked examples
Example 1
A car travels 180 km in 3 hours. Work out its average speed.
2 marks
Recall speed formula: speed = distance / time.
Divide distance by time: 180 / 3 = 60 km/h.
The speed is 60 km/h.
Answer: 60
Common slips
Slip: Multiply distance by time directly. Speed is the rate of distance covered per unit of time.
Slip: Ben multiplied 180 × 3 = 540. Multiplication gives km·hours, which is not speed.
Slip: Conclude 540 km/h. 180 divided by 3 gives 60.
Example 2
A block has mass 250 g and volume 50 cm³. Work out its density in g/cm³.
2 marks
Recall density formula: density = mass / volume.
Divide mass by volume: 250 / 50 = 5 g/cm³.
The density is 5 g/cm³.
Answer: 5
Common slips
Slip: Subtract volume from mass. Density measures mass per unit volume via division.
Slip: Cara subtracted 250 - 50 = 200. Subtraction does not calculate density.
Slip: Conclude 200 g/cm³. 250 divided by 50 gives 5.
Example 3
A van travels at 60 km/h for 3 hours. Work out the distance it travels.
3 marks
Recall distance formula: distance = speed × time.
Multiply speed by time: 60 × 3 = 180 km.
The distance is 180 km.
Answer: 180
Common slips
Slip: Divide speed by time. Total distance covered is speed multiplied by elapsed time.
Slip: Dan divided 60 / 3 = 20. Division gives km/h per hour, not distance.
Slip: Conclude 20 km. 60 multiplied by 3 gives 180.
Questions and answers
GCSE Maths speed, density and pressure questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A train travels 240 km in 4 hours. Work out its average speed in km/h.
Show answer
Answer: 60
Formula: speed = distance / time.
Calculate 240 / 4 = 60 km/h.
M1 — Formula: speed = distance / time.
A1 — Calculate 240 / 4 = 60 km/h.
Question 2 Easy2 marks
A coach travels 150 km in 2 hours. Work out its average speed in km/h.
Show answer
Answer: 75
Formula: speed = distance / time.
Calculate 150 / 2 = 75 km/h.
M1 — Formula: speed = distance / time.
A1 — Calculate 150 / 2 = 75 km/h.
Question 3 Medium2 marks
A stone has mass 120 g and volume 40 cm³. Work out its density in g/cm³.
Show answer
Answer: 3
Formula: density = mass / volume.
Calculate 120 / 40 = 3 g/cm³.
M1 — Formula: density = mass / volume.
A1 — Calculate 120 / 40 = 3 g/cm³.
Question 4 Medium2 marks
A metal bar has mass 80 g and volume 20 cm³. Work out its density in g/cm³.
Show answer
Answer: 4
Formula: density = mass / volume.
Calculate 80 / 20 = 4 g/cm³.
M1 — Formula: density = mass / volume.
A1 — Calculate 80 / 20 = 4 g/cm³.
Question 5 Hard2 marks
A lorry travels at 40 km/h for 5 hours. Work out the distance it travels.
Show answer
Answer: 200
Formula: distance = speed × time.
Calculate 40 × 5 = 200 km.
M1 — Formula: distance = speed × time.
A1 — Calculate 40 × 5 = 200 km.
Question 6 Hard2 marks
A car travels at 70 km/h for 2 hours. Work out the distance it travels.
Show answer
Answer: 140
Formula: distance = speed × time.
Calculate 70 × 2 = 140 km.
M1 — Formula: distance = speed × time.
A1 — Calculate 70 × 2 = 140 km.
Question 7 Exam-style2 marks
A metal block has mass 120 g and volume 30 cm³. Work out its density in g/cm³.
Show answer
Answer: 4
Density = mass ÷ volume.
Substitute: 120 ÷ 30 = 4 g/cm³.
M1 — 120 ÷ 30
A1 — 4
Common mistakes
Most lost marks on this topic are one slip.
Multiplying distance by time to get speed
Divide distance by time
Subtracting mass and volume
Divide mass by volume, in g/cm³
Dividing speed by time when the question asks for distance
Multiply speed by time
Spot the slip
A car travels 180 km in 3 hours. Ada multiplies and says the speed is 540 km/h. What is the average speed?
60
540
183
Show the slip
60 Speed is distance divided by time: 180 ÷ 3 = 60 km/h.
Exam tips
A calculator is useful here. Show the calculation you typed, not only the final line.
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.
Write the formula in words before you substitute; the marker can then award the method mark even if a number slips.
Put units on every line, not just the answer — it stops you dividing km by minutes by accident.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.