Speed density and pressure
Ratio, proportion and rates of change
- Crossover
- Non-calculator
- 8 questions
- 29 marks
Questions marked Higher are aimed at the Higher tier.
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
-
A journey of $150$ km takes $3$ hours. Find the average speed.
2 marks
-
A block has mass $240$ g and volume $80$ cm$^{3}$. Find the density.
2 marks
-
A force of $400$ N acts on an area of $8$ m$^{2}$. Find the pressure.
3 marks
-
A car travels at $60$ km/h for $2.5$ hours. How far does it travel?
3 marks
-
A block has mass $540$ g and density $2.7$ g/cm$^{3}$. Find the volume.
4 marks
-
A journey of $45$ miles takes $1$ hour $30$ minutes. Find the average speed in miles per hour.
4 marks
-
A metal prism has volume $125$ cm$^{3}$ and density $8$ g/cm$^{3}$. Find the mass. The metal is recast as a cube. Find the side length of the cube. Higher
5 marks
-
A cyclist travels $12$ km at $16$ km/h and then $20$ km at $10$ km/h. Find the time for each part and the average speed for the whole journey, as a mixed number. Explain why the average speed is not the mean of $16$ and $10$. Higher
6 marks
Mark scheme
-
Answer. $50$ km/h
- Speed $= \dfrac{\text{distance}}{\text{time}}$
- $\dfrac{150}{3} = 50$ km/h
-
Answer. $3$ g/cm$^{3}$
- Density $= \dfrac{\text{mass}}{\text{volume}}$
- $\dfrac{240}{80} = 3$ g/cm$^{3}$
-
Answer. $50$ N/m$^{2}$
- Pressure $= \dfrac{\text{force}}{\text{area}}$
- $\dfrac{400}{8} = 50$ N/m$^{2}$
-
Answer. $150$ km
- Distance $= \text{speed} \times \text{time}$
- $60 \times 2.5 = 150$ km
-
Answer. $200$ cm$^{3}$
- Volume $= \dfrac{\text{mass}}{\text{density}}$
- $\dfrac{540}{2.7} = 200$ cm$^{3}$
-
Answer. $30$ mph
- $1$ hour $30$ minutes $= 1.5$ hours.
- $\dfrac{45}{1.5} = 30$ mph
-
Answer. Mass $1000$ g, side $5$ cm
- Mass $= 125 \times 8 = 1000$ g.
- The volume is still $125$ cm$^{3}$.
- $5^{3} = 125$, so the side is $5$ cm.
-
Answer. Times $\dfrac{3}{4}$ hour and $2$ hours. Average speed $11\dfrac{7}{11}$ km/h. The slower part took longer.
- First time $= \dfrac{12}{16} = \dfrac{3}{4}$ hour.
- Second time $= \dfrac{20}{10} = 2$ hours.
- Average speed $= \dfrac{32}{2.75} = \dfrac{128}{11} = 11\dfrac{7}{11}$ km/h.
- The mean of the speeds would give equal weight to each part, but the slower part lasted longer.