Rates: past paper questions

Where the questions come from

• Question 10May/June 2026, paper 43Structured4 marksHas a diagram

  Llew cycles to school. The speed–time graph shows the first 10 seconds of his journey. By drawing a suitable tangent, estimate the acceleration at $t=2$.

  Try this question
• Question 9Oct/Nov 2025, paper 41Structured2 marks

  An athlete runs at a speed of $9.5\text{ m/s}$. Convert this speed into $\text{km/h}$. An athlete runs at a speed of $9.5\text{ m/s}$.

  Try this question
• Question 14Oct/Nov 2024, paper 21Structured4 marks

  Two solid steel statues are mathematically similar. The smaller statue has height $12\text{ cm}$ and the larger statue has height $15\text{ cm}$. The larger statue has a mass $2.5\text{ kg}$.

  Try this question
• Question 11Oct/Nov 2023, paper 23Structured4 marks

  A bronze sphere has radius $3.6\text{ cm}$. The density of bronze is $8.05{\text{ g/cm}}^3$. Find the mass of the sphere.

  Try this question
• Question 4Oct/Nov 2025, paper 42Structured4 marks

  Pedro makes cards. He makes cards at a rate of 9 cards every 20 minutes. Work out the number of cards he makes in 8 hours.

  Try this question
• Question 4Oct/Nov 2024, paper 41Structured17 marks

  Enzo, Rashid and Blessy each swim as many lengths of a swimming pool as they can in 15 minutes. The results are shown in the table.

  Try this question
• Question 2May/June 2023, paper 41Structured16 marksHas a diagram

  The diagram shows a solid triangular prism $ABCDEF$ of length $15\text{ cm}$. $AB=6.4\text{ cm}$, $EB=5.7\text{ cm}$ and the volume of the prism is $145{\text{ cm}}^3$. Show that angle $EBA={32}^{\circ }$, correct to the nearest degree.

  Try this question
• Question 21Oct/Nov 2025, paper 43Structured4 marksHas a diagram

  A dressmaker takes 75 hours to make 31 dresses. In week 1, she takes a total of 12 hours 30 minutes to make the first 4 dresses. In week 2, she makes the remaining 27 dresses at a constant hourly rate.

  Try this question
• Question 1Oct/Nov 2024, paper 42Structured12 marks

  Anvi buys a new car. The price of the car is $28240$. She is given a 7.5% discount.

  Try this question
• Question 5May/June 2023, paper 42Structured13 marksHas a diagram

  A cone has base diameter $8\text{ cm}$ and perpendicular height $15\text{ cm}$. Calculate the volume of the cone.

  Try this question
• Question 3May/June 2025, paper 41Structured3 marksHas a diagram

  In the USA, one gallon of fuel costs $4.83 . In the UK, one litre of fuel costs £1.62 . The exchange rate is £1 = $1.215 . 1 gallon = 3.785 litres In which country does 1 litre of fuel cost more and by how much?

  Try this question
• Question 5Oct/Nov 2024, paper 42Structured15 marksHas a diagram

  The cumulative frequency diagram shows information about the distance travelled by each of 80 motorists in a month. Use the cumulative frequency diagram to find an estimate for the median

  Try this question
• Question 7May/June 2023, paper 42Structured11 marksHas a diagram

  The diagram shows the straight roads between town $A$, town $B$ and town $C$. $AC=60\text{ km}$, $CB=87\text{ km}$ and $B$ is due east of $A$. The bearing of $C$ from $A$ is ${038}^{\circ }$.

  Try this question
• Question 6May/June 2025, paper 42Structured3 marks

  A solid wooden cone has base radius $4\text{ cm}$ and height $12\text{ cm}$. The density of the wood is $0.74{\text{ g/cm}}^3$. Calculate the mass of the cone.

  Try this question
• Question 4Oct/Nov 2024, paper 43Structured15 marksHas a diagram

  A box contains 50 cuboids. Each cuboid has a mass of $135\text{ g}$. The total mass of the cuboids and the box is $7\text{ kg}$.

  Try this question
• Question 24May/June 2025, paper 42Structured8 marks

  Ahmed walks $2\text{ km}$ at a speed of $x\text{ km/h}$. He then walks a further $3\text{ km}$ at a speed of $(x+1)\text{ km/h}$. The total time he takes to walk the $5\text{ km}$ is $1\frac{1}{4}\text{ hours}$.

  Try this question
• Question 5Oct/Nov 2024, paper 43Structured8 marks

  Naomi runs $100\text{ m}$ in 15 seconds. Calculate Naomi's average speed in kilometres per hour.

  Try this question
• Question 7May/June 2024, paper 41Structured15 marksHas a diagram

  The diagram shows a box in the shape of a cuboid. The box is open at the top. Work out the surface area of the inside of the open box.

  Try this question
• Question 4May/June 2024, paper 42Structured15 marksHas a diagram

  The diagram shows a tank in the shape of a half-cylinder of radius 12 cm and length 1 metre. The tank is fixed horizontally and is completely filled with water. Calculate the volume of water in the tank.

  Try this question
• Question 7May/June 2024, paper 43Structured11 marks

  A car travels $50\text{ km}$ at an average speed of $75\text{ km/h}$. Find the time taken.

  Try this question