Year 9 Ratio and Proportion Worksheet - Intermediate

Year 9 Ratio and Proportion worksheet for Year 9 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Ratio and Proportionintermediate

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Year 9 Ratio & Proportion: Make the Connections

Ages 13–14 | Intermediate | UK National Curriculum

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Instructions: Work through each activity, showing clear working in the answer boxes. Include units where appropriate and give a brief reason when interpreting a graph. Check that your answers are sensible in context.

Inverse Proportion in Context

For each problem, identify the quantities that vary inversely. Use a constant product or an equivalent method, then show your working and include units. Check that your answer makes sense.

1. Six identical pumps empty a tank in 14 hours. How long would 8 pumps take? [3 marks]

2. A journey takes 3 hours at an average speed of 80 km/h. How long would the same journey take at 96 km/h? [3 marks]

3. Twelve workers complete a job in 15 days. At the same rate, how many days would 20 workers take? [3 marks]

4. The pressure on a fixed area is 240 kPa when a force of 600 N is applied. What pressure results from a force of 900 N on the same area? [3 marks]

Compound Measures: Speed, Density and Pressure

Use the relevant relationship: speed = distance ÷ time, density = mass ÷ volume, and pressure = force ÷ area. Rearrange the relationship if needed, show your calculation and include the correct units.

1. A cyclist travels 27 km in 1.5 hours. Calculate the average speed in km/h. [2 marks]

2. A metal block has a mass of 540 g and a volume of 200 cm³. Calculate its density in g/cm³. [2 marks]

3. A force of 1,200 N acts on an area of 0.4 m². Calculate the pressure in N/m². [2 marks]

4. A car travels at 18 m/s for 25 seconds. Calculate the distance travelled in metres. [2 marks]

Similar Shapes and Scale Factors

Corresponding lengths in similar shapes are related by the linear scale factor. Remember that area scales by the square of the linear scale factor. Show the factor you use and include units in your answers.

1. Two similar triangles have corresponding sides of 6 cm and 15 cm. The smaller triangle has another side of 8 cm. Find the corresponding side of the larger triangle. [2 marks]

2. A photograph is enlarged using a linear scale factor of 1.5. Its original width is 12 cm. Find the enlarged width. [2 marks]

3. Two similar shapes have a linear scale factor of 3 from the smaller shape to the larger shape. The smaller shape has area 14 cm². Find the larger area. [3 marks]

4. A model car is 9 cm long. The real car is 4.5 m long. Find the scale factor from model to real car, using the same units. [3 marks]

Recognising Direct and Inverse Proportion

For each relationship, decide whether it is direct or inverse proportion. Use the paired values to test for a constant ratio or a constant product. Then complete the statement or calculation requested.

1. For a fixed-price item, the cost is £4 for 2 items, £10 for 5 items and £16 for 8 items. Is cost directly proportional to the number of items? State the constant of proportionality in pounds per item. [2 marks]

2. For a fixed journey, speed and time are paired as (40 km/h, 6 h), (60 km/h, 4 h) and (80 km/h, 3 h). Is speed inversely proportional to time? Give the constant product. [2 marks]

3. Which relationship has a straight-line graph through the origin: y is directly proportional to x, or y is inversely proportional to x? [1 mark]

4. The graph of y = k/x passes through the point (4, 6). Find k, then find y when x = 8. [3 marks]

Interpret Proportion Data

Read the table carefully. For direct proportion, compare each output with its input; for inverse proportion, multiply the paired values. Answer the questions using the table and show any calculations.