Year 11 rates of change and areas under graphs test to download as PDF

This Year 11 rates of change and areas under graphs test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 15-16, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Distance-time graph
A graph has corner points \((0,0)\), \((1.5,45)\), \((2,45)\), \((3.5,90)\) with time in hours and distance in km.
1. Find the speed in the first section. (1 mark)
2. What happens between 1.5 and 2 hours? (1 mark)
3. Find the average speed for the whole journey. (2 marks)
Question 2 – Units
Convert and calculate.
1. 90 km/h into m/s. (2 marks)
2. 12 m/s into km/h. (2 marks)
Question 3 – Area under a graph
A velocity-time graph has corner points \((0,0)\), \((6,18)\), \((14,18)\), \((20,0)\) with time in seconds and velocity in m/s.
1. Find the acceleration in the first 6 seconds. (1 mark)
2. Find the total distance travelled. (3 marks)
Question 4 – Rate
A graph shows that 150 litres flow into a tank in 5 minutes at a steady rate.
1. Find the rate in litres per minute. (1 mark)
2. How long does a 600-litre tank take to fill? (1 mark)
3. What does a steeper line mean? (2 marks)
Question 5 – Trapezium estimate (Higher)
A particle has speed 0, 8, 11, 12 m/s at times 0, 3, 6, 9 seconds.
1. Use trapezia to estimate the distance travelled. (3 marks)
2. State whether it is an under- or overestimate and why. (1 mark)

How to use this Year 11 rates of change and areas under graphs test

First, revise with the rates of change and areas under graphs lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the rates of change and areas under graphs test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 11 rates of change and areas under graphs test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Rates of change and areas under graphs – Year 11 GCSE maths test to download as PDF

Question 1 – Distance-time graph

Question 2 – Units

Question 3 – Area under a graph

Question 4 – Rate

Question 5 – Trapezium estimate (Higher)

How to use this Year 11 rates of change and areas under graphs test

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