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Year 8 Maths • AC9M8M03 • Authored homework

Circumference and area of circles

Practise Circumference and area of circles through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.

10
Short-answer questions
10
Long-answer questions
1
Research/application task

Part A

Short-answer questions

  1. Find the circumference of a circle with radius 7 cm in terms of π.

  2. Find the area of a circle with diameter 10 m.

  3. Explain the difference between radius, diameter, circumference and area.

  4. A student uses 2πr for area. Correct the formula choice.

  5. Write the rule or formula most useful for Circumference and area of circles.

  6. Show how to check one answer using estimation, substitution or inverse operations.

  7. Write one common mistake students make in Circumference and area of circles and correct it.

  8. Create a small table, diagram or equation that represents this topic.

  9. State where units, exact form or rounding matter in this topic.

  10. Write one exam-style short question on Circumference and area of circles and solve it.

Part B

Long-answer questions

  1. A circular path surrounds a pond of radius 4 m and has width 1 m. Find the area of the path.

  2. Compare exact answers in terms of π with decimal approximations for two circle problems.

  3. Solve a multi-step problem involving Circumference and area of circles and explain every step clearly.

  4. Create a realistic word problem for Circumference and area of circles, solve it and interpret the answer.

  5. Compare two methods for a problem in Circumference and area of circles and explain which is more efficient.

  6. Write a worked solution that includes a check for reasonableness.

  7. Create a problem with a deliberate trap, then solve it correctly and explain the trap.

  8. Use a diagram, table, graph or equation to model a situation involving Circumference and area of circles.

  9. Explain how this topic connects to a previous Year 7 or Year 8 maths skill.

  10. Write a full-mark response to a challenging Circumference and area of circles question, including reasoning and final answer.

Part C

Research and understanding task

Research a circular object or space. Measure it and calculate circumference and area.