Proof and circle geometry — Topic Review | Year 11

QUICK RECAP

Connect the ideas

State the assumptions and the conclusion before beginning a proof.

An implication and its converse are different claims. One counterexample disproves a universal statement.

A diagram suggests a relationship; named theorems and a justified argument establish it.

Check the positions of circle angles and use whole secant lengths in power-of-a-point equations.

Complete each paper and show your working.

Proof and circle geometry — Practice test 1
10 questions · 48 marks · 75 minutes · By hand
A balanced paper moving from logical statements and exact number arguments to circle geometry and a final congruence proof.
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Proof and circle geometry — Practice test 2
10 questions · 52 marks · 75 minutes · By hand
A second balanced paper emphasising converse arguments, divisibility, constructions and similarity.
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Proof and circle geometry — Applications test
10 questions · 56 marks · 75 minutes · By hand
Use logical claims, exact arithmetic and circle theorems to analyse practical designs and identify errors.
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Proof and circle geometry — Reasoning test
10 questions · 52 marks · 75 minutes · By hand
Explain why methods work, judge the information in a diagram, and combine algebra with circle properties.
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Proof and circle geometry — Challenge test
10 questions · 61 marks · 75 minutes · By hand
A final synthesis paper requiring careful domains, valid converses and multi-step geometric reasoning.
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