YEAR 11 · PROOF AND CIRCLE GEOMETRY

Topic review.

Connect the key ideas, then choose a practice paper.

01 / 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.

02 / PRACTICE TESTS

Choose a paper and show your working.

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

SACE Board of South Australia

Stage 1 Mathematics: geometric reasoning and real-number/proof material, regrouped into a school chapter; all exercises are original.