Real Polynomials — Topic Review | Year 12

QUICK RECAP

Connect the ideas

Write polynomials in descending powers and include zero coefficients when dividing.

A root a corresponds to a factor x-a; repeated roots affect crossing behaviour.

Use identities, division and the remainder/factor theorems with clear justification.

Check real solutions, intercepts, multiplicities and leading-term behaviour together.

Complete each paper and show your working.

Real Polynomials — Practice Test 1
10 questions · 43 marks · 65 minutes · Scientific calculator
Build from polynomial operations to factor theorems, graphs and a volume application.
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Real Polynomials — Practice Test 2
10 questions · 45 marks · 65 minutes · Scientific calculator
Use identities, remainders and repeated roots to reason about polynomial structure.
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Real Polynomials — Practice Test 3
10 questions · 51 marks · 65 minutes · Scientific calculator
Apply polynomial models to geometry, intersections and reconstruction problems.
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Real Polynomials — Practice Test 4
10 questions · 45 marks · 65 minutes · Scientific calculator
Explain why polynomial methods work, and diagnose claims that need stronger justification.
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Real Polynomials — Practice Test 5
10 questions · 49 marks · 75 minutes · Scientific calculator
Connect exact algebra, restricted domains and numerical evidence without losing solutions.
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Real Polynomials — Practice Test 6
10 questions · 58 marks · 75 minutes · Scientific calculator
Combine coefficient constraints, repeated-root arguments and parameter-dependent real roots.
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