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.
Put it together.
Choose a paper and show your working.
Real Polynomials — Practice Test 1
Build from polynomial operations to factor theorems, graphs and a volume application.
10 questions · 43 marks · 65 minutes · Scientific calculatorReal Polynomials — Practice Test 2
Use identities, remainders and repeated roots to reason about polynomial structure.
10 questions · 45 marks · 65 minutes · Scientific calculatorReal Polynomials — Practice Test 3
Apply polynomial models to geometry, intersections and reconstruction problems.
10 questions · 51 marks · 65 minutes · Scientific calculatorReal Polynomials — Practice Test 4
Explain why polynomial methods work, and diagnose claims that need stronger justification.
10 questions · 45 marks · 65 minutes · Scientific calculatorReal Polynomials — Practice Test 5
Connect exact algebra, restricted domains and numerical evidence without losing solutions.
10 questions · 49 marks · 75 minutes · Scientific calculatorReal Polynomials — Practice Test 6
Combine coefficient constraints, repeated-root arguments and parameter-dependent real roots.
10 questions · 58 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Board of South Australia
A recognisable real-polynomial chapter supporting Stage 2 Specialist polynomial factorisation and graph analysis; original lessons use current SACE scope and the school chapter structure requested by the user.
Official curriculum source ↗