01 / QUICK RECAP
Connect the ideas.
- Average change gives a secant gradient; a derivative gives a local tangent gradient.
- Find a tangent point from f and its gradient from f′.
- Classify stationary points by a sign change, not merely f′=0.
- Model the objective in one variable and check the physical domain and boundaries.
- Velocity is signed; speed and total distance are nonnegative.
02 / PRACTICE TESTS
Put it together.
Choose a paper and show your working.
Introduction to calculus — Topic test 1
A balanced first paper: rates, derivative rules, tangent lines, graph behaviour, optimisation and motion.
10 questions · 48 marks · 65 minutes · Scientific calculatorIntroduction to calculus — Topic test 2
Move between numerical data, derivative information and polynomial graphs, then interpret models.
10 questions · 52 marks · 65 minutes · Scientific calculatorIntroduction to calculus — Topic test 3
Select and evaluate constrained models, including non-turning stationary points and boundary optima.
10 questions · 52 marks · 65 minutes · Scientific calculatorIntroduction to calculus — Topic test 4
Analyse different representations, tangent conditions, changes of direction and the validity of solutions.
10 questions · 49 marks · 65 minutes · Scientific calculatorIntroduction to calculus — Topic test 5
A harder synthesis paper with exact tangent conditions, parameters, weighted constraints and model evaluation.
10 questions · 56 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 Mathematics topic 6: rates of change, derivatives and applications. Introductory polynomial calculus with explicit modelling and interpretation.
Official curriculum source ↗