Introduction to calculus — Topic Review | Year 11

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.

Complete each paper and show your working.

Introduction to calculus — Topic test 1
10 questions · 48 marks · 65 minutes · Scientific calculator
A balanced first paper: rates, derivative rules, tangent lines, graph behaviour, optimisation and motion.
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Introduction to calculus — Topic test 2
10 questions · 52 marks · 65 minutes · Scientific calculator
Move between numerical data, derivative information and polynomial graphs, then interpret models.
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Introduction to calculus — Topic test 3
10 questions · 52 marks · 65 minutes · Scientific calculator
Select and evaluate constrained models, including non-turning stationary points and boundary optima.
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Introduction to calculus — Topic test 4
10 questions · 49 marks · 65 minutes · Scientific calculator
Analyse different representations, tangent conditions, changes of direction and the validity of solutions.
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Introduction to calculus — Topic test 5
10 questions · 56 marks · 75 minutes · Scientific calculator
A harder synthesis paper with exact tangent conditions, parameters, weighted constraints and model evaluation.
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