IB Math AA SL Unit 5: Calculus

IB Maths AA SL Unit 5: Calculus, topic by topic

Each topic in this unit has a free page with step-by-step worked examples and the key formulas, then exam-style questions with mark schemes.

• Applications of Differentiation questions42 questions · 3 worked examples
• Definite Integrals questions32 questions · 3 worked examples
• Graphical Behaviour and the Second Derivative questions22 questions · 3 worked examples
• Integration questions41 questions · 3 worked examples
• Kinematics questions34 questions · 3 worked examples
• Limits and Rates of Change questions41 questions · 2 worked examples
• Rules of Differentiation questions51 questions · 3 worked examples

Learn it first: AA SL Unit 5 notes

• Kinematics

Where marks go in AA SL Unit 5

From the IB subject reports we summarise on AA SL Examiner Insights, in our own words:

• Kinematics: speed vs velocity, change of direction, distance vs displacement. Speed is |v|: graph |v| (or check the largest and smallest v) over the whole interval. Change of direction means v = 0 with a sign change. Distance is ∫|v| dt. Radians for calculus.
• Integration: missing +C, substituting into the derivative, and area limits. From f′ to f: integrate, add + C, use the given point to find C, then write f(x) = … in full. For a definite integral, write F(upper) − F(lower) with both values shown.
• Modelling in context: not setting up the expression, and answers that ignore the context. Translate the words first: fastest rate means maximise the derivative; closest means minimise a distance. End with a sentence in the units and form the context needs (a year, a whole number, one value).

The questions here are original, written in the style of IB papers with IB-style mark schemes; for real papers see the IB Maths AA SL past papers page.

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