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Pattern-Based Math Practice

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DifferentiationHigh Frequency

Chain Rule

ddx[sin⁡(x2+1)]=?\frac{d}{dx}\bigl[\sin(x^2 + 1)\bigr] = ?

Composite function differentiation

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Applications

Related Rates

dVdt=4πr2 drdt\frac{dV}{dt} = 4\pi r^{2}\,\frac{dr}{dt}

Connecting changing quantities

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Analytical

Optimization

max⁡x∈[a,b]f(x)  ⟺  f′(x)=0\max_{x \in [a,b]} f(x) \;\Longleftrightarrow\; f'(x)=0

Maxima/minima problems

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Integration

u-Substitution

∫2xcos⁡(x2) dx\int 2x\cos(x^{2})\,dx

Reverse chain rule for integrals

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Apps of Integration

Volume — Disk/Washer

V=π ⁣∫ab ⁣[f(x)]2dxV = \pi\!\int_{a}^{b}\!\bigl[f(x)\bigr]^{2}dx

Solids of revolution

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IntegrationBC only

Integration by Parts

∫u dv=uv−∫v du\int u\,dv = uv - \int v\,du

Product rule for integrals

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Complete AP Calculus AB / BC Coverage

10 units · 51 topics · 20 BC-only

1

Limits & Continuity

5 topics

2

Differentiation — Rules

6 topics

3

Differentiation — Composite, Implicit, Inverse

3 topics

4

Contextual Applications of Differentiation

3 topics

5

Analytical Applications of Differentiation

4 topics

6

Integration & Accumulation

8 topics· 3 BC

7

Differential Equations

4 topics· 2 BC

8

Applications of Integration

4 topics· 1 BC

9

Parametric, Polar & Vector

8 topicsBC

10

Infinite Sequences & Series

6 topicsBC

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