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Calculus 1 · Lessons

Calculus 1 lessons

8 sections · 87 skills · work through the full outline skill by skill — read the long-form lesson or flip through the slide-style version.
Long-form lessonsSlide-style lessons

Calculus 1

Practice 87 skills across this outline.

Recommended next
Limits via Algebraic Properties
Limits & Continuity · Limit Evaluation and Graphical Limits
Long-form lesson
Weighting distribution
26 categories
Limits & Continuity · Limit Evaluation and Graphical Limits
8%
Applications of Derivatives: Contextual · Motion Along a Line
7%
Applications of Derivatives: Analytical · Optimization
6%
Differential Equations (Intro) · Differential Equations Basics
6%
Derivatives: Definition & Rules · Derivative Definition and Estimation
6%
Applications of Integration · Volumes of Solids
6%

Skills

The comprehensive taxonomy of calculus 1 — drill into a card to work its skills.

Limits & Continuity · Limit Evaluation and Graphical Limits

10 core skills8% total weight
0/10 completed
10 skills to mastery
1
Limits via Algebraic PropertiesRecommended
Long-form
2
Estimating Limits from GraphsAvailable
Long-form
3
Limits at Infinity & Horizontal AsymptotesAvailable
Long-form
4
Squeeze TheoremAvailable
Long-form
5
Limits via Algebraic ManipulationAvailable
Long-form
6
Selecting Limit ProceduresAvailable
Long-form
7
Infinite Limits & Vertical AsymptotesAvailable
Long-form
8
Limit Definition & NotationAvailable
Long-form
9
Multiple Limit RepresentationsAvailable
Long-form
10
Estimating Limits from TablesAvailable
Long-form

Limits & Continuity · Continuity

5 core skills4% total weight
0/5 completed
5 skills to mastery
1
Continuity over an IntervalAvailable
Long-form
2
Removing DiscontinuitiesAvailable
Long-form
3
Types of DiscontinuitiesAvailable
Long-form
4
Intermediate Value TheoremAvailable
Long-form
5
Continuity at a PointAvailable
Long-form

Limits & Continuity · General Skills

1 core skills1% total weight
0/1 completed
1 skill to mastery
1
Intro to Calculus: Instantaneous ChangeAvailable
Long-form

Applications of Derivatives: Analytical · Derivative Applications

3 core skills4% total weight
0/3 completed
3 skills to mastery
1
EVT, Extrema & Critical PointsAvailable
Long-form
2
Implicit Relation BehaviorsAvailable
Long-form
3
Connecting f, f', and f''Available
Long-form

Applications of Derivatives: Analytical · General Skills

2 core skills3% total weight
0/2 completed
2 skills to mastery
1
Graphing Functions & DerivativesAvailable
Long-form
2
Mean Value TheoremAvailable
Long-form

Applications of Derivatives: Analytical · Optimization

7 core skills6% total weight
0/7 completed
7 skills to mastery
1
Determining ConcavityAvailable
Long-form
2
Increasing/Decreasing IntervalsAvailable
Long-form
3
Second Derivative TestAvailable
Long-form
4
Solving Optimization ProblemsAvailable
Long-form
5
Intro to OptimizationAvailable
Long-form
6
First Derivative TestAvailable
Long-form
7
Candidates Test for Global ExtremaAvailable
Long-form

Applications of Derivatives: Contextual · Motion Along a Line

2 core skills7% total weight
0/2 completed
2 skills to mastery
1
Motion: Position, Velocity, AccelerationAvailable
Long-form
2
Non-Motion Rates of ChangeAvailable
Long-form

Applications of Derivatives: Contextual · Related Rates

3 core skills3% total weight
0/3 completed
3 skills to mastery

Applications of Derivatives: Contextual · General Skills

3 core skills3% total weight
0/3 completed
3 skills to mastery
1
L'Hospital's RuleAvailable
Long-form
2
Linear ApproximationAvailable
Long-form
3
Derivative Meaning in ContextAvailable
Long-form

Differential Equations (Intro) · Separable Differential Equations

2 core skills4% total weight
0/2 completed
2 skills to mastery
1
Particular Solutions: Initial ConditionsAvailable
Long-form
2
General Solutions: Separation of VariablesAvailable
Long-form

Differential Equations (Intro) · Slope Fields and Qualitative Solutions

2 core skills3% total weight
0/2 completed
2 skills to mastery
1
Sketching Slope FieldsAvailable
Long-form
2
Reasoning with Slope FieldsAvailable
Long-form

Differential Equations (Intro) · Differential Equations Basics

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Exponential DE ModelsAvailable
Long-form
2
Verifying DE SolutionsAvailable
Long-form
3
Modeling with Differential EquationsAvailable
Long-form

Derivatives: Definition & Rules · Derivative Definition and Estimation

6 core skills6% total weight
0/6 completed
6 skills to mastery
1
Estimating DerivativesAvailable
Long-form
2
Derivative Definition & NotationAvailable
Long-form
3
Differentiability & ContinuityAvailable
Long-form
4
Derivatives of tan, cot, sec, cscAvailable
Long-form
5
Derivatives of cos, sin, e^x, ln xAvailable
Long-form
6
Basic Derivative RulesAvailable
Long-form

Derivatives: Definition & Rules · Trigonometric Derivatives

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Derivatives of sin & cosAvailable
Long-form
2
Derivatives of tan & Other TrigAvailable
Long-form

Derivatives: Definition & Rules · Derivative Rules

4 core skills4% total weight
0/4 completed
4 skills to mastery
1
Average & Instantaneous RatesAvailable
Long-form
2
Quotient RuleAvailable
Long-form
3
Power RuleAvailable
Long-form
4
Product RuleAvailable
Long-form

Applications of Integration · Volumes of Solids

6 core skills6% total weight
0/6 completed
6 skills to mastery
1
Washer Method: x- or y-AxisAvailable
Long-form
2
Cross Sections: Triangles & SemicirclesAvailable
Long-form
3
Disc Method: x- or y-AxisAvailable
Long-form
4
Washer Method: Other AxesAvailable
Long-form
5
Disc Method: Other AxesAvailable
Long-form
6
Cross Sections: Squares & RectanglesAvailable
Long-form

Applications of Integration · General Skills

4 core skills5% total weight
0/4 completed
4 skills to mastery
1
Work & Fluid ForceAvailable
Long-form
2
Average Value of a FunctionAvailable
Long-form
3
Position, Velocity, Acceleration via IntegralsAvailable
Long-form
4
Accumulation Functions in ContextAvailable
Long-form

Applications of Integration · Area Between Curves

3 core skills2% total weight
0/3 completed
3 skills to mastery
1
Area Between Curves (y-functions)Available
Long-form
2
Area Between Multiple IntersectionsAvailable
Long-form
3
Area Between Curves (x-functions)Available
Long-form

Derivatives: Composite, Implicit & Inverse · Inverse Functions and Inverse Differentiation

2 core skills5% total weight
0/2 completed
2 skills to mastery
1
Differentiating Inverse FunctionsAvailable
Long-form
2
Inverse Trig DerivativesAvailable
Long-form

Derivatives: Composite, Implicit & Inverse · Composite Functions and Chain Rule Extensions

3 core skills6% total weight
0/3 completed
3 skills to mastery
1
Higher-Order DerivativesAvailable
Long-form
2
Chain RuleAvailable
Long-form
3
Selecting Derivative ProceduresAvailable
Long-form

Derivatives: Composite, Implicit & Inverse · General Skills

1 core skills2% total weight
0/1 completed
1 skill to mastery
1
Implicit DifferentiationAvailable
Long-form

Integration: Accumulation & FTC · Fundamental Theorem of Calculus

2 core skills1% total weight
0/2 completed
2 skills to mastery
1
FTC & Accumulation FunctionsAvailable
Long-form
2
FTC & Definite IntegralsAvailable
Long-form

Integration: Accumulation & FTC · Integration Foundations

5 core skills5% total weight
0/5 completed
5 skills to mastery
1
Accumulation Function BehaviorAvailable
Long-form
2
Selecting Integration TechniquesAvailable
Long-form
3
Properties of Definite IntegralsAvailable
Long-form
4
Accumulations of ChangeAvailable
Long-form
5
Integration: Long Division & Completing SquareAvailable
Long-form

Integration: Accumulation & FTC · Riemann Sums and Numerical Integration

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Riemann Sum ApproximationsAvailable
Long-form
2
Riemann Sums & NotationAvailable
Long-form

Integration: Accumulation & FTC · Antiderivatives and Basic Integrals

2 core skills2% total weight
0/2 completed
2 skills to mastery
1
Basic Trig IntegralsAvailable
Long-form
2
Antiderivatives & Indefinite IntegralsAvailable
Long-form

Integration: Accumulation & FTC · u-Substitution

2 core skills3% total weight
0/2 completed
2 skills to mastery
1
u-SubstitutionAvailable
Long-form
2
Integration by SubstitutionAvailable
Long-form