IXL skill plan | Calculus plan for Calculus AP Edition Second Edition

Skill plan for Calculus AP Edition Second Edition - Calculus

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1	Chapter 1 Functions
1.1: Review of Functions		Identify and evaluate functions 1. Identify functions 2. Find values using function graphs 3. Evaluate functions Domain and range 4. Domain and range 5. Domain and range of linear functions: word problems Composition of functions 6. Composition of functions Average rate of change 7. Average rate of change I 8. Average rate of change II
1.1: Review of Functions
Identify and evaluate functions 1. Identify functions 2. Find values using function graphs 3. Evaluate functions Domain and range 4. Domain and range 5. Domain and range of linear functions: word problems Composition of functions 6. Composition of functions Average rate of change 7. Average rate of change I 8. Average rate of change II

1.2: Representing Functions		Linear functions 1. Linear functions: mixed review Piecewise functions 2. Graph piecewise-defined functions Function transformations 3. Function transformation rules 4. Transformations of functions 5. Describe function transformations
1.2: Representing Functions
Linear functions 1. Linear functions: mixed review Piecewise functions 2. Graph piecewise-defined functions Function transformations 3. Function transformation rules 4. Transformations of functions 5. Describe function transformations

1.3: Inverse, Exponential, and Logarithmic Functions		Inverse functions 1. Identify inverse functions 2. Find values of inverse functions from tables 3. Find values of inverse functions from graphs 4. Find inverse functions and relations Exponential and logarithmic functions 5. Domain and range of logarithmic functions 6. Convert between exponential and logarithmic form 7. Match exponential functions and graphs 8. Exponential growth and decay: word problems Properties of logarithms 9. Change of base formula 10. Properties of logarithms: mixed review 11. Evaluate logarithms using properties Solve exponential and logarithmic equations 12. Solve exponential equations by rewriting the base 13. Solve exponential equations using logarithms 14. Solve logarithmic equations with one logarithm 15. Solve logarithmic equations with multiple logarithms
1.3: Inverse, Exponential, and Logarithmic Functions
Inverse functions 1. Identify inverse functions 2. Find values of inverse functions from tables 3. Find values of inverse functions from graphs 4. Find inverse functions and relations Exponential and logarithmic functions 5. Domain and range of logarithmic functions 6. Convert between exponential and logarithmic form 7. Match exponential functions and graphs 8. Exponential growth and decay: word problems Properties of logarithms 9. Change of base formula 10. Properties of logarithms: mixed review 11. Evaluate logarithms using properties Solve exponential and logarithmic equations 12. Solve exponential equations by rewriting the base 13. Solve exponential equations using logarithms 14. Solve logarithmic equations with one logarithm 15. Solve logarithmic equations with multiple logarithms

1.4: Trigonometric Functions and Their Inverses		Radians and degrees 1. Convert between radians and degrees Find trigonometric ratios 2. Find trigonometric ratios using right triangles 3. Find trigonometric ratios using the unit circle 4. Find trigonometric ratios using reference angles 5. Convert between trigonometric ratios Inverses of trigonometric functions 6. Inverses of trigonometric functions Trigonometric equations 7. Solve trigonometric equations Graphs of sine and cosine functions 8. Find properties of sine and cosine functions 9. Write equations of sine and cosine functions from graphs 10. Write equations of sine and cosine functions using properties 11. Graph sine and cosine functions
1.4: Trigonometric Functions and Their Inverses
Radians and degrees 1. Convert between radians and degrees Find trigonometric ratios 2. Find trigonometric ratios using right triangles 3. Find trigonometric ratios using the unit circle 4. Find trigonometric ratios using reference angles 5. Convert between trigonometric ratios Inverses of trigonometric functions 6. Inverses of trigonometric functions Trigonometric equations 7. Solve trigonometric equations Graphs of sine and cosine functions 8. Find properties of sine and cosine functions 9. Write equations of sine and cosine functions from graphs 10. Write equations of sine and cosine functions using properties 11. Graph sine and cosine functions

2	Chapter 2 Limits
2.1: The Idea of Limits		1. Average velocity
2.1: The Idea of Limits
1. Average velocity

2.2: Definitions of Limits		1. Find limits using graphs 2. Find one-sided limits using graphs 3. Determine if a limit exists
2.2: Definitions of Limits
1. Find limits using graphs 2. Find one-sided limits using graphs 3. Determine if a limit exists

2.3: Techniques for Computing Limits		1. Find limits using limit laws 2. Find limits of polynomials and rational functions 3. Find limits involving factorization and rationalization Also consider: • Find limits involving absolute value functions • Find limits using addition, subtraction, and multiplication laws • Find limits using the division law • Find limits using power and root laws
2.3: Techniques for Computing Limits
1. Find limits using limit laws 2. Find limits of polynomials and rational functions 3. Find limits involving factorization and rationalization Also consider: • Find limits involving absolute value functions • Find limits using addition, subtraction, and multiplication laws • Find limits using the division law • Find limits using power and root laws

2.4: Infinite Limits		1. Find limits at vertical asymptotes using graphs 2. Find the limit at a vertical asymptote of a rational function I 3. Find the limit at a vertical asymptote of a rational function II
2.4: Infinite Limits
1. Find limits at vertical asymptotes using graphs 2. Find the limit at a vertical asymptote of a rational function I 3. Find the limit at a vertical asymptote of a rational function II

2.5: Limits at Infinity		1. Determine end behavior using graphs 2. Determine end behavior of polynomial and rational functions
2.5: Limits at Infinity
1. Determine end behavior using graphs 2. Determine end behavior of polynomial and rational functions

2.6: Continuity		1. Identify graphs of continuous functions 2. Determine continuity at a point 3. Determine continuity on an interval using graphs 4. Intermediate Value Theorem Also consider: • Find and analyze points of discontinuity using graphs • Make a piecewise function continuous
2.6: Continuity
1. Identify graphs of continuous functions 2. Determine continuity at a point 3. Determine continuity on an interval using graphs 4. Intermediate Value Theorem Also consider: • Find and analyze points of discontinuity using graphs • Make a piecewise function continuous

2.7: Precise Definitions of Limits
2.7: Precise Definitions of Limits

3	Chapter 3 Derivatives
3.1: Introducing the Derivative		1. Find values of derivatives using limits 2. Find the slope of a tangent line using limits 3. Find equations of tangent lines using limits
3.1: Introducing the Derivative
1. Find values of derivatives using limits 2. Find the slope of a tangent line using limits 3. Find equations of tangent lines using limits

3.2: Working with Derivatives		1. Identify the graph of the derivative from the graph of the function
3.2: Working with Derivatives
1. Identify the graph of the derivative from the graph of the function

3.3: Rules of Differentiation		1. Sum and difference rules 2. Power rule I 3. Find derivatives of polynomials Also consider: • Find higher derivatives of polynomials
3.3: Rules of Differentiation
1. Sum and difference rules 2. Power rule I 3. Find derivatives of polynomials Also consider: • Find higher derivatives of polynomials

3.4: The Product and Quotient Rules		1. Product rule 2. Find derivatives using the product rule 3. Quotient rule 4. Find derivatives using the quotient rule
3.4: The Product and Quotient Rules
1. Product rule 2. Find derivatives using the product rule 3. Quotient rule 4. Find derivatives using the quotient rule

3.5: Derivatives of Trigonometric Functions		1. Find limits involving trigonometric functions 2. Find derivatives of sine and cosine functions 3. Find derivatives of trigonometric functions using the product and quotient rules
3.5: Derivatives of Trigonometric Functions
1. Find limits involving trigonometric functions 2. Find derivatives of sine and cosine functions 3. Find derivatives of trigonometric functions using the product and quotient rules

3.6: Derivatives as Rates of Change		1. Relate position, velocity, speed, and acceleration using derivatives
3.6: Derivatives as Rates of Change
1. Relate position, velocity, speed, and acceleration using derivatives

3.7: The Chain Rule		1. Chain rule 2. Find derivatives using the chain rule Also consider: • Find higher derivatives of exponential and trigonometric functions
3.7: The Chain Rule
1. Chain rule 2. Find derivatives using the chain rule Also consider: • Find higher derivatives of exponential and trigonometric functions

3.8: Implicit Differentiation		1. Find derivatives using implicit differentiation 2. Find tangent lines using implicit differentiation 3. Find derivatives of radical functions Also consider: • Power rule II • Find higher derivatives of rational and radical functions
3.8: Implicit Differentiation
1. Find derivatives using implicit differentiation 2. Find tangent lines using implicit differentiation 3. Find derivatives of radical functions Also consider: • Power rule II • Find higher derivatives of rational and radical functions

3.9: Derivatives of Logarithmic and Exponential Functions		1. Find derivatives of exponential and logarithmic functions I 2. Find derivatives of exponential and logarithmic functions II 3. Find derivatives using logarithmic differentiation Also consider: • Find higher derivatives of logarithmic and power functions
3.9: Derivatives of Logarithmic and Exponential Functions
1. Find derivatives of exponential and logarithmic functions I 2. Find derivatives of exponential and logarithmic functions II 3. Find derivatives using logarithmic differentiation Also consider: • Find higher derivatives of logarithmic and power functions

3.1: Derivatives of Inverse Trigonometric Functions		1. Inverse function rule 2. Find derivatives of inverse trigonometric functions Also consider: • Find second derivatives of trigonometric, exponential, and logarithmic functions
3.1: Derivatives of Inverse Trigonometric Functions
1. Inverse function rule 2. Find derivatives of inverse trigonometric functions Also consider: • Find second derivatives of trigonometric, exponential, and logarithmic functions

3.11: Related Rates		1. Introduction to related rates
3.11: Related Rates
1. Introduction to related rates

4	Chapter 4 Applications of the Derivative
4.1: Maxima and Minima		1. Find absolute extrema on a closed interval 2. Find critical points of functions
4.1: Maxima and Minima
1. Find absolute extrema on a closed interval 2. Find critical points of functions

4.2: What Derivatives Tell Us		Relationship between a function and its first derivative 1. Identify the graph of a function from the graph of its derivative 2. Find local extrema using the first derivative test Relationship between a function and its second derivative 3. Identify the graph of the second derivative from the graph of the function
4.2: What Derivatives Tell Us
Relationship between a function and its first derivative 1. Identify the graph of a function from the graph of its derivative 2. Find local extrema using the first derivative test Relationship between a function and its second derivative 3. Identify the graph of the second derivative from the graph of the function

4.3: Graphing Functions
4.3: Graphing Functions


4.4: Optimization Problems		1. Introduction to optimization
4.4: Optimization Problems
1. Introduction to optimization

4.5: Linear Approximation and Differentials		1. Linear approximation
4.5: Linear Approximation and Differentials
1. Linear approximation

4.6: Mean Value Theorem		1. Mean Value Theorem
4.6: Mean Value Theorem
1. Mean Value Theorem

4.7: L'Hôspital's Rule		1. L'Hospital's rule: indeterminate forms involving quotients
4.7: L'Hôspital's Rule
1. L'Hospital's rule: indeterminate forms involving quotients

4.8: Newton's Method
4.8: Newton's Method

5	Chapter 5 Integration
5.1: Antiderivatives		1. Find antiderivatives Indefinite Integrals 2. Find indefinite integrals using the power rule 3. Find indefinite integrals involving exponential and logarithmic functions 4. Find indefinite integrals involving trigonometric functions 5. Find indefinite integrals: mixed review Differential equations 6. Solve first-order initial value problems
5.1: Antiderivatives
1. Find antiderivatives Indefinite Integrals 2. Find indefinite integrals using the power rule 3. Find indefinite integrals involving exponential and logarithmic functions 4. Find indefinite integrals involving trigonometric functions 5. Find indefinite integrals: mixed review Differential equations 6. Solve first-order initial value problems

5.2: Approximating Areas under Curves		1. Approximate the area under a curve: left and right endpoints 2. Approximate the area under a curve: midpoints
5.2: Approximating Areas under Curves
1. Approximate the area under a curve: left and right endpoints 2. Approximate the area under a curve: midpoints

5.3: Definite Integrals		1. Properties of definite integrals 2. Evaluate definite integrals using graphs 3. Definite integrals and net area
5.3: Definite Integrals
1. Properties of definite integrals 2. Evaluate definite integrals using graphs 3. Definite integrals and net area

5.4: Fundamental Theorem of Calculus		1. Fundamental Theorem of Calculus, Part 1 2. Evaluate definite integrals: mixed review 3. Fundamental Theorem of Calculus, Part 2 Also consider: • Evaluate definite integrals using the power rule • Evaluate definite integrals involving exponential and logarithmic functions • Evaluate definite integrals involving trigonometric functions • Areas of regions bounded by graphs and the x-axis
5.4: Fundamental Theorem of Calculus
1. Fundamental Theorem of Calculus, Part 1 2. Evaluate definite integrals: mixed review 3. Fundamental Theorem of Calculus, Part 2 Also consider: • Evaluate definite integrals using the power rule • Evaluate definite integrals involving exponential and logarithmic functions • Evaluate definite integrals involving trigonometric functions • Areas of regions bounded by graphs and the x-axis

5.5: Properties of Integrals and Average Value		1. Find the average value of a function
5.5: Properties of Integrals and Average Value
1. Find the average value of a function

5.6: Substitution Rule		1. Find indefinite integrals using substitution Also consider: • Integrals involving inverse trigonometric functions
5.6: Substitution Rule
1. Find indefinite integrals using substitution Also consider: • Integrals involving inverse trigonometric functions

5.7: Numerical Integration		1. Approximate the area under a curve: trapezoids
5.7: Numerical Integration
1. Approximate the area under a curve: trapezoids

6	Chapter 6 Applications of Integration
6.1: Velocity and Net Change
6.1: Velocity and Net Change


6.2: Regions Between Curves
6.2: Regions Between Curves


6.3: Volume by Slicing
6.3: Volume by Slicing


6.4: Volume by Shells
6.4: Volume by Shells


6.5: Length of Curves
6.5: Length of Curves


6.6: Physical Applications
6.6: Physical Applications

7	Chapter 7 Integration Techniques
7.1: Basic Approaches		1. Integrate using long division 2. Integrate by completing the square
7.1: Basic Approaches
1. Integrate using long division 2. Integrate by completing the square

7.2: Integration by Parts
7.2: Integration by Parts


7.3: Partial Fractions
7.3: Partial Fractions


7.4: Improper Integrals
7.4: Improper Integrals


7.5: Trigonometric Substitutions
7.5: Trigonometric Substitutions

8	Chapter 8 Differential Equations
8.1: Basic Ideas		1. Verify solutions to differential equations 2. Solve higher-order initial value problems
8.1: Basic Ideas
1. Verify solutions to differential equations 2. Solve higher-order initial value problems

8.2: Slope Fields and Euler's Method
8.2: Slope Fields and Euler's Method


8.3: Separable Differential Equations
8.3: Separable Differential Equations


8.4: Exponential Models
8.4: Exponential Models

9	Chapters 9-11
Skills covering these topics are not yet available on IXL.
Skills covering these topics are not yet available on IXL.

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