IXL skill plan | Precalculus plan for Precalculus with Limits: A Graphing Approach

Skill plan for Precalculus with Limits: A Graphing Approach - Precalculus

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1	Chapter 1 Functions and Their Graphs
1.1: Lines in the Plane		Linear functions 1. Graph a linear function 2. Find the slope of a linear function 3. Write the equation of a linear function Parallel and perpendicular lines 4. Slopes of parallel and perpendicular lines 5. Equations of parallel and perpendicular lines
1.1: Lines in the Plane
Linear functions 1. Graph a linear function 2. Find the slope of a linear function 3. Write the equation of a linear function Parallel and perpendicular lines 4. Slopes of parallel and perpendicular lines 5. Equations of parallel and perpendicular lines

1.2: Functions		1. Identify functions 2. Evaluate functions 3. Evaluate piecewise-defined functions
1.2: Functions
1. Identify functions 2. Evaluate functions 3. Evaluate piecewise-defined functions

1.3: Graphs of Functions		1. Domain and range 2. Find values using function graphs 3. Identify functions: vertical line test 4. Graph piecewise-defined functions 5. Even and odd functions
1.3: Graphs of Functions
1. Domain and range 2. Find values using function graphs 3. Identify functions: vertical line test 4. Graph piecewise-defined functions 5. Even and odd functions

1.4: Shifting, Reflecting, and Stretching Graphs		1. Function transformation rules 2. Translations of functions 3. Reflections of functions 4. Dilations of functions 5. Transformations of functions 6. Describe function transformations
1.4: Shifting, Reflecting, and Stretching Graphs
1. Function transformation rules 2. Translations of functions 3. Reflections of functions 4. Dilations of functions 5. Transformations of functions 6. Describe function transformations

1.5: Combinations of Functions		1. Add, subtract, multiply, and divide functions 2. Composition of functions
1.5: Combinations of Functions
1. Add, subtract, multiply, and divide functions 2. Composition of functions

1.6: 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
1.6: 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

1.7: Linear Models and Scatter Plots		Scatter plots 1. Create scatter plots 2. Identify trends with scatter plots Regression lines 3. Find the equation of a regression line 4. Interpret regression lines 5. Analyze a regression line of a data set Correlation coefficients 6. Match correlation coefficients to scatter plots 7. Calculate correlation coefficients
1.7: Linear Models and Scatter Plots
Scatter plots 1. Create scatter plots 2. Identify trends with scatter plots Regression lines 3. Find the equation of a regression line 4. Interpret regression lines 5. Analyze a regression line of a data set Correlation coefficients 6. Match correlation coefficients to scatter plots 7. Calculate correlation coefficients

2	Chapter 2 Polynomial and Rational Functions
2.1: Quadratic Functions		1. Characteristics of quadratic functions 2. Graph a quadratic function 3. Match quadratic functions and graphs 4. Write a quadratic function in vertex form 5. Write a quadratic function in vertex form from its vertex and another point 6. Solve quadratic equations: word problems Also consider: • Interpret parts of quadratic expressions: word problems
2.1: Quadratic Functions
1. Characteristics of quadratic functions 2. Graph a quadratic function 3. Match quadratic functions and graphs 4. Write a quadratic function in vertex form 5. Write a quadratic function in vertex form from its vertex and another point 6. Solve quadratic equations: word problems Also consider: • Interpret parts of quadratic expressions: word problems

2.2: Polynomial Functions of Higher Degree		1. Match polynomials and graphs 2. Find the roots of factored polynomials 3. Write a polynomial from its roots 4. Find the eccentricity of an ellipse
2.2: Polynomial Functions of Higher Degree
1. Match polynomials and graphs 2. Find the roots of factored polynomials 3. Write a polynomial from its roots 4. Find the eccentricity of an ellipse

2.3: Real Zeros of Polynomial Functions		1. Divide polynomials using long division 2. Divide polynomials using synthetic division 3. Evaluate polynomials using synthetic division 4. Rational root theorem 5. Descartes' Rule of Signs
2.3: Real Zeros of Polynomial Functions
1. Divide polynomials using long division 2. Divide polynomials using synthetic division 3. Evaluate polynomials using synthetic division 4. Rational root theorem 5. Descartes' Rule of Signs

2.4: Complex Numbers		1. Add and subtract complex numbers 2. Complex conjugates 3. Multiply and divide complex numbers 4. Powers of i Also consider: • Add, subtract, multiply, and divide complex numbers • Solve a quadratic equation with complex solutions
2.4: Complex Numbers
1. Add and subtract complex numbers 2. Complex conjugates 3. Multiply and divide complex numbers 4. Powers of i Also consider: • Add, subtract, multiply, and divide complex numbers • Solve a quadratic equation with complex solutions

2.5: The Fundamental Theorem of Algebra		1. Complex conjugate theorem 2. Conjugate root theorems 3. Fundamental Theorem of Algebra
2.5: The Fundamental Theorem of Algebra
1. Complex conjugate theorem 2. Conjugate root theorems 3. Fundamental Theorem of Algebra

2.6: Rational Functions and Asymptotes		1. Rational functions: asymptotes and excluded values
2.6: Rational Functions and Asymptotes
1. Rational functions: asymptotes and excluded values

2.7: Graphs of Rational Functions
2.7: Graphs of Rational Functions


2.8: Quadratic Models
2.8: Quadratic Models

3	Chapter 3 Exponential and Logarithmic Functions
3.1: Exponential Functions and Their Graphs		1. Solve exponential equations by rewriting the base 2. Match exponential functions and graphs Also consider: • Match exponential functions and graphs
3.1: Exponential Functions and Their Graphs
1. Solve exponential equations by rewriting the base 2. Match exponential functions and graphs Also consider: • Match exponential functions and graphs

3.2: Logarithmic Functions and Their Graphs		1. Convert between exponential and logarithmic form 2. Evaluate logarithms 3. Domain and range of logarithmic functions
3.2: Logarithmic Functions and Their Graphs
1. Convert between exponential and logarithmic form 2. Evaluate logarithms 3. Domain and range of logarithmic functions

3.3: Properties of Logarithms		1. Change of base formula 2. Product property of logarithms 3. Quotient property of logarithms 4. Power property of logarithms 5. Evaluate logarithms using properties
3.3: Properties of Logarithms
1. Change of base formula 2. Product property of logarithms 3. Quotient property of logarithms 4. Power property of logarithms 5. Evaluate logarithms using properties

3.4: Solving Exponential and Logarithmic Equations		1. Solve exponential equations using logarithms 2. Solve logarithmic equations with one logarithm 3. Solve logarithmic equations with multiple logarithms
3.4: Solving Exponential and Logarithmic Equations
1. Solve exponential equations using logarithms 2. Solve logarithmic equations with one logarithm 3. Solve logarithmic equations with multiple logarithms

3.5: Exponential and Logarithmic Models		1. Exponential growth and decay: word problems 2. Compound interest: word problems 3. Continuously compounded interest: word problems
3.5: Exponential and Logarithmic Models
1. Exponential growth and decay: word problems 2. Compound interest: word problems 3. Continuously compounded interest: word problems

3.6: Nonlinear Models		1. Exponential regression
3.6: Nonlinear Models
1. Exponential regression

4	Chapter 4 Trigonometric Functions
4.1: Radian and Degree Measure		1. Quadrants 2. Convert between radians and degrees 3. Radians and arc length 4. Coterminal angles
4.1: Radian and Degree Measure
1. Quadrants 2. Convert between radians and degrees 3. Radians and arc length 4. Coterminal angles

4.2: Trigonometric Functions: The Unit Circle		1. Find trigonometric ratios using the unit circle
4.2: Trigonometric Functions: The Unit Circle
1. Find trigonometric ratios using the unit circle

4.3: Right Triangle Trigonometry		1. Find trigonometric ratios using right triangles 2. Find trigonometric ratios of special angles 3. Trigonometric ratios: find a side length 4. Trigonometric ratios: find an angle measure 5. Solve a right triangle
4.3: Right Triangle Trigonometry
1. Find trigonometric ratios using right triangles 2. Find trigonometric ratios of special angles 3. Trigonometric ratios: find a side length 4. Trigonometric ratios: find an angle measure 5. Solve a right triangle

4.4: Trigonometric Functions of Any Angle		1. Reference angles 2. Find trigonometric ratios using reference angles 3. Find trigonometric functions using a calculator
4.4: Trigonometric Functions of Any Angle
1. Reference angles 2. Find trigonometric ratios using reference angles 3. Find trigonometric functions using a calculator

4.5: Graphs of Sine and Cosine Functions		Sine functions 1. Find properties of sine functions 2. Write equations of sine functions from graphs 3. Write equations of sine functions using properties Cosine functions 4. Find properties of cosine functions 5. Write equations of cosine functions from graphs 6. Write equations of cosine functions using properties Sine and cosine functions 7. Graph sine and cosine functions 8. Graph translations of sine and cosine functions
4.5: Graphs of Sine and Cosine Functions
Sine functions 1. Find properties of sine functions 2. Write equations of sine functions from graphs 3. Write equations of sine functions using properties Cosine functions 4. Find properties of cosine functions 5. Write equations of cosine functions from graphs 6. Write equations of cosine functions using properties Sine and cosine functions 7. Graph sine and cosine functions 8. Graph translations of sine and cosine functions

4.6: Graphs of Other Trigonometric Functions
4.6: Graphs of Other Trigonometric Functions


4.7: Inverse Trigonometric Functions		1. Inverses of trigonometric functions 2. Inverses of trigonometric functions using a calculator
4.7: Inverse Trigonometric Functions
1. Inverses of trigonometric functions 2. Inverses of trigonometric functions using a calculator

4.8: Applications and Models
4.8: Applications and Models

5	Chapter 5 Analytic Trigonometry
5.1: Using Fundamental Identities		1. Find trigonometric ratios using a Pythagorean or reciprocal identity 2. Find trigonometric ratios using multiple identities
5.1: Using Fundamental Identities
1. Find trigonometric ratios using a Pythagorean or reciprocal identity 2. Find trigonometric ratios using multiple identities

5.2: Verifying Trigonometric Identities
5.2: Verifying Trigonometric Identities


5.3: Solving Trigonometric Equations		1. Solve trigonometric equations
5.3: Solving Trigonometric Equations
1. Solve trigonometric equations

5.4: Sum and Difference Formulas
5.4: Sum and Difference Formulas


5.5: Multiple-Angle and Product-to-Sum Formulas
5.5: Multiple-Angle and Product-to-Sum Formulas

6	Chapter 6 Additional Topics in Trigonometry
6.1: Law of Sines		1. Law of Sines 2. Area of a triangle: sine formula
6.1: Law of Sines
1. Law of Sines 2. Area of a triangle: sine formula

6.2: Law of Cosines		1. Law of Cosines 2. Area of a triangle: Heron's formula 3. Solve a triangle
6.2: Law of Cosines
1. Law of Cosines 2. Area of a triangle: Heron's formula 3. Solve a triangle

6.3: Vectors in the Plane		Introduction to vectors 1. Find the magnitude of a vector 2. Find the direction angle of a vector Component form 3. Find the component form of a vector 4. Find the component form of a vector from its magnitude and direction angle Addition and subtraction 5. Graph a resultant vector using the triangle method 6. Graph a resultant vector using the parallelogram method 7. Add vectors 8. Subtract vectors 9. Find the magnitude and direction of a vector sum Scalar multiples 10. Multiply a vector by a scalar 11. Find the magnitude of a vector scalar multiple 12. Determine the direction of a vector scalar multiple Unit vectors 13. Find a unit vector Linear combinations 14. Linear combinations of vectors
6.3: Vectors in the Plane
Introduction to vectors 1. Find the magnitude of a vector 2. Find the direction angle of a vector Component form 3. Find the component form of a vector 4. Find the component form of a vector from its magnitude and direction angle Addition and subtraction 5. Graph a resultant vector using the triangle method 6. Graph a resultant vector using the parallelogram method 7. Add vectors 8. Subtract vectors 9. Find the magnitude and direction of a vector sum Scalar multiples 10. Multiply a vector by a scalar 11. Find the magnitude of a vector scalar multiple 12. Determine the direction of a vector scalar multiple Unit vectors 13. Find a unit vector Linear combinations 14. Linear combinations of vectors

6.4: Vectors and Dot Products
6.4: Vectors and Dot Products


6.5: The Complex Plane		Introduction to the complex plane 1. Introduction to the complex plane Graphing with complex numbers 2. Graph complex numbers 3. Graph complex conjugates Operations in the complex plane 4. Addition in the complex plane 5. Subtraction in the complex plane Distance and midpoints in the complex plane 6. Absolute value in the complex plane 7. Midpoints in the complex plane 8. Distance in the complex plane
6.5: The Complex Plane
Introduction to the complex plane 1. Introduction to the complex plane Graphing with complex numbers 2. Graph complex numbers 3. Graph complex conjugates Operations in the complex plane 4. Addition in the complex plane 5. Subtraction in the complex plane Distance and midpoints in the complex plane 6. Absolute value in the complex plane 7. Midpoints in the complex plane 8. Distance in the complex plane

6.6: Trigonometric Form of a Complex Number		1. Find the modulus and argument of a complex number 2. Convert complex numbers from rectangular to polar form 3. Convert complex numbers from polar to rectangular form
6.6: Trigonometric Form of a Complex Number
1. Find the modulus and argument of a complex number 2. Convert complex numbers from rectangular to polar form 3. Convert complex numbers from polar to rectangular form

7	Chapter 7 Linear Systems and Matrices
7.1: Solving Systems of Equations		Solve the system by graphing 1. Solve a system of linear and quadratic equations by graphing: parabolas 2. Solve a system of equations by graphing Solve the system by substitution 3. Solve a system of equations using substitution 4. Solve a system of linear and quadratic equations: parabolas 5. Solve a system of linear and quadratic equations: circles Solve word problems with systems 6. Solve a system of equations by graphing: word problems 7. Solve a system of equations using substitution: word problems
7.1: Solving Systems of Equations
Solve the system by graphing 1. Solve a system of linear and quadratic equations by graphing: parabolas 2. Solve a system of equations by graphing Solve the system by substitution 3. Solve a system of equations using substitution 4. Solve a system of linear and quadratic equations: parabolas 5. Solve a system of linear and quadratic equations: circles Solve word problems with systems 6. Solve a system of equations by graphing: word problems 7. Solve a system of equations using substitution: word problems

7.2: Systems of Linear Equations in Two Variables		1. Classify a system of equations 2. Solve a system of equations using elimination 3. Solve a system of equations using elimination: word problems Also consider: • Find the number of solutions to a system of equations
7.2: Systems of Linear Equations in Two Variables
1. Classify a system of equations 2. Solve a system of equations using elimination 3. Solve a system of equations using elimination: word problems Also consider: • Find the number of solutions to a system of equations

7.3: Multivariable Linear Systems		1. Solve a system of equations in three variables using substitution 2. Solve a system of equations in three variables using elimination 3. Determine the number of solutions to a system of equations in three variables Also consider: • Write a quadratic function from three points
7.3: Multivariable Linear Systems
1. Solve a system of equations in three variables using substitution 2. Solve a system of equations in three variables using elimination 3. Determine the number of solutions to a system of equations in three variables Also consider: • Write a quadratic function from three points

7.4: Matrices and Systems of Equations		1. Matrix vocabulary 2. Solve a system of equations using augmented matrices 3. Solve a system of equations using augmented matrices: word problems
7.4: Matrices and Systems of Equations
1. Matrix vocabulary 2. Solve a system of equations using augmented matrices 3. Solve a system of equations using augmented matrices: word problems

7.5: Operations with Matrices		1. Add and subtract matrices 2. Multiply a matrix by a scalar 3. Add and subtract scalar multiples of matrices 4. Multiply two matrices 5. Solve matrix equations Also consider: • Matrix operation rules • Simplify matrix expressions • Properties of matrices • Identify transformation matrices
7.5: Operations with Matrices
1. Add and subtract matrices 2. Multiply a matrix by a scalar 3. Add and subtract scalar multiples of matrices 4. Multiply two matrices 5. Solve matrix equations Also consider: • Matrix operation rules • Simplify matrix expressions • Properties of matrices • Identify transformation matrices

7.6: The Inverse of a Square Matrix		1. Is a matrix invertible? 2. Inverse of a 2 x 2 matrix 3. Inverse of a 3 x 3 matrix 4. Identify inverse matrices
7.6: The Inverse of a Square Matrix
1. Is a matrix invertible? 2. Inverse of a 2 x 2 matrix 3. Inverse of a 3 x 3 matrix 4. Identify inverse matrices

7.7: The Determinant of a Square Matrix		1. Determinant of a matrix
7.7: The Determinant of a Square Matrix
1. Determinant of a matrix

7.8: Applications of Matrices and Determinants		1. Identify transformation matrices
7.8: Applications of Matrices and Determinants
1. Identify transformation matrices

8	Chapter 8 Sequences, Series, and Probability
8.1: Sequences and Series		1. Find terms of a sequence 2. Find terms of a recursive sequence 3. Introduction to sigma notation 4. Find a recursive formula Also consider: • Factorials
8.1: Sequences and Series
1. Find terms of a sequence 2. Find terms of a recursive sequence 3. Introduction to sigma notation 4. Find a recursive formula Also consider: • Factorials

8.2: Arithmetic Sequences and Partial Sums		1. Introduction to partial sums 2. Find the sum of an arithmetic series 3. Partial sums of arithmetic series 4. Write a formula for an arithmetic sequence
8.2: Arithmetic Sequences and Partial Sums
1. Introduction to partial sums 2. Find the sum of an arithmetic series 3. Partial sums of arithmetic series 4. Write a formula for an arithmetic sequence

8.3: Geometric Sequences and Series		1. Find the sum of a finite geometric series 2. Find the value of an infinite geometric series 3. Write a formula for a geometric sequence Also consider: • Write a repeating decimal as a fraction
8.3: Geometric Sequences and Series
1. Find the sum of a finite geometric series 2. Find the value of an infinite geometric series 3. Write a formula for a geometric sequence Also consider: • Write a repeating decimal as a fraction

8.4: The Binomial Theorem		1. Pascal's triangle 2. Pascal's triangle and the Binomial Theorem 3. Binomial Theorem I 4. Binomial Theorem II
8.4: The Binomial Theorem
1. Pascal's triangle 2. Pascal's triangle and the Binomial Theorem 3. Binomial Theorem I 4. Binomial Theorem II

8.5: Counting Principles		1. Counting principle 2. Combinations and permutations 3. Combinations and permutations: word problems
8.5: Counting Principles
1. Counting principle 2. Combinations and permutations 3. Combinations and permutations: word problems

8.6: Probability		1. Theoretical probability 2. Probability of independent and dependent events 3. Find probabilities using combinations and permutations
8.6: Probability
1. Theoretical probability 2. Probability of independent and dependent events 3. Find probabilities using combinations and permutations

9	Chapter 9 Topics in Analytic Geometry
9.1: Circles and Parabolas		Circles 1. Find properties of circles 2. Write equations of circles in standard form 3. Graph circles Parabolas 4. Find properties of parabolas 5. Write equations of parabolas in vertex form 6. Graph parabolas
9.1: Circles and Parabolas
Circles 1. Find properties of circles 2. Write equations of circles in standard form 3. Graph circles Parabolas 4. Find properties of parabolas 5. Write equations of parabolas in vertex form 6. Graph parabolas

9.2: Ellipses		1. Find properties of ellipses 2. Find the eccentricity of an ellipse 3. Write equations of ellipses in standard form
9.2: Ellipses
1. Find properties of ellipses 2. Find the eccentricity of an ellipse 3. Write equations of ellipses in standard form

9.3: Hyperbolas and Rotation of Conics		Hyperbolas 1. Find properties of hyperbolas 2. Find the eccentricity of a hyperbola 3. Write equations of hyperbolas in standard form Conic sections 4. Convert equations of conic sections from general to standard form
9.3: Hyperbolas and Rotation of Conics
Hyperbolas 1. Find properties of hyperbolas 2. Find the eccentricity of a hyperbola 3. Write equations of hyperbolas in standard form Conic sections 4. Convert equations of conic sections from general to standard form

9.4: Parametric Equations
9.4: Parametric Equations


9.5: Polar Coordinates
9.5: Polar Coordinates


9.6: Graphs of Polar Equations		1. Match polar equations and graphs
9.6: Graphs of Polar Equations
1. Match polar equations and graphs

9.7: Polar Equations of Conics
9.7: Polar Equations of Conics

10	Chapter 10 Analytic Geometry in Three Dimensions
10.1: The Three-Dimensional Coordinate System
10.1: The Three-Dimensional Coordinate System


10.2: Vectors in Space		Introduction to three-dimensional vectors 1. Find the magnitude of a three-dimensional vector 2. Find the component form of a three-dimensional vector Three-dimensional vector operations 3. Add and subtract three-dimensional vectors 4. Scalar multiples of three-dimensional vectors 5. Find a three-dimensional unit vector 6. Linear combinations of three-dimensional vectors
10.2: Vectors in Space
Introduction to three-dimensional vectors 1. Find the magnitude of a three-dimensional vector 2. Find the component form of a three-dimensional vector Three-dimensional vector operations 3. Add and subtract three-dimensional vectors 4. Scalar multiples of three-dimensional vectors 5. Find a three-dimensional unit vector 6. Linear combinations of three-dimensional vectors

11	Chapter 11 Limits and an Introduction to Calculus
11.1: Introduction to Limits		Introduction to limits 1. Find limits using graphs 2. Determine if a limit exists Limit laws 3. Find limits using addition, subtraction, and multiplication laws 4. Find limits using the division law 5. Find limits using power and root laws 6. Find limits using limit laws Limits of polynomials and rational functions 7. Find limits of polynomials and rational functions
11.1: Introduction to Limits
Introduction to limits 1. Find limits using graphs 2. Determine if a limit exists Limit laws 3. Find limits using addition, subtraction, and multiplication laws 4. Find limits using the division law 5. Find limits using power and root laws 6. Find limits using limit laws Limits of polynomials and rational functions 7. Find limits of polynomials and rational functions

11.2: Techniques for Evaluating Limits		1. Find one-sided limits using graphs 2. Find limits involving factorization and rationalization
11.2: Techniques for Evaluating Limits
1. Find one-sided limits using graphs 2. Find limits involving factorization and rationalization

11.3: The Tangent Line Problem		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
11.3: The Tangent Line Problem
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

11.4: Limits at Infinity and Limits of Sequences		1. Find limits at vertical asymptotes using graphs 2. Determine end behavior using graphs 3. Determine end behavior of polynomial and rational functions
11.4: Limits at Infinity and Limits of Sequences
1. Find limits at vertical asymptotes using graphs 2. Determine end behavior using graphs 3. Determine end behavior of polynomial and rational functions

11.5: The Area Problem		1. Approximate the area under a curve: right endpoints
11.5: The Area Problem
1. Approximate the area under a curve: right endpoints

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