IXL Skill Plan | Pennsylvania Core Standards: Algebra II

Pennsylvania Core Standards: Algebra II

Skills available for Pennsylvania Algebra 2 standards

Section

Numbers and Operations
Algebraic Concepts
Measurement, Data, and Probability

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CC.2.1.HS	Numbers and Operations
CC.2.1.HS.F Number and Quantity
CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.		Evaluate expressions 1. Evaluate rational exponents Apply properties of exponents 2. Multiplication with rational exponents 3. Division with rational exponents 4. Power rule 5. Simplify expressions involving rational exponents I 6. Simplify expressions involving rational exponents II
CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.
Evaluate expressions 1. Evaluate rational exponents Apply properties of exponents 2. Multiplication with rational exponents 3. Division with rational exponents 4. Power rule 5. Simplify expressions involving rational exponents I 6. Simplify expressions involving rational exponents II

CC.2.1.HS.F.3 Apply quantitative reasoning to choose and Interpret units and scales in formulas, graphs and data displays.		1. Find the equation of a regression line 2. Interpret regression lines
CC.2.1.HS.F.3 Apply quantitative reasoning to choose and Interpret units and scales in formulas, graphs and data displays.
1. Find the equation of a regression line 2. Interpret regression lines

CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.		Precision 1. Precision Percent error 2. Percent error 3. Percent error: area and volume Limitations 4. Greatest possible error 5. Minimum and maximum area and volume
CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Precision 1. Precision Percent error 2. Percent error 3. Percent error: area and volume Limitations 4. Greatest possible error 5. Minimum and maximum area and volume

CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers.		Understand complex numbers 1. Introduction to complex numbers 2. Complex conjugates 3. Absolute values of complex numbers Operations with complex numbers 4. Add and subtract complex numbers 5. Multiply complex numbers 6. Divide complex numbers 7. Add, subtract, multiply, and divide complex numbers 8. Powers of i
CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers.
Understand complex numbers 1. Introduction to complex numbers 2. Complex conjugates 3. Absolute values of complex numbers Operations with complex numbers 4. Add and subtract complex numbers 5. Multiply complex numbers 6. Divide complex numbers 7. Add, subtract, multiply, and divide complex numbers 8. Powers of i

CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.		1. Solve a quadratic equation using square roots 2. Solve a quadratic equation using the quadratic formula 3. Solve polynomial equations 4. Complex conjugate theorem 5. Conjugate root theorems
CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.
1. Solve a quadratic equation using square roots 2. Solve a quadratic equation using the quadratic formula 3. Solve polynomial equations 4. Complex conjugate theorem 5. Conjugate root theorems

CC.2.2.HS	Algebraic Concepts
CC.2.2.HS.D Algebra
CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context.		1. Polynomial vocabulary 2. Interpret parts of quadratic expressions: word problems
CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context.
1. Polynomial vocabulary 2. Interpret parts of quadratic expressions: word problems

CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.		Variable expressions 1. Simplify variable expressions using properties Factor polynomials 2. Factor out a monomial 3. Factor quadratics 4. Factor using a quadratic pattern 5. Factor by grouping 6. Factor sums and differences of cubes 7. Factor polynomials Rational exponents 8. Multiplication with rational exponents 9. Division with rational exponents 10. Power rule 11. Simplify expressions involving rational exponents I 12. Simplify expressions involving rational exponents II Rational expressions 13. Simplify rational expressions Logarithms and exponents 14. Convert between exponential and logarithmic form: rational bases 15. Convert between natural exponential and logarithmic form 16. Convert between exponential and logarithmic form: all bases 17. Evaluate logarithms
CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
Variable expressions 1. Simplify variable expressions using properties Factor polynomials 2. Factor out a monomial 3. Factor quadratics 4. Factor using a quadratic pattern 5. Factor by grouping 6. Factor sums and differences of cubes 7. Factor polynomials Rational exponents 8. Multiplication with rational exponents 9. Division with rational exponents 10. Power rule 11. Simplify expressions involving rational exponents I 12. Simplify expressions involving rational exponents II Rational expressions 13. Simplify rational expressions Logarithms and exponents 14. Convert between exponential and logarithmic form: rational bases 15. Convert between natural exponential and logarithmic form 16. Convert between exponential and logarithmic form: all bases 17. Evaluate logarithms

CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.		Add and subtract polynomials 1. Add and subtract polynomials Multiply polynomials 2. Multiply polynomials Divide polynomials 3. Divide polynomials using long division 4. Divide polynomials using synthetic division
CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.
Add and subtract polynomials 1. Add and subtract polynomials Multiply polynomials 2. Multiply polynomials Divide polynomials 3. Divide polynomials using long division 4. Divide polynomials using synthetic division

CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.		Solve equations 1. Solve a quadratic equation using the zero product property 2. Solve a quadratic equation by factoring 3. Solve polynomial equations Roots and factors 4. Find the roots of factored polynomials 5. Write a polynomial from its roots 6. Rational root theorem Graphs 7. Match quadratic functions and graphs 8. Match polynomials and graphs Pascal's triangle and the Binomial Theorem 9. Pascal's triangle 10. Pascal's triangle and the Binomial Theorem 11. Binomial Theorem I 12. Binomial Theorem II
CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.
Solve equations 1. Solve a quadratic equation using the zero product property 2. Solve a quadratic equation by factoring 3. Solve polynomial equations Roots and factors 4. Find the roots of factored polynomials 5. Write a polynomial from its roots 6. Rational root theorem Graphs 7. Match quadratic functions and graphs 8. Match polynomials and graphs Pascal's triangle and the Binomial Theorem 9. Pascal's triangle 10. Pascal's triangle and the Binomial Theorem 11. Binomial Theorem I 12. Binomial Theorem II

CC.2.2.HS.D.5 Use polynomial identities to solve problems.		Greatest common factors 1. Factor out a monomial Factor quadratics 2. Factor quadratics 3. Factor using a quadratic pattern Sums and differences of cubes 4. Factor sums and differences of cubes Factor polynomials 5. Factor by grouping 6. Factor polynomials
CC.2.2.HS.D.5 Use polynomial identities to solve problems.
Greatest common factors 1. Factor out a monomial Factor quadratics 2. Factor quadratics 3. Factor using a quadratic pattern Sums and differences of cubes 4. Factor sums and differences of cubes Factor polynomials 5. Factor by grouping 6. Factor polynomials

CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.		1. Simplify rational expressions
CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.
1. Simplify rational expressions

CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships.		Linear equations 1. Graph a linear function 2. Write the equation of a linear function Two-variable linear inequalities 3. Write two-variable linear inequalities: word problems 4. Graph a two-variable linear inequality Quadratic equations 5. Graph a quadratic function 6. Write a quadratic function in vertex form from its vertex and another point Exponential equations 7. Write exponential functions: word problems 8. Exponential growth and decay: word problems 9. Compound interest: word problems 10. Continuously compounded interest: word problems
CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships.
Linear equations 1. Graph a linear function 2. Write the equation of a linear function Two-variable linear inequalities 3. Write two-variable linear inequalities: word problems 4. Graph a two-variable linear inequality Quadratic equations 5. Graph a quadratic function 6. Write a quadratic function in vertex form from its vertex and another point Exponential equations 7. Write exponential functions: word problems 8. Exponential growth and decay: word problems 9. Compound interest: word problems 10. Continuously compounded interest: word problems

CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.		Linear equations 1. Solve linear equations Absolute value equations 2. Solve absolute value equations Multi-variable equations 3. Rearrange multi-variable equations Quadratic equations 4. Solve a quadratic equation using square roots 5. Solve a quadratic equation using the zero product property 6. Solve a quadratic equation by factoring 7. Complete the square Radical equations 8. Solve radical equations Rational equations 9. Solve rational equations Exponential equations 10. Solve exponential equations by rewriting the base 11. Solve exponential equations using common logarithms 12. Solve exponential equations using natural logarithms Logarithmic equations 13. Solve logarithmic equations I 14. Solve logarithmic equations II
CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.
Linear equations 1. Solve linear equations Absolute value equations 2. Solve absolute value equations Multi-variable equations 3. Rearrange multi-variable equations Quadratic equations 4. Solve a quadratic equation using square roots 5. Solve a quadratic equation using the zero product property 6. Solve a quadratic equation by factoring 7. Complete the square Radical equations 8. Solve radical equations Rational equations 9. Solve rational equations Exponential equations 10. Solve exponential equations by rewriting the base 11. Solve exponential equations using common logarithms 12. Solve exponential equations using natural logarithms Logarithmic equations 13. Solve logarithmic equations I 14. Solve logarithmic equations II

CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.		Linear equations 1. Solve linear equations: complete the solution Quadratic equations 2. Solve a quadratic equation using square roots 3. Solve a quadratic equation using the zero product property 4. Solve a quadratic equation by factoring 5. Complete the square 6. Solve a quadratic equation using the quadratic formula
CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.
Linear equations 1. Solve linear equations: complete the solution Quadratic equations 2. Solve a quadratic equation using square roots 3. Solve a quadratic equation using the zero product property 4. Solve a quadratic equation by factoring 5. Complete the square 6. Solve a quadratic equation using the quadratic formula

CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.		Quadratic equations 1. Solve a quadratic equation using square roots 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring 4. Solve a quadratic equation by completing the square 5. Solve quadratic equations: word problems Radical equations 6. Solve radical equations Rational equations 7. Solve rational equations Exponential equations 8. Write exponential functions: word problems 9. Exponential growth and decay: word problems 10. Compound interest: word problems 11. Continuously compounded interest: word problems Systems of equations 12. Solve a system of equations by graphing (Algebra 1) 13. Solve a system of equations by graphing (Algebra 2) 14. Solve a system of equations by graphing: word problems 15. Solve a system of equations using substitution 16. Solve a system of equations using substitution: word problems 17. Solve a system of equations using elimination 18. Solve a system of equations using elimination: word problems 19. Solve a system of equations using any method 20. Solve a system of equations using any method: word problems Systems of inequalities 21. Solve a system of equations using any method 22. Solve a system of equations using any method: word problems 23. Solve a system of linear and quadratic equations 24. Is (x, y) a solution to the system of inequalities? 25. Solve systems of linear inequalities by graphing 26. Solve a system of linear and quadratic equations by graphing: parabolas
CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
Quadratic equations 1. Solve a quadratic equation using square roots 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring 4. Solve a quadratic equation by completing the square 5. Solve quadratic equations: word problems Radical equations 6. Solve radical equations Rational equations 7. Solve rational equations Exponential equations 8. Write exponential functions: word problems 9. Exponential growth and decay: word problems 10. Compound interest: word problems 11. Continuously compounded interest: word problems Systems of equations 12. Solve a system of equations by graphing (Algebra 1) 13. Solve a system of equations by graphing (Algebra 2) 14. Solve a system of equations by graphing: word problems 15. Solve a system of equations using substitution 16. Solve a system of equations using substitution: word problems 17. Solve a system of equations using elimination 18. Solve a system of equations using elimination: word problems 19. Solve a system of equations using any method 20. Solve a system of equations using any method: word problems Systems of inequalities 21. Solve a system of equations using any method 22. Solve a system of equations using any method: word problems 23. Solve a system of linear and quadratic equations 24. Is (x, y) a solution to the system of inequalities? 25. Solve systems of linear inequalities by graphing 26. Solve a system of linear and quadratic equations by graphing: parabolas
CC.2.2.HS.C Functions
CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context.		Identify functions 1. Identify functions Evaluate functions 2. Evaluate functions 3. Find values using function graphs 4. Complete a table for a function graph 5. Complete a function table: quadratic functions Domain and range 6. Domain and range 7. Domain and range of quadratic functions: graphs 8. Domain and range of quadratic functions: equations 9. Domain and range of polynomials 10. Domain and range of radical functions 11. Domain and range of logarithmic functions
CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context.
Identify functions 1. Identify functions Evaluate functions 2. Evaluate functions 3. Find values using function graphs 4. Complete a table for a function graph 5. Complete a function table: quadratic functions Domain and range 6. Domain and range 7. Domain and range of quadratic functions: graphs 8. Domain and range of quadratic functions: equations 9. Domain and range of polynomials 10. Domain and range of radical functions 11. Domain and range of logarithmic functions

CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations.		Linear functions 1. Find the slope of a linear function 2. Graph a linear function Quadratic functions 3. Characteristics of quadratic functions: graphs 4. Characteristics of quadratic functions: equations 5. Graph a quadratic function 6. Match quadratic functions and graphs Polynomial functions 7. Match polynomials and graphs Exponential functions 8. Graph exponential functions 9. Match exponential functions and graphs Word problems 10. Identify graphs: word problems
CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations.
Linear functions 1. Find the slope of a linear function 2. Graph a linear function Quadratic functions 3. Characteristics of quadratic functions: graphs 4. Characteristics of quadratic functions: equations 5. Graph a quadratic function 6. Match quadratic functions and graphs Polynomial functions 7. Match polynomials and graphs Exponential functions 8. Graph exponential functions 9. Match exponential functions and graphs Word problems 10. Identify graphs: word problems

CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities.		Sequences 1. Find terms of an arithmetic sequence 2. Find terms of a geometric sequence 3. Evaluate explicit formulas for sequences 4. Write a formula for an arithmetic sequence 5. Write a formula for a geometric sequence 6. Sequences: mixed review Linear functions 7. Write the equation of a linear function Quadratic functions 8. Write a quadratic function from its zeros 9. Write a quadratic function in vertex form from its vertex and another point 10. Write a quadratic function in factored form from its x-intercepts and another point 11. Write a quadratic function from three points
CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities.
Sequences 1. Find terms of an arithmetic sequence 2. Find terms of a geometric sequence 3. Evaluate explicit formulas for sequences 4. Write a formula for an arithmetic sequence 5. Write a formula for a geometric sequence 6. Sequences: mixed review Linear functions 7. Write the equation of a linear function Quadratic functions 8. Write a quadratic function from its zeros 9. Write a quadratic function in vertex form from its vertex and another point 10. Write a quadratic function in factored form from its x-intercepts and another point 11. Write a quadratic function from three points

CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions.		Transformations of functions 1. Function transformation rules 2. Translations of functions 3. Reflections of functions 4. Dilations of functions 5. Transformations of functions 6. Describe function transformations Inverse functions 7. Identify inverse functions 8. Find inverse functions and relations
CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions.
Transformations of functions 1. Function transformation rules 2. Translations of functions 3. Reflections of functions 4. Dilations of functions 5. Transformations of functions 6. Describe function transformations Inverse functions 7. Identify inverse functions 8. Find inverse functions and relations

CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems.		1. Identify linear, quadratic, and exponential functions from graphs 2. Identify linear, quadratic, and exponential functions from tables 3. Write linear, quadratic, and exponential functions
CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems.
1. Identify linear, quadratic, and exponential functions from graphs 2. Identify linear, quadratic, and exponential functions from tables 3. Write linear, quadratic, and exponential functions

CC.2.2.HS.C.6 Interpret functions in terms of the situation they model.		1. Slope-intercept form: write an equation from a word problem 2. Interpret parts of quadratic expressions: word problems 3. Interpret the graph of a function: word problems 4. Interpret functions using everyday language
CC.2.2.HS.C.6 Interpret functions in terms of the situation they model.
1. Slope-intercept form: write an equation from a word problem 2. Interpret parts of quadratic expressions: word problems 3. Interpret the graph of a function: word problems 4. Interpret functions using everyday language

CC.2.2.HS.C.7 Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.		1. Convert between radians and degrees 2. Radians and arc length 3. Find trigonometric ratios using the unit circle
CC.2.2.HS.C.7 Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.
1. Convert between radians and degrees 2. Radians and arc length 3. Find trigonometric ratios using the unit circle

CC.2.2.HS.C.8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.		Sine functions 1. Find properties of sine functions 2. Write equations of sine functions from graphs 3. Write equations of sine functions using properties 4. Graph sine functions Cosine functions 5. Find properties of cosine functions 6. Write equations of cosine functions from graphs 7. Write equations of cosine functions using properties 8. Graph cosine functions Sine and cosine functions 9. Graph sine and cosine functions
CC.2.2.HS.C.8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.
Sine functions 1. Find properties of sine functions 2. Write equations of sine functions from graphs 3. Write equations of sine functions using properties 4. Graph sine functions Cosine functions 5. Find properties of cosine functions 6. Write equations of cosine functions from graphs 7. Write equations of cosine functions using properties 8. Graph cosine functions Sine and cosine functions 9. Graph sine and cosine functions

CC.2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate trigonometric ratios.		1. Find trigonometric ratios using a Pythagorean or reciprocal identity 2. Find trigonometric ratios using multiple identities
CC.2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate trigonometric ratios.
1. Find trigonometric ratios using a Pythagorean or reciprocal identity 2. Find trigonometric ratios using multiple identities

CC.2.4.HS	Measurement, Data, and Probability
CC.2.4.HS.B Statistics and Probability
CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.		1. Variance and standard deviation
CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.
1. Variance and standard deviation

CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.		1. Interpret stem-and-leaf plots 2. Interpret a scatter plot 3. Interpret bar graphs, line graphs, and histograms 4. Create bar graphs, line graphs, and histograms 5. Interpret circle graphs
CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.
1. Interpret stem-and-leaf plots 2. Interpret a scatter plot 3. Interpret bar graphs, line graphs, and histograms 4. Create bar graphs, line graphs, and histograms 5. Interpret circle graphs

CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data.		1. Find the equation of a regression line 2. Interpret regression lines 3. Analyze a regression line of a data set
CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data.
1. Find the equation of a regression line 2. Interpret regression lines 3. Analyze a regression line of a data set

CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments.		Games of chance 1. Write the probability distribution for a game of chance 2. Expected values for a game of chance Choose the better bet 3. Identify probability distributions 4. Choose the better bet
CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments.
Games of chance 1. Write the probability distribution for a game of chance 2. Expected values for a game of chance Choose the better bet 3. Identify probability distributions 4. Choose the better bet

CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.		1. Identify biased samples 2. Experiment design 3. Analyze the results of an experiment using simulations
CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
1. Identify biased samples 2. Experiment design 3. Analyze the results of an experiment using simulations

CC.2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data.		Independent and dependent events 1. Identify independent events 2. Probability of independent and dependent events Conditional probability 3. Find conditional probabilities 4. Independence and conditional probability 5. Find conditional probabilities using two-way frequency tables
CC.2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data.
Independent and dependent events 1. Identify independent events 2. Probability of independent and dependent events Conditional probability 3. Find conditional probabilities 4. Independence and conditional probability 5. Find conditional probabilities using two-way frequency tables

CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.		Counting principle, permutations, and combinations 1. Counting principle 2. Combinations and permutations Calculate probabilities 3. Calculate probabilities of events 4. Find probabilities using combinations and permutations
CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.
Counting principle, permutations, and combinations 1. Counting principle 2. Combinations and permutations Calculate probabilities 3. Calculate probabilities of events 4. Find probabilities using combinations and permutations