Illinois Priority Learning Standards: Mathematics II
Skills available for Illinois Integrated 2 math standards
Section
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9-12.HSN
Number and Quantity
9-12.HSN-RN The Real Number System
9-12.HSN-RN.A Extend the properties of exponents to rational exponents.
9-12.HSN-RN.A Extend the properties of exponents to rational exponents.
9-12.HSN-RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents
Radical expressions
9-12.HSN-RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents
Radical expressions
9-12.HSN-CN The Complex Number System
9-12.HSN-CN.A Perform arithmetic operations with complex numbers.
9-12.HSN-CN.A Perform arithmetic operations with complex numbers.
9-12.HSN-CN.A.1: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
9-12.HSN-CN.A.1: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
9-12.HSN-CN.A.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
9-12.HSN-CN.A.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
9-12.HSN-CN.C Use complex numbers in polynomial identities and equations.
9-12.HSN-CN.C Use complex numbers in polynomial identities and equations.
9-12.HSN-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
9-12.HSN-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
9-12.HSA
Algebra
9-12.HSA-SSE Seeing Structure in Expressions
9-12.HSA-SSE.A Interpret the structure of expressions.
9-12.HSA-SSE.A Interpret the structure of expressions.
9-12.HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
9-12.HSA-SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
9-12.HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
9-12.HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
9-12.HSA-SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
9-12.HSA-SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
9-12.HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Quadratic expressions
Integer exponents
Rational exponents
Radical expressions
9-12.HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Quadratic expressions
Integer exponents
Rational exponents
Radical expressions
9-12.HSA-SSE.B Write expressions in equivalent forms to solve problems.
9-12.HSA-SSE.B Write expressions in equivalent forms to solve problems.
9-12.HSA-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
9-12.HSA-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
9-12.HSA-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics
Solve quadratics
9-12.HSA-SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics
Solve quadratics
9-12.HSA-SSE.B.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
9-12.HSA-SSE.B.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
9-12.HSA-SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
Integer exponents
Rational exponents
Evaluate functions
9-12.HSA-SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
Integer exponents
Rational exponents
Evaluate functions
9-12.HSA-APR Arithmetic with Polynomials and Rational Expressions
9-12.HSA-APR.A Perform arithmetic operations on polynomials.
9-12.HSA-APR.A Perform arithmetic operations on polynomials.
9-12.HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Model polynomials
Addition and subtraction
Multiplication
9-12.HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Model polynomials
Addition and subtraction
Multiplication
9-12.HSA-CED Creating Equations
9-12.HSA-CED.A Create equations that describe numbers or relationships.
9-12.HSA-CED.A Create equations that describe numbers or relationships.
9-12.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
9-12.HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
9-12.HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quadratic equations
Linear, quadratic, and exponential equations
9-12.HSA-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quadratic equations
Linear, quadratic, and exponential equations
9-12.HSF
Functions
9-12.HSF-IF Interpreting Functions
9-12.HSF-IF.B Interpret functions that arise in applications in terms of the context.
9-12.HSF-IF.B Interpret functions that arise in applications in terms of the context.
9-12.HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Quadratic functions
Linear, quadratic, and exponential functions
Word problems
9-12.HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Quadratic functions
Linear, quadratic, and exponential functions
Word problems
9-12.HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Absolute value functions
Quadratic functions
9-12.HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Absolute value functions
Quadratic functions
9-12.HSF-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
9-12.HSF-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
9-12.HSF-IF.C Analyze functions using different representations.
9-12.HSF-IF.C Analyze functions using different representations.
9-12.HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.HSF-IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Linear functions
Quadratic functions
9-12.HSF-IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Linear functions
Quadratic functions
9-12.HSF-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
9-12.HSF-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
9-12.HSF-IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
9-12.HSF-IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
9-12.HSF-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
9-12.HSF-IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
9-12.HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
9-12.HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
9-12.HSF-BF Building Functions
9-12.HSF-BF.A Build a function that models a relationship between two quantities.
9-12.HSF-BF.A Build a function that models a relationship between two quantities.
9-12.HSF-BF.A.1: Write a function that describes a relationship between two quantities.
9-12.HSF-BF.A.1: Write a function that describes a relationship between two quantities.
9-12.HSF-BF.A.1b: Combine standard function types using arithmetic operations.
9-12.HSF-BF.A.1b: Combine standard function types using arithmetic operations.
9-12.HSF-BF.B Build new functions from existing functions.
9-12.HSF-BF.B Build new functions from existing functions.
9-12.HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Quadratic functions
Absolute value functions
Function transformations
9-12.HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Quadratic functions
Absolute value functions
Function transformations
9-12.HSF-LE Linear, Quadratic, and Exponential Models
9-12.HSF-LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
9-12.HSF-LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
9-12.HSF-LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
9-12.HSF-LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
9-12.HSF-TF Trigonometric Functions
9-12.HSF-TF.A Extend the domain of trigonometric functions using the unit circle.
9-12.HSF-TF.A Extend the domain of trigonometric functions using the unit circle.
9-12.HSF-TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
9-12.HSF-TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
9-12.HSG
Geometry
9-12.HSG-CO Congruence
9-12.HSG-CO.C Prove geometric theorems.
9-12.HSG-CO.C Prove geometric theorems.
9-12.HSG-CO.C.9: Prove theorems about lines and angles.
Angles
Parallel lines
Perpendicular bisectors
9-12.HSG-CO.C.9: Prove theorems about lines and angles.
Angles
Parallel lines
Perpendicular bisectors
9-12.HSG-CO.C.10: Prove theorems about triangles.
Isosceles triangles
Angles in triangles
Segments in triangles
Centroids or orthocenters of triangles
9-12.HSG-CO.C.10: Prove theorems about triangles.
Isosceles triangles
Angles in triangles
Segments in triangles
Centroids or orthocenters of triangles
9-12.HSG-SRT Similarity, Right Triangles, and Trigonometry
9-12.HSG-SRT.A Understand similarity in terms of similarity transformations.
9-12.HSG-SRT.A Understand similarity in terms of similarity transformations.
9-12.HSG-SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
9-12.HSG-SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
9-12.HSG-SRT.B Prove theorems involving similarity.
9-12.HSG-SRT.B Prove theorems involving similarity.
9-12.HSG-SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Congruent triangles
Proofs involving congruent triangles
Isosceles, equilateral, and right triangles
Similar triangles
Proofs involving similar triangles
9-12.HSG-SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Congruent triangles
Proofs involving congruent triangles
Isosceles, equilateral, and right triangles
Similar triangles
Proofs involving similar triangles
9-12.HSG-SRT.C Define trigonometric ratios and solve problems involving right triangles.
9-12.HSG-SRT.C Define trigonometric ratios and solve problems involving right triangles.
9-12.HSG-SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
9-12.HSG-SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
9-12.HSG-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
9-12.HSG-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
9-12.HSG-C Circles
9-12.HSG-C.A Understand and apply theorems about circles.
9-12.HSG-C.A Understand and apply theorems about circles.
9-12.HSG-C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.
Central and inscribed angles
Chords, secants, and tangents
9-12.HSG-C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.
Central and inscribed angles
Chords, secants, and tangents
9-12.HSG-GPE Expressing Geometric Properties with Equations
9-12.HSG-GPE.A Translate between the geometric description and the equation for a conic section.
9-12.HSG-GPE.A Translate between the geometric description and the equation for a conic section.
9-12.HSG-GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Complete the square
Write equations and graph circles
9-12.HSG-GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Complete the square
Write equations and graph circles