### I: Students will use the language and operations of algebra to evaluate, analyze and solve problems.

#### I.1: Evaluate, analyze, and solve mathematical situations using algebraic properties and symbols.

I.1.a: Solve and graph first-degree absolute value equations of a single variable.

I.1.b: Solve radical equations of a single variable, including those with extraneous roots.

I.1.c: Solve absolute value and compound inequalities of a single variable.

I.1.e: Simplify algebraic expressions involving negative and rational exponents.

#### I.2: Solve systems of equations and inequalities.

I.2.a: Solve systems of linear, absolute value, and quadratic equations algebraically and graphically.

I.2.b: Graph the solutions of systems of linear, absolute value, and quadratic inequalities on the coordinate plane.

I.2.c: Solve application problems involving systems of equations and inequalities.

#### I.3: Represent and compute fluently with complex numbers.

I.3.b: Simplify expressions involving complex numbers and express them in standard form, a + bi.

#### I.4: Model and solve quadratic equations and inequalities.

I.4.a: Model real-world situations using quadratic equations.

I.4.c: Solve quadratic equations of a single variable over the set of complex numbers by factoring, completing the square, and using the quadratic formula.

I.4.e: Write a quadratic equation when given the solutions of the equation.

### II: Students will understand and represent functions and analyze function behavior.

#### II.1: Represent mathematical situations using relations.

II.1.a: Model real-world relationships with functions.

II.1.c: Determine when a relation is a function.

II.1.d: Determine the domain and range of relations.

#### II.2: Evaluate and analyze functions.

II.2.c: Add, subtract, multiply, and divide functions.

II.2.d: Determine whether or not a function has an inverse, and find the inverse when it exists.

#### II.3: Define and graph exponential functions and use them to model problems in mathematical and real-world contexts.

II.3.a: Define exponential functions as functions of the form y = abx ,b > 0,b ?? 1.

II.3.b: Model problems of growth and decay using exponential functions.

II.3.c: Graph exponential functions.

#### II.4: Define and graph logarithmic functions and use them to solve problems in mathematics and real-world contexts.

II.4.a: Relate logarithmic and exponential functions.

II.4.d: Solve exponential and logarithmic equations.

II.4.e: Graph logarithmic functions.

II.4.f: Solve problems involving growth and decay.

### III: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

#### III.1: Examine the behavior of functions using coordinate geometry.

III.1.a: Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions.

III.1.c: Graph functions using transformations of parent functions.

III.1.d: Write an equation of a parabola in the form y = a(x − h)2 + k when given a graph or an equation..

#### III.2: Determine radian and degree measures for angles.

III.2.a: Convert angle measurements between radians and degrees.

III.2.b: Find angle measures in degrees and radians using inverse trigonometric functions, including exact values for special triangles.

#### III.3: Determine trigonometric measurements using appropriate techniques, tools, and formulas.

III.3.a: Define the sine, cosine, and tangent functions using the unit circle.

III.3.b: Determine the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle using reference angles.

### IV: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

#### IV.1: Apply basic concepts of probability.

IV.1.a: Distinguish between permutations and combinations and identify situations in which each is appropriate.

IV.1.b: Calculate probabilities using permutations and combinations to count events.

IV.1.c: Compute conditional and unconditional probabilities in various ways, including by definitions, the general multiplication rule, and probability trees.

#### IV.2: Use percentiles and measures of variability to analyze data.

IV.2.a: Compute different measures of spread, including the range, standard deviation, and interquartile range.

IV.2.b: Compare the effectiveness of different measures of spread, including the range, standard deviation, and interquartile range in specific situations.

Correlation last revised: 5/24/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.