### 1: Number and Operations

#### 1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.1.1: Solve problems and equations that require the number system to be extended from real to complex numbers.

1.1.2: Convert between radical and exponential forms of numerical expressions.

### 2: Data Analysis, Probability, and Discrete Mathematics

#### 2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.2: Compare data sets using graphs and summary statistics, including variance and standard deviation, with or without technology.

2.1.3: Compute and explain summary statistics for distributions of data including measures of center and spread, including variance and standard deviation.

2.1.7: Determine when arguments based on data mistake correlation for causation.

2.1.8: Draw a line of best fit for a scatterplot with or without technology, describe how the correlation coefficient relates to fit, and explain when it is appropriate to use the regression equation to make predictions.

#### 2.2: Understand and apply the basic concepts of probability.

2.2.1: Apply probability concepts to calculate the probability of events and to make informed decisions in practical situations.

2.2.2: Use the principal characteristics of the normal distribution to estimate probabilities.

2.2.3: Estimate probabilities and predict outcomes using one- and two-variable data.

#### 2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.1: Use the binomial theorem and Pascal's Triangle to solve problems.

2.3.2: Demonstrate the connections between the binomial coefficients, entries of Pascal's triangle, and combinations.

### 3: Patterns, Algebra, and Functions

#### 3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Analyze sequences and series and use them in modeling, including

3.1.1.a: explicit formulas for nth terms,

3.1.2: Apply recursive formulas for arithmetic and geometric sequences to solve problems.

3.1.4: Solve problems involving recursion.

#### 3.2: Describe and model functions and their relationships.

3.2.1: Express and solve problems that can be modeled using linear, quadratic, logarithmic, exponential, cubic, reciprocal, absolute value, and step and other piecewise-defined functions; interpret their solutions in terms of the context.

3.2.3: Graph absolute value, and step and other piecewise-defined functions identifying their key characteristics.

3.2.4: Graph exponential functions identifying their key characteristics.

3.2.6: Graph polynomial functions identifying their key characteristics.

3.2.7: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions.

3.2.8: Find the major and minor axes, intercepts and asymptotes of conic sections.

3.2.9: Find domain, range, intercepts, period, amplitude, and asymptotes of trigonometric functions.

3.2.10: Given a function

3.2.10.a: find the inverse of the function,

3.2.12: Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes Rule of Signs, the Conjugate Root Theorem) to find the zeros of a polynomial function.

3.2.14: Combine functions by composition, as well as by addition, subtraction, multiplication, and division including any necessary restrictions on the domain.

3.2.16: Identify the degree of a given polynomial function and write a polynomial function of a given degree.

#### 3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.1: Rewrite and describe the need for equivalent forms of algebraic expressions.

3.3.2: Apply the laws of exponents including rational and negative exponents to rewrite expressions in alternative forms.

3.3.4: Use matrices to represent everyday problems that involve systems of linear equations.

3.3.5: Simplify radical expressions by performing operations on them.

3.3.6: Divide a polynomial by a lower degree polynomial.

3.3.7: Find complex solutions for quadratic equations.

3.3.8: Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression with and without technology.

3.3.11: Add, subtract, and compute the dot product of two-dimensional vectors; multiply a two-dimensional vector by a scalar.

#### 3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.5: Solve problems involving compound interest.

3.4.6: Demonstrate the relationship between

3.4.6.a: simple interest and linear growth

3.4.6.b: compound interest and exponential growth.

### 4: Geometry and Measurement

#### 4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Perform basic geometric constructions using a variety of methods, including

4.1.1.a: perpendicular bisector of a line segment,

4.1.1.b: bisector of an angle

4.1.1.c: perpendicular or parallel lines.

#### 4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Describe how changing the parameters of a quadratic function affects the shape and position of its graph (f(x) = a(x-h)²+k).

4.2.2: Describe how changing the parameters of an exponential function affects the shape and position of its graph (f(x) = ab to the x power).

#### 4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.2: Determine an equation of a circle given its center and radius; given an equation of a circle, find its center and radius.

4.3.3: Graph equations of conic sections explaining the relationship between their algebraic form and key characteristics of the graph.

4.3.4: Graph all six trigonometric functions identifying their key characteristics.

4.3.5: Evaluate all six trigonometric functions at angles between (0 degrees and 360 degrees, 0 and 2π radians) using the unit circle in the coordinate plane.

#### 4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.1: Explain, use, and convert between degree and radian measures for angles.

Correlation last revised: 1/20/2017

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