Academic Standards

P.N.NE.A: Represent, interpret, compare, and simplify number expressions.

P.N.NE.A.1: Use the laws of exponents and logarithms to expand or collect terms in expressions; simplify expressions or modify them in order to analyze them or compare them.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions II

P.N.NE.A.2: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

P.N.NE.A.3: Classify real numbers and order real numbers that include transcendental expressions, including roots and fractions of pi and e.

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

P.N.NE.A.4: Simplify complex radical and rational expressions; discuss and display understanding that rational numbers are dense in the real numbers and the integers are not.

Operations with Radical Expressions

Rational Numbers, Opposites, and Absolute Values

Simplifying Radical Expressions

P.N.CN.A: Perform complex number arithmetic and understand the representation on the complex plane.

P.N.CN.A.1: Perform arithmetic operations with complex numbers expressing answers in the form a + bi.

P.N.CN.A.2: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane

Roots of a Quadratic

P.N.CN.A.3: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

P.N.CN.A.4: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

P.N.VM.A: Represent and model with vector quantities.

P.N.VM.A.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

P.N.VM.B: Understand the graphic representation of vectors and vector arithmetic.

P.N.VM.B.4: Add and subtract vectors.

P.N.VM.B.4.a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

P.N.VM.B.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

P.N.VM.B.4.c: Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

P.N.VM.B.6: Calculate and interpret the dot product of two vectors.

P.N.VM.C: Perform operations on matrices and use matrices in applications.

P.N.VM.C.9: Add, subtract, and multiply matrices of appropriate dimensions.

P.N.VM.C.13: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

P.A.S.A: Understand and use sequences and series.

P.A.S.A.1: Demonstrate an understanding of sequences by representing them recursively and explicitly.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

P.A.S.A.5: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

P.A.REI.A: Solve systems of equations and nonlinear inequalities.

P.A.REI.A.1: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

P.A.REI.A.2: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Solving Linear Systems (Matrices and Special Solutions)

P.A.C.A: Understand the properties of conic sections and model real-world phenomena.

P.A.C.A.2: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

P.A.C.A.3: From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics.

Circles

Ellipses

Hyperbolas

Parabolas

P.A.C.A.4: Transform equations of conic sections to convert between general and standard form.

Circles

Ellipses

Hyperbolas

Parabolas

P.F.BF.A: Build new functions from existing functions.

P.F.BF.A.1: Understand how the algebraic properties of an equation transform the geometric properties of its graph.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Parabolas

Quadratics in Vertex Form

Translating and Scaling Sine and Cosine Functions

P.F.BF.A.2: Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.

Addition and Subtraction of Functions

P.F.BF.A.5: Find inverse functions (including exponential, logarithmic, and trigonometric).

P.F.BF.A.5.c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

P.F.BF.A.5.d: Recognize a function is invertible if and only if it is one-to-one. Produce an invertible function from a non-invertible function by restricting the domain.

P.F.IF.A: Analyze functions using different representations.

P.F.IF.A.2: Analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real-world problems that can be modeled with these functions (by hand and with appropriate technology).

Compound Interest

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Rational Functions

P.F.IF.A.4: Identify the real zeros of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (exponential, polynomial, logarithmic, trigonometric, and rational).

Polynomials and Linear Factors

P.F.IF.A.5: Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c.

Absolute Value with Linear Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Parabolas

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

P.F.IF.A.8: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences

Geometric Sequences

P.F.TF.A: Extend the domain of trigonometric functions using the unit circle.

P.F.TF.A.1: Convert from radians to degrees and from degrees to radians.

Cosine Function

Sine Function

Tangent Function

P.F.TF.A.2: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

P.F.TF.A.3: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

P.F.TF.A.4: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

P.F.GT.A: Model periodic phenomena with trigonometric functions.

P.F.GT.A.1: Interpret transformations of trigonometric functions.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

P.F.GT.A.2: Determine the difference made by choice of units for angle measurement when graphing a trigonometric function.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

P.F.GT.A.3: Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

P.G.AT.A: Use trigonometry to solve problems.

P.G.AT.A.1: Use the definitions of the six trigonometric ratios as ratios of sides in a right triangle to solve problems about lengths of sides and measures of angles.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

P.G.TI.A: Apply trigonometric identities to rewrite expressions and solve equations.

P.G.TI.A.1: Apply trigonometric identities to verify identities and solve equations. Identities include: Pythagorean, reciprocal, quotient, sum/difference, double-angle, and half-angle.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

P.G.TI.A.2: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

P.S.MD.A: Model data using regressions equations.

P.S.MD.A.1: Create scatter plots, analyze patterns, and describe relationships for bivariate data (linear, polynomial, trigonometric, or exponential) to model real-world phenomena and to make predictions.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

P.S.MD.A.2: Determine a regression equation to model a set of bivariate data. Justify why this equation best fits the data.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

P.S.MD.A.3: Use a regression equation, modeling bivariate data, to make predictions. Identify possible considerations regarding the accuracy of predictions when interpolating or extrapolating.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Correlation last revised: 8/17/2021

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