Download Pre-Calculus

CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
N-CN
The Complex Number System
Perform arithmetic operations with complex numbers.
Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
N-CN.3
Edgenuity Lesson Name
Complex Numbers
N-CN.4
Represent complex numbers and their operations on the complex plane.
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.
Complex Numbers
Polar Coordinates
N-CN.5
Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the
complex plane; use properties of this representation for computation.
Complex Numbers
N-CN.6
Calculate the distance between numbers in the complex plane as the modulus of the difference, and the
midpoint of a segment as the average of the numbers at its endpoints.
Distance and Midpoints in the Complex
Plane
N-VM
N-VM.1
Vector and Matrix Quantities
Represent and model with vector quantities.
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).
Algebraic Vectors
Vectors in Three-Dimensional Space
N-VM.2
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a
terminal point.
Algebraic Vectors
N-VM.3
Solve problems involving velocity and other quantities that can be represented by vectors.
Algebraic Vectors
Geometric Vectors
N-VM.4
N-VM.4.a
Perform operations on vectors.
Add and subtract vectors.
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.
Geometric Vectors
N-VM.4.b
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
Algebraic Vectors
©Edgenuity, Inc.
Confidential
Page 1 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
Edgenuity Lesson Name
N-VM.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.
Geometric Vectors
N-VM.5
N-VM.5.a
Multiply a vector by a scalar.
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform
scalar multiplication component-wise, e.g., as c(v subscript x, v subscript y) = (cv subscript x, cv subscript y).
Dot Products of Vectors
Vectors in Three-Dimensional Space
N-VM.5.b
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that
when |c|v is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Vectors in Geometry
N-VM.6
Perform operations on matrices and use matrices in applications.
Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a
network.
Matrices
Networks
Organizing Data Into Matrices
N-VM.7
Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
N-VM.8
Add, subtract, and multiply matrices of appropriate dimensions.
Multiplication Matrix
Adding and Subtracting Matrices
Multiplication Matrix
N-VM.9
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a
commutative operation, but still satisfies the associative and distributive properties.
Multiplication Matrix
.N-VM.10
Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the
role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix
has a multiplicative inverse.
Determinants
Identity and Inverse Matrices
N-VM.11
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce
another vector. Work with matrices as transformations of vectors.
Vector Multiplication Using Matrices
©Edgenuity, Inc.
Confidential
Page 2 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
Edgenuity Lesson Name
N-VM.12
Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the
determinant in terms of area.
Determinants
Geometric Transformations with Matrices
Modeling Motion with Matrices
A-CED
A-CED.2
Creating Equations
Create equations that describe numbers or relationships
Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales.
Direct, Inverse, and Joint Variation
Writing Equations of Parallel and
Perpendicular Lines
Writing Linear Equations
A-REI
A-REI.3
Reasoning with Equations and Inequalities
Solve equations and inequalities in one variable
Solve linear equations and inequalities in one variable, including equations with coefficients represented by
letters.
Applications of Equations
Inequalities
Linear Inequalities
Solving Equations Graphically
A-REI.5
Solve systems of equations
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that
equation and a multiple of the other produces a system with the same solutions.
Solving Systems of Equations in Three
Variables
Solving Systems of Equations in Two
Variables
A-REI.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
Solving Systems of Equations in Two
Variables
A-REI.8
Represent a system of linear equations as a single matrix equation in a vector variable.
A-REI.9
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 Systems With Matrix Equations
Solving Systems With Matrix Equations
©Edgenuity, Inc.
Confidential
Page 3 of 9
CA- Common Core Pre-Calculus
Standard ID
A-REI.12
Selected Standards from the Common Core State Standards
Standard Text
Edgenuity Lesson Name
Represent and solve equations and inequalities graphically
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case
of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the
intersection of the corresponding half-planes.
Graphing Linear Inequalities
Linear Programming
Solving Systems of Linear Inequalities
F-IF
F-IF.2
Interpreting Functions
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use
function notation in terms of a context.
Functions and Their Properties
Operations with Functions
F-IF.4
F-IF.5
F-IF.7
F-IF.7.b
©Edgenuity, Inc.
Interpret functions that arise in applications in terms of the context
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.
Functions and Their Properties
Parabolas
Piecewise Functions
Symmetry and Coordinate Graphs
Twelve Basic Functions
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes.
Functions and Their Properties
Piecewise Functions
Twelve Basic Functions
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and
using technology for more complicated cases.
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value
functions.
Families of Graphs
Graphs and Transformations
Graphs of Nonlinear Inequalities
Piecewise Functions
Vertical and Horizontal Translations
Confidential
Page 4 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
Edgenuity Lesson Name
F-IF.7.c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end
behavior.
Fundamental Polynomial Connections
Locating Zeros of a Polynomial Function
F-IF.7.d
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and
showing end behavior.
Graphs of Rational Functions
F-IF.7.e
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric
functions, showing period, midline, and amplitude.
Twelve Basic Functions
F-IF.8
F-IF.8.a
Write a function defined by an expression in different but equivalent forms to reveal and explain different
properties of the function.
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.
Solving Quadratic Equations Algebraically
F-BF
F-BF.1
F-BF.1.b
Building Functions
Build a function that models a relationship between two quantities
Write a function that describes a relationship between two quantities.
Combine standard function types using arithmetic operations.
Operations with Functions
F-BF.1.c
Compose functions.
Operations with Functions
F-BF.3
Build new functions from existing functions
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.
Analyzing Graphs of Quadratic Functions
Families of Graphs
Graphs and Transformations
Vertical and Horizontal Translations
F-BF.4
F-BF.4.b
Find inverse functions.
Verify by composition that one function is the inverse of another.
F-BF.4.d
Produce an invertible function from a non-invertible function by restricting the domain.
Inverse Functions and Relations
Trigonometric Inverses and Their Graphs
©Edgenuity, Inc.
Confidential
Page 5 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
Edgenuity Lesson Name
F-LE
F-LE.1
Linear, Quadratic, and Exponential Models
Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.1.a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions
grow by equal factors over equal intervals.
F-LE.1.b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Exponential and Logistic Functions
Direct, Inverse, and Joint Variation
Graphing Linear Equations
F-LE.1.c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative
to another.
Exponential and Logistic Functions
F-LE.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs (include reading these from a table).
Exponential and Logistic Functions
The Number e
F-LE.4
For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are
numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Logarithmic Functions and Their Graphs
F-TF
F-TF.1
Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Angles and Radian Measure
F-TF.3
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.
Applying Trigonometric Functions
Circular Functions
The Unit Circle
F-TF.4
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Amplitude and Period
The Cosine Function
The Sine Function
©Edgenuity, Inc.
Confidential
Page 6 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
Edgenuity Lesson Name
F-TF.6
Model periodic phenomena with trigonometric functions
Understand that restricting a trigonometric function to a domain on which it is always increasing or always
decreasing allows its inverse to be constructed.
Trigonometric Inverses and Their Graphs
F-TF.7
Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions
using technology, and interpret them in terms of the context.
Inverse Functions
F-TF.9
Prove and apply trigonometric identities
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Double-Angle and Half-Angle Identities
Sum and Difference Identities
Verifying Trigonometric Identities
G-SRT
G-SRT.9
Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations
Apply trigonometry to general triangles
Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
Area and The Law of Sines
G-SRT.10
Prove the Laws of Sines and Cosines and use them to solve problems.
Law of Sines and Law of Cosines — a Deeper
Look
The Law of Cosines
The Law of Sines
G-SRT.11
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and
non-right triangles (e.g., surveying problems, resultant forces).
The Ambiguous Case for the Law of Sines
The Law of Cosines
The Law of Sines
G-GPE
G-GPE.1
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
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.
Circles
Circles and Parabolas
©Edgenuity, Inc.
Confidential
Page 7 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
G-GPE.2
Derive the equation of a parabola given a focus and directrix.
Edgenuity Lesson Name
Circles and Parabolas
Parabolas
G-GPE.3
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.
Ellipses
Hyperbolas
S-CP
Conditional Probability and the Rules of Probability
Use the rules of probability to compute probabilities of compound events in a uniform probability model
S-CP.8
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B),
and interpret the answer in terms of the model.
Multiplying Probabilities
S-CP.9
Use permutations and combinations to compute probabilities of compound events and solve problems.
Probability with Combinations or
Permutations
S-MD
S-MD.1
Using Probability to Make Decisions
Calculate expected values and use them to solve problems
Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample
space; graph the corresponding probability distribution using the same graphical displays as for data
distributions.
Probability
S-MD.2
Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
Probability
S-MD.3
Develop a probability distribution for a random variable defined for a sample space in which theoretical
probabilities can be calculated; find the expected value.
Basic Statistics
S-MD.4
Develop a probability distribution for a random variable defined for a sample space in which probabilities are
assigned empirically; find the expected value.
Basic Statistics
Normal Distributions
S-MD.5
S-MD.5.a
Use probability to evaluate outcomes of decisions
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected
values.
Find the expected payoff for a game of chance.
Basic Statistics
©Edgenuity, Inc.
Confidential
Page 8 of 9
CA- Common Core Pre-Calculus
Selected Standards from the Common Core State Standards
Standard ID
Standard Text
S-MD.5.b
Evaluate and compare strategies on the basis of expected values.
Edgenuity Lesson Name
Decision Making Using Probability
S-MD.6
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Probability with Combinations and
Permutations
S-MD.7
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game).
Decision Making Using Probability
©Edgenuity, Inc.
Confidential
Page 9 of 9