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Antelope Valley Union High School District
Algebra II
Curriculum Outline
Course Title: Algebra II
Date Adopted: March 17, 1999
Department: Mathematics
Fulfills UC/CSU Requirement: Yes
Pre-Requisite: Geometry with a grade
of C or better or consent
of the course instructor
Fulfills CSF Requirement: Yes
Length of Course: 2 Semesters
Fulfills H/S Graduation Credit As:
Required X Elective
Semester Units/Credits: 5
Course No.: 10402A
Grade Level: 9-12
I.
Course Description
Algebra II deepens and extends the Algebra I course which studies the structure of the real
number system and problem solving using equations, inequalities, and graphs and the
simplification of algebraic expressions. The course covers all of the California Mathematics
Academic Content Standards (1998) for Algebra II.
II.
Rationale
Algebra II is a must course for students planning to major in math, science, or engineering. It
is the third course in the college required three years of high school mathematics.
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
1. Number and Number Theory
The student will demonstrate an understanding of number concepts and number theory, by
identifying and using the forms of complex numbers, by applying number properties and
algebraic procedures, and by using concepts of discrete math to solve algebraic problems.
1.1
Understands Real Number System
The student will demonstrate understanding of the real number system.
001
1.1.1
Explains Similarities/Differences of Subsystems
The student will explain the similarities and differences in the subsystems of
real numbers (e.g., rational, complex, prime, factors, multiples). (Expected)
002
1.1.2
Defines Abstract Math Concepts
The student will define abstract mathematical concepts (e.g., imaginary
numbers, absolute value, irrational numbers). (Expected)
1.2
Performs Operations With Real Numbers
The student will perform operations on number sentences containing exponents.
007
1.2.1
Performs Operations With Scientific Notation
The student will perform operations on numbers written in scientific
notation. (Essential)
008
1.2.2
Reduces Fractions With Positive/Negative Exponents
The student will reduce fractions with positive and negative exponents in the
denominator. (Essential)
009
1.2.3
Performs Operations - Exponents
The student will perform operations on number sentences containing integral
and fractional exponents. (Essential)
1.3
Understands Complex Numbers
The student will demonstrate understanding of complex numbers.
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
019
1.3.1
Relates Complex Numbers to Real/Imaginary
The student will describe the complex number system in relation to real
numbers and imaginary numbers. (Expected)
020
1.3.2
Performs Operations on Complex Numbers
The student will add, subtract, multiply, and divide complex numbers.
(Expected)
2. Geometry
The student will demonstrate an understanding of geometry appropriate to algebra by using
coordinate geometry to solve problems.
2.1
Understands Geometric Relationships
The student will demonstrate understanding of relationships among geometric figures.
039
2.1.1
Solves Word Problems Using Trigonometry
The student will solve word problems involving the missing sides and
angles of a right triangle, using trigonometric ratios. (Expected)
3. Functions
The student will demonstrate an understanding of functions by translating among tabular,
symbolic, and graphic representations of functions, by classifying and performing operations on
linear, quadratic, and exponential functions, and by applying trigonometric functions.
3.1
Defines/Analyzes Functional Relationships
The student will define and analyze functional relationships.
044
3.1.1
Distinguishes Between Arithmetic/Geometric Sequence
The student will distinguish between an arithmetic and geometric sequence.
(Expected)
045
3.1.2
Finds Terms in Arithmetic/Geometric Sequences
The student will find the missing term or the nth term in arithmetic or
geometric sequences. (Expected)
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
3.1.3
Derives Formula/Finds Sum of Arithmetic Series
The student will derive the formula and find the sum of an arithmetic series.
(Expected)
3.1.4
Derives Formula/Finds Sum of Geometric Series
The student will derive the formula and find the sum of a finite geometric
series or infinite geometric series. (Expected)
048
3.1.5
Applies Binomial Theorem
The student will apply the binomial theorem. (Essential)
3.2
Applies Functions to Real World
The student will apply a variety of functions to model real-world phenomena.
054
3.2.1
Draws Graph/Writes Situation
The student will draw a graph to represent a problem situation or write a
possible problem situation that a graph could represent. (Essential)
055
3.2.2
Writes Function/Situation
The student will write a linear, quadratic, or exponential function to
represent a problem situation or will write a possible situation that a linear,
quadratic, or exponential function could represent. (Expected)
3.3
Understands Tabular/Symbolic/Graphic Representations
The student will demonstrate understanding of tabular, symbolic, and graphic
representations of functions.
061
3.3.1
Creates Tables/Graphs/Diagrams/Ordered Pairs
The student will create tables, graphs, mapping diagrams, input-output
diagrams, and ordered pairs from a function. (Essential)
062
3.3.2
Determines Domain/Range
The student will determine the domain and range of a function. (Expected)
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
063
3.3.3
Identifies Function/Inverse
The student will identify a function and its inverse from ordered pairs,
equations, and graphs. (Expected)
3.4
Analyzes Effects of Parameter Changes
The student will analyze the effects of parameter changes on the graphs of functions.
070
3.4.1
Recognizes Effect of Changing Slope/y-Intercept
The student will recognize the effect of changing the slope or y-intercept of
a linear equation. (Essential)
071
3.4.2
Recognizes Changes - Horizontal/Vertical Shifts/Reflections
The student will recognize changes in a function resulting in horizontal or
vertical shifts or reflections about an axis. (Essential)
072
3.4.3
Recognizes/Explains Effect of Changing Coefficient
The student will recognize and explain how the graph of a quadratic
equation changes as the coefficients in the equation change. (Expected)
3.5
Understands Classes of Functions
The student will demonstrate understanding of operations on, and the general
properties and behavior of, classes of functions.
077
3.5.1
Performs Operations on Functions
The student will perform operations on functions (e.g., sum, product, and
composition of functions) and justify the steps used. (Essential)
078
3.5.2
Classifies Functions
The student will classify functions (e.g., linear, quadratic, exponential).
(Essential)
079
3.5.3
Describes Characteristics/Properties - Functions
The student will describe the characteristics and properties of classes of
functions. (Essential)
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
056
3.5.4
Uses Exponential Functions
The student will use exponential functions to solve exponential growth and
decay problems. (Expected)
4. Algebra
The student will demonstrate an understanding of algebra by simplifying expressions containing
exponents and imaginary numbers, by solving and graphing inequalities, by evaluating, solving,
and graphing equations involving radicals, exponents, polynomials, and conic sections, by
solving systems of equations, and by applying the binomial theorem.
4.1
Understands Algebraic Representation
The student will demonstrate understanding of the use of variables and symbols in
algebraic expressions and equations.
085
4.1.1
Translates English Phrase/Sentence
The student will translate an English phrase or sentence into an algebraic
expression or equation (linear, quadratic, or exponential) to solve a problem.
(Essential)
086
4.1.2
Uses Mathematical Symbols
The student will use appropriate mathematical symbols. (Essential)
088
4.1.3
Restates Equation in Alternate/Standard Form
The student will restate an equation in an alternate form or standard form.
(Essential)
089
4.1.4
Uses Logarithms/Antilogarithms to Convert
The student will use logarithms and antilogarithms to convert an expression
to an equivalent expression. (Expected)
090
4.1.5
Converts Between Logarithmic/Exponential Forms
The student will convert a logarithmic equation to an exponential equation
and vice versa. (Essential)
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
091
4.1.6
Uses Properties of Logarithms
The student will use the properties of logarithms to simplify logarithmic
expressions. (Essential)
4.2
Simplifies Expressions - Real/Complex Numbers
The student will simplify algebraic expressions containing real or complex numbers.
096
4.2.1
Simplifies Imaginary/Complex Numbers
The student will simplify expressions involving imaginary or complex
numbers. (Expected)
097
4.2.2
Simplifies Negative/Fractional Exponents
The student will simplify expressions containing negative or fractional
exponents. (Essential)
098
4.2.3
Simplifies Radical Expressions
The student will simplify expressions containing radicals. (Essential)
4.3
Solves Equations
The student will solve equations.
106
4.3.1
Solves Fractional/Radical Equations
The student will solve fractional and radical equations. (Essential)
107
4.3.2
Solves Logarithmic/Exponential Equations
The student will solve logarithmic and exponential equations. (Expected)
108
4.3.3
Solves Complex Number Equations
The student will solve equations containing complex numbers. (Expected)
109
4.3.4
Solves Systems of Linear Equations
The student will solve systems of linear equations in two variables.
(Essential)
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5/4/2017
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
111
4.3.5
Finds Solution for Set of Linear Equations
The student will find the solution for a set of linear equations and determine
if the equations are consistent/inconsistent or dependent/independent.
(Essential)
112
4.3.6
Solves Systems of Three Linear Equations
The student will solve systems of three linear equations with or without
matrices. (Expected)
4.4
Understands Inequalities
The student will demonstrate understanding of how to solve inequalities.
117
4.4.1
Solves Absolute Value Inequalities
The student will solve absolute value inequalities. (Expected)
118
4.4.2
Solves Compound Inequalities
The student will solve compound inequalities. (Expected)
119
4.4.3
Solves Systems of Linear Inequalities
The student will solve systems of linear inequalities. (Expected)
4.5
Represents With Charts/Tables/Graphs
The student will represent expressions, equations, and inequalities with charts, tables,
and graphs.
125
4.5.1
Creates Tables/Graphs to Interpret Equations
The student will create tables and graphs to interpret equations. (Essential)
126
4.5.2
Identifies Graph of Linear/Absolute Value Equation
The student will identify the graph of a linear or absolute value equation.
(Essential)
127
4.5.3
Graphs Equations/Determines Equations From Graph
The student will graph linear and absolute value equations and will
determine the equations from a graph. (Expected)
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5/4/2017
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
128
4.5.4
Graphs Inequalities/Determines Inequality From Graph
The student will graph linear or absolute value inequalities and will
determine an inequality from a graph. (Expected)
129
4.5.5
Identifies Graph of Logarithmic/Exponential Function
The student will identify the graph of a logarithmic or exponential function.
(Expected)
148
4.5.6
Graphs Quadratic Function
The student will graph a quadratic function and determine the discriminant,
maximum point, minimum point, and zeros (or roots) of the equation.
(Essential)
4.6
Simplifies/Factors/Solves Polynomials
The student will simplify and factor polynomial expressions and solve polynomial
equations.
135
4.6.1
Simplifies Polynomials
The student will simplify polynomial expressions by performing operations,
including synthetics and long division. (Expected)
136
4.6.2
Factors Polynomials
The student will factor polynomials, including perfect squares, perfect
square trinomials, and the sum and difference of two cubes. (Essential)
137
4.6.3
Performs Operations on Polynomial Fractions
The student will use operations to simplify and evaluate rational expressions
with monomial and polynomial denominators. (Essential)
138
4.6.4
Solves Polynomial Equations
The student will solve polynomial equations of degree two or greater.
(Expected)
4.7
Solves Quadratic Equations
The student will solve quadratic equations.
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5/4/2017
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
143
4.7.1
Solves Quadratic Equations
The student will solve quadratic equations by factoring, completing the
square, or using the quadratic formula. (Essential)
144
4.7.2
Identifies Sum and Product of Quadratics
The student will identify the sum and product of a quadratic equation.
(Expected)
149
4.7.3
Solves/Graphs Quadratic Inequalities
The student will solve and graph quadratic inequalities. (Expected)
145
4.7.4
Determines Equation From Graph
The student will determine the equation from a graph that is not a straight
line (parabola, circle, ellipse, hyperbola). (Expected)
146
4.7.5
Identifies/Describes Conic Graphs/Equations
The student will identify and describe the graphs and equations of the conic
sections (circle, parabola, ellipse, hyperbola). (Expected)
150
4.7.6
Solves Quadratic Equations - Complex Numbers
The student will solve quadratic equations in the complex number system.
(Expected)
4.8
Applies Discrete Math
The student will apply discrete structures such as finite graphs, matrices, and
algorithms to the solution of mathematical problems.
158
4.8.1
Performs Operations on Matrices
The student will perform operations on a set of matrices. (Essential)
159
4.8.2
Uses Properties of 0 to Solve Matrices
The student will use the properties of 0 when solving matrices. (Essential)
160
4.8.3
Evaluates Matrix Properties
The student will evaluate the properties of matrices. (Essential)
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
161
4.8.4
Uses Cramer’s Rule to Solve Matrices
The student will solve matrices of equations using Cramer’s rule.
(Expected)
164
4.8.5
Uses Matrices to Solve Word Problems
The student will use matrices to solve word problems. (Extended)
165
4.8.6
Uses Algorithms to Solve Math Problems
The student will use a variety of algorithms to solve mathematical problems.
(Expected)
5. Statistics and Probability
The student will demonstrate an understanding of statistics and probability by finding measures
of central tendency, by determining the probability of dependent and independent simple and
compound events, and by computing combinations and permutations.
5.1
Organizes/Interprets Data
The student will organize and interpret mathematical data in several forms.
171
5.1.1
Constructs or Interprets Graphs/Charts
The student will construct or interpret graphs, charts, and other forms of
organized data. (Expected)
172
5.1.2
Finds Line of Regression
The student will choose the equation that best represents the line of
regression when applied to a statistical model represented by a scatter plot.
(Essential)
173
5.1.3
Uses Curve Fitting
The student will use curve fitting to identify the equation of a line that best
describes data on the coordinate plane. (Extended)
5.2
Determines/Applies Measures of Central Tendency
The student will determine and apply measures of central tendency.
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Algebra II
Curriculum Outline
180
5.2.1
Computes Variance/Standard Deviation
The student will compute the variance and standard deviation of a
distribution of data. (Expected)
5.3
Understands Prediction/Probability/Counting
The student will demonstrate understanding of the prediction and counting of
outcomes based on data.
185
5.3.1
Identifies/Determines Independent and Dependent Probabilities
The student will identify and determine independent and dependent
probabilities. (Essential)
187
5.3.2
Uses Counting Techniques
The student will use counting techniques, including permutations and
combinations, to determine the number of possible outcomes in a
mathematical situation and will use the information to determine
probabilities. (Essential)
5.4
Designs/Conducts Probability Experiment
The student will design and/or conduct an experiment in probability.
192
5.4.1
Gathers/Graphs Data
The student will gather and graph data in real-life situations. (Expected)
193
5.4.2
Experiments to Study Problem
The student will design and/or conduct an experiment to study a problem by
making predictions, by forming hypotheses, and by compiling data.
(Expected)
6. Reasoning and Problem Solving
The student will use inductive or deductive reasoning to solve mathematical and financial
management problems, formulating problems from situations, developing and applying strategies
(including algebraic, geometric, and technological), verifying solutions, and applying strategies,
or solutions to new problems.
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Algebra II
Curriculum Outline
6.1
Formulates Problems
The student will formulate problems from everyday and mathematical situations.
202
6.1.1
Formulates Mathematical Word Problems
The student will create mathematical word problems from everyday and
mathematical situations. (Expected)
6.1.2
Identifies Equations/Inequality to Represent Problem
The student will identify the equation or inequality that represents a problem
situation. (Extended)
6.2
Uses Logical Reasoning/Constructs Arguments
The student will use logical reasoning and construct valid arguments
198
6.2.1
Uses Logic to Evaluate Validity of Argument/Conclusion
The student will use logic to evaluate the validity of a mathematical
argument or conclusion (e.g., using properties of numbers, exponents, and
logarithms).
201
6.2.2
Uses Induction
The student will use mathematical induction to prove statements.
6.3
Develops/Applies Problem-Solving Strategies
The student will develop and apply strategies to solve a variety of problems.
203
6.3.1
Identifies Missing/Extraneous Information
The student will identify missing and/or extraneous information in a given
problem. (Essential)
209
6.3.2
Uses Tools in Problem Solving
The student will use calculators, computers, spreadsheets, and graphing
utilities in problem solving. (Essential)
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Algebra II
Curriculum Outline
7. Communication and Connections
The student will communicate his or her understanding of mathematical ideas, using
mathematical language, symbols, technology, and models and illustrating the connections among
mathematical concepts.
7.1
Communicates Ideas/Reasoning
The student will communicate mathematical ideas and reasoning processes, using
appropriate mathematical language and symbols.
214
7.1.1
Expresses Math Ideas Orally/in Writing
The student will express his or her mathematical ideas both orally and in
writing. (Essential)
215
7.1.2
Applies Terminology of Algebra
The student will apply the terminology of algebra (e.g., polynomials,
functions, conics, sets). (Expected)
7.2
Relates Mathematical Concepts to Representations
The student will relate mathematical concepts to mathematical representations.
220
7.2.1
Identifies Problems Represented by Models
The student will identify problem situations that could be represented by
given mathematical models (e.g., number sentences, equations, graphs,
tables, diagrams). (Expected)
7.3
Responds to Math Presentations
The student will respond to written, visual, or oral presentations of mathematics.
225
7.3.1
Asks Clarifying/Extending Questions
The student will ask clarifying and extending questions related to
mathematics presentations. (Expected)
7.4
Demonstrates Connections Between Math/Other Disciplines
The student will demonstrate the connections between mathematics and other
disciplines.
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Antelope Valley Union High School District
Algebra II
Curriculum Outline
230
7.4.1
Applies Math to Other Disciplines
The student will apply mathematical concepts to solving problems in other
disciplines (e.g., physics, chemistry, biology). (Expected)
232
7.4.2
Identifies Historical Relevance
The student will identify historical relevance of important mathematical
accomplishments. (Extended)
7.5
Demonstrates Connections Among Strands
The student will display his or her achievement in understanding the connections
among mathematical strands through investigations, performance tasks, writing, openended questions, portfolios, and other active assessments.
238
7.5.1
Applies Mathematical Strands to Solve Problems
The student will apply algebra, geometry, and other mathematical strands
together in order to solve real-world problems, using mathematical language
and representation (Expected)
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MCAD® is a registered trademark of NCS.
5/4/2017