Download ALG 2 Topics

1.1 Properties of Real Numbers
 Graph and order real numbers
 Identify and use properties of real numbers
1.2 Algebraic Expressions
 Evaluate algebraic expressions
 Simplify algebraic expressions
1.3 Solving Equations
 Solve equations
 Solve problems by writing equations
1.4 Solving Inequalities
 Solve and graph inequalities
 Solve and write compound inequalities
1.5 Absolute Value Equations and Inequalities
 Solve absolute value equations
 Solve absolute value inequalities
1.6 Probability
 Find experimental probabilities
 Find theoretical probabilities
2.1 Relations and Functions
 Graph relations
 Identify functions
2.2 Linear Equations
 Graph linear equations
 Write equations of lines
2.3 Direct Variation
 Write and interpret direct variation equations
2.4 Using Linear Models
 Write linear equations that model real-world
data
 Make predictions from linear models
2.5 Absolute Value Functions and Graphs
 Graph absolute value functions
2.6 Families of Functions
 Analyze translations
 Analyze stretches, shrinks, and reflections
2.7 Two-Variable Inequalities
 Graph linear inequalities
 Graph absolute value inequalities
3.1 Graphing Systems of Equations
 Solve a system by graphing
3.2 Solving Systems Algebraically
 Solve a system by substitution
 Solve a system by elimination
3.3 Systems of Inequalities
 Solve systems of linear inequalities
3.4 Linear Programming
 Find maximum and minimum values
 Solve problems with linear programming
3.5 Graphs in Three Dimensions
 Graph points in three dimensions
 Graph equations in three dimensions
3.6 Systems With Three Variables
 Solve systems in three variables by elimination
 Solve systems in three variables by substitution
4.1 Organizing Data Into Matrices
 Identify matrices and their elements
 Organize data into matrices
4.2 Adding and Subtracting Matrices
 Add and subtract matrices
 Solve certain matrix equations
4.3 Matrix Multiplication
 Multiply a matrix by a scalar
 Multiply two matrices
4.4 Geometric Transformations with Matrices
 Represent translations and dilations with
matrices
 Represent reflections and rotations with matrices
4.5 2x2 Matrices, Determinants, and Inverses
 Evaluate determination of 2x2 matrices and find
inverse matrices
 Use inverse matrices in solving matrix equations
4.6 3x3 Matrices, Determinants, and Inverses
 Evaluate determinants of 3x3 matrices
 Use inverse matrices in solving matrix equations
4.7 Inverse Matrices and Systems
 Solve systems of equations using inverse
matrices
4.8 Augmented Matrices and Systems
 Solve a system of equations using Cramer’s
Rule
 Solve a system of equations using augmented
matrices
5.1 Modeling Data With Quadratic Functions
 Identify quadratic functions and graphs
 Model data with quadratic functions
5.2 Properties of Parabolas
 Graph quadratic functions
 Find maximum and minimum values of
quadratic functions
5.3 Transforming Parabolas
 Use the vertex form of a quadratic function
5.4 Factoring Quadratic Expressions
 Find common and binomial factors of quadratic
expressions
 Factor special quadratic expressions
5.5 Quadratic Equations
 Solve quadratic equations by factoring and by
finding square roots
 Solve quadratic equations by graphing
5.6 Complex Numbers
 Identify and graph complex numbers
 Add, subtract, and multiply complex numbers
5.7 Completing the Square
 Solve equations by completing the square
 Rewrite functions by completing the square
5.8 The Quadratic Formula
 Solve quadratic equations by using the
Quadratic Formula
 Determine types of solutions by using the
discriminant
6.1 Polynomial Functions
 Classify polynomials
 Model data using polynomial functions
6.2 Polynomials and Linear Factors
 Analyze the factored form of a polynomial
 Write a polynomial function from its zeros
6.3 Dividing Polynomials
 Divide polynomials using long division
 Divide polynomials using synthetic division
6.4 Solving Polynomial Equations
 Solve polynomial equations by graphing
 Solve polynomial equations by factoring
6.5 Theorems About Roots of Polynomial Equations
 Solve equations using the Rational Root
Theorem
 Use the Irrational Root Theorem and the
Imaginary Root Theorem
6.6 The Fundamental Theorem of Algebra
 Use the Fundamental Theorem of Algebra in
solving polynomial equations with complex
roots
6.7 Permutations and Combinations
 Count permutations
 Count combinations
6.8 The Binomial Theorem
 Use Pascal’s Triangle
 Use the Binomial Theorem
7.1 Roots and Radical Expressions
 Simplify nth roots
7.2 Multiplying and Dividing Radical Expressions
 Multiply radical expressions
 Divide radical expressions
7.3 Binomial Radical Expressions
 Add and subtract radical expressions
 Multiply and divide binomial radical expressions
7.4 Rational Exponents
 Simplify expressions with rational exponents
7.5 Solving Square Root and Other Radical Equations
 Solve square root and other radical equations
7.6 Function Operations
 Add, subtract, multiply, and divide functions
 Find the composite of two functions
7.7 Inverse Relations and Functions
 Find the inverse of a relation or function
7.8 Graphing Square Root and Other Radical Functions
 Graph square root and other radical functions
8.1 Exploring Exponential Models
 Model exponential growth
 Model exponential decay
8.2 Properties of Exponential Functions
 Identify the role of constants in y  abcx
 Use e as a base
8.3 Logarithmic Functions as Inverses
 Write and evaluate logarithmic expressions
 Graph logarithmic functions
8.4 Properties of Logarithms
 Use the properties of logarithms
8.5 Exponential and Logarithmic Equations
 Solve exponential equations
 Solve logarithmic equations
8.6 Natural Logarithms
 Evaluate natural logarithmic expressions
 Solve equations using natural logarithms
9.1 Inverse Variation
 Use inverse variation
 Use joint and other variations
9.2 The Reciprocal Function Family
 Graph reciprocal functions
 Graph translations of reciprocal functions
9.3 Rational Functions and Their Graphs
 Identify properties of rational functions
 Graph rational functions
9.4 Rational Expressions
 Simplify rational expressions
 Multiply and divide rational expressions
9.5 Adding and Subtracting Rational Expressions
 Add and subtract rational expressions
 Simplify complex fractions
9.6 Solving Rational Equations
 Solve rational equations
 Use rational equations in solving problems
9.7 Probability of Multiple Events
 Find the probability of the event A and B
 Find the probability of the event A or B
10.1 Exploring Conic Sections
 Graph conic sections
 Identify conic sections
10.2 Parabolas
 Write the equation of a parabola
 Graph parabolas
10.3 Circles
 Write and graph the equation of a circle
 Find the center and radius of a circle and use it
to graph the circle
10.4 Ellipses
 Write the equation of an ellipse
 Find the foci of an ellipse and graph an ellipse
10.5 Hyperbolas
 Graph hyperbolas
 Find and use the foci of a hyperbola
10.6 Translating Conic Sections
 Write the equation of a translated conic section
 Identify a translated conic section from an
equation
11.1 Mathematical Patterns
 Identify mathematical patterns
 Use a formula for finding the nth term of a
sequence
11.2 Arithmetic Sequences
 Identify and generate arithmetic sequences
11.3 Geometric Sequences
 Identify and generate geometric sequences
11.4 Arithmetic Series
 Write and evaluate arithmetic series
 Use summation notation
11.5 Geometric Series
 Evaluate a finite geometric series
 Evaluate an infinite geometric series
11.6 Area Under a Curve
 Find area under a curve
12.1 Probability Distributions
 Make a probability distribution
 Use a probability distribution in conducting a
simulation
12.2 Conditional Probability
 Find conditional probabilities
 Use formulas and tree diagrams
12.3 Analyzing Data
 Calculate measures of central tendency
 Draw and interpret box-and-whisker plots
12.4 Standard Deviation
 Find the standard deviation of a set of values
 Use standard deviation in real-world situations
12.5 Working with Samples
 Find sample proportions
 Find the margin of error
12.6 Binomial Distributions
 Find binomial probabilities
 Use binomial distributions
12.7 Normal Distributions
 Use a normal distribution
 Use the standard normal curve
13.1 Exploring Periodic Data
 Identify cycles and periods of periodic functions
 Find the amplitude of periodic functions
13.2 Angles and the Unit Circle
 Work with angles in standard position
 Find coordinates of points on the unit circle
13.3 Radian Measure
 Use radian measure for angles
 Find the length of an arc of a circle
13.4 The Sine Function
 Identify properties of the sine function
 Graph Sine curves
13.5 The Cosine Function
 Graph and write cosine functions
 Solve trigonometric equations
13.6 The Tangent Function
 Graph the tangent function
13.7 Translating Sine and Cosine Functions
 Graph translations of trigonometric functions
 Write equations of translations
13.8 Reciprocal Trigonometric Functions
 Evaluate reciprocal trigonometric functions
 Graph reciprocal trigonometric functions
14.1 Trigonometric Identities
 Verify trigonometric identities
14.2 Solving Trigonometric Equations Using Inverses
 Evaluate inverses of trigonometric functions
 Solve trigonometric equations
14.3 Right Triangles and Trigonometric Ratios
 Find lengths of sides in a right triangle
 Find measures of angles in a right triangle
14.4 Area and the Law of Sines
 Find the area of any triangle and use the Law of
Sines
14.5 Law of Cosines
 Use the Law of Cosines in finding the measures
of sides and angles of a triangle
14.6 Angle Identities
 Verify and use angle identities
 Verify and use sum and difference identities
14.7 Double-Angle and Half-Angle Identities
 Verify and use double-angle identities
 Verify and use half-angle identities