Algebra II
Problem Solving Methods:
Simplify algebraic expressions by using the operations with expressions and the order of operations
Solve linear equations and inequalities and graph the solutions of inequalities
Graph equations
Use function notation
Apply the midpoint and distance formulas
Multiply a matrix by a scalar
Solve matrix equations
Add, subtract and multiply matrices
Linear Functions
Determine and interpret the slope of a line
Use the slope-intercept, point-slope and standard form of the equation of a line
Use the slopes to determine whether two lines are parallel, perpendicular or neither
Solve systems of linear equations graphically
Solve systems of linear equations algebraically
Graph linear inequalities
Find the union and the intersection of graphs defined by inequalities
Recognize direct variation and express it as a proportion
Fit a line to data
Recognize and graph composite functions, including absolute value functions
Quadratic Functions:
Recognize quadratic equations and expression
Factor quadratic expressions by various methods
Find the real zeros of quadratic equations
Solve quadratic equations by graphing, factoring and by applying the quadratic formula
Complete the square to find the maximum or the minimum of a function and use it to solve real-life optimization problems
Analyze and solve projectile motion problems
Properties of Functions
Recognize and represent relations and functions
Find the domain and the range of a function and identify restrictions on a domain of a function
Recognize inverse functions and find the inverse of a function
Interpret recursive definitions of functions
Transformations of Graphs
Graph parabolas and absolute value functions
Stretch, shrink and reflect graphs Shift graphs horizontally and vertically
Recognize symmetry with respect to a point or a line
Graph cubic and quartic functions
Graph reciprocal functions
Graph exponential functions
Find the asymptotes of a graph and holes in a graph
Systems of Equations and Inequalities
Use systems of equations to solve problems
Solve systems of equations in three variables
Solve systems of inequalities
Use the method of linear programming to solve optimization problems
Solve inverse variation problems and graph inverse variations
Solve systems of non-linear equations
Solve systems of equations involving rational expressions
Number Systems
Apply the properties of negative and fractional exponents
Solve equations that contain square roots
Solve equations that contain fractional exponents
Identify complex numbers
Find the conjugate and the magnitude of complex numbers
Plot complex numbers in the number plane
Perform operations with complex numbers
Polynomial Functions:
Write a polynomial in nested form
Divide a polynomial by a binomial
Apply the remainder and factor theorems
Performs synthetic division
Find the zeros of a polynomial function by factoring
Apply the rational zeros theorem
Apply the relationship between the roots and coefficients of a quadratic function
Use graphs to find the approximate values of a polynomial function
Rational Functions
Recognize rational expressions
Simplify, multiply and divide rational expressions
Add and subtract rational expressions
Simplify complex fractions
Solve rational equations
Exponential and Logarithmic Functions
Graph exponential functions
Graph logarithmic functions
Use base 10 and base e exponential and logarithmic functions to solve problems
Use the definition and the properties of a logarithm to simplify expressions and solve exponential and logarithmic equations
Use exponential and logarithmic functions to model real-life phenomena
Analyze exponentially related data
Probability and Statistics:
Read, interpret and create data displays to analyze the data
Construct and interpret stem and leaf plots
Construct and interpret box and whisker plots
Use the measures of central tendencies to analyze data
Interpret percentiles and percentile ranks
Apply the Basic Counting Principle
Use permutations and combinations
Identify events and calculate their probabilities
Calculate probabilities of mutually exclusive events
Calculate probabilities of independent events
Use the Binomial Theorem to expand powers of binomials.
Sequences and Series
Apply the definition of a sequence and describe a sequence
Form sequences of partial sums
Compute finite series
Use sigma notation to express a series
Compute arithmetic and geometric means
Find elements of arithmetic and geometric sequences
Evaluate arithmetic and geometric series
Evaluate infinite geometric series