Algebra Part One

 Language of Algebra

Classify numbers into number sets. 4.1 A-1

Evaluate algebraic expressions. 4.3 D-1

Simplify algebraic expressions using the commutative, associative, and distributive properties. 4.3 D-1

Evaluate expressions containing more than one operational symbol. 4.3 D-1

Exponents and Radicals

Evaluate algebraic expressions using the power and product rules. 4.1 B-2

Simplify and evaluate expressions using the quotient rule and negative exponents. 4.1 B-2

Determine the meaning of roots and radicals. 4.1 B-4

Evaluate algebraic expressions involving rational exponents. 4.1 B-4

Factoring Polynomials

Combine polynomials by addition or subtraction. 4.3 D-1

Multiply polynomials using the distributive property. 4.3 D-1

Factor a polynomial by extracting the greatest common factor of terms. 4.3 D-1

Extract binomial factors of trinomials. 4.3 D-1

Factor perfect square trinomials. 4.3 D-1

Linear Equations

Solve linear equations. 4.3 D-2

Solve linear equations containing decimals and fractions. 4.3 D-2

Express word problems as equations and solve them. 4.3 D-2, 4.5 A-1, 4.5 A-5

Express the relationships in proportion problems and solve them. 4.3 D-2, 4.5 A-1, 4.5 A-5

Express simple word problems as equations and solve them. 4.3 D-2, 4.5 A-1, 4.5 A-5

 Complex Numbers

Perform basic operations with imaginary numbers.

Recognize complex numbers in the complex plane.

Add and subtract complex numbers.

Multiply and divide complex numbers.

Quadratic Equations

Solve simple quadratic equations by trial and error. Solve quadratic equations by factoring the difference of two squares.

Solve quadratic equations by factoring perfect square trinomials.

Solve quadratic equations by completing the square.

Solve quadratic equations by using the quadratic formula.

 Inequalities

Solve problems of simple inequalities.

Solve real-world problems involving inequalities.

Solve quadratic inequalities. Solve rational inequalities.

Absolute Value and Review

Interpret basic absolute value expressions.

Solve absolute value equations. Solve absolute value inequalities.

Use the basic algebra concepts you have learned to solve real-world problems.

Linear Relations

Interpret equations and their graphs.

Develop a linear equation using a graph.

Interpret graphs and their linear equations.

Write equations from ordered pairs and determine the distance between two points.

Circles and Parabolas

Determine the radius and coordinates of a circle given an equation of a circle.

Identify the characteristics of parabolas.

Interpret graphs of parabolas using the general form of the equation for the parabola.

Ellipse and Hyperbola

Determine the equation of an ellipse.

Graph an ellipse when given its equation.

Determine the characteristics of hyperbolas when using their graphs or equations.

Algebra Part Two

Functions

Determine whether a given relationship is a function or not.

Represent a function by using ordered pairs and graphs.

Determine range values for given values in the domain using the equation of a function.

Identify four types of functions: linear, step, absolute value, and quadratic.

Composition and Inverse Functions

Combine functions arithmetically to obtain new functions.

Perform a composition of functions.

Find the inverse of a function.

Identify functions that do not have an inverse.

Variation

Recognize and use direct variation in solving problems.

Recognize and use inverse relationships in solving problems.

Solve problems involving combined and joint variation.

Polynomial Functions

Identify polynomial functions by their general features and degrees.

Find the zero values of polynomial functions by factoring and using the factor theorem.

Interpret graphs of polynomials.

Identify the number of zero values in polynomial functions using the Fundamental Theorem of Algebra.

 Rational Functions

Identify the main characteristics of rational functions.

Interpret and graph rational functions with horizontal and vertical asymptotes.

Interpret and graph rational functions that have horizontal, no horizontal, or oblique asymptotes.

Exponential Functions

Solve problems involving exponential growth functions.

Solve real-world problems involving exponential decay functions.

Solve some real-world problems involving the compounding effect.

Logarithmic Functions

Identify and interpret logarithmic notation.

Solve equations using logarithms.

Solve equations using natural logarithms.

Systems of Equations

Solve systems of linear equations with two variables using the substitution method.

Solve systems of consistent linear equations that have more than two variables.

Solve systems of nonlinear equations.

Systems of Linear Inequalities

Identify the feasible region or solution of a system of linear inequalities.

Find the point that maximizes or minimizes the objective function by using the corner principle.

Sequences, Series, and Induction

Recognize an arithmetic sequence and find any term in its sequence.

Identify and work with different types of natural sequences.

Determine the sum of the terms in a finite arithmetic sequence.

Apply the procedure for mathematical induction and disprove statements by producing a counterexample.

Geometric Sequences and Series

Find any term in a geometric sequence and find the common ratio of the sequence.

Determine the first term and common ratio of a geometric sequence from any two known terms.

Find the sum of any finite geometric series.

Find the sum of an infinite geometric series.

Permutations and Combinations

Apply the fundamental principle of counting to determine possible outcomes.

Apply permutations in appropriate problems.

Calculate combinations in appropriate problems.

Probability

Define terms dealing with probability and calculate simple probabilities.

Calculate expected values.

Calculate probabilities when independence is an issue.