ALGEBRA LEARNING OBJECTIVES
Book 1 – Language of Algebra
• Classify numbers into number sets.
• Evaluate algebraic expressions.
• Simplify algebraic expressions using the commutative, associative, and distributive properties.
• Evaluate expressions containing more than one operational symbol.
Book 2 – Exponents and Radicals
• Evaluate algebraic expressions using the power and product rules.
• Simplify and evaluate expressions using the quotient rule and negative exponents.
• Determine the meaning of roots and radicals.
• Evaluate algebraic expressions involving rational exponents.
Book 3 – Factoring Polynomials
• Combine polynomials by addition or subtraction.
• Multiply polynomials using the distributive property.
• Factor a polynomial by extracting the greatest common factor of terms.
• Extract binomial factors of trinomials.
• Factor perfect square trinomials.
Book 4 – Linear Equations
• Solve linear equations.
• Solve linear equations containing decimals and fractions.
• Express word problems as equations and solve them.
• Express the relationships in proportion problems and solve them.
• Express simple work problems as equations and solve them.
Book 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.
Book 6 – 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.
Book 7 – Inequalities
• Solve problems of simple inequalities.
• Solve real-world problems involving inequalities.
• Solve quadratic inequalities.
• Solve rational inequalities.
Book 8 – Absolute Value
• Interpret basic absolute value expressions.
• Solve absolute value equations and inequalities.
• Use the basic algebra concepts you have learned to solve real-world problems.
Book 9 – 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.
Book 10 – 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.
Book 11 – 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.
Book 1 – 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.
• Identify four types of functions: linear, step, absolute value, and quadratic.
Book 2 – Composition of 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.
Book 3 – Variation
• Recognize and use direct variation in solving problems.
• Recognize and use inverse relationships in solving problems.
• Solve problems involving combined and joint variation.
Book 4 – Polynomials
• Identify polynomial functions by their general features and degrees.
• Find the zero values of polynomial functions.
• Interpret graphs of polynomials.
• Identify the number of zero values in polynomial functions.
Book 5 – Rational Functions
• Identify the main characteristics of rational functions.
• Interpret and graph rational functions with horizontal and vertical asymptotes.
• Interpret and graph rational functions with no horizontal, or oblique asymptotes.
Book 6 – 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.
Book 7 – Logarithmic Functions
• Identify and interpret logarithmic notation.
• Solve equations using logarithms.
• Solve equations using natural logarithms.
Book 8 – 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.
Book 9 – Systems of Linear Inequalities
• Identify the feasible region or solution of a system of linear inequalities.
• Find the point which maximizes or minimizes the objective function by using the corner principle.
Book 10 – Arithmetic Sequences and 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 counter example
Book 11 – 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 an infinite geometric series.
Book 12 – Permutations and Combinations
• Apply the fundamental principle of counting to determine possible outcomes.
• Apply permutations in appropriate problems.
• Calculate combinations in appropriate problems.
Book 13 – Probability
• Define terms dealing with probability and calculate simple probabilities.
• Calculate expected values.
• Calculate probabilities when independence is an issue.