**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.