ALGEBRA LEARNING OBJECTIVES

ALGEBRA PART 1

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.

ALGEBRA PART 2

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.

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