| Algebra Part One |
| 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.
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| 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.
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| 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.
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| 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 word problems as equations and solve them.
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| 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.
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| 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.
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| Book 7 - Inequalities |
- Solve problems of simple inequalities.
- Solve real-world problems involving inequalities.
- Solve quadratic inequalities.
- Solve rational inequalities.
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| Book 8 - 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.
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| 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.
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| 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.
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| 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.
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| Algebra Part Two |
| 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 using the equation of a function.
- Identify four types of functions: linear, step, absolute value, and quadratic.
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| Book 2 - 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.
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| 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.
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| Book 4 - 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.
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| 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 that have horizontal, no horizontal, or oblique asymptotes.
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| 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.
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| Book 7 - Logarithmic Functions |
- Identify and interpret logarithmic notation.
- Solve equations using logarithms.
- Solve equations using natural logarithms.
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| 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.
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| Book 9 - 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.
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| Book 10 - 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.
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| 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 any finite geometric series.
- Find the sum of an infinite geometric series.
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| 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.
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| 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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