List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015)

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1 List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015) MAT 155P MAT Absolute Value Equations P 7 P 3 2 Absolute Value Inequalities P 9 P 4 3 Algebraic Expressions: Combining Like Terms P 1 * * 4 Algebraic Expressions: Distributive Property P 1 * * 5 Algebraic Expressions: Distributive Property and Combining Like Terms P 1 * * 6 Algebraic Expressions: Evaluating P 1 * * 7 Algebraic Expressions: Translating Word Expressions P 1 * * 8 Complex Functions: Applying the Concepts 2 * P 5 9 Complex Numbers: Adding and Subtracting 2 1 P 5 10 Complex Numbers: Dividing 2 1 P 5 11 Complex Numbers: Multiplying 2 1 P 5 12 Exponent Rule: Integer (Zero) P 2 P 1 13 Exponent Rule: Negative P 2 P 1 14 Exponent Rule: Power-to-a-Power P 2 P 1 15 Exponent Rule: Product-to-a-Power P 2 P 1 16 Exponent Rule: Product P 2 P 1 17 Exponent Rule: Quotient P 2 P 1 18 Exponent Rule: Quotient -to-a-power P 2 P 1 19 Exponential Equations: Solve Exponential Equation of Quadratic Form Exponential Equations: Solve Exponential Equation with Different Bases (use logarithms) Exponential Equations: Solve Exponential Equation with Like Bases Exponential Functions: Applying the Concepts Exponential Functions: Compound Interest Formula Finding Future Value Exponential Functions: Continuous Compound Interest Formula Exponential Functions: Evaluating Exponential Functions Exponential Functions: Graphing Exponential Inequalities: Solve * * 3 4

2 28 Exponents: Basics P 1 P 1 29 Exponents: Evaluate Expressions with Rational Exponents P 3 P 2 30 Exponents: Simplify Expressions with Rational Exponents P 3 P 2 31 Function Notation: Evaluating a Piecewise Function Function Notation: Finding Average Rate of Change Function Notation: Finding Difference Quotient Function Notation: Graphing Piecewise Functions Function Notation: Read a Graph (Decreasing, Increasing, Intercepts, Domain, Range, Symmetry) Function Notation: Use Function Notation Inverse Functions: Finding Inverse Functions Inverse Functions: Graph of an Inverse of a Function from the Graph of that Function Inverse Functions: Horizontal Line Test Inverse Functions: Verifying Inverse Functions Linear Equations: Containing Fractions P 7 P 3 42 Linear Equations: Solving by Addition and Multiplication Property P 7 P 3 43 Linear Equations: Solving by Addition Property P 7 P 3 44 Linear Equations: Solving by Multiplication Property P 7 P 3 45 Linear Functions: Applying the Concepts for Linear Equations and Inequalities P 1 P 3 46 Linear Inequalities: Solve by Addition Property Linear Inequalities in One Variable P 9 P 4 47 Linear Inequalities: Solve by Both Add. and Multi. Prop. Linear Inequalities in One Variable P 9 P 4 48 Linear Inequalities: Solve by Multiplication Property Linear Inequalities in One Variable P 9 P 4 49 Logarithmic Equations: Solve Using One-to-One Property of Logarithms Logarithmic Equations: Solve Using the Definition of a Logarithm Logarithmic Functions: Applying the Concepts Logarithmic Functions: Compound Interest Formula Finding Time Logarithmic Functions: Continuous Compound Interest Formula Finding Time Logarithmic Functions: Convert from Exponential to Logarithmic Form Logarithmic Functions: Convert from Logarithmic to Exponential Form Logarithmic Functions: Evaluating Logarithms Logarithmic Functions: Finding the Domain

3 58 Logarithmic Inequalities: Solve * * Logarithms Rule: Condense - Combination of All Rules Logarithms Rule: Condense - Product Logarithms Rule: Condense - Quotient Logarithms Rule: Expand - Combination of All Rules Logarithms Rule: Expand - Power Logarithms Rule: Expand - Product Logarithms Rule: Expand - Quotient Logarithms Rule: Using a Change of Base to Compute Logarithms Order of Operations P 1 * * 68 Polynomial Expressions: Adding and Subtracting P 4 * * 69 Polynomial Expressions: Dividing Monomial by a Monomial * * * * 70 Polynomial Expressions: Dividing Polynomials by a Monomial * * * * 71 Polynomial Expressions: Dividing Polynomials by a Polynomial (Long Division) Polynomial Expressions: Multiplying Binomials P 4 * * 73 Polynomial Expressions: Multiplying Polynomials P 4 * * 74 Polynomial Functions: Applying the Concepts P 1 P 3 75 Polynomial Functions: Constructing a Polynomial Whose Zeros Are Given Polynomial Functions: Dividing Polynomials Synthetic Division Polynomial Functions: Factoring Algebraic Expressions Containing Fractional and Negative Exp. P 5 P 3 78 Polynomial Functions: Factoring By Grouping P 5 P 3 79 Polynomial Functions: Factoring Greatest Common Factor P 5 P 3 80 Polynomial Functions: Factoring Perfect Square Trinomials P 5 P 3 81 Polynomial Functions: Factoring the Difference of Two Squares P 5 P 3 82 Polynomial Functions: Factoring the Sum and Difference of Two Cubes P 5 P 3 83 Polynomial Functions: Factoring Trinomial with Leading Coefficient of 1 P 5 P 3 84 Polynomial Functions: Factoring Trinomial with Leading Coefficient Other than 1 P 5 P 3 85 Polynomial Functions: Finding All Solutions Polynomial Functions: Finding All the Zeros Quadratic Equations: Complex Imaginary Solutions 2 1 * *

4 88 Quadratic Equations: Converting a Quadratic from Standard to Vertex Form Quadratic Equations: Writing the Equation of a Quadratic Function Given Vertex and a Point Quadratic Equations: Solving by Completing the Square P 7 P 3 91 Quadratic Equations: Solving by Factoring P 7 P 3 92 Quadratic Equations: Solving by Quadratic Formula P 7 P 3 93 Quadratic Equations: Solving by Square Root Property P 7 P 3 94 Quadratic Functions: Applying the Concepts P 1 P 3 95 Quadratic Inequalities: Solve 2 7 P 4 96 Radical Equations: Solving P 7 P 2 97 Radical Expressions: Dividing P 3 * * 98 Radical Expressions: Multiplying P 3 * * 99 Radical Expressions: Rationalizing P 3 P Radical Expressions: Simplify by Adding and Subtracting P 3 P Radical Functions: Applying the Concepts P 1 P Rational Equations: Solving P 7 P Rational Expressions: Adding and Subtracting with Common Denominators P 6 * * 104 Rational Expressions: Adding and Subtracting with Uncommon Denominators P 6 * * 105 Rational Expressions: Dividing P 6 * * 106 Rational Expressions: Multiplying P 6 * * 107 Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Distinct Linear Factors * * Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Nonrepeated Linear Factors * * Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Repeated Linear Factors * * Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Repeated Quadratic Factors * * Rational Expressions: Simplify Complex Rational Expressions P 6 * * 112 Rational Expressions: Simplify Rational Expressions P 6 * * 113 Rational Functions: Find Horizontal Asymptotes Rational Functions: Find the Domains P Rational Functions: Find Vertical Asymptotes Rational Functions: Arrow Notation 2 6 * * 117 Rational Inequalities: Solve 2 7 P 4

5 118 Solving Formulas for Specified Variables P 7 * * 119 Systems of Equations Two Variables: Solve by Elimination/Addition * * Systems of Equations Two Variables: Solve by Graphing * * Systems of Equations Two Variables: Solve by Substitution * * The Algebra of Functions: Composition The Algebra of Functions: Finding the Domain of Composite Functions The Algebra of Functions: Product The Algebra of Functions: Quotient The Algebra of Functions: Sum and Difference Variations: Combined 2 8 * * 128 Variations: Direct 2 8 * * 129 Variations: Inverse 2 8 * * 130 Variations: Joint 2 8 * * 131 Write Equation of Line: Parallel and Perpendicular Lines Write Equation of a Line: Given a Slope and a Point Write Equation of a Line: Given a Slope and y-intercept Write Equation of a Line: Given Two Points

6 List of PreCalculus Trigonometry Mathematical Concept Practice Sheets (Updated Spring 2015) MAT 155P MAT 155 TRIGONOMETRY SKILLS 1 Angles: Convert Degrees to Radians-Approximate Angles: Convert Degrees to Radians-Exact Angles: Convert Radians to Degrees-Approximate Angles: Convert Radians to Degrees-Exact Angles: Draw Angles in Standard Position Angles: Find Arc Length of a Circle Given Radius and Central Angle Angles: Find Central Angle Given Radius and Arc Length Angles: Find Coterminal Angles Angles: Finding Complements and Supplements Inverse Trig. Functions: Evaluate Inverse Cosine Inverse Trig. Functions: Evaluate Inverse Secant, Cosecant, Cotangent Inverse Trig. Functions: Evaluate Inverse Sine Inverse Trig. Functions: Evaluate Inverse Tangent Inverse Trig. Functions: Find Exact Values of Composite Functions Involving Inverse Trig Oblique Triangles: The Law of Cosines (SAS, SSS) No Figures Oblique Triangles: The Law of Cosines (SAS, SSS) With Figures Oblique Triangles: The Law of Sines (AAS, ASA, SSA) No Figures Oblique Triangles: The Law of Sines (AAS, ASA, SSA) With Figures Right-Triangle Trig.: Finding the Remaining Trig. Function Values from a Given Value 4 * Right-Triangle Trig.: Solve Right Triangles 4 * Right-Triangle Trig.: Use Right Triangles to Evaluate Trigonometric Functions Trigonometric Equations: Find All Solutions of a Trigonometric Equation Trigonometric Equations: Solve Equations With Multiple Angles Trigonometric Formulas: Express as Power Reducing Trigonometric Formulas: Express as Product-to-Sum 5 4 * * 26 Trigonometric Formulas: Express as Sum-to-Product 5 4 * * 27 Trigonometric Formulas: Verify Identities Using Double Angle

7 TRIGONOMETRY SKILLS 28 Trigonometric Formulas: Verify Identities Using Sum and Difference for Sines, Cosines, and Tangents Trigonometric Formulas: Verify Trignometric Equations Trigonometric Functions of Any Angle: Find Exact Value of Remaining Trig Function Given Information Trigonometric Functions of Any Angle: Find Reference Angles Trigonometric Functions of Any Angle: Name the Quadrant in Which the Angle Lies Unit Circle: Find Exact Trig. Function Values Using Point on the Unit Circle