List of PreCalculus Algebra Mathematical Concept Practice Sheets (Updated Spring 2015) MAT 155P MAT 155 1 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 3 4 3 4 20 Exponential Equations: Solve Exponential Equation with Different Bases (use logarithms) 3 4 3 4 21 Exponential Equations: Solve Exponential Equation with Like Bases 3 4 3 4 22 Exponential Functions: Applying the Concepts 3 1 3 3 23 Exponential Functions: Compound Interest Formula Finding Future Value 3 1 3 1 24 Exponential Functions: Continuous Compound Interest Formula 3 1 3 1 25 Exponential Functions: Evaluating Exponential Functions 3 1 3 1 26 Exponential Functions: Graphing 3 1 3 1 27 Exponential Inequalities: Solve * * 3 4
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 1 3 1 4 32 Function Notation: Finding Average Rate of Change 1 5 1 4 33 Function Notation: Finding Difference Quotient 1 3 1 4 34 Function Notation: Graphing Piecewise Functions 1 3 1 4 35 Function Notation: Read a Graph (Decreasing, Increasing, Intercepts, Domain, Range, Symmetry) 1 3 1 4 36 Function Notation: Use Function Notation 1 2 1 3 37 Inverse Functions: Finding Inverse Functions 1 8 1 7 38 Inverse Functions: Graph of an Inverse of a Function from the Graph of that Function 1 8 1 7 39 Inverse Functions: Horizontal Line Test 1 8 1 7 40 Inverse Functions: Verifying Inverse Functions 1 8 1 7 41 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 3 4 3 4 50 Logarithmic Equations: Solve Using the Definition of a Logarithm 3 4 3 4 51 Logarithmic Functions: Applying the Concepts 3 2 3 3 52 Logarithmic Functions: Compound Interest Formula Finding Time 3 4 3 2 53 Logarithmic Functions: Continuous Compound Interest Formula Finding Time 3 4 3 2 54 Logarithmic Functions: Convert from Exponential to Logarithmic Form 3 2 3 2 55 Logarithmic Functions: Convert from Logarithmic to Exponential Form 3 2 3 2 56 Logarithmic Functions: Evaluating Logarithms 3 2 3 2 57 Logarithmic Functions: Finding the Domain 3 2 3 2
58 Logarithmic Inequalities: Solve * * 3 4 59 Logarithms Rule: Condense - Combination of All Rules 3 3 3 3 60 Logarithms Rule: Condense - Product 3 3 3 3 61 Logarithms Rule: Condense - Quotient 3 3 3 3 62 Logarithms Rule: Expand - Combination of All Rules 3 3 3 3 63 Logarithms Rule: Expand - Power 3 3 3 3 64 Logarithms Rule: Expand - Product 3 3 3 3 65 Logarithms Rule: Expand - Quotient 3 3 3 3 66 Logarithms Rule: Using a Change of Base to Compute Logarithms 3 3 3 3 67 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) 2 4 2 3 72 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 2 5 2 4 76 Polynomial Functions: Dividing Polynomials Synthetic Division 2 4 2 3 77 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 2 5 2 4 86 Polynomial Functions: Finding All the Zeros 2 5 2 4 87 Quadratic Equations: Complex Imaginary Solutions 2 1 * *
88 Quadratic Equations: Converting a Quadratic from Standard to Vertex Form 2 2 2 1 89 Quadratic Equations: Writing the Equation of a Quadratic Function Given Vertex and a Point 2 2 2 1 90 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 2 100 Radical Expressions: Simplify by Adding and Subtracting P 3 P 2 101 Radical Functions: Applying the Concepts P 1 P 2 102 Rational Equations: Solving P 7 P 3 103 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 * * 6 5 108 Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Nonrepeated Linear Factors * * 6 5 109 Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Repeated Linear Factors * * 6 5 110 Rational Expressions: Partial Fraction Decomposition P/Q, Where Q Has Repeated Quadratic Factors * * 6 5 111 Rational Expressions: Simplify Complex Rational Expressions P 6 * * 112 Rational Expressions: Simplify Rational Expressions P 6 * * 113 Rational Functions: Find Horizontal Asymptotes 2 6 2 5 114 Rational Functions: Find the Domains P 6 2 5 115 Rational Functions: Find Vertical Asymptotes 2 6 2 5 116 Rational Functions: Arrow Notation 2 6 * * 117 Rational Inequalities: Solve 2 7 P 4
118 Solving Formulas for Specified Variables P 7 * * 119 Systems of Equations Two Variables: Solve by Elimination/Addition * * 6 4 120 Systems of Equations Two Variables: Solve by Graphing * * 6 4 121 Systems of Equations Two Variables: Solve by Substitution * * 6 4 122 The Algebra of Functions: Composition 1 7 1 6 123 The Algebra of Functions: Finding the Domain of Composite Functions 1 7 1 6 124 The Algebra of Functions: Product 1 7 1 6 125 The Algebra of Functions: Quotient 1 7 1 6 126 The Algebra of Functions: Sum and Difference 1 7 1 6 127 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 1 4 1 2 132 Write Equation of a Line: Given a Slope and a Point 1 4 1 2 133 Write Equation of a Line: Given a Slope and y-intercept 1 4 1 2 134 Write Equation of a Line: Given Two Points 1 4 1 2
List of PreCalculus Trigonometry Mathematical Concept Practice Sheets (Updated Spring 2015) MAT 155P MAT 155 TRIGONOMETRY SKILLS 1 Angles: Convert Degrees to Radians-Approximate 4 1 4 1 2 Angles: Convert Degrees to Radians-Exact 4 1 4 1 3 Angles: Convert Radians to Degrees-Approximate 4 1 4 1 4 Angles: Convert Radians to Degrees-Exact 4 1 4 1 5 Angles: Draw Angles in Standard Position 4 1 4 1 6 Angles: Find Arc Length of a Circle Given Radius and Central Angle 4 1 4 1 7 Angles: Find Central Angle Given Radius and Arc Length 4 1 4 1 8 Angles: Find Coterminal Angles 4 1 4 2 9 Angles: Finding Complements and Supplements 4 1 4 1 10 Inverse Trig. Functions: Evaluate Inverse Cosine 4 7 4 5 11 Inverse Trig. Functions: Evaluate Inverse Secant, Cosecant, Cotangent 4 7 4 5 12 Inverse Trig. Functions: Evaluate Inverse Sine 4 7 4 5 13 Inverse Trig. Functions: Evaluate Inverse Tangent 4 7 4 5 14 Inverse Trig. Functions: Find Exact Values of Composite Functions Involving Inverse Trig. 4 7 4 5 15 Oblique Triangles: The Law of Cosines (SAS, SSS) No Figures 6 2 5 1 16 Oblique Triangles: The Law of Cosines (SAS, SSS) With Figures 6 2 5 1 17 Oblique Triangles: The Law of Sines (AAS, ASA, SSA) No Figures 6 1 5 1 18 Oblique Triangles: The Law of Sines (AAS, ASA, SSA) With Figures 6 1 5 1 19 Right-Triangle Trig.: Finding the Remaining Trig. Function Values from a Given Value 4 * 4 6 20 Right-Triangle Trig.: Solve Right Triangles 4 * 4 6 21 Right-Triangle Trig.: Use Right Triangles to Evaluate Trigonometric Functions 4 3 4 6 22 Trigonometric Equations: Find All Solutions of a Trigonometric Equation 5 5 4 7 23 Trigonometric Equations: Solve Equations With Multiple Angles 5 5 4 7 24 Trigonometric Formulas: Express as Power Reducing 5 3 4 8 25 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 5 3 4 8
TRIGONOMETRY SKILLS 28 Trigonometric Formulas: Verify Identities Using Sum and Difference for Sines, Cosines, and Tangents 5 2 4 8 29 Trigonometric Formulas: Verify Trignometric Equations 5 1 4 7 30 Trigonometric Functions of Any Angle: Find Exact Value of Remaining Trig Function Given Information 4 4 4 2 31 Trigonometric Functions of Any Angle: Find Reference Angles 4 4 4 2 32 Trigonometric Functions of Any Angle: Name the Quadrant in Which the Angle Lies 4 4 4 2 33 Unit Circle: Find Exact Trig. Function Values Using Point on the Unit Circle 4 2 4 2