AP Pre-Calculus Easy Worksheet™

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Select the number of each type of objective: (Selecting Random will randomly generate all subtypes) Click on any title to see the free sample worksheet. (only the first few samples are free) Pre (Random) Prerequisites a. Solving Multi-Step Linear Equations b. Graphing Linear Inequalities c. Factoring: Pulling out the GCF d. Factoring: Trinomials (a=1) e. Factoring: Trinomials (a>1) f. Factoring: Difference of Squares g. Factoring: Perfect Square Trinomials h. Factoring: Sum and Difference of Cubes i. Factoring: Group Factorable j. Factoring: Combination -- Hard Factorable k. Solving Quadratics by Factoring l. Using Trigonometry (Sin, Cos, Tan) to find Side Lengths m. Solving Linear Equations in Two or Three Variables with Linear Combination n. Solving Two Linear Equations in Two or Three Variables with Substitution o. Applying Rules of Exponents to Multiplying and Dividing Monomials p. Simplifying Radicals q. Fixing Radicals into Imaginary Numbers r. Solving Quadratics A (Random) Polynomial and Rational Functions - Linear and Quadratic a. LO 1.1A Change in Tandem - Domain and Range b. LO 1.1A Change in Tandem - Increasing and Decreasing c. LO 1.1B Change in Tandem - Concave up vs Concave down d. LO 1.1B Change in Tandem - Zeros and x-Intercepts e. LO 1.1B Change in Tandem - Identifying Parent graphs f. LO 1.2A Rates of Change - Finding a Rate of Change g. LO 1.2B Rates of Change - Understanding Rates of Change h. LO 1.3A Rates of Change in Linear and Quadratic Functions - Finding Rate of Change for Linear functions i. LO 1.3A Rates of Change in Linear and Quadratic Functions - Finding Rate of Change for Quadratic functions j. LO 1.3B Rates of Change in Linear and Quadratic Functions - Finding the change of average rates of change for Linear functions k. LO 1.3B Rates of Change in Linear and Quadratic Functions - Finding the change of average rates of change for Quadratic functions l. LO 1.3B Rates of Change in Linear and Quadratic Functions - Identifying the function type from the Rates of Change B (Random) Polynomial and Rational Functions- Polynomial Functions a. LO 1.4A Polynomial Functions - Increasing b. LO 1.4A Polynomial Functions - Decreasing c. LO 1.4A Polynomial Functions - Local Maxima and Minima d. LO 1.4A Polynomial Functions - Absolute Maxima and Minima e. LO 1.4A Polynomial Functions - Finding Maxima and Minima in other cases f. LO 1.4A Polynomial Functions - Concavity g. LO 1.4A Polynomial Functions - Concavity given Charts h. LO 1.5A Polynomial Functions and Complex Zeros - Factors, Roots and Zeros i. LO 1.5A Polynomial Functions and Complex Zeros - Finding another Complex Root j. LO 1.5A Polynomial Functions and Complex Zeros - Effects of Multiplicity of roots k. LO 1.5A Polynomial Functions and Complex Zeros - Finding the Polynomial given a sequence l. LO 1.5B Polynomial Functions and Complex Zeros - Even vs Odd Functions m. LO 1.6A Polynomial Functions and End Behaviors C (Random) Polynomial and Rational Functions- Rational Functions a. LO 1.7A Rational Functions and End Behavior b. LO 1.8A Rational Functions and Zeros c. LO 1.9A Rational Functions and Vertical Asymptotes d. LO 1.10A Rational Functions and Holes e. LO 1.11A Equivalent Representations of Polynomials and Rational Functions - Factored vs Standard form f. LO 1.11B Equivalent Representations of Polynomials and Rational Functions - Using Long Division with Polynomials g. LO 1.11B Equivalent Representations of Polynomials and Rational Functions - Finding Slant Asymptotes h. LO 1.11B Equivalent Representations of Polynomials and Rational Functions - Partial Fraction Decomposition (Extension Topic) i. LO 1.11B Equivalent Representations of Polynomials and Rational Functions - Using the Binomial Theorem to expand Powers of Polynomials j. LO 1.12A Transformations of Functions - Identifying Transformations k. LO 1.12A Transformations of Functions - Domain and Range changes D (Random) Polynomial and Rational Functions- Modeling Functions a. LO 1.13A Function Model Selection and Assumption Articulation - Linear Word Problems b. LO 1.13A Function Model Selection and Assumption Articulation - Quadratic Word Problems c. LO 1.13A Function Model Selection and Assumption Articulation - Cubic Word Problems d. LO 1.13A Function Model Selection and Assumption Articulation - Finding a Polynomial Given a Sequence e. LO 1.13B Function Model Selection and Assumption Articulation - Changes in Domain or Range due to modeling data f. LO 1.14A Function Model Construction and Application - Identifying the Best Fit Equation type from a Data Set or a Scatterplot g. LO 1.14A Function Model Construction and Application - Finding the Best Fit Curve from a Data Set h. LO 1.14B Function Model Construction and Application - Direct Variation and Inverse Variation Word Problems i. LO 1.14C Function Model Construction and Application - Rate of Change Word Problems E (Random) Exponentionals and Logarithmic Functions a. LO 2.1A Change in Arithmetic and Geometric Sequences - Arithmetic b. LO 2.1A Change in Arithmetic and Geometric Sequences - Arithmetic Sequences with Variables c. LO 2.1B Change in Arithmetic and Geometric Sequences - Geometric d. LO 2.1A Change in Arithmetic and Geometric Sequences - Geometric Sequences with Variables e. LO 2.2A Change in Linear and Exponential Functions - Similarity between Arithmetic Sequences and Linear Functions f. LO 2.2A Change in Linear and Exponential Functions - Similarity between Geometric Sequences and Exponential Functions g. LO 2.2A Change in Linear and Exponential Functions - Writing the equation of an Exponential given a table (including shifts!) h. LO 2.2B Change in Linear and Exponential Functions - Determine an Arithmetic Sequence, Linear Function, Geometric Sequence, or Exponential Function based upon just 2 points i. LO 2.2B Change in Linear and Exponential Functions - Variables within tables for Exponential and Linear functions j. LO 2.1&2.2 Extension - Finding Partial Sums k. LO 2.1&2.2 Extension - Evaluating Arithmetic Series l. LO 2.1&2.2 Extension - Evaluating Finite Geometric Series m. LO 2.1&2.2 Extension - Evaluating Infinite Geometric Series n. LO 2.1&2.2 Extension - Sequences of Sums F (Random) Exponential and Logarithmic Functions - Exponential Functions a. LO 2.3A Exponential Functions - General Form b. LO 2.3A Exponential Functions - Limits at Infinity c. LO 2.3A Exponential Functions - Increasing / Decreasing / Concavity / Inflection Points d. LO 2.4A Exponential Function Manipulation - Transformations e. LO 2.4A Exponential Function Manipulation - Fractional Exponents and their effect f. LO 2.5A Exponential Function Context and Data Modeling - Modeling Growth and Decay Patterns g. LO 2.5B Exponential Function Context and Data Modeling - Effect of Changing units h. LO 2.5A Exponential Function Context and Data Modeling - Predicting Values i. LO 2.6A Competing Function Model Validation - Construct linear, quadratic, and exponential models based upon data (using scatterplot's pictures/calculator) j. LO 2.6A Competing Function Model Validation - Construct linear, quadratic, and exponential models based upon data (using differences) k. LO 2.6B Competing Function Model Validation - Checking residuals of regression l. LO 2.6B Competing Function Model Validation - Error as the difference between predicted and actual values G (Random) Exponential and Logarithmic Functions - Compositions and Inverses a. LO 2.7A Composition of Functions - Calculating Composite functions via tables and graphs b. LO 2.7B Composition of Functions - Calculating the Results of a Composition c. LO 2.7C Composition of Functions - Rewrite a given function as a composition of 2 or more functions d. LO 2.8A Inverse Functions - Finding an Inverse e. LO 2.8B Inverse Functions - Determining if functions are inverses f. LO 2.8B Inverse Functions - Domain and Range g. LO 2.8B Inverse Functions - Graphing Inverses H (Random) Exponential and Logarithmic Functions - Logarithmic Functions a. LO 2.9A Logarithmic Expressions - Understanding Logs b. LO 2.9A Logarithmic Expressions - Changing Forms c. LO 2.9A Logarithmic Expressions - Graphing Logarithms d. LO 2.10A Inverses of Exponential Functions - Understanding Inverses of Logs e. LO 2.11A Logarithmic Functions - Domain and Range f. LO 2.11A Logarithmic Functions - Increasing / Decreasing / Concavity / Inflection Points g. LO 2.12A Logarithmic Function Manipulation - Expanding Logs h. LO 2.12A Logarithmic Function Manipulation - Compressing Logs i. LO 2.12A Logarithmic Function Manipulation - Change of Base j. LO 2.12A Logarithmic Function Manipulation - Changing Bases with Variables k. LO 2.13A Exponential and Logarithmic Equations and Inequalities - Solving equations with Logs on both sides l. LO 2.13A Exponential and Logarithmic Equations and Inequalities - Solving inequalities m. LO 2.13B Exponential and Logarithmic Equations and Inequalities - Solving equations by using an Inverse n. LO 2.13B Exponential and Logarithmic Equations and Inequalities - Solving inequalities using an Inverse o. LO 2.14A Logarithmic Function Context and Data Modeling - Construct a logarithmic function for a model p. LO 2.15A Semi-log Plots - Determine if an exponential model is appropriate by examining a semi-log plot q. LO 2.15A Semi-log Plots - Figuring out the linear rate of change and initial linear value of a semi-log plot given an exponential model r. LO 2.15A Semi-log Plots - Identifying Parallel Exponential Functions plotted on a semi-log plot I (Random) Trigonometric and Polar Functions - Intro to Trig a. LO 3.1A Periodic Phenomena - Graphing Periodic Functions b. LO 3.1B Periodic Phenomena - Figuring out the Period c. LO 3.1B Periodic Phenomena - Intervals of Increase/Decrease, Concavities, and Maxima and Minima d. LO 3.2A Sine, Cosine, and Tangent - Converting from Radians to Degrees e. LO 3.2A Sine, Cosine, and Tangent - Converting from Degrees to Radians f. LO 3.2A Sine, Cosine, and Tangent - Draw an angle in Standard position g. LO 3.2A Sine, Cosine, and Tangent - Finding Sin/Cos/Tan given coordinates on the Unit Circle h. LO 3.2A Sine, Cosine, and Tangent - Finding Sin/Cos/Tan of Special Angles (Degrees) i. LO 3.2A Sine, Cosine, and Tangent - Finding Sin/Cos/Tan of Special Angles (Radians) j. LO 3.3A Sine and Cosine Function Values - Finding Sin/Cos/Tan given coordinates on the terminal side of an angle in Standard Position k. LO 3.3A Sine and Cosine Fuction Values - Finding Trigonometric Functions in a Triangle J (Random) Trigonometric and Polar Functions - Graphing Sine and Cosine a. LO 3.4A Sine and Cosine Functions - Basic Facts and Graphs of parent Functions b. LO 3.4A Sine and Cosine Functions - Basic Facts about Sine/Cosine c. LO 3.4A Sine and Cosine Functions - Graphing Sin/Cos by Chart d. LO 3.5A Sinusoidal Functions - Writing Equations with Period and Frequency e. LO 3.5A Sinusoidal Functions - Writing Equations with Amplitude Changes f. LO 3.5A Sinusoidal Functions - Writing Equations with Midline Changes g. LO 3.6A Sinusoidal Function Transformations - Sketching Graphs with Period Changes h. LO 3.6A Sinusoidal Functions Transformations - Sketching Graphs with Phase Shift Changes i. LO 3.6A Sinusoidal Functions Transformations - Sketching Graphs with Vertical Shift Changes j. LO 3.6A Sinusoidal Functions Transformations - Sketching Sin/Cos Graphs k. LO 3.7A Sinusoidal Function Context and Modeling - Using sinusoidal to find Max and Min values l. LO 3.7A Sinusoidal Function Context and Modeling - Using Max and Min values to Model a sinusoidal m. LO 3.7A Sinusoidal Function Context and Modeling - Writing an equation from a Graph n. LO 3.7A Sinusoidal Function Context and Modeling - Modeling a sinusoidal (identifying facts and writing equations)	K (Random) Trigonometric and Polar Functions - Tangent a. LO 3.8A The Tangent Function - Comparing Tangent to Sin/Cos b. LO 3.8A The Tangent Function - Tangent compared to slope to a terminal point c. LO 3.8B The Tangent Function - Period of a Tangent Function d. LO 3.8B The Tangent Function - Asymptotes of Tangent Functions e. LO 3.8C The Tangent Function - Graphing Tan by chart f. LO 3.8C The Tangent Function - Sketching Graphs with Period Changes g. LO 3.8C The Tangent Function - Sketching Graphs with Vertical Stretches Changes h. LO 3.8C The Tangent Function - Sketching Graphs with Phase Shift Changes i. LO 3.8C The Tangent Function - Sketching Graphs with Vertical Shift Changes j. LO 3.8C The Tangent Function - Sketching Graphs L (Random) Trigonometric and Polar Functions - Other Functions a. LO 3.9A Inverse Trigonometric Functions - Inverses of Sin, Cos and Tan b. LO 3.10A Trigonometric Equations and Inequalities - Equations c. LO 3.10A Trigonometric Equations and Inequalities - Inequalities d. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Values on the Unit Circle (Degrees) e. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Values on the Unit Circle (Radians) f. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Values found given coordinates on the terminal side of an angle in standard position g. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Graphing sec/csc by chart h. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Graphing cot by chart i. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Relating cotangent with sine and cosine j. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Sketching Graphs with Period Changes k. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Sketching Graphs with Vertical Stretches l. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Sketching Graphs with Phase Shifts m. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Sketching Graphs with Vertical Shifts n. LO 3.11A The Secant, Cosecant, and Cotangent Functions - Sketching Graphs M (Random) Trigonometric and Polar Functions - Equivalent Representations a. LO 3.12A - Equivalent Representations of Trigonometric Functions - Simplifying Pythagorean Identities b. LO 3.12A - Equivalent Representations of Trigonometric Functions - Proving Pythagorean Identities c. LO 3.12A - Equivalent Representations of Trigonometric Functions - Simplifying Basic Trigonometric Identities d. LO 3.12A - Equivalent Representations of Trigonometric Functions - Proving Basic Trigonometric Identities e. LO 3.12A - Equivalent Representations of Trigonometric Functions - Simplifying Harder Basic Trigonometric Identities f. LO 3.12A - Equivalent Representations of Trigonometric Functions - Proving Harder Basic Trigonometric Identities g. LO 3.12B - Equivalent Representations of Trigonometric Functions - Using Pythagorean Identities h. LO 3.12B - Equivalent Representations of Trigonometric Functions - Proving Identities involving Sum/Difference Formulas i. LO 3.12B - Equivalent Representations of Trigonometric Functions - Proving Identities involving Double/Half Angle Formulas j. LO 3.12B - Equivalent Representations of Trigonometric Functions - Using Sum and Difference Formulas k. LO 3.12B - Equivalent Representations of Trigonometric Functions - Using Double Angle Formulas l. LO 3.12B - Equivalent Representations of Trigonometric Functions - Using Half Angle Formulas m. LO 3.12C - Equivalent Representations of Trigonometric Functions - Simplifying Identities involving CoFunction and Even/Odd n. LO 3.12C - Equivalent Representations of Trigonometric Functions - Proving Identities involving CoFunction and Even/Odd o. LO 3.12C - Equivalent Representations of Trigonometric Functions - Using Reciprocal Identities N (Random) Trigonometric and Polar Functions - Polar a. LO 3.13A Trigonometry and Polar Coordinates - Changing Points to Rectangular Form b. LO 3.13A Trigonometry and Polar Coordinates - Changing Points to Polar Form c. LO 3.13A Trigonometry and Polar Coordinates - Writing a Complex Number in Trigonometric Form (and visa-versa) d. LO 3.14A Polar Function Graphs - Plotting Complex Numbers e. LO 3.14A Polar Function Graphs - Changing Equations to Rectangular Form f. LO 3.14A Polar Function Graphs - Changing Equations to Polar Form g. LO 3.14A Polar Function Graphs - Classifying Polar Equations h. LO 3.14A Polar Function Graphs - Drawing Polar Equations i. LO 3.14A Polar Function Graphs - Testing for Symmetry in Polar Equations j. LO 3.14A Polar Function Graphs - Transformations k. LO 3.15A Rates of Change in Polar Functions - What increasing/decreasing means l. LO 3.15A Rates of Change in Polar Functions - What a Maxima / Minima means m. LO 3.15A Rates of Change in Polar Functions - End Behavior for a polar graph n. LO 3.15A Rates of Change in Polar Functions - Finding the average rate of change o. LO 3.15A Rates of Change in Polar Functions - Using the average rate of change O (Random) Functions Involving Parameters, Vectors, and Matrices - Parametrics a. LO 4.1A Parametric Functions - Graphing Parametric Equations b. LO 4.1A Parametric Functions - Eliminating Parameters to Convert Parametric Equations c. LO 4.2A Parametric Fuctions Modeling Planar Motion - Solving Motion over Time Problems (Equations Given) d. LO 4.3A Parametric Functions and Rates of Change - Finding Orientation of Parametric Equations e. LO 4.3A Parametric Functions and Rates of Change - Identifying Different Parameterizations f. LO 4.3A Parametric Functions and Rates of Change - Average rate of change between x and y g. LO 4.4A Parametrically Defined Circles and Lines - Modeling a circle with center (h,k) h. LO 4.4A Parametrically Defined Circles and Lines - Modeling a line from (a,b) to (c,d) in multiple ways i. LO 4.4A Parametrically Defined Circles and Lines - Modeling Motion over Time Problems j. LO 4.4A Parametrically Defined Circles and Lines - Solving Motion over Time Problems P (Random) Functions Involving Parameters, Vectors, and Matrices - Implicitly defined Functions and Conics a. LO 4.5A Implicitly Defined Functions - Graphing by plugging in points b. LO 4.5B Implicitly Defined Functions - Looking at the rate of change c. LO 4.6A Conic Sections - Graphing a Circle d. LO 4.6A Conic Sections - Graphing an Ellipse e. LO 4.6A Conic Sections - Graphing a Parabola f. LO 4.6A Conic Sections - Graphing a Hyperbola g. LO 4.6A Conic Sections - Identifying the Type of Conic from an Equation or a Picture h. LO 4.6A Conic Sections - Changing Equations to Standard Form (Completing the Square) i. LO 4.6A Conic Sections - Changing Equations to Standard Form (Another Method) j. LO 4.6A Conic Sections - Graphing Pictures of Conics (Equations in General form) k. LO 4.7A Parameterization of Implicitly Defined Functions - Represent a curve in the plane parametrically l. LO 4.7A Parameterization of Implicitly Defined Functions - Represent Circles parametrically m. LO 4.7A Parameterization of Implicitly Defined Functions - Represent Parabolas parametrically n. LO 4.7A Parameterization of Implicitly Defined Functions - Represent Ellipses parametrically o. LO 4.7A Parameterization of Implicitly Defined Functions - Represent Hyperbolas parametrically Q (Random) Functions Involving Parameters, Vectors, and Matrices - Vectors a. LO 4.8A Vectors - Using Vector Notation b. LO 4.8A Vectors - Identifying Parallel Vectors c. LO 4.8A Vectors - Finding Magnitude of a Vector d. LO 4.8A Vectors - Finding the Direction e. LO 4.8B Vectors - Multiplying a Vector by a Constant f. LO 4.8B Vectors - Adding and Subtracting Vectors g. LO 4.8B Vectors - Finding the Dot Product h. LO 4.8B Vectors - Identifying Orthogonal Vectors i. LO 4.8C Vectors - Finding a Unit Vector j. LO 4.8D Vectors - Finding the Angle between Two Vectors k. LO 4.8D Vectors - Using Law of Sines l. LO 4.8D Vectors - Using Law of Cosines m. LO 4.9A Vector-Valued Functions - Represent planar motion in terms of vector-valued functions R (Random) Functions Involving Parameters, Vectors, and Matrices - Matrices a. LO 4.10A Matrices - Identifying Matrix Elements and Size b. LO 4.10A Matrices - Adding/Subtracting Matrices c. LO 4.10A Matrices - Adding/Subtracting Matrices with Variables d. LO 4.10A Matrices - Multiplying Matrices e. LO 4.10A Matrices - Multiplying Matrices with Variables f. LO 4.11B The Inverse and Determinant of a Matrix - Finding Matrix Inverses for a 2x2 matrix g. LO 4.11B The Inverse and Determinant of a Matrix - Verifying Inverse Matrices h. LO 4.11B The Inverse and Determinant of a Matrix - Finding Matrix Determinants 2x2 i. LO 4.11B The Inverse and Determinant of a Matrix - Using Matrix Determinants to determine invertability j. LO 4.12A Linear Transformations and Matrices - Linear Transformations k. LO 4.12A Linear Transformations and Matrices - Applying Linear Transformations to multiple Vectors l. LO 4.13A Matrices as Functions - Examining Basic Matrix Transformations m. LO 4.13A Matrices as Functions - Matrices of Linear Transformations n. LO 4.13A Matrices as Functions - Matrices of Rotational Transformations o. LO 4.13A Matrices as Functions - Comparing Area p. LO 4.13B Matrices as Functions - Composing 2 Linear Functions q. LO 4.13C Matrices as Functions - Finding an inverse to a Linear Transformation r. LO 4.14A Matrices Modeling Contexts - Matrix Word Problems s. LO 4.14B Matrices Modeling Contexts - Apply Adjacency Matrices t. LO 4.14B Matrices Modeling Contexts - Apply the Leslie matrix model to population models u. LO 4.14B Matrices Modeling Contexts - Apply the Markov chain to probability models v. LO 4.14B Matrices Modeling Contexts - Apply the Leontief model to economic situations S (Random) Extension: Limits, Continuity, and the Derivative a. Finding the Limit of (f(x+h)-f(x))/h for a Polynomial b. Finding the Limit of (f(x+h)-f(x))/h for a Radical c. Finding the Limit of (f(x+h)-f(x))/h for a Rational d. Finding Points of Discontinuity (Graphs) e. Finding Points of Discontinuity (Expressions) f. Definition of the Derivative g. Definition of the Derivative Graphically h. Finding the Derivative of a Polynomial i. Finding the Derivative of a Radical j. Finding the Derivative of a simple Rational k. Finding the Derivative of a Polynomial at a point l. Finding points where the Tangent Line is Horizontal (Polynomials) m. Estimating the Derivative at a Point Numerically n. Finding points of Differentiability o. Differentiability vs. Continuity p. Constant Rule and Power Rule q. Constant Multiple Rule r. Sum and Difference Rules T (Random) Free Response! a. AP Pre-Calculus Free Response Question 1 (Calculator Based) b. AP Pre-Calculus Free Response Question 2 (Calculator Based) c. AP Pre-Calculus Free Response Question 3 (No Calculator) d. AP Pre-Calculus Free Response Question 4 (No Calculator)
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