Unit O: AP Precalculus Prerequisites
Summer Packet
Unit 1: Polynomial & Rational Functions
Topic 1.1-1.2-1.3: Change in Tandem, Rates of Change, Rates of Change in Linear & Quadratic Functions.
Video 1: Topic 1.1-1.2-1.3: Average Rate of Change - Rates of Change in Linear and Quadratic Functions - Concavity - Increasing/Decreasing Functions.
Topic 1.4: Polynomial Functions & Rate of Change.
Video 2: Topic 1.4: Polynomial Functions and Rates of Change | Local (Relative) Min/Max | Global (Absolute) Min/Max | Points of Inflection | Turning Points.
Must watch Videos 3 - 7 since they are prerequisites for Topic 1.5 - 1.11.
Video 3: Factoring trinomials by Trial and Error Method.
Video 4: New Method of Factoring Trinomials WITHOUT Guessing and Checking.
Video 5: Factoring Special Cases of polynomials.
Video 6: Long Division & Synthetic Division with 8 Specific Examples - The easy way!
Video 7: Dividing Polynomials using 3 methods: Factoring - Long Division - Synthetic Division.
Topic 1.5: Polynomial Functions & Complex Zeros.
Video 8: Topic 1.5 (A): Polynomial Functions and Complex Zeros | Complex Roots, Multiplicity, Polynomial Inequalities, Fundamental Theorem of Algebra, Conjugate Pairs | Write the Polynomial Function given a Graph.
Video 9: Topic 1.5 (B): Determine if the Function is EVEN or ODD?
Video 10: Topic 1.5 (C): The EASIEST Way to Solve Polynomial Inequalities!
Topic 1.6: Polynomial Functions & End Behavior.
Video 11: Topic 1.6 (A): Polynomial Functions and End Behavior | The Easy Way!
Video 12: Topic 1.6 (B): Polynomial Functions and End Behavior (Foldable Activity) - Easy way to memorize!
Topic 1.7: Rational Functions & End Behavior.
Video 13: Topic 1.7: Rational Functions and End Behavior - Horizontal Asymptotes and Slant Asymptotes.
Topic 1.8: Rational Functions & Zeros.
Video 14: Topic 1.8: Rational Functions and Zeros | Solving Rational Inequalities.
Topic 1.9 - 10: Rational Functions |Vertical Asymptotes - Holes.
Video 15: Topic 1.9-1.10 (A): Vertical Asymptotes and Holes - Horizontal Asymptotes and Slant Asymptotes - Graphing Rational Functions
Video 16: Topic 1.9-1.10 (B): If Vertical Asymptotes, Holes, and Zeros (x-intercepts) occur simultaneously, which one beats?
Video 17: Topic 1.9-1.10 (sub): Find the Domain & Range of Continuous Functions and Discontinuous Functions.
Must watch Videos 18 since it is a prerequisite for Topic 1.11.
Video 18: Permutations & Combinations
Topic 1.11: Equivalent Representations of Polynomial and Rational Expressions.
Video 19: Topic 1.11 (A): How to Write a Rational Function Given a Graph.
Video 20: Topic 1.11 (B): Use the Binomial Theorem to find the coefficient of the term containing x^3 or x^4...?
Video 21: Topic 1.11 (C): Use the Pascal Triangle to find the coefficient of the term containing x^3 or x^4...?
If you're looking to deepen your understanding of advanced concepts, give this a watch.
Video 22: Binomial Theorem Challenging Problem 1
Video 23: Binomial Theorem Challenging Problem 2
If you're looking to deepen your understanding of advanced concepts, give this a read.
Topic 1.12: Transformations of Functions.
Video 24: Topic 1.12: Transformations of Functions (Translation, Reflection, Dilation)
Topic 1.13 - 1.14: Function Model | Selection and Assumption Articulation | Construction and Application.
Video 25: Topic 1.13 - 1.14: Modeling Functions and Applications | Best-fitting Regression Model with TI-Nspire & TI-84 Plus CE Calculator.
Video 26: Topic 1.13 - 1.14 (sub): Scatter Plots and Trend Lines - Association vs. Causation - Correlation Coefficient.
Unit 2: Exponential & Logarithmic Functions
Topic 2.1: Change in Arithmetic and Geometric Sequences.
Video 27: Topic 2.1: Change in Arithmetic and Geometric Sequences.
Topic 2.2: Change in Linear and Exponential Functions.
Video 28: Topic 2.2: Change in Linear and Exponential Functions. How to Predict the Future Values?
Topic 2.3: Exponential Functions.
Video 29: Topic 2.3: Exponential Functions | Characteristics, End Behavior & Concavity |Determine if the function is increasing/decreasing at an increasing/decreasing rate?
Must watch Videos 30 - 33 since they are prerequisites for Topic 2.4 - 2.5.
Video 30: Find the Domain, Range, Y-intercept, Asymptote of an Exponential Function.
Video 31: Find the Domain, Range, Y-intercept, Asymptote of an Exponential Function Word Problems.
Video 32: Exponential Growth & Decay Functions.
Video 33: Modeling Exponential Functions in Finance | Compound Interest.
Topic 2.4: Exponential Function Manipulation.
Video 34: Topic 2.4: Exponential Function Manipulation | Why is the Horizontal Translation the same as Vertical Dilation?
Topic 2.5: Exponential Function Context and Data Modeling.
Video 35: Topic 2.5: Exponential Function Context and Data Modeling with a TI-Nspire & TI-84 Plus CE Calculator.
Topic 2.6: Competing Function Model Validation.
Video 36: Topic 2.6: Competing Function Model Validation.
Topic 2.7: Compositions of Functions.
Video 37: Topic 2.7 (A): Composition of Functions.
Video 38: Topic 2.7 (B): Domain of Composite Functions.
Topic 2.8: Inverse Functions.
Video 39: Topic 2.8: Inverse Functions.
Topic 2.9: Logarithmic Expressions.
Video 40: Topic 2.9: Logarithmic Expressions.
Topic 2.10: Inverses of Exponential Functions.
Video 41: Topic 2.10: Inverses of Exponential Functions & Logarithmic Functions.
Topic 2.11: Logarithmic Functions.
Video 42: Topic 2.11: Logarithmic Functions |Characteristics, End Behavior, Concavity, and Transformations |Determine if the function is increasing/decreasing at an increasing/decreasing rate?
Topic 2.12: Logarithmic Function Manipulation.
Video 43: Topic 2.12 (A): Properties of Logarithms | Proof and Walkthrough Examples.
Video 44: Topic 2.12 (B): Logarithmic Function Manipulation | Is the Horizontal Dilation the same as the Vertical Translation?
Topic 2.13: Exponential and Logarithmic Equations and Inequalities.
Video 45: Topic 2.13 (A): Exponential and Logarithmic Equations.
Video 46: Topic 2.13 (B): Mastering Compound Interest: Step-by-Step Proofs & Real-Life Examples.
Video 47: Topic 2.13 (C): Exponential and Logarithmic Equations Word Problems in Finance| Interest Compounded Annually & Continuously.
Video 48: Topic 2.13 (D): Exponential and Logarithmic Inequalities.
Topic 2.14: Logarithmic Function Context & Data Modeling.
Video 49: Topic 2.14: Logarithmic Function Context and Data Modeling with TI-Nspire & TI-84 Plus CE Calculator.
Topic 2.15: Semi-log Plots.
Video 50: Topic 2.15: Mastering Semi-Log Plots: Simplify Exponential Data in Minutes!
Unit 3: Trigonometric & Polar Functions
Topic 3.1: Periodic Phenomena.
Video 51 : Topic 3.1: Unlocking the Secrets of Periodic Phenomena 🌊
Topic 3.2: Sine, Cosine, and Tangent.
Video 52: Topic 3.2: Using the Unit Circle Activity to Verify Why π = 180?
Video 53: Topic 3.2 (A): Trigonometry in Right Triangles - Sine, Cosine, and Tangent - SOH, CAH - TOA Explained!
Video 54: Topic 3.2 (B): Reference & Coterminal Angles EXPLAINED! 🔥 (Easy Tricks!)
Video 55: Topic 3.2 (C): Unlock Trigonometry: Sine, Cosine & Tangent in the Circle! 🚀
Video 56: Topic 3.2 (D): Crack the Unit Circle & Radians Like a Pro! 🔥
Topic 3.3: Sine and Cosine Function Values.
Video 57: Topic 3.3 (A): Struggling with Sine & Cosine? This Unit Circle Trick Will Help! ✅
Video 58: Topic 3.3 (B): A Complete Guide to Deriving the Unit Circle from Scratch - Evaluate the Value of Sine & Cosine of BIG Angles.
Video 59: Topic 3.3 (C): Cool Trick to memorize the Unit Circle in Seconds! 🚀
Video 60: Topic 3.3 (D): Cool Trick to memorize the Trigonometric Values of Special Angles! 🚀
Practice: Follow this link to quiz yourself about finding the value of the Sine & Cosine w/wo the Unit Circle after you watch the videos 57-60.
Topic 3.4 - 3.5: Sine and Cosine Function Graphs | Sinusoidal Functions.
Video 61: Topic 3.4 - 3.5: Sinusoidal Functions Demystified! Master Sine & Cosine Graphs | Finding Maximum, Minimum, Midline, Amplitude, Period, Frequency, Increasing, Decreasing, and Concavity.
Topic 3.6: Sinusoidal Function Transformations.
Video 62: Topic 3.6 (A): Writing Sine & Cosine Functions Given Amplitude, Period, Phase Shift, and Vertical Shift.
Video 63: Topic 3.6 (B): Graphing Sine & Cosine Functions.
Video 64: Topic 3.6 (C): Writing Sine & Cosine Functions Given a Graph.
Topic 3.7: Sinusoidal Function Context and Data Modeling.
Video 65: Topic 3.7 (A): How to Write Sinusoidal Functions Given a Data Set with a TI-Nspire Calculator and TI-84 Plus CE Calculator?
Video 66: Topic 3.7 (B): Unlock the Power of Sinusoidal Function Context and Data Modeling.
Video 67: Topic 3.7 (C): Sinusoidal Function Word Problems.
Video 68: Topic 3.7 (D): Sinusoidal Regression with TI-Nspire & TI-84 Plus CE Calculators and Related Questions.
Topic 3.8: The Tangent Function.
Video 69: Topic 3.8 (A): How to Evaluate the Value of the Tangent Function?
Practice: Follow this link to quiz yourself about finding the value of the Tangent function w/wo the Unit Circle after you watch the video 69.
Video 70: Topic 3.8 (B): Mastering Tangent Functions: Period, Inflection Points, Asymptotes & Graphing Made Easy!
Video 71: Topic 3.8 (C): Writing the Tangent Function Given A Graph, Finding the Formula for the Vertical Asymptotes, and Finding the Slope of the Terminal Ray.
Topic 3.9: Inverse Trigonometric Functions.
Video 72: Topic 3.9 (A): Mastering the Graphs of Inverse Trigonometric Functions arcsin, arccos, arctan.
Video 73: Topic 3.9 (B): Evaluating (Finding the Exact) Value of the Composition of Inverse Trigonometric Functions.
Video 74: Topic 3.9 (C): The ULTIMATE Guide to Finding Inverse Trigonometric Functions! 📚
Video 75: Topic 3.9 (D): Exploring Graphs of Inverse Sine and Cosine Functions & Their Transformation.
Must watch Videos 76 - 78, and video 10 of Topic 1.5C - Solving Polynomial Inequalities since they are prerequisites for Topic 3.10.
Video 76: Solving Quadratic Equations by Factoring.
Video 77: Solving Quadratic Equations by Taking Square Root and Completing Squares.
Video 78: Solving Quadratic Equations Using Quadratic Formula and Graphing Calculator.
Topic 3.10: Trigonometric Equations and Inequalities.
Video 79: Topic 3.10 (A): Solving Trigonometric Equations.
Video 80: Topic 3.10 (B): Solving Trigonometric Inequalities.
Video 81: Topic 3.10 (C): Mastering Trigonometric Inequalities with Double & Triple Angles.
Topic 3.11: The Secant, Cosecant, and Cotangent Functions.
Video 82: Topic 3.11 (A): Identifying characteristics & Finding Exact Values of Secant, Cosecant, and Cotangent Functions.
Video 83: Topic 3.11 (B): Graphing Secant, Cosecant, and Cotangent Functions.
Video 84: Topic 3.11 (C): Solving Secant, Cosecant, and Cotangent Equations.
Topic 3.12: Equivalent Representations of Trigonometric Functions.
Video 85: Topic 3.12 (A): How to Prove Fundamental Trigonometric Identities | Step-by-Step Guide.
Video 86: Topic 3.12 (B): Trick to Memorize Trigonometric Identities | Super Hexagon for Trigonometric Identities.
Video 87: Topic 3.12 (C): Verifying Trigonometric Identities | Step-by-Step Guide.
Video 88: Topic 3.12 (D): Finding the Exact Values of Trigonometric Functions Using Trigonometric Identities.
Video 89: Topic 3.12 (E): Solving Trigonometric Equations Involving Fundamental Trigonometric Identities.
If you're looking to deepen your understanding of advanced concepts, give this a read:
Topic 3.13: Trigonometry and Polar Coordinates.
Video 90: Topic 3.13 (A): How to Find Multiple Representations of Polar Coordinates.
Video 91: Topic 3.13 (B): How to Convert between Polar and Rectangular Coordinates.
Topic 3.14: Polar Function Graphs.
Video 92: Topic 3.14 (A): Tests for Symmetry.
Video 93: Topic 3.14 (B): Graphs of Polar Equations of Circles.
Video 94: Topic 3.14 (C): Graphs of Limacon Curves.
Video 95: Topic 3.14 (D): Graphs of Rose Curves.
Video 96: Topic 3.14 (E): Graphs of Lemniscate Curves.
Video 97: Topic 3.14 (F): Graphs of Archimedean Spirals: TI-Nspire, TI-84, & Desmos Made Easy!
After learning how to graph polar functions by hand from Videos 93–97, use the following link to practice graphing them on Desmos.
Video 98: Topic 3.14 (G): Polar Function Graph Related Problems.
Here's a link to a Desmos demonstration that beautifully illustrates the relationship between polar and rectangular graphs on the same xy-coordinate plane - definitely worth exploring!
Topic 3.15: Rates of Change in Polar Functions.
Video 99: Topic 3.15: Mastering the Rate of Change in Polar Functions 🚀
AP Precalculus Exam Prep - Road to a 5!
Yay! We've reached the end of the AP Precalculus curriculum—now it's time for review. Use the three slideshares of unit 1, 2, 3 below to revisit key concepts and activate your prior knowledge. Then, summarize them using the AP Precalculus Exam Review by Unit Summary Student Pages found at the bottom of this page.
Unit 1: Polynomial & Rational Functions.
Unit 2: Exponential & Logarithmic Functions.
Unit 3: Trigonometric & Polar Functions.
Below is a series of videos that review the entire AP Precalculus curriculum. If there's any concept you've missed or want to strengthen your understanding of, be sure to check out the corresponding videos above.
Video 100: Last Minute Lock In: Everything you need to know before the AP Precalculus exam.
Unit 1 Review: Polynomial & Rational Functions
Video 101: Topics 1.1 - 1.6 Review: Polynomial Review Summary | Characteristics of Polynomial Functions | Writing Polynomial Functions | Factoring Polynomials | Solving Polynomial Equations and Inequalities | Polynomial Behavior and Modeling.
Video 102: Topics 1.7 - 1.11 Review (Part 1): Asymptotes, Holes & End Behavior | Rational Functions.
Video 103: Topics 1.7 - 1.11 Review (Part 2): Asymptotes, Holes & Zeros | Long Division | Synthetic Division | Pascal Triangle | Binomial Theorem | Rational Functions.
Video 104: Topics 1.12 - 1.14 Review: Transformations (Translation, Reflection, Dilation) & Modeling with TI-84 Plus CE & TI-Nspire Calculator.
Video 105: Unit 1 Review: Mastering Polynomials & Rational Functions for the AP Exam.
Unit 2 Review: Exponential & Logarithmic Functions
Video 106: Topics 2.1 - 2.4 Review: Sequences & Exponential Functions Made Easy!
Video 107: Topics 2.3 - 2.9 Review: Mastering Exponential & Logarithmic Functions!
Video 108: Topic 2.8 - 2.10 Review: Mastering Inverses: Exponential & Logarithmic Functions!
Video 109: Topics 2.3, 2.10 - 2.11 Review: Exponential & Logarithmic Rates of Change Explained!
Video 110: Topic 2.12 Review: Logarithmic Function Manipulation | Is the Horizontal Dilation the same as the Vertical Translation?
Video 111: Topic 2.13 Review: Exponential and Logarithmic Inequalities.
Video 112: Topics 2.13 - 2.15 Review: Master Log Equations and Semi-Log Graphs in Minutes!
Video 113: Unit 2 Review: Mastering Exponential and Logarithmic Functions for the AP Exam!
Unit 3 Review: Trigonometric & Polar Functions
Video 114: Topics 3.1 - 3.3 Review: Sine, Cosine, Tangent, Periods & Unit Circle Explained!
Video 115: Topics 3.4 - 3.7 Review: Sinusoidal Functions, Graphs, and Modeling.
Video 116: Unit 3.8 Review: The Tangent Function & Its Transformations.
Video 117: Unit 3.9 Review: Everything You Need for Inverse Trigonometric Functions.
Video 118: Unit 3.10 Review: Trigonometric Equations and Inequalities.
Video 119: Unit 3.11 Review: Unlocking Secant, Cosecant, and Cotangent Functions.
Video 120: Unit 3.12 Review: Equivalent Representations of Trigonometric Functions.
Video 121: Unit 3.13 Review: Trigonometry & Polar Coordinates.
Video 122: Unit 3.14 Review: Polar Function Graphs.
Video 123: Unit 3.15 Review: Rates of Change in Polar Functions.
Video 124: Unit 3 Review: Trigonometric & Polar Functions.
Video 125: AP Precalculus Full Course Review with AP-Style MCQs: Everything You Need Before the Exam!
Video 126: FRQ#1 Review: AP Precalculus FRQ #1 Walkthrough | Ace the Free Response!
Video 127: FRQ#2 Review: AP Precalculus FRQ #2 Walkthrough | Ace the Free Response!
Video 128: FRQ#3 Review: AP Precalculus FRQ #3 Walkthrough | Ace the Free Response!
Video 129: FRQ#4 Review: AP Precalculus FRQ #4 Walkthrough | Ace the Free Response!
Video 130: FRQ Review: Full AP Precalculus FRQs in One Video — How to Ace Every Free Response Question!
Past AP Precalculus Exams
Use the past AP Precalculus exams below to sharpen your skills and get familiar with the test format. Reviewing real exam questions helps build familiarity with the format, reinforce key concepts, and boost confidence. Practicing with these resources is one of the best ways to identify strengths and target areas for growth - use them to your full advantage! If there's any concept you've missed or want to strengthen your understanding of, be sure to check out the corresponding videos above.
Video 131: Full Solutions to the AP Precalculus FRQ 2024.
Video 132: Full Solutions to the AP Precalculus FRQ 2025.
Assorted Advanced Concepts
Dive into a collection of advanced math concepts!
This series of videos covers a variety of challenging topics designed to deepen your understanding and sharpen your problem-solving skills. Whether you’re preparing for competitions, exams, or just love advanced math, these concepts will push your thinking and expand your toolkit. Ready to level up? Let’s get started!
Video 1: Don’t Let Composition of Inverse Trig Confuse You! Try This Trick!
Video 2: A Tricky Trigonometry Equation sin(theta + pi/3) = (sqrt of 6 + sqrt of 2)/4
Video 3: Given sin^6(x) + cos^6(x) = 1/4. Evaluate 1/sin^6(x) + 1/cos^6(x)=?
Video 4: STOP Struggling with Logs! Solve This Like a Pro💡
Video 5: A Challenging Logarithmic Equation from Viet Nam log_3(5 - 3^x) + x = 0.
Video 6: A Insane Trigonometric Equation Everyone's Stressing Out.
Video 7: The Best Trick to Solve This Challenging Logarithmic Equation.
Video 8: How to solve log_2(log_3(log_4x)) = log_4(log_3(log_2x))?
Video 9: Find the sum of the combination using the Binomial theorem.
Video 10: Can you solve this tricky problem using the Binomial theorem?
Video 11: A Simple Exponential Equation: Solve 16^(x^2+y) +16^(x+y^2) = 1
Video 12: A Simple Exponential Equation: 4 + 9(3^x) = (4 + 9^x)(7^(2-x)
Video 13: An Insane Logarithmic Equation (x/3)^(3+logx) = 3(10^4)
Video 14: A Trigonometry Math Olympiad Problem from Viet Nam that my stress you out.
Video 15: Find all solutions to the equation 3^x = x^9.
Video 16: Most students stuck with this exponential problem 3^x = 7^y = 11^z = 231
Video 17: Can you solve this exponential equation: 4^x+9^x = 6^x
Video 18: Can you solve this exponential equation: 4^x+6^x = 9^x
Video 19: Finding All 6 Roots of 𝑥^6 + 64 = 0
Explore my playlist of nearly 1000 Math Olympiad problem videos, with new content added regularly. Dive in and challenge yourself!
AP Precalculus Score Calculator
The AP Precalculus Exam is divided into two sections: Multiple Choice and Free Response. Scores range from 1 to 5, with 5 being the highest possible score. The results provided by this calculator are estimates based on historical scoring curves. Actual scoring may vary from year to year. Use this link to estimate your score.
