Problem Sets | Precalculus

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Problem Sets

This course contains problem sets that accompany each module. In these problem sets, students are given an opportunity to apply the quantitative-reasoning skills they learned throughout the module.

Module 1: Introduction to Functions
- Problem Set 1: Functions and Function Notation
- Problem Set 2: Domain and Range
- Problem Set 3: Rates of Change and Behavior of Graphs
- Problem Set 4: Composition of Functions
- Problem Set 5: Transformation of Functions
- Problem Set 6: Absolute Value Functions
- Problem Set 7: Inverse Functions
Module 2: Linear Functions
- Problem Set 8: Linear Functions
- Problem Set 9: Graphs of Linear Functions
- Problem Set 10: Modeling with Linear Functions
- Problem Set 11: Fitting Linear Models to Data
Module 3: Polynomial and Rational Functions
- Problem Set 12: Complex Numbers
- Problem Set 13: Quadratic Functions
- Problem Set 14: Power Functions and Polynomial Functions
- Problem Set 15: Graphs of Polynomial Functions
- Problem Set 16: Dividing Polynomials
- Problem Set 17: Zeros of Polynomial Functions
- Problem Set 18: Rational Functions
- Problem Set 19: Inverse and Radical Functions
- Problem Set 20: Modeling Using Variation
Module 4: Exponential and Logarithmic Functions
- Problem Set 21: Exponential Functions
- Problem Set 22: Graphs of Exponential Functions
- Problem Set 23: Logarithmic Functions
- Problem Set 24: Graphs of Logarithmic Functions
- Problem Set 25: Logarithmic Properties
- Problem Set 26: Exponential and Logarithmic Equations
- Problem Set 27: Exponential and Logarithmic Models
- Problem Set 28: Fitting Exponential Models to Data
Module 5: Systems of Equations and Inequalities
- Problem Set 29: Systems of Linear Equations: Two Variables
- Problem Set 30: Systems of Linear Equations: Three Variables
- Problem Set 31: Systems of Nonlinear Equations and Inequalities: Two Variables
- Problem Set 32: Partial Fractions
- Problem Set 33: Matrices and Matrix Operations
- Problem Set 34: Solving Systems with Gaussian Elimination
- Problem Set 35: Solving Systems with Inverses
- Problem Set 36: Solving Systems with Cramer’s Rule
Module 6: Sequences, Probability, and Counting Theory
- Problem Set 37: Sequences and Their Notations
- Problem Set 38: Arithmetic Sequences
- Problem Set 39: Geometric Sequences
- Problem Set 40: Series and Their Notations
- Problem Set 41: Counting Principles
- Problem Set 42: Binomial Theorem
- Problem Set 43: Probability
Module 7: Trigonometric Functions
- Problem Set 44: Angles
- Problem Set 45: Unit Circle: Sine and Cosine Functions
- Problem Set 46: The Other Trigonometric Functions
- Problem Set 47: Right Triangle Trigonometry
Module 8: Periodic Functions
- Problem Set 48: Graphs of the Sine and Cosine Function
- Problem Set 49: Graphs of the Other Trigonometric Functions
- Problem Set 50: Inverse Trigonometric Functions
Module 9: Trigonometric Identities and Equations
- Problem Set 51: Solving Trigonometric Equations With Identities
- Problem Set 52: Sum and Difference Identities
- Problem Set 53: Double Angle, Half Angle, and Reduction Formulas
- Problem Set 54: Sum-to-Product and Product-to-Sum Formulas
- Problem Set 55: Solving Trigonometric Equations
- Problem Set 56: Modeling with Trigonometric Equations
Module 10: Further Applications of Trigonometry
- Problem Set 57: Non-right Triangles: Law of Sines
- Problem Set 58: Non-right Triangles: Law of Cosines
- Problem Set 59: Polar Coordinates
- Problem Set 60: Polar Coordinates: Graphs
- Problem Set 61: Polar Form of Complex Numbers
- Problem Set 62: Parametric Equations
- Problem Set 63: Parametric Equations: Graphs
- Problem Set 64: Vectors
Module 11: Analytic Geometry
- Problem Set 65: The Ellipse
- Problem Set 66: The Hyperbola
- Problem Set 67: The Parabola
- Problem Set 68: Rotation of Axes
- Problem Set 69: Conic Sections in Polar Coordinates
Module 12: Introduction to Calculus
- Problem Set 70: Finding Limits: Numerical and Graphical Approaches
- Problem Set 71: Finding Limits: Properties of Limits
- Problem Set 72: Continuity
- Problem Set 73: Derivatives