Algebraic Notation, Substitution, and Simplifying
Use algebraic notation accurately, substitute values, collect like terms, and simplify expressions.
AI ← Back to AP Mathematics
AP Precalculus
Strengthen your prerequisites, explore all 14 Unit 1 topics, then try one of five fixed Unit 1 simulations.
Each simulation combines 20 multiple-choice questions with two multipart free-response questions, adjustable timers, worked solutions, and a personal skills summary. Units 2–4 and their simulations are coming soon.
AIThis new course resource was assembled with AI and has not yet been independently verified by Topey. Please report anything unclear or incorrect.
Expanding Polynomial Expressions
Expand single, double, and repeated parentheses and simplify the result.
AIFactoring Polynomial Expressions
Factor out greatest common factors and factor quadratic expressions completely.
AIExponent Rules
Apply product, quotient, power, zero, and negative exponent rules.
AIRadicals and Rational Exponents
Simplify radicals and move fluently between radical and rational-exponent forms.
AILinear Equations and Inequalities
Solve multistep linear equations and inequalities, including variables on both sides.
AIRearranging Formulas
Make a chosen variable the subject of a formula and preserve stated restrictions.
AISolving Quadratic Equations
Solve quadratics by factoring, completing the square, and using the quadratic formula.
AISolving Simple Polynomial Equations
Solve polynomial equations by first factoring out a common power of x.
AICoordinate Geometry
Find slope, distance, midpoint, and geometric relationships in the coordinate plane.
AILinear Functions and Graphs
Work with equations of lines, intercepts, and parallel or perpendicular slopes.
AISystems of Equations
Solve systems in two and three variables and interpret the solution.
AIQuadratic Functions and Graphs
Connect standard, vertex, and factored forms to key features of a parabola.
AIFunction Notation and Representations
Evaluate functions and connect formulas, tables, graphs, and verbal descriptions.
AIPiecewise-Defined Functions
Evaluate and interpret functions whose rules change across parts of their domain.
AIExponential Functions
Recognize, evaluate, and interpret basic exponential growth and decay models.
AIComplex Numbers
Use i, simplify powers of i, and perform arithmetic with complex numbers.
AIRight-Triangle Trigonometry
Use sine, cosine, tangent, and the Pythagorean theorem in right triangles.
AIChange in Tandem
Describe how two quantities vary together using values, signs, intervals, and context.
AIRates of Change
Calculate, compare, and interpret average rates of change from multiple representations.
AIRates of Change in Linear and Quadratic Functions
Connect constant and changing rates to the structure of linear and quadratic functions.
AIPolynomial Functions and Rates of Change
Analyze polynomial behavior, turning points, and changing rates across intervals.
AIPolynomial Functions and Complex Zeros
Use factors, multiplicity, and conjugate pairs to reason about real and complex zeros.
AIPolynomial Functions and End Behavior
Determine polynomial end behavior from degree, leading coefficient, and equivalent forms.
AIRational Functions and End Behavior
Use degree comparison and division to identify horizontal and polynomial asymptotes.
AIRational Functions and Zeros
Identify rational-function zeros and use multiplicity to describe local behavior.
AIRational Functions and Vertical Asymptotes
Locate vertical asymptotes and analyze one-sided behavior with sign reasoning.
AIRational Functions and Holes
Find removable discontinuities and determine the coordinates of holes.
AIEquivalent Representations of Polynomial and Rational Expressions
Rewrite expressions to expose zeros, holes, asymptotes, and end behavior.
AITransformations of Functions
Track points and features through translations, reflections, and stretches.
AIFunction Model Selection and Assumption Articulation
Select defensible polynomial or rational models and state their assumptions and limitations.
AIFunction Model Construction and Application
Construct, apply, and interpret polynomial and rational models in context.
AIUnit 1 Simulations
Choose from five tests, each with 20 multiple-choice questions and two multipart free-response questions. Set your timer and see which skills to work on next.
AI Unit 2
Coming soonExponential and Logarithmic Functions
Topic practice and unit simulations are coming soon.
Unit 2 Simulations
Choose from five tests, each with 20 multiple-choice questions and two multipart free-response questions. Set your timer and see which skills to work on next.
Coming soon
AI Unit 3
Coming soonTrigonometric and Polar Functions
Topic practice and unit simulations are coming soon.
Unit 3 Simulations
Choose from five tests, each with 20 multiple-choice questions and two multipart free-response questions. Set your timer and see which skills to work on next.
Coming soon
AI Unit 4
Coming soonFunctions Involving Parameters, Vectors, and Matrices
Topic practice and unit simulations are coming soon.
Unit 4 Simulations
Choose from five tests, each with 20 multiple-choice questions and two multipart free-response questions. Set your timer and see which skills to work on next.
Coming soon
AI How to use the practice
Choose a card, work through the questions in order or jump directly to any number, select an answer where appropriate, and press Check answer only when you are ready. Use Worked solution for staged reasoning.
Question design
- Neutral A–D choices until checking
- Distractors tied to common misconceptions
- Specific micro-skill shown on every question
- Calculator mode shown where relevant