Representation fluency
Move among equations, graphs, tables, and contexts without changing the model.
Independent AP Precalculus study
See the function before you reach for a formula.
A bilingual, calculation-first guide for students moving between Chinese mathematics classrooms and AP reasoning. Twelve complete original questions are public; your private Learn workspace stays separate.
AP evidence
Learn what determine, justify, and interpret require you to put on the page.
Calculator judgment
Use TI-84 Plus CE and Bluebook Desmos as tools, not substitutes for reasoning.
Open sample set
Twelve questions, fully worked.
01
Unit 1 · 1.2.A
1.2 Rates of Change
foundational · context · no calculator02Unit 1 · 1.6.A
1.6 Polynomial Functions and End Behavior
foundational · graph · no calculator03Unit 1 · 1.11.A
1.11 Equivalent Representations
foundational · equation · no calculator04Unit 1 · 1.14.A
1.14 Function Model Construction and Application
moderate · shared_stimulus · calculator05Unit 2 · 2.2.B
2.2 Change in Linear and Exponential Functions
foundational · graph · no calculator06Unit 2 · 2.5.A
2.5 Exponential Function Context and Data Modeling
moderate · shared_stimulus · no calculator07Unit 2 · 2.6.B
2.6 Competing Function Model Validation
challenging · table · calculator08Unit 2 · 2.13.A
2.13 Exponential and Logarithmic Equations and Inequalities
challenging · graph · calculator09Unit 3 · 3.1.A
3.1 Periodic Phenomena
foundational · table · no calculator10Unit 3 · 3.7.A
3.7 Sinusoidal Function Context and Data Modeling
challenging · shared_stimulus · calculator11Unit 3 · 3.8.C
3.8 The Tangent Function
moderate · equation · no calculator12Unit 3 · 3.12.C