Directions: This module contains 20 advanced multiple-choice items covering Units 1–4 (Polynomial & Rational Functions, Exponential & Logarithmic Functions, Trigonometric & Polar Functions, Parametric Functions & Vectors). Items were selected for error patterns most common among Korean AP Precalculus students. Select an answer to see immediate feedback. A graphing calculator is available at top left.

Advanced Item Set — Units 1–4

20 Questions • No calculator restriction • Answer choices reveal explanations instantly

0 / 20 answered

Review flagged items using the number palette above before printing.

Graphing Calculator

Reference

Unit Circle & Identities

sin²θ + cos²θ = 1

tan θ = sin θ / cos θ

sin(A±B) = sinA cosB ± cosA sinB

cos(A±B) = cosA cosB ∓ sinA sinB

Logs & Exponentials

log_b(xy) = log_b x + log_b y

log_b(x/y) = log_b x − log_b y

log_b(x^k) = k·log_b x

change of base: log_b x = ln x / ln b

Polar / Parametric / Vectors

x = r cosθ, y = r sinθ

speed = √[(dx/dt)² + (dy/dt)²]

|v| = √(v₁² + v₂²)