AP Precalculus study plan
AP Precalculus · Give each week a clear focus.
8 weeks · About 6 hours per week
General Functions (non-analytical) & Polynomial and Rational Functions
Identify domain and range of algebraic, piecewise, and absolute value functions from equations and graphs
Compute and simplify difference quotients for polynomial and rational functions
Determine even, odd, or neither symmetry algebraically and confirm graphically
Sketch transformations (shifts, reflections, stretches) of parent functions without a graphing tool
Your checkpoint
A 20-problem self-graded worksheet on domain/range, difference quotients, and transformations with written corrections for each miss
Polynomial and Rational Functions
Factor and solve polynomial equations of degree 3 and higher using grouping and rational root reasoning
Analyze end behavior, zeros, and multiplicity to sketch polynomial graphs
Find vertical asymptotes, holes, and horizontal or slant asymptotes of rational functions
Solve polynomial and rational inequalities using sign charts
Your checkpoint
One-page summary sheet of polynomial and rational graphing rules plus 15 solved problems, including 3 inequalities with sign charts
Polynomial and Rational Functions & Exponential and Logarithmic Functions
Construct exponential and logarithmic functions from tables and word-problem contexts
Apply properties of logarithms to expand and condense expressions
Solve exponential and logarithmic equations, checking for extraneous solutions
Model growth and decay scenarios and interpret parameters in context
Your checkpoint
A timed 45-minute mixed problem set (polynomials, rationals, exponentials, logs) scored and error-analyzed by topic
Exponential and Logarithmic Functions
Determine inverse functions algebraically and verify with composition
Graph logarithmic and exponential functions and state domain, range, and asymptotes
Interpret average rate of change of exponential functions over equal intervals
Solve contextual half-life and compound-interest problems
Your checkpoint
A cumulative mid-plan practice test (30 questions) covering Domains 1-3, scored with a written list of the three weakest skills
Trigonometric and Polar Functions
Convert fluently between degrees and radians and locate angles on the unit circle
Evaluate all six trig functions at standard angles without a calculator
Graph sine, cosine, and tangent with amplitude, period, phase shift, and midline identified
Model periodic phenomena with sinusoidal functions from given data
Your checkpoint
A completed unit-circle reference card (from memory, then corrected) plus 15 graphing and modeling problems
Trigonometric and Polar Functions
Solve trigonometric equations over a specified interval
Verify trigonometric identities using fundamental identities
Apply inverse trig functions and state restricted ranges
Translate between polar and rectangular coordinates and equations
Your checkpoint
A 25-problem trig and polar worksheet with full worked solutions written out for every item
General Functions (non-analytical) & Polynomial and Rational Functions & Exponential and Logarithmic Functions & Trigonometric and Polar Functions
Classify missed problems from prior weeks by domain and error type
Re-solve every previously missed problem without notes
Complete mixed-domain problems under timed conditions
Identify and drill the two lowest-accuracy skills across all domains
Your checkpoint
An error log covering all prior worksheets with each item re-solved correctly and a ranked list of remaining weak skills
Polynomial and Rational Functions & Exponential and Logarithmic Functions & Trigonometric and Polar Functions
Complete two full-length timed practice exams under test conditions
Review each exam and correct every error with a written explanation
Confirm mastery of the previously ranked weak skills
Finalize a one-page formula and strategy sheet for exam day
Your checkpoint
Two scored full-length practice exams with corrections and a finished one-page exam-day reference sheet
Milestones
Week 2: Score at least 80% on a self-made 15-question polynomial/rational quiz, including two inequality sign charts solved correctly
Week 4: Score at least 75% on the 30-question cumulative practice test for Domains 1-3, with no more than two errors from careless arithmetic
Week 6: Evaluate all six trig functions at standard angles from memory with 90% accuracy and complete the 25-problem trig/polar worksheet
Week 8: Score at least 80% on both full-length practice exams and show zero repeated error types from the week 7 error log