AP Precalculus 1-Month Study Plan

title: "AP Precalculus 1-Month Study Plan" description: "A month-long AP Precalculus calendar: 4 weeks structured by unit, daily practice, weekly full mocks, and cumulative review. Target a 4-5 with steady effort." date: "2026-01-15" examDate: "May AP Exam" topics:

• Polynomial Functions
• Rational Functions
• Exponential & Logarithmic Functions
• Trigonometric Functions
• Polar & Parametric

You have 4 weeks until exam day. This calendar breaks the AP Precalculus curriculum into manageable daily chunks, with progressive difficulty and three full mock exams. Aim for 1–2 hours per day of focused study.

Week 1: Polynomial & Rational Foundations

| Day | Topic | Review (20 min) | Practice (40 min) | Key Goal | |---|---|---|---|---| | Mon | Polynomial end behavior & zeros | Degree + leading coeff rule; factored form | 12 MCQs + sketch 2 graphs | End behavior automatic | | Tue | Polynomial local extrema | Critical points, turning points | 10 MCQs + analyze turning behavior | Distinguish multiplicity (touch vs cross) | | Wed | Rational asymptotes (vertical & horizontal) | Set denom = 0; compare degrees for $y = \frac{\text{const}}{1}$ | 15 MCQs; identify asymptotes from equations | Spot vertical asymptotes in 10 sec | | Thu | Rational holes & slant asymptotes | Common factors; polynomial long division | 10 MCQs + 1 division problem | Perform division cleanly | | Fri | Polynomial long division applications | Use to reduce rational functions | 8 MCQs + 1 full FRQ analyzing a rational function | Write asymptotes + sketch from analysis | | Sat | Cumulative review: Poly & Rational | Skim all Week 1 formulas | 20 mixed MCQs (no calc) | Fluency across both topics | | Sun | Light day or rest | Review errors from Sat | 5 quick drill problems on weak area | Consolidate learning |

Week 1 checkpoint: You should identify end behavior and all asymptotes of a rational function in under 3 minutes.

Week 2: Exponential, Logarithmic & Growth Models

| Day | Topic | Review (20 min) | Practice (40 min) | Key Goal | |---|---|---|---|---| | Mon | Exponential functions & growth/decay | $a \cdot b^t$ vs $a e^{kt}$; identify $b$ or $k$ | 12 MCQs + interpret 3 models | Know growth factor vs growth rate | | Tue | Logarithm properties & change of base | Product, quotient, power rules; $\log_b(x) = \frac{\ln(x)}{\ln(b)}$ | 14 MCQs + expand/condense 4 log expressions | Apply all properties fluently | | Wed | Solving exponential & log equations | Isolate, take log; exponentiate to clear log | 15 MCQs + solve 5 equations | Solve $2^x = 50$ and $\ln(x+3) = 2$ in your head | | Thu | Exponential modeling (FRQ-style) | Set up model, interpret initial/growth, predict | 1 full FRQ + 8 MCQs verifying predictions | Write complete model with interpretation | | Fri | Logarithmic modeling (real-world context) | Interpret log model; solve for time/quantity | 1 full FRQ + 8 MCQs | Scale model interpretation (e.g., decibels, pH) | | Sat | Mock Exam 1 | 30 min: skim all formulas from Weeks 1–2 | Full 80-min timed practice exam (40 MCQ + 4 FRQ) | Measure readiness; identify weak units | | Sun | Error analysis + rest | Review Mock Exam 1; categorize errors | Re-solve 5 problems you missed | Build error-fixing habit |

Week 2 checkpoint: You can write a complete exponential or log model and make predictions from it.

Week 3: Trigonometry & Sinusoidal Modeling

| Day | Topic | Review (20 min) | Practice (40 min) | Key Goal | |---|---|---|---|---| | Mon | Unit circle & special angles | Reference angles; $\sin(\pi/6) = 1/2$, etc. | 15 MCQs on trig values + exact circle | Recall all special angles instantly | | Tue | Basic trig graphs: sine & cosine | Amplitude, period, domain, range | 12 MCQs + sketch $y = \sin(x)$ and $y = \cos(x)$ | Draw graphs from memory | | Wed | Trig transformations | Apply $a$, $b$, $c$, $d$ to $f(x) = a\sin(b(x-c)) + d$ | 18 MCQs; sketch $y = 3\sin(2(x - \pi/4)) - 1$ | Identify all 4 parameters from a graph | | Thu | Inverse trig functions | Ranges of $\sin^{-1}$, $\cos^{-1}$, $\tan^{-1}$; solving equations | 10 MCQs + solve $\sin^{-1}(0.5)$ and $\tan^{-1}(1)$ | Know inverse ranges cold; avoid sign traps | | Fri | Sinusoidal modeling (FRQ focus) | Real-world periodic context; write model + interpret | 2 full modeling FRQs (e.g., temperature, light) | Identify amplitude, period, midline, phase shift correctly | | Sat | Mock Exam 2 | 30 min: skim Weeks 1–3 | Full 80-min timed exam | Track improvement; focus on trig speed | | Sun | Review trig transformations + rest | Re-work any transformation problems you rushed | Light drill: 5 phase-shift problems | Solidify transformation intuition |

Week 3 checkpoint: You write a sinusoidal model and identify all parameters from a real-world description (no calculator).

Week 4: Polar, Parametric, Vectors, Matrices & Final Prep

| Day | Topic | Review (20 min) | Practice (40 min) | Key Goal | |---|---|---|---|---| | Mon | Parametric equations & conversion | Eliminate parameter; recognize ellipse, circle, line | 10 MCQs + convert 4 parametric systems | Convert parametric → Cartesian smoothly | | Tue | Polar coordinates & conversion | $x = r\cos(\theta)$, $y = r\sin(\theta)$; polar → Cartesian | 12 MCQs + convert $r = 4\cos(\theta)$ | Identify polar curves (circles, roses, spirals) | | Wed | Vectors: magnitude, direction, operations | $\|{\bf v}\|$, dot product, angle between vectors | 10 MCQs + compute 3 dot products & magnitudes | Fluent vector arithmetic | | Thu | Matrices & transformations | Multiplication, inverses (2×2), solving $A{\bf x} = {\bf b}$ | 8 MCQs + compute 2 matrix inverses + 1 system | Solve systems via matrix inverse confidently | | Fri | Full cumulative review | Skim all 4 units; prioritize your weak topic | 25 mixed MCQs (all topics) + skim 2 FRQ templates | Fluency across all units | | Sat | Mock Exam 3 | 20 min: bullet-point formula review only | Full 80-min timed exam under exam conditions | Final diagnostic; measure final readiness | | Sun | Error analysis + light review | Review Mock 3; drill ONLY the 2–3 topics where you lost points | Last-Minute Review checklist | Rest, confidence-building |

Week 4 checkpoint: You score 65%+ on Mock 3 (equivalent to a 4 or 5 on the actual exam).

If you're behind schedule

• Weak on polynomials/rationals? Extend Week 1 by 3 days; compress Week 4 to 2 days (parametric is lower-yield).
• Struggling with trig? Extend Week 3 by 4 days; reduce parametric/polar practice.
• Short on time before exam? Skip Week 4 detailed topics and run two full mocks (Weeks 2 and 3), focusing error analysis.

Study habits for success

💡 Daily rhythm: Study at the same time each day. Consistency beats cramming.

| Habit | Reason | |---|---| | Use the graphing calculator for every graph | You'll have one on exam day; don't learn it then. | | Write every FRQ solution fully (not shorthand) | FRQ rubrics demand written work; practice the habit. | | Time yourself on each practice set | Speed + accuracy both matter; rushing loses points. | | Review wrong answers only | Don't waste time re-reading correct ones. |

Before exam week

• Days 21–28: Run one full mock every 2 days (time yourself; full 80 min, no breaks except stretch).
• 2 days before exam: Last-Minute Review only. No new problems.
• Night before: Sleep 8+ hours. Do not study.

Ready to start Week 1?

Open polynomial end behavior practice →. Commit to the calendar. Trust the process. 🎯

Need daily check-ins? Review the FRQ practice guide after each mock to strengthen weak FRQ types.