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Exam Blueprint
AP Precalculus Exam · May 2026 · 2 hr 20 min total
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Section I · Part A
Multiple Choice — No Calculator
~44%28 questions50 min
- ›Function analysis, transformations, and algebraic manipulation
- ›Tests deep conceptual understanding without computational shortcuts
- ›Covers all 4 units with emphasis on reasoning
💡 For Part A, focus on the WHY behind each function type. Know interval notation, domain/range, and end behavior cold — these appear every year without a calculator.
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Section I · Part B
Multiple Choice — Calculator
~19%12 questions30 min
- ›Use your graphing calculator to find intersections, zeros, and extrema
- ›Regression modeling (linear, quadratic, exponential, sinusoidal)
- ›Interpret graphical and numerical results in context
💡 Practice regression on your calculator before the exam. Store equations in Y1, find zeros with [2nd][TRACE][Zero]. Calculator fluency saves 30+ seconds per question.
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Section II · Part A
Free Response — Calculator
~19%2 FRQs30 min
- ›Modeling real-world scenarios with appropriate function types
- ›Interpreting parameters (a, b, c, d) in context of the situation
- ›Multi-part questions requiring algebraic work AND graphical support
💡 Always state your regression equation before using it. Show all calculator work — write 'Using calculator, f(x) = ...' to earn process points even if you make an error.
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Section II · Part B
Free Response — No Calculator
~19%2 FRQs30 min
- ›Algebraic manipulation of exponential, logarithmic, and trig functions
- ›Proof-style reasoning about function properties
- ›Inverse functions, composition, and rate of change analysis
💡 For Part B FRQs, show every algebraic step. A correct process with an arithmetic error earns partial credit; a missing step earns nothing. Write out ln(e^x) = x explicitly.
Score Distribution
5
Master
20%
4
Proficient
22%
3
Qualified
28%
2
Developing
18%
1
Beginning
12%
4 Units — Everything You Need for a 5
Click any unit to expand topics, vocabulary, and curated video resources.
FRQ Mastery Suite
4 free-response types · 37.5% of your score. Master each format.
1
Modeling with Functions
12 points
Identify which function family models the scenario (exponential for growth/decay, sinusoidal for periodic, polynomial for bounded). State the model explicitly, interpret every parameter in context, and use calculus-readiness language about rates of change.
Model Opener
Let f(t) represent [quantity] in [units] as a function of t [time units] after [reference point]. Based on the given data, an exponential model of the form f(t) = a·b^t is appropriate because...
2
Function Analysis
12 points
Analyze function behavior (domain, range, increasing/decreasing, concavity, zeros, asymptotes). Show algebraic work for each property. Connect graphical features to algebraic structure.
Model Opener
The function f has a vertical asymptote at x = [value] because the denominator equals zero there while the numerator is nonzero. As x approaches this value from the left/right, f(x) → ...
3
Rate of Change
10 points
Calculate average rate of change as (f(b)-f(a))/(b-a). Interpret the result in context with appropriate units. Compare rates across intervals to describe concavity. Connect to the idea of instantaneous rate as a bridge to calculus.
Model Opener
The average rate of change of f on the interval [a, b] is (f(b)-f(a))/(b-a) = [calculation] [units]. This means that [quantity] is [increasing/decreasing] by approximately [value] [units] per [time unit] over this interval.
4
Transformation and Composition
10 points
Apply transformations in the correct order (horizontal then vertical, or inside-out). For composition, evaluate inner function first. For inverses, swap x and y then solve — and verify by checking f(f⁻¹(x)) = x.
Model Opener
To find f⁻¹(x): replace f(x) with y, swap x and y to get x = [expression], then solve for y. Therefore f⁻¹(x) = [expression], with domain [domain] and range [range].
Score 5 Strategy Guide
1
Master the 4 function families cold
Polynomial, rational, exponential/log, and trig — know their graphs, transformations, key features, and real-world models. Every exam question connects to one of these.
2
Learn the transformation toolkit
f(x-h)+k shifts, af(x) stretches/reflects, f(bx) horizontal compression. Practice applying ALL transformations simultaneously to one function.
3
Trig identities are non-negotiable
Memorize the Pythagorean identities, double angle formulas, and the unit circle. Know how sin²θ + cos²θ = 1 leads to all others.
4
Connect every problem to rate of change
AP Precalculus bridges algebra and calculus. The exam loves average rate of change (AROC) and comparing AROC across intervals.
5
Write full units and context in FRQs
If f(t) models temperature in °C after t hours, your answer isn't just '3.5' — it's '3.5°C per hour.' Context sentences earn points.
6
Regression fluency wins Part A-B problems
Practice regression on your graphing calculator weekly. Know which model to choose (exponential for decay/growth, sinusoidal for cycles, quadratic for parabolic data).
Practice Resources
AP Classroom (College Board)
Free · Official
Desmos Graphing Calculator
Free · Calculator
Khan Academy — Precalculus
Free · Video + Practice
Paul's Online Math Notes
Free · Notes
Fiveable AP Precalculus
Free · Study Guides
3Blue1Brown — Essence of Calculus
Free · Conceptual
Albert.io AP Precalculus
Paid · Practice Tests
16-Week Score 5 Study Plan
Phase 1 (Weeks 1–4)
Unit 1: Polynomial and Rational Functions
- Graph polynomial functions by hand — zeros, multiplicity, end behavior
- Practice simplifying rational expressions and finding asymptotes
- Master polynomial long division and synthetic division
- Complete 2 timed Unit 1 MC sections per week
Phase 2 (Weeks 5–8)
Unit 2: Exponential and Logarithmic Functions
- Build fluency with log properties — expand, condense, change-of-base
- Solve exponential and logarithmic equations algebraically
- Practice regression on your graphing calculator with real datasets
- Model growth/decay scenarios with correct parameter interpretation
Phase 3 (Weeks 9–12)
Unit 3: Trigonometric and Polar Functions
- Memorize the unit circle through patterns (not brute force)
- Graph one full period of sin/cos/tan with all transformations
- Solve sinusoidal modeling problems with amplitude/period/phase shift
- Practice polar coordinate plots and conversions
Phase 4 (Weeks 13–16)
Unit 4 + Full Practice Exams
- Master parametric equations and eliminate the parameter
- Practice vector operations and matrix multiplication
- Take 3 complete AP Precalculus practice exams under timed conditions
- Review every missed problem — identify the concept, not just the answer
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