Multiple choice
42 questions · 1 hour 45 minutes · 62.5%
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AP Precalculus exam prep
Master function behavior, modeling, transformations, and multiple representations before practicing calculator and non-calculator decisions.
AP4units
AP Precalculus exam format
Hybrid digital. Formats can change, so verify the linked official page before exam day.
Official College Board exam page ↗Free response
4 questions · 1 hour 10 minutes · 37.5%
AP Precalculus unit roadmap
Each unit is a connected part of the course, not an isolated chapter. The focus says what you must know and the weighting says how much exam time it is worth. Use the weighting to order your review, never as permission to skip a prerequisite.
Polynomial and Rational Functions
Zeros, rates of change, end behavior, transformations, and models
- Define the vocabulary you need to explain zeros, rates of change, end behavior, transformations, and models.
- Draw and label the graph, model, diagram, or evidence that best represents polynomial and rational functions.
- Solve one direct polynomial and rational functions question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Function transformations and composition
Exponential and Logarithmic Functions
Growth, decay, inverses, semi-log reasoning, and models
- Define the vocabulary you need to explain growth, decay, inverses, semi-log reasoning, and models.
- Draw and label the graph, model, diagram, or evidence that best represents exponential and logarithmic functions.
- Solve one direct exponential and logarithmic functions question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Exponential versus polynomial behavior
Trigonometric and Polar Functions
Periodic behavior, identities, equations, and polar representation
- Define the vocabulary you need to explain periodic behavior, identities, equations, and polar representation.
- Draw and label the graph, model, diagram, or evidence that best represents trigonometric and polar functions.
- Solve one direct trigonometric and polar functions question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Sinusoidal model parameters
Functions Involving Parameters, Vectors, and Matrices
Course extension; not assessed on the end-of-course exam
- Define the vocabulary you need to explain course extension; not assessed on the end-of-course exam.
- Draw and label the graph, model, diagram, or evidence that best represents functions involving parameters, vectors, and matrices.
- Solve one direct functions involving parameters, vectors, and matrices question, then change one assumption and predict how the answer moves.
- Tie this unit to the course priority: Justification from tables and graphs
Use a diagnostic to find the first knowledge gap
This short check is not a score prediction. It identifies which part of the course deserves your next focused session.
- Answer without notes.
- Explain your choice before revealing feedback.
- Record every uncertain answer, including lucky guesses.
Question 1 of 3
Scored skills for the AP Precalculus exam
Knowing an idea internally is not enough. Practice producing observable evidence under time pressure.
Translate among graphical, numerical, analytical, and verbal representations
Build and validate function models
Describe covariation and rates of change
Use technology strategically and interpret output
Highest-value review targets
- Function transformations and composition
- Exponential versus polynomial behavior
- Sinusoidal model parameters
- Justification from tables and graphs
AP Precalculus formulas and reference relationships
A useful sheet records meaning and conditions, not isolated symbols. Rebuild it from a blank page until every line comes back with its conditions attached.
Average rate of change
\[\frac{f(b)-f(a)}{b-a}\]
What it tells you: Measures output change per input unit across an interval.
Use it when: $a\ne b$; retain input and output units in the interpretation.
Example: For $f(x)=x^2$ on $[1,3]$, the rate is $(9-1)/2=4$.
Exponential model
\[y=ab^x=a(1+r)^x\]
What it tells you: Models a constant multiplicative or percentage change per equal input interval.
Use it when: $a$ is the initial value, $b>0$, and growth uses $b>1$ while decay uses $0<b<1$.
Example: Six-percent growth uses $b=1.06$, so $y=a(1.06)^x$.
Sinusoidal model
\[y=A\sin(B(x-C))+D\]
What it tells you: Connects amplitude, period, phase shift, and midline to periodic behavior.
Use it when: $B\ne0$; period is $2\pi/|B|$ in radians.
Example: $3\sin(2x)+1$ has amplitude $3$, period $\pi$, and midline $y=1$.
Function composition
\[(f\circ g)(x)=f(g(x))\]
What it tells you: Feeds the output of one function into another function.
Use it when: $x$ must lie in the domain of $g$ and $g(x)$ in the domain of $f$.
Example: If $f(x)=x^2$ and $g(x)=x+1$, then $(f\circ g)(x)=(x+1)^2$.
What the AP Precalculus exam hands you, and what you have to recall
| Section or part | What you may use | What that means for your work |
|---|---|---|
| Multiple choice, Part A | No calculator | Algebra by hand: factoring, end behavior, log rules, exact unit-circle values. |
| Multiple choice, Part B | Graphing calculator required | Graph, find intersections, and evaluate models numerically. |
| Free response, Part A | Graphing calculator required | Regression models, intersections, and decimal answers you must store, not retype. |
| Free response, Part B | No calculator | Exact answers, transformations, and reasoning about function behavior. |
Anything the table does not hand you, you have to remember. The AP Precalculus study plan puts these rules on a week-by-week schedule.
Your AP Precalculus preparation plan
Repeat this loop weekly: retrieve, diagnose, repair, mix, time, and reflect.
01
AP-style practice
Original questions, immediate explanations, and local progress.
Start →02Full course test
A timed mixed-unit test with a complete answer review.
Test →03Study plan and strategy
Eight weeks, plus the timing, calculator, and task-verb decisions.
Plan →04Unit roadmap
Every unit, its weighting, and what mastery looks like.
Review →05Formula review
Key relationships, their conditions, and what the exam provides.
Recall →Questions about the AP Precalculus exam
Can I use a graphing calculator on the AP Precalculus exam?
Rules change from section to section. Multiple choice, Part A: no calculator. Multiple choice, Part B: graphing calculator required. Free response, Part A: graphing calculator required. Free response, Part B: no calculator. Practise each section under its own rule.
How long is the AP Precalculus exam?
Multiple choice: 1 hour 45 minutes, 42 questions. Free response: 1 hour 10 minutes, 4 questions. Multiple choice — About 2.5 minutes each. The no-calculator part is faster, so bank time there for Part B. Free response — Roughly 17 minutes per question. Every question has parts a, b, and c, so budget by part, not by question.
Which AP Precalculus unit is weighted most heavily?
Polynomial and Rational Functions (30–40%) and Exponential and Logarithmic Functions (27–40%) tie for the largest published weighting. Use the weighting to order your review, not to skip a prerequisite that a heavier unit depends on.
What does “Describe how the function changes” mean on the AP Precalculus exam?
Direction AND concavity: 'increasing at a decreasing rate' scores; 'increasing' alone often does not. Answering a different verb can be mathematically correct and still score zero.
Use AI responsibly during AP exam preparation
Attempt first. Ask for a hint or critique. Close the explanation and solve again from memory. Never use outside help on a live or prohibited assessment.
Turn the guide into exam-day skill
Start a focused AP Precalculus practice set, check each explanation, and use every miss to choose your next review session.
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