If $f(x)$ has a simple zero at $x=2$, what happens to its graph at that point?
Correct answer: It crosses the $x$-axis
Why: A simple zero has odd multiplicity, so the graph crosses the $x$-axis at $x=2$.
AP Precalculus Practice Questions
Answer original AP-style diagnostic questions, review explanations, and identify the next unit to study.
AP Precalculus diagnostic practice set
These are original practice questions, not copied College Board items. Use official released questions for final calibration.
Question 1 of 3
Review the reasoning after you finish
The interactive set keeps answers hidden while you work. This review section remains crawlable and gives every student a complete correction path after the attempt.
Which expression models a quantity that grows by $6\%$ each period?
Correct answer: $A(1.06)^t$
Why: Repeated percentage growth uses the growth factor $1+0.06=1.06$, giving $A(1.06)^t$.
For $y=3\sin(2x)+1$, what is the equation of the midline?
Correct answer: $y=1$
Why: In $y=A\sin(Bx)+D$, the midline is $y=D$. Here, $D=1$.
Practise each section under its own calculator rule
Practising with a calculator you will not be handed is the most common way a practice score stops predicting an exam score. Set each practice block up to match the section it rehearses.
| 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. |
How practice should cover the complete course
Polynomial and Rational Functions
Zeros, rates of change, end behavior, transformations, and models
30–40%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Exponential and Logarithmic Functions
Growth, decay, inverses, semi-log reasoning, and models
27–40%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Trigonometric and Polar Functions
Periodic behavior, identities, equations, and polar representation
30–35%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Functions Involving Parameters, Vectors, and Matrices
Course extension; not assessed on the end-of-course exam
Course only: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Use the result to focus your AP Precalculus review
Read the score as a map, not a verdict
Each answer shows a relationship between course knowledge and an exam decision. A miss may mean that a definition is unclear, a representation was misread, or the right method was not selected. Compare each miss with these AP Precalculus priorities before choosing the next unit or practice set.
- Function transformations and composition
- Exponential versus polynomial behavior
- Sinusoidal model parameters
- Justification from tables and graphs
Next steps after the AP Precalculus diagnostic
Use a four-step correction cycle
- Write the rule or idea behind every miss.
- Solve a second problem of the same type without looking back.
- Mix that skill with two older units tomorrow.
- Complete official released questions under authentic timing.
Questions about AP Precalculus exam practice
How many questions are on the AP Precalculus exam?
The published format is 42 questions on multiple choice and 4 questions on free response. 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 units should I practise first?
Start with the heaviest published weightings: Polynomial and Rational Functions (30–40%), Exponential and Logarithmic Functions (27–40%), Trigonometric and Polar Functions (30–35%). Then repair whichever earlier unit those depend on.
Can I use a graphing calculator while I practise for AP Precalculus?
Only where the exam allows one, and practising otherwise builds the wrong habit. Multiple choice, Part A: Algebra by hand: factoring, end behavior, log rules, exact unit-circle values. Multiple choice, Part B: Graph, find intersections, and evaluate models numerically. Free response, Part A: Regression models, intersections, and decimal answers you must store, not retype. Free response, Part B: Exact answers, transformations, and reasoning about function behavior.
What is the most common way students lose points on AP Precalculus?
Unit 4 (parameters, vectors, and matrices) is taught in class but is not tested on the AP exam. Do not spend April on it.
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