AP Precalculus · 24 questions
Past multiple-choice questions
Every multiple-choice question College Board has published for AP Precalculus, sorted by the unit and topic each one tests in the current course. Each one opens College Board's own page beside four choices, and tells you right away whether your pick matches College Board's answer key.
College Board printed these questions as samples in its course and exam description. We checked every earlier edition the Internet Archive saved (5 of them): each one carries the same questions, so every question opens from the current edition on College Board's site. Your picks stay in this browser and are never sent anywhere.
Unit 1: Polynomial and Rational Functions
- Topic 1.1 · Question 2 · No calculator Where a lake gets deeper more and more slowly Read a graph of water depth over a month and find every interval where the depth rises while its rate of increase shrinks.
- Topic 1.5 · Question 4 · No calculator A relative maximum on an odd polynomial An odd polynomial has a relative maximum of negative 4 at x equals 3. Use odd symmetry to decide the value and kind of extremum at x equals negative 3.
- Topic 1.5 · Question 6 · No calculator Matching a polynomial graph to its factored form From where a polynomial graph crosses or touches the x axis, choose the factored expression with the right zeros and multiplicities.
- Topic 1.6 · Question 1 · No calculator End behavior of a fifth degree polynomial From the sign of its leading coefficient and whether its highest power is odd or even, decide what a polynomial does as x grows without bound in each direction.
- Topic 1.11 · Question 3 · No calculator Building a rational function from a zero, asymptote and hole Pick the rational function whose factored form gives a zero at 3, a vertical asymptote at 2, and a removable hole at 1.
- Topic 1.11 · Question 5 · No calculator Domain of a quotient of two polynomials Factor a cubic in the denominator of a quotient of polynomials and find every input the domain must leave out.
- Topic 1.12 · Question 7 · No calculator Three transformations applied to a table of values A horizontal stretch, a vertical stretch and an upward shift turn f into g. Use a table of f to evaluate g at negative 4.
- Topic 1.14 · Question 20 · Calculator allowed Time for a rational temperature model to climb With a graphing calculator, find when a rational model of afternoon temperature reaches two given values and how long the climb takes.
Unit 2: Exponential and Logarithmic Functions
- Topic 2.1 · Question 9 · No calculator Formula for a geometric sequence read from a graph Read terms of a geometric sequence off a plotted graph, find the common ratio, and choose the matching formula for the nth term.
- Topic 2.5 · Question 12 · No calculator Quarterly growth written as a function of years Payments grow by a fixed percent every quarter. Choose the exponential model in years with the right growth factor and exponent.
- Topic 2.5 · Question 13 · No calculator Iodine half life rewritten in hours Convert an exponential decay model written in days into an equivalent model where time is measured in hours.
- Topic 2.5 · Question 21 · Calculator allowed Prediction from an exponential regression Fit an exponential regression to four data points on a calculator and use the model to predict a value between two inputs.
- Topic 2.6 · Question 11 · No calculator Judging a linear sales model from its residual plot A linear model of sandwich sales comes with a plot of its residuals. Decide whether the linear model is appropriate and why.
- Topic 2.7 · Question 10 · No calculator Composing a table function with a formula Look up g of 3 in a table, then put that output into a function that adds a power of 3 and a square.
- Topic 2.12 · Question 8 · No calculator Expanding a base 10 logarithm of a quotient Rewrite the logarithm of a product over a square as sums and differences of single logarithms using the product, quotient and power rules.
- Topic 2.13 · Question 14 · No calculator Solving an equation with two natural logarithms Combine two natural logs into one and solve the equation for x.
Unit 3: Trigonometric and Polar Functions
- Topic 3.5 · Question 22 · Calculator allowed Daylight on day 150 of the year A cosine model gives minutes of daylight by day of the year. Decide whether daylight is rising or falling on day 150 and how its rate changes.
- Topic 3.6 · Question 16 · No calculator Period and amplitude of a sinusoid from its graph Read a sinusoid off its plotted curve to find how long one cycle takes and how far it rises above its midline.
- Topic 3.7 · Question 24 · Calculator allowed Modeling a bouncing thrill ride with a sinusoid Use the highest point, lowest point and time per bounce of a drop tower ride to choose a sinusoidal model for its height.
- Topic 3.9 · Question 23 · Calculator allowed Restricting a sinusoid so it has an inverse Choose an interval on which the difference of sine and cosine has an inverse, and the reason that interval works.
- Topic 3.10 · Question 15 · No calculator Where a secant graph meets a horizontal line Set a shifted and stretched secant function equal to a constant, rewrite it as a cosine equation, and solve on one full period.
- Topic 3.10 · Question 18 · No calculator Two trig inequalities that must hold at once Find the angles on one full turn where a cosine condition and a sine condition are both true, using the unit circle.
- Topic 3.14 · Question 17 · No calculator Choosing the graph of a limacon Match a polar function built from cosine to its graph by following how r changes as theta goes around.
- Topic 3.15 · Question 19 · No calculator How a polar curve moves as the angle grows For a polar function built from sine, decide which side of the horizontal axis the points lie on and whether they move toward the origin.
The questions and answer key are College Board's, from AP Precalculus Course and Exam Description, Effective Fall 2026. The titles and summaries on this page are ours.