Algebraic expressions, equations, and inequalities 12
Simplify (1/x − 1/3)/(x − 3).College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), operations on algebraic expressions
Simplify (x³ − 8)/(x² − 4).College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), operations on algebraic expressions
Solve 1/x + 1/(x + 3) = 1/2.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve 2 cos x + √3 = 0 for 0 ≤ x < 2π.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve 3^(2x − 1) = 27.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve log₅(x) + log₅(x + 20) = 3.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve x(x − 2)(x + 3) > 0.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve x³ − 4x² − x + 4 = 0.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve |2x − 5| = 9.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Solve √(2x + 3) = x − 6.College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
What are all the solutions of sin(2x) = sin x for 0 ≤ x < 2π?College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), solving equations and inequalities
Which points lie on both y = x² − 5 and y = 4x?College Board, CLEP Precalculus outline: Algebraic expressions, equations, and inequalities (20% of the exam), systems of equations, linear and nonlinear
Show all 60 questions (48 more)
Functions: concept, properties, and operations 9
For f(x) = 3x² − x and h ≠ 0, simplify (f(x + h) − f(x))/h.College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
If f(x) = (2x − 1)/(x + 3), what is f⁻¹(x)?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
If f(x) = 1/(x − 2) and g(x) = √x, what is the domain of (f ∘ g)(x)?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
If f(x) = 2x² − 5x, what is f(a + 1)?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
If f(x) = √(x + 1) and g(x) = x² − 2x, what is (f ∘ g)(4)?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
What is arcsin(sin(2π/3))?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
What is the domain of f(x) = ln(x² − 4x)?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
What is the range of f(x) = 3 − 2 sin x?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
Which function satisfies f(−x) = −f(x) for every x?College Board, CLEP Precalculus outline: Functions: concept, properties, and operations (15% of the exam), the concept of a function, domain and range, function notation, evaluation and inverse functions
Representations of functions: symbolic, graphical, and tabular 18
A polynomial p has p(0) = −5, p(1) = −1, p(2) = 4 and p(3) = 11. Between which two inputs must p have a zero?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
A table gives f(0) = 5, f(1) = 10, f(2) = 20 and f(3) = 40. Which rule fits every entry?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
At which zero does the graph of f(x) = (x + 2)³(x − 1)² cross the x-axis?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
f(x) = |x| when x ≤ 0 and f(x) = 2^x when x > 0. What is f(−3) · f(3)?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
For x = 0, 1, 2, 3, 4 a table gives h(x) = 1, 4, 11, 22, 37. Which kind of function fits the table exactly?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
For x = 1, 2, 3, 4 a table gives f(x) = 3, 1, 4, 2 and g(x) = 2, 3, 4, 1. What is f(g(2))?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
The graph of y = sin(x − π/2) is the same as the graph of which function?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
The graph of y = √x is reflected across the x-axis and then moved 5 units right. Which equation gives the new graph?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
How does the graph of f(x) = −x⁵ + 4x³ − 2 behave at its two ends?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
What is the average rate of change of f(x) = log₂ x from x = 2 to x = 16?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
What is the lowest point on the graph of y = |x + 1| − 4?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
What is the maximum value of y = 1 − 4 cos x?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
What is the period of y = 2 cos(πx/3)?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), operations and transformations on functions presented symbolically, graphically, or in tabular form
What is the range of y = arccos x?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
Where does the graph of y = log₃(x − 2) cross the x-axis?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
Where is the lowest point of the graph of f(x) = 3x² − 12x + 7?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
Which line is a vertical asymptote of the graph of f(x) = (3x² − 3)/(x² + x − 2)?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
Which line is a vertical asymptote of the graph of y = tan(2x)?College Board, CLEP Precalculus outline: Representations of functions: symbolic, graphical, and tabular (30% of the exam), basic properties of functions and recognizing elementary functions
Analytic geometry 6
The graph of x² − 4y² + 2x − 3 = 0 is which curve?College Board, CLEP Precalculus outline: Analytic geometry (10% of the exam), the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
What are the asymptotes of the hyperbola x²/16 − y²/9 = 1?College Board, CLEP Precalculus outline: Analytic geometry (10% of the exam), the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
What are the center and radius of the circle x² + y² + 14x − 4y + 17 = 0?College Board, CLEP Precalculus outline: Analytic geometry (10% of the exam), the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
Where are the foci of the ellipse x²/25 + y²/9 = 1?College Board, CLEP Precalculus outline: Analytic geometry (10% of the exam), the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
Where is the focus of the parabola x² = 8y?College Board, CLEP Precalculus outline: Analytic geometry (10% of the exam), the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
Which line is the perpendicular bisector of the segment from (0, 0) to (4, 2)?College Board, CLEP Precalculus outline: Analytic geometry (10% of the exam), the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas
Trigonometry and its applications 9
A circle has radius 4. What is the area of the sector cut off by a central angle of 135°?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
From the top of a cliff 60 m above the sea, the angle of depression of a boat is 30°. How far is the boat from the foot of the cliff?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), applying trigonometry in problem-solving contexts
If sin θ = 1/3, what is cos(2θ)?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
θ is an acute angle with cos θ = 8/17. What is tan θ?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
Simplify sin x tan x + cos x.College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
tan θ = −5/12 and θ lies in quadrant II. What is sin θ?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
Two hikers leave camp on straight trails that form a 120° angle. One walks 7 km and the other 8 km. How far apart are they?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), applying trigonometry in problem-solving contexts
What is cos(7π/6)?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
What is the exact value of cos 75°?College Board, CLEP Precalculus outline: Trigonometry and its applications (15% of the exam), the basic trigonometric functions and their inverses, ratios and identities in right triangles and on the unit circle
Functions as models 6
A boat bought for $18,500 loses 12% of its value each year. Which function gives its value in dollars after t years?College Board, CLEP Precalculus outline: Functions as models (10% of the exam), interpreting and constructing functions as models
A rectangle has a perimeter of 40 cm and width w cm. Which function gives its area?College Board, CLEP Precalculus outline: Functions as models (10% of the exam), interpreting and constructing functions as models
A sample has mass A(t) = 80e^(−0.1t) grams after t years. After how many years are 40 grams left?College Board, CLEP Precalculus outline: Functions as models (10% of the exam), interpreting and constructing functions as models
The depth of water at a dock is d(t) = 3 cos(πt/6) + 7 meters, t hours after midnight. How many hours pass from one high tide to the next?College Board, CLEP Precalculus outline: Functions as models (10% of the exam), interpreting and constructing functions as models
Over a 24-hour cycle a temperature swings between a low of 10° at t = 0 and a high of 30°. Which function models it, with t in hours?College Board, CLEP Precalculus outline: Functions as models (10% of the exam), interpreting and constructing functions as models
Two ships leave a port together. One sails north at 30 km/h and the other east at 40 km/h. How far apart are they after t hours?College Board, CLEP Precalculus outline: Functions as models (10% of the exam), interpreting and constructing functions as models
How this list was compiled: Our own questions, written to the College Board's published outline of the CLEP Precalculus exam (https://clep.collegeboard.org/clep-exams/precalculus, read 2026-10-11): algebraic expressions, equations, and inequalities 20%; functions: concept, properties, and operations 15%; representations of functions: symbolic, graphical, and tabular 30%; analytic geometry 10%; trigonometry and its applications 15%; functions as models 10%. The bank holds 12, 9, 18, 6, 9 and 6 questions, the same shares, and 20 of the 60 need trigonometry. Every answer is worked out from what the question itself prints and was worked out a second time on 2026-10-11. Identities and definitions are those of the NIST Digital Library of Mathematical Functions, sections 4.14, 4.21 and 4.23 (https://dlmf.nist.gov/4.21). Licence: Questions, choices and explanations are original work of this site.
How it works
Sixty questions of our own cover the six areas of the Precalculus outline in the College Board's proportions, and each answer comes with its working. This CLEP Precalculus practice test is unofficial and not affiliated with, endorsed by or sponsored by the College Board.
Read the full guide
Six areas and their weights
The College Board's outline, read October 11, 2026: algebraic expressions, equations and inequalities (20%); functions and their properties (15%); representations of functions (30%); analytic geometry (10%); trigonometry (15%); functions as models (10%). The bank holds 12, 9, 18, 6, 9 and 6 questions.
Two timed sections
The real exam has about 48 questions in about 90 minutes: 25 in 50 minutes with an online graphing calculator, then 23 in 40 minutes with none. Exam mode asks 48 in 90 minutes as one round.
How the math is written
Powers are written x² or 2^x, and angles are in radians unless a degree sign is shown. Functions come as a rule or a small table, so no question needs a drawn graph.
Trigonometry runs through most topics: the College Board says 30% to 40% of the real questions need it. Here 20 of the 60 do.
Some real questions ask you to enter a number in place of picking a choice. Every question here is multiple choice.
Questions and answers
Can you use a calculator on the CLEP Precalculus exam?
In Section 1 only. An online TI-84 Plus CE graphing calculator is built into the exam software for those 25 questions, and only some of them need it. Section 2, 23 questions, allows no calculator.
What is on the precalculus CLEP test?
Functions above all: linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions, presented symbolically, graphically, verbally or in tables, the College Board says.
How many questions are on the CLEP Precalculus exam?
About 48 in about 90 minutes, in two sections of 25 and 23 questions, the College Board's exam page says. Most are multiple choice.
Is this CLEP practice test for precalculus the real exam?
No. All 60 questions are our own, written to the published outline, and none is copied or reworded from a real exam or an official sample question. A score here is a count of right answers and nothing more.
What score do you need on the CLEP Precalculus exam?
Colleges decide. The American Council on Education recommends 3 semester hours of credit for a scaled score of 50, on a scale of 20 to 80, and the College Board notes that each institution may set its own policy.