Pre-Calculus Knowledge Test — Mathematics Practice on Functions, Limits & Trigonometry
Covers functions, limits, and trigonometric concepts.
Prepare for algebra II, calculus, or standardized placement exams with the Pre-Calculus Knowledge Test. This Mathematics quiz focuses on essential pre-calculus topics including functions, domain and range, limits, continuity, and trigonometric concepts. Whether you're a high school student, college applicant, or lifelong learner, this practice test helps you identify strengths and gaps in core pre-calculus skills.
This timed-free assessment contains multiple-choice questions that emphasize conceptual understanding and problem-solving strategies. Use the results to target review in functions, limits, and trigonometry — key areas that form the foundation for calculus. The quiz and feedback are SEO-optimized for learners searching for pre-calculus practice, math placement prep, and trig review resources.
Which of the following best defines a mathematical function?
Select the definition that correctly characterizes a function in mathematics.
What is the domain of f(x) = sqrt(x - 2)?
Consider real-valued functions and real square roots.
If f(x) = x^2 and g(x) = sqrt(x) (principal square root), what is the domain of (f ◦ g)(x) = f(g(x))?
Find domain considering composition f(g(x)).
Evaluate the limit: lim_{x→2} (x^2 - 4) / (x - 2).
Simplify algebraically to remove the removable discontinuity.
Which condition must hold for f to be continuous at x = a?
Basic definition of continuity at a point.
Which identity is always true for all real x?
Select the fundamental trigonometric identity.
Solve for θ in [0°, 360°): sin(θ) = 1/2.
Provide all solutions in the given interval.
What is arcsin(1) in radians?
Return the principal value of the inverse sine.
What are the coordinates on the unit circle for angle π/4?
Recall unit circle values for common angles.
Determine the horizontal asymptote of (2x^2 + 1) / (x^2 - 3) as x → ±∞.
Compare degrees and leading coefficients of numerator and denominator.
Frequently asked questions
This Mathematics test covers key pre-calculus areas including functions (definition, domain/range, composition), limits and continuity, trigonometric identities, unit-circle values, inverse trig functions, and basic asymptote/limit behavior. It is designed to diagnose readiness for calculus and to highlight which topics need review.
Each question has assigned numeric values for the provided options. The results_function sums the values of selected answers to produce a total score. Higher scores indicate stronger mastery of pre-calculus concepts.
Most learners finish this 10-question multiple-choice quiz in about 10–20 minutes depending on pace. Take your time on limit and trig questions — accuracy is more important than speed for diagnostic purposes.
Students preparing for calculus, college math placement tests, teachers assessing class readiness, and self-learners who want to check their understanding of pre-calculus fundamentals should take this quiz. It is suitable for late high school and early college-level review.
Review the areas where you scored lower: consult targeted lessons on functions, limits, or trigonometry, practice problems and worked solutions, and consider retaking the test after focused study to track improvement. Use textbooks, video tutorials, and practice problem sets to strengthen weak topics.
Yes. Retaking the quiz after studying targeted topics will help you measure progress. Compare scores and review explanations or notes from previous attempts to focus your practice.
Most questions on this diagnostic can be solved without a calculator by applying algebraic simplification and known trig values. For practice, attempt the quiz without a calculator to test conceptual understanding; use a calculator later for numerical checks if desired.
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