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Quizzes > Mathematics

Pre Calculus Questions: Practice Quiz with Answers

Quick pre calculus quiz with instant results to spot gaps and track progress.

Editorial: Review CompletedCreated By: Cartoon LoversUpdated Aug 27, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art layers of math symbols and question marks on teal background promoting free precalc quiz

This pre-calculus quiz helps you practice key skills and see what to study next. Solve mixed problems and get instant feedback to build speed and confidence before a test. Want more targeted review? Brush up with an algebra quiz, step up to a calculus quiz, or sharpen rules with a derivative quiz.

What is the domain of f(x) = sqrt(x - 3)?
(3, infinity)
[3, infinity)
(-infinity, infinity)
(-infinity, 3)
undefined
Find the slope of the line through (1, 2) and (3, 6).
1
2
-2
4
undefined
Evaluate f(x) = 2x^2 - 3 at x = -2.
-11
5
-5
13
undefined
Convert 60 degrees to radians.
2pi/3
pi/2
pi/6
pi/3
undefined
What is sin(30 degrees)?
1
1/2
sqrt(3)/2
0
undefined
Find the domain of f(x) = 1/(x^2 - 1).
(-infinity, -1] U [1, infinity)
(-infinity, infinity)
(-infinity, -1) U (-1, 1) U (1, infinity)
(-1, 1)
undefined
Find the inverse function of f(x) = 3x - 4.
f^{-1}(x) = 3x + 4
f^{-1}(x) = (x + 4)/3
f^{-1}(x) = (x - 4)/3
f^{-1}(x) = (x/3) - 4
undefined
Solve log_2(x) + log_2(x - 1) = 3 (domain x > 1).
4
8
3
2
undefined
What is the period of y = sin(2x)?
2pi
pi
pi/2
4pi
undefined
What is the vertex of y = (x - 2)^2 + 5?
(-2, -5)
(2, 5)
(2, -5)
(-2, 5)
undefined
Solve 2^x = 5. Give the exact value.
x = log_5(2)
x = 5 ln(2)
x = log_2(5)
x = ln(5)
undefined
Identify the zeros and their multiplicities of f(x) = (x - 1)^2(x + 2).
x = 1 (mult 3) only
x = 1 (mult 2), x = -2 (mult 1)
x = -1 (mult 2), x = 2 (mult 1)
x = 1 (mult 1), x = -2 (mult 2)
undefined
Solve log_3(2x - 1) = log_3(7 - x).
x = 3
x = 2
x = 7/2
x = 8/3
undefined
Find the inverse of f(x) = (x - 2)/(x + 3).
f^{-1}(x) = (2 - x)/(x + 3)
f^{-1}(x) = (x - 3)/(x + 2)
f^{-1}(x) = (3x + 2)/(1 - x)
f^{-1}(x) = (x + 3)/(x - 2)
undefined
What is the domain of (f ∘ g)(x) if f(x) = sqrt(x - 1) and g(x) = x^2 - 4?
(-infinity, -sqrt(5)] U [sqrt(5), infinity)
[1, infinity)
(-infinity, infinity)
(-infinity, -2] U [2, infinity)
undefined
Eliminate the parameter: x = 2t + 1, y = 3t - 2.
y = (x + 7)/3
y = (2x - 7)/3
y = (x - 7)/6
y = (3x - 7)/2
undefined
Convert the polar point (r, θ) = (4, 135°) to rectangular coordinates (x, y).
(-2sqrt(2), 2sqrt(2))
(2sqrt(2), 2sqrt(2))
(-4, 0)
(0, 4)
undefined
For the ellipse x^2/16 + y^2/9 = 1, what is c (the focal distance)?
sqrt(7)
sqrt(13)
5
sqrt(25)
undefined
Find the asymptotes of the hyperbola x^2/9 - y^2/4 = 1.
y = +/-(3/2)x
x = +/-(3/2)y
y = +/-(2/3)x
x = +/-(2/3)y
undefined
In a triangle with sides a = 7, b = 5 and included angle C = 60 degrees, find side c.
sqrt(14)
sqrt(39)
sqrt(74)
6
undefined
0

Study Outcomes

  1. Understand key function concepts -

    By completing the pre calc questions and answers quiz, you will be able to identify domains, ranges, and types of functions with confidence.

  2. Apply limit evaluation techniques -

    Practice computing limits using algebraic and graphical methods to enhance your skills for the precalc quiz.

  3. Analyze and interpret graphs -

    Learn to determine intercepts, asymptotes, and overall behavior to accurately graph functions in pre calc test problems.

  4. Solve algebraic and trigonometric problems -

    Tackle a variety of pre calc practice questions to master algebraic manipulations and trigonometric identities.

  5. Evaluate problem-solving strategies -

    Identify and apply the most efficient methods for diverse pre calculus review quiz questions to improve speed and accuracy.

  6. Track progress and pinpoint weaknesses -

    Use instant feedback from each question to monitor your performance and focus revision on areas needing improvement.

Cheat Sheet

  1. Function Notation & Transformations -

    Master the language of functions by practicing f(x), f ❻¹(x), and composite functions; recognizing that f(x - h)+k shifts graphs horizontally and vertically is key (MIT OpenCourseWare). A quick mnemonic is "H-V" for horizontal then vertical shifts, helping you breeze through pre calc practice questions involving transformations.

  2. Limits & Continuity Fundamentals -

    Learn to evaluate limits algebraically and recognize removable vs. infinite discontinuities, as outlined in Stewart's Calculus textbooks. Plug in values, factor or use rational conjugates, and always check left- and right-hand limits to ace your pre calc test problems.

  3. Analyzing Graphical Features -

    Identify intercepts, asymptotes, and end behavior by sketching functions from key characteristics (source: Khan Academy Precalculus). Practice reading domain and range directly from graphs, a skill that boosts your confidence on any precalc quiz.

  4. Algebraic Manipulation & Factoring -

    Solidify techniques for expanding, factoring, and simplifying polynomials and rational expressions, drawing on exercises from University of California's online resources. Mastering these tricks underpins smooth solutions to complex pre calculus review quiz problems.

  5. Trigonometric Identities & Applications -

    Memorize core identities like SOH-CAH-TOA and the Pythagorean identity (sin²x + cos²x = 1) using flashcards or mnemonic devices. Applying these formulas to solve triangles and verify equations will streamline your performance on pre calc questions and answers.

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