AP Precalculus Unit 3 Part B Passwater's MCQ Exam Review
Authored by Stefanie Frey
Mathematics
12th Grade
CCSS covered
Used 35+ times
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This comprehensive exam covers trigonometric functions and their properties at the AP Precalculus level, appropriate for grade 12 students. The quiz systematically addresses four major areas: trigonometric function analysis and transformations, inverse trigonometric functions, trigonometric equations and inequalities, and coordinate system conversions. Students must demonstrate mastery of sinusoidal functions by determining parameters like amplitude, period, and vertical shifts from given maximum and minimum points. They need to identify vertical asymptotes for tangent, secant, cosecant, and cotangent functions, analyze function transformations including dilations and translations, and interpret graphical representations of trigonometric functions. The content requires strong algebraic manipulation skills, understanding of function composition, and the ability to work fluently with radian measure and special angle values. Created by Stefanie Frey, a Mathematics teacher in US who teaches grade 12. This exam serves as a comprehensive review tool for students preparing for the AP Precalculus exam, specifically targeting Unit 3 Part B content on advanced trigonometric concepts. Teachers can use this quiz for cumulative assessment, exam preparation, or as a diagnostic tool to identify areas where students need additional practice. The multiple-choice format mirrors the AP exam structure, helping students develop test-taking strategies while reinforcing conceptual understanding. This assessment aligns with Common Core standards HSF-TF.5 (modeling periodic phenomena), HSF-TF.6 (understanding radian measure), HSF-TF.7 (using inverse trigonometric functions), and HSF-TF.8 (proving and applying trigonometric identities), making it ideal for formative assessment or as a capstone review before the AP examination.
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65 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function g is defined by g(x) = a*sin(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (3, -1) and (7, 3) represent a minimum value and a maximum value, respectively, on the graph of g. What are the values of a and d?
a = 2 and d = -1
a = 2 and d = 1
a = 4 and d = -1
a = 4 and d = 1
Tags
CCSS.HSF-IF.C.7E
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function h is defined by h(x) = a*sin(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (2, 4) and (4, 10) represent consecutive minimum and maximum values, respectively, on the graph of h. What is the value of b?
b = 2
b = 4
b = π/2
b = π
Tags
CCSS.HSF-IF.C.7E
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function f is defined by f(x) = a*cos(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (π, 6) and (2π, 2) represent consecutive maximum and minimum values, respectively, on the graph of f. What are the values of b and d?
b = 2π and d = 2
b = 1 and d = 2
b = 2π and d = 4
b = 1 and d = 4
Tags
CCSS.HSF-IF.C.7E
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function k is defined by k(x) = a*cos(b*(x+c))+d, for constants a, b, c, and d. In the xy-plane, the points (π/4, 10) and (3π/4, 40) represent a minimum value and a maximum value, respectively, on the graph of k. What are the period and amplitude of the function k?
The period is π/2 and the amplitude is 15.
The period is π/2 and the amplitude is 30.
The period is π and the amplitude is 15.
The period is π and the amplitude is 30.
Tags
CCSS.HSF-IF.C.7E
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function f is given by f(x) = 1 + 2 tan x. Which of the following gives the vertical asymptotes of f?
pi/2 + pi k, where k is an integer
pi/2 + 2pi k, where k is an integer
pi/4 + pi/2 k, where k is an integer
pi + 2pi k, where k is an integer
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function k is given by k(x) = tan(1/2 x). Which of the following gives the vertical asymptotes of k?
pi/4 + pi/2 k, where k is an integer
pi/2 + pi k, where k is an integer
pi + 2pi k, where k is an integer
pi + 4pi k, where k is an integer
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The function g is given by g(x) = tan(pi x). Which of the following gives the vertical asymptotes of g?
1/2 + 2k, where k is an integer
1/2 + k, where k is an integer
1 + pi k, where k is an integer
1 + 2pi k, where k is an integer
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