Unit 4 AP Calculus
Authored by S W
Mathematics
12th Grade
25 Questions
CCSS covered
Used 85+ times
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About
This quiz covers differentiation techniques in Advanced Placement Calculus, specifically focusing on the chain rule, product rule, implicit differentiation, and derivatives of exponential and logarithmic functions. The content is designed for grade 12 students who have mastered basic derivative rules and are ready to tackle composite functions and more complex differentiation scenarios. Students need a solid understanding of the power rule, trigonometric derivatives, and exponential functions as prerequisites. The problems require students to recognize when to apply the chain rule for composite functions like (x⁶ + 4)⁵, use the product rule for expressions such as x⁷(5 + 8x)³, and navigate implicit differentiation when variables cannot be easily separated. The inclusion of logarithmic differentiation and exponential functions with variable exponents demonstrates the comprehensive nature of differential calculus at the AP level. Created by S W, a Mathematics teacher in US who teaches grade 12. This assessment serves as an excellent unit review or practice tool for students preparing for the AP Calculus exam, particularly for Unit 4 content covering advanced differentiation techniques. Teachers can deploy this quiz as a formative assessment to identify students who need additional support with chain rule applications or implicit differentiation before moving to integration topics. The variety of problem types makes it ideal for homework assignments, allowing students to practice different differentiation scenarios independently, or as a warm-up activity to reinforce previously learned concepts. This quiz aligns with Common Core standards HSF-IF.C.7 and HSA-CED.A.2, as well as College Board AP Calculus AB standards covering derivatives of composite, implicit, and transcendental functions.
Content View
Student View
1.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Find the derivative of f(x) = (x6 + 4)5
2.
MULTIPLE CHOICE QUESTION
5 mins • 12 pts
Find the derivative of f(x)=(x3-2x)2
Tags
CCSS.HSA.APR.A.1
3.
MULTIPLE CHOICE QUESTION
5 mins • 12 pts
A
B
C
D
Tags
CCSS.HSA.SSE.A.2
CCSS.HSN.RN.A.2
4.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
find y' for y=(e5x)+1
5e5x+1
e5x
5e5x
1
Tags
CCSS.HSF-IF.C.8B
5.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
find y' for y= sin(2x2)
4sin(2x2)
4xcos(2x2)
2xcos(2x2)
xcos(4x2)
6.
MULTIPLE CHOICE QUESTION
15 mins • 12 pts
Differentiate:
f(x) = x7 (5 + 8x)3
7.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Find dy/dx by Implicit Differentiation
x3 +y3 = 36
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