
Unit 3 - Calculus AB
Quiz
•
10th - 12th Grade
•
Practice Problem
•
Medium
Standards-aligned
Isaac Townsend
Used 322+ times
FREE Resource
About this resource
This quiz covers advanced differential calculus concepts appropriate for 11th or 12th grade students enrolled in AP Calculus AB. The questions assess mastery of implicit differentiation, chain rule applications, related rates problems, derivatives of inverse functions, and logarithmic/exponential differentiation. Students must demonstrate fluency with fundamental differentiation rules while applying them to complex, multi-step problems that mirror real-world scenarios. The related rates problems require students to set up equations modeling geometric relationships, apply the chain rule to find rates of change, and interpret results in context. Success on these problems demands strong algebraic manipulation skills, geometric reasoning, and the ability to connect abstract mathematical concepts to practical situations involving moving objects and changing quantities. Created by Isaac Townsend, a mathematics teacher in the US who teaches grades 10-12. This comprehensive assessment serves multiple instructional purposes, from formative evaluation during the implicit differentiation and related rates unit to summative review before AP examinations. Teachers can deploy individual sections as targeted practice for specific concepts, use the related rates word problems as collaborative group work to develop problem-solving strategies, or assign the entire quiz as homework to reinforce classroom instruction. The variety of question types makes this particularly effective for identifying students who need additional support with chain rule applications or conceptual understanding of rate problems. This quiz aligns with Common Core standards HSF-IF.B.6 for calculating average rate of change and HSA-CED.A.3 for representing constraints with systems of equations, while supporting AP Calculus AB learning objectives related to differentiation techniques and applications.
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17 questions
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1.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Find dy/dx by Implicit Differentiation
x3 +y3 = 36
2.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Find dy/dx
xy+y2=2
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Find dy/dx at a given point.
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?
Tags
CCSS.8.G.B.8
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm3/sec. How fast is the diameter changing when the diameter is 8 cm?
6.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft3/sec. How fast is the height of the water changing when the water is 2 ft deep?
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area changing when the circumference is 4 in?
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