AP Calc Unit 3
Authored by William Bell
Mathematics
12th Grade
CCSS covered
Used 109+ times
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This quiz covers differential calculus, specifically focusing on derivatives and their applications to motion problems. The content is appropriate for 12th-grade students enrolled in Advanced Placement Calculus AB. Students need a solid foundation in algebraic manipulation, function notation, and the power rule for differentiation. The core concepts assessed include finding derivatives of polynomial, rational, and trigonometric functions using differentiation rules, evaluating derivatives at specific points, understanding the geometric interpretation of derivatives as slopes of tangent lines, and applying derivatives to analyze motion through position, velocity, and acceleration functions. Students must also grasp the relationship between continuity and differentiability, recognize when functions are continuous but not differentiable, and solve optimization problems involving maximum and minimum values. Created by William Bell, a Mathematics teacher in US who teaches grade 12. This comprehensive assessment serves multiple instructional purposes, from formative assessment during the derivatives unit to summative evaluation of student understanding. Teachers can use individual questions as warmup problems to activate prior knowledge, assign sections for homework practice, or deploy the entire quiz for unit review before the AP exam. The variety of question types—from basic derivative calculations to complex motion analysis—makes it particularly valuable for differentiated instruction and identifying areas where students need additional support. The quiz aligns with Common Core standards HSF-IF.A.2 and HSF-IF.B.4 for function analysis, as well as AP Calculus curriculum standards covering limits, derivatives, and applications of differentiation to motion and optimization problems.
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40 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the derivative of the given equation
f(x) = 7
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Find the derivative of the given function
f(x) = 1/x2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find f '(2) if
f(x) = x2 + 2x
Tags
CCSS.HSF.IF.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the derivative of the given equation
f(x) = x3 + x2 + 3
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The derivative of a function is its
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Find the slope of the tangent line of y= 3x2 - 5 when x = 2
7.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.SSE.B.3
CCSS.HSN.RN.A.2
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