Antiderivative Practice
Authored by Katherine Tarnowski
Mathematics
11th - 12th Grade
CCSS covered
Used 206+ times
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About
This quiz focuses on integral calculus, specifically antiderivatives and integration techniques, appropriate for grades 11-12 in Advanced Placement Calculus AB or BC courses. The questions systematically assess students' mastery of fundamental integration rules including basic antiderivatives of polynomial, exponential, logarithmic, and trigonometric functions. Students must demonstrate proficiency with advanced integration techniques such as u-substitution and integration by parts, requiring them to identify appropriate substitutions and apply the integration by parts formula correctly. The quiz also tests recognition of inverse trigonometric integration patterns and the critical skill of determining which integration method to apply for different types of functions. To succeed, students need solid understanding of derivative-antiderivative relationships, algebraic manipulation skills, and the ability to recognize function compositions that indicate specific integration strategies. Created by Katherine Tarnowski, a Mathematics teacher in US who teaches grade 11-12. This comprehensive assessment serves multiple instructional purposes in the calculus classroom, functioning effectively as a formative assessment tool to gauge student understanding before major tests, as targeted practice for homework assignments, or as a warm-up activity to activate prior knowledge before introducing more complex integration topics. The quiz's structure allows teachers to identify specific areas where students struggle, whether with basic antiderivative rules, u-substitution techniques, or integration by parts methodology. Teachers can use individual question analysis to provide differentiated instruction and reteaching opportunities. This assessment aligns with Common Core State Standards for Mathematics F-IF.8 and A-CED.2, as well as College Board AP Calculus standards covering techniques of antidifferentiation and applications of integration.
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28 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
∫ - sinx dx
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
∫ 1/x dx
Tags
CCSS.HSF.BF.B.5
3.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
∫(4/x - ex ) dx
Tags
CCSS.HSA.APR.D.6
CCSS.HSA.APR.D.7
CCSS.HSF.BF.B.5
4.
MULTIPLE CHOICE QUESTION
45 sec • 1 pt
∫ x(x2 - 4) dx
Tags
CCSS.HSA.SSE.B.3
CCSS.HSA.APR.A.1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
∫-csc2x dx
6.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
For u-substitution, what should be used for u here:
∫ (tan4xsec2x)dx
7.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
For u-substitution what should bethe u here?
∫(5xsin(2x2))dx
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