Author:
Melissa Leng, Greg Mayer
Subject:
Mathematics
Material Type:
Homework/Assignment
Level:
Community College / Lower Division
Tags:
  • Multivariable Calculus
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    Interactive

    Practice Tests for OpenStax Calculus Volume 3

    Practice Tests for OpenStax Calculus Volume 3

    Overview

    This resources contains four tests and one final exam that are aligned to the OpenStax Calculus Volume 3 textbook, which focuses on multivariable calculus. All of the tests are in QTI format so they can be imported to platforms that support that format. Most questions in the tests have explanations, and many questions have different versions.

    Practice Tests in QTI format

    As stated in the Overview, the tests follow the OpenStax Calculus Volume 3 textbook. Note that in the OpenStax Calculus 3 textbook that Cylindrical and Spherical Coordinates were introduced in Chapter 2. We did not cover these coordinate systems in our Test 1. 

    All tests in this resources were only used for formative assessment. Please feel free to let students view the answers in these quizzes. 

    Thank you for considering the use of these materials! The authors would be happy to know if you found these resources useful. 

    Practice Tests in QTI format

    Gregory Mayer and Melissa Leng

    Georgia Institute of Technology, School of Mathematics, College of Sciences

    This resources contains four tests and one final exam. The content is aligned to the OpenStax Calculus Volume 3 textbook, which focuses on multivariable calculus. 

    All of the tests are in QTI format so they can be imported to platforms that support that format. Most questions in the tests have explanations, and many questions have different versions.

    All questions are open for public use. These tests have only been used to give students additional practice to learn multivariable calculus. 

    Quiz questions use a mix of multiple choice and numeric responses. 

    Test 1 has 16 questions and looks at Chapters 2 and 3, covering the following topics:

    • Dot products, cross products, and projections
    • Equations for lines, planes, and curves
    • Parametric representations of vector-valued functions
    • Tangent/normal vectors, arc length, and curvature

    Test 2 has 14 questions and looks at Chapter 4, covering the following topics:

    • Partial derivatives
    • Tangent planes and linear approximations
    • Critical points and Lagrange multipliers
    • Gradients and directional derivatives

    Test 3 has 15 questions and looks at Chapter 5, covering the following topics:

    • Double integrals (in Cartesian and polar coordinates)
    • Triple integrals (in Cartesian, cylindrical, and spherical coordinates)
    • Order of integration
    • Change of variables using the Jacobian

    Test 4 has 13 questions and looks at Chapter 6, covering the following topics:

    • Line integrals and vector fields
    • Green's Theorem
    • Conservative vector fields and potential functions
    • Stokes' Theorem, Divergence Theorem

    The final exam incorporates questions from all of the above topics.

    Each test uses question banks. In total, there are 132 questions in the question banks.