# MATH 131

Deborah Hughes-Hallett, et al. Applied Calculus for Loyola University Chicago Custom (packaged with WileyPlus).

Chapter 1: Foundations For Calculus: Functions and Limits
1.1    Functions and Change
1.2    Exponential Functions
1.3    New Functions from Old
1.4    Logarithmic Functions
1.5    Trigonometric Functions
1.6    Powers, Polynomials, and Rational Functions
1.7    Introduction to Continuity
1.8    Limits
Chapter 2: Key Concept: The Derivative
2.1    How Do We Measure Speed?
2.2    The Derivative at a Point
2.3    The Derivative Function
2.4    Interpretations of the Derivative
2.5    The Second Derivative
Chapter 3: Short-Cuts to Differentiation
3.1    Powers and Polynomials
3.2    The Exponential Function
3.3    The Product and Quotient Rules
3.4    The Chain Rule
3.5    The Trigonometric Functions
3.6    The Chain Rule and Inverse Functions
Chapter 4: Using the Derivative
4.1    Using First and Second Derivatives
4.2    Optimization
4.3    Optimization and Modeling
4.4    Families of Functions and Modeling
4.5    Applications to Marginality
4.7    L’Hopital’s Rule, Growth, and Dominance
Chapter 5: Key Concept: The Definite Integral
5.1    How Do We Measure Distance Traveled?
5.2    The Definite Integral
5.3    The Fundamental Theorem and Interpretations
Chapter 6: Constructing Antiderivatives
6.1    Antiderivatives Graphically and Numerically
6.2    Constructing Antiderivatives Analytically
6.3    [Optional] Differential Equations and Motion

Below are “core problems” that we expect students to be able to solve to ensure understanding of the material in the course syllabus. The problems are taken from Applied & Single Variable Calculus for Loyola University Chicago (packaged with WebAssign), 4th ed., Hughes-Hallett, Deborah, et al.

Chapter 1. A Library of Functions
1.1 1, 8, 13, 16, 23, 27, 31, 33, 53, 55, 70(No WP*)
1.2 2, 5, 6, 8, 10, 16, 17, 31, 38, 39
1.3 9, 13, 14, 28, 32, 43, 45, 50, 51, 52, 56, 61, 68, 19, 71
1.4 2, 4, 6, 7, 12, 16, 19, 24, 26, 30, 36, 45, 47, 48
1.5 6, 10, 12, 18, 20, 30, 31, 33, 62, 63, 68
1.6 3, 6, 8, 9 , 12, 15, 17, 19, 47 (No WP), 50, 52, 54
1.7 2, 3, 12 (No WP), 14 (No WP), 24( No WP), 26(No WP), 28 (No WP), 31 (No WP), 39 (No WP), 43 (No WP), 49 (No WP)
1.8 4, 6, 31, 33, 38, 45, 52 (No WP)
Chapter 2. Key Concept: The Derivative
2.1 1, 3, 5, 7, 10, 15, 16, 17, 21, 22, 29, 31, 33
2.2 1, 3, 4, 8, 10, 19, 22, 23(No WP), 32, 37, 47, 56, 60, 63
2.3 1, 2, 5, 13, 20, 22, 33, 49, 50, 52
2.4 2, 3, 9, 12(No WP), 17, 19, 24 (No WP), 27, 33, 38, 51, 54 (No WP)
2.5 2, 3, 8, 9, 12, 14, 15, 25, 37, 38, 41
Chapter 3. Short-Cuts to Differentiation
3.1 6, 10, 11, 14, 18, 23, 25, 28, 30, 32, 35, 38, 48, 58, 70, 75, 99
3.2 2, 4, 6, 8, 10, 12, 13, 17, 24, 42, 44, 46, 49, 58
3.3 4, 6, 7, 10, 12, 16, 19, 20, 24, 28, 31, 43, 47, 52, 90
3.4 2, 4, 7, 11, 17, 18, 28, 33, 43, 45, 48, 58, 60, 61, 67, 70, 73, 77, 86
3.5 4, 8, 10, 12, 16, 19, 22, 24, 26, 30, 36, 38, 45, 61
3.6 1, 9, 12, 13, 17, 22, 25, 26, 28, 30, 32, 35, 38, 39, 41, 50
Chapter 4. Using the Derivative
4.1 1, 5, 18, 25, 32, 34, 35, 36, 37, 40, 52, 53, 59
4.2 4, 6, 7, 8, 10, 13, 18, 19, 30, 37, 39, 40, 43
4.3 5, 6, 7, 9, 11, 14, 18, 22, 25, 27, 38, 39, 45
4.4 3, 4, 16, 25, 26, 47, 49, 50, 51, 57, 63
4.5 1, 4, 7, 12, 13, 15, 16, 18
4.7 6, 11, 35, 41, 42, 48, 53, 58, 59, 65, 67, 76, 87
Chapter 5. Using the Derivative
5.1 1, 2, 4, 8, 14 ,15, 23, 25, 28
5.2 4, 8, 12, 24, 29, 30, 32, 36
5.3 1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 16, 18, 22, 30
5.4 1, 2, 3, 4, 6, 7, 8, 11, 14, 16, 19, 25, 26, 28, 30, 33
Chapter 6. Constructing Antiderivatives
6.1 3, 6, 13, 15, 20, 25, 33
6.2 7, 9, 10, 11, 12, 15, 18, 20, 21, 26, 28, 30, 31, 35, 41, 44, 50, 55, 56, 57, 58, 60, 65

* No WP means the problem is not in WileyPlus and should be completed from the textbook.

Math 131 Common Final Study Materials

Calculators will be permitted on the exam, however no internet-capable devices will be permitted during the exam. CAS (computer algebra system) calculator features will not be needed on the exam.We provide sample exams and study materials here from previous academic years. Please note that some of these exams were administered online. We plan for the Spring 2023 final exam to be administered in person on the Loyola campus.

We provide the following pdf files:

## Should you choose Math 161/162 or Math 131/132?

Any questions about placement in calculus or other 100-level courses that remain after reading that section should be directed to John Houlihan, Mathematics Placement Director. Please e-mail him to set up an appointment.

Math 161/162 (Calculus I, Calculus II) is a traditional calculus sequence covering all the basic topics of one-variable calculus. This sequence is a prerequisite for Multivariable Calculus (Math 263) as well as for almost all higher-level math courses. It is required for all students majoring in Chemistry, Engineering Science, Mathematics, Physics and Statistics. It is highly recommended, although not required, for students majoring in Biology, Computer Science and Economics.

Math 131/132 (Applied Calculus I, Applied Calculus II) is more of a survey sequence covering many of the basic topics in one-variable calculus as well as some topics in multivariable calculus and differential equations. It is a terminal sequence in that it does not satisfy the prerequisites of upper-level mathematics and statistics courses. Students who enjoyed mathematics in high school and earned ACT math scores of 28 and higher or SAT math scores of 660 and higher are encouraged to choose the Math 161/162 sequence.

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