MATH 131: Mathematics and Statistics: Loyola University Chicago

Deborah Hughes-Hallett, et al. Applied Calculus, 7th Edition (packaged with WileyPlus). ISBN: 978-1-119-799085.

Chapter 1: Functions and Change
1.1 What is a Function
1.2 Linear Functions
1.3 Average Rate of Change and Relative Change
1.5 Exponential Functions
1.6 The Natural Logarithm
1.7 Exponential Growth and Decay
1.8 New Functions from Old
1.10 Periodic Functions

Chapter 2: Rate of Change: The Derivative
2.1 Instantaneous Rate of Change
2.2 The Derivative Function
2.3 Interpretations of the Derivative
2.4 The Second Derivative

Chapter 3: Shortcuts to Differentiation
3.1 Derivative Formulas for Powers and Polynomials
3.2 Exponential and Logarithmic Functions
3.3 The Chain Rule
3.4 The Product and Quotient Rules
3.5 Derivatives of Periodic Functions

Chapter 4: Using the Derivative
4.1 Local Maximum and Minima
4.2 Inflection Points
4.3 Global Maxima and Minima
4.4 Profit, Cost, and Revenue

Chapter 5: Accumulated Change: The Definite Integral
5.1 Distance and Accumulated Change
5.2 The Definite Integral
5.3 The Definite Integral as Area
5.4 Total Change and the Fundamental Theorem of Calculus
5.6 Average Value

Chapter 6: Antiderivatives and Applications
6.1 Analyzing Antiderivatives Graphically and Numerically
6.2 Antiderivatives and the Indefinite Integral
6.3 Using the Fundamental Theorem of Calculus to Find Definite Integrals

Core Problems

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.

Final Exam

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.

We provide the following pdf files:

Math 131/132 vs Math 161/162

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.

Available Tutoring Resources

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