Loyola University Chicago

Mathematics and Statistics

MATH 161

Textbook for MATH 161 and MATH 162: Dwyer and Grunwald, “Calculus: Resequenced for Students in STEM”, Preliminary Edition, Wiley.


Note: MATH 162A uses a different textbook. Namely, James Stewart. Calculus, Early Transcendentals (WebAssign eBook) 8th ed. Cengage Learning. Be sure you are reading the correct information.

Chapter 1: Functions
1.1 Functions and Their Graphs
1.2 Library of Functions
1.3 Implicit Functions and Conic Sections
1.4 Polar Functions
1.5 Parametric Functions


Chapter 2: Limits
2.1 Limits in Calculus
2.2 Limits: Numerical & Graphical Approaches
2.3 Calculating Limits Using Limit Laws
2.4 Limits at Infinity & Horizontal Asymptotes
2.5 Continuity & the Intermediate Value Theorem
2.6 Formal Definition of Limit


Chapter 3: The Derivative
3.1 Tangents, Velocities, Other Rates of Change
3.2 Derivatives
3.3 Rules for Differentiation
3.4 Product and Quotient Rules
3.5 Trigonometric Fn’s and Their Derivatives
3.6 Chain Rule
3.7 Tangents to Parametric and Polar Curves
3.8 Implicit Differentiation
3.9 Inverse Functions and Their Derivatives
3.10 Logarithmic Functions & Their Derivatives


Chapter 4: Applications of the Derivative
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 Derivatives and Graphs
4.4 Optimization
4.5 Applications to Rates of Change
4.6 Indeterminate Limits and L’Hopital’s Rule
4.7 Polynomial Approximations
4.8 Tangent Line Approximations: Differentials and Newton’s Method


Chapter 5: The Integral
5.1 Antiderivatives and Indefinite Integrals
5.2 Area Under a Curve and Total Change
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Integration by Substitution

Math 161 Common Final Study Materials 

Calculators will not be permitted on the exam. We provide sample exams and study materials here from previous academic years. Please note that this exam was 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: 

  1. MATH 161 Exam questions from Fall 2021
  2. MATH 161 Exam questions from Spring 2022
  3. MATH 161 Exam questions from Spring 2022 solutions
  4. MATH 161 Exam questions from Fall 2022
  5. MATH 161 Exam questions from Fall 2023
  6. MATH 161 Practice final exam problems 
  7. MATH 161 Practice final exam solutions

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.

Center for Tutoring and Academic Excellence

The Center for Tutoring & Academic Excellence offers free collaborative learning opportunities that include small group tutoring and tutor-led study halls to Loyola students. To learn more or request tutoring services, visit the Center for Tutoring & Academic Excellence online at http://www.luc.edu/tutoring.

Loyola Math Club Tutoring

The Loyola Math Club offers free tutoring to students in 100-level MATH courses (and others). 

Click here to see when it is offered this semester.