Loyola University Chicago

Mathematics and Statistics

MATH 118: Precalculus II

Course Details
Credit Hours: 3
Prerequisites: MATH 117 with a grade of C- or higher, or Math Placement Assessment
Description:  A continuation of MATH 117 focusing on exponential, logarithmic, trigonometric, and inverse trigonometric functions, their graphs, and their properties. Techniques for solving equalities involving these functions are examined. Trigonometric identities, sum and difference formulas, double and half-angle formulas, the Laws of Sines and Cosines, and polar coordinates are also considered.

Functions Modeling Change (6th ed.) by Connally, Hughes-Hallett, Gleason, et al.

Common Syllabus for MATH 118

Textbook:  Functions Modeling Change (6th ed.) by Connally, Hughes-Hallett, Gleason, et al.   

Chapter 4: Exponential functions
   4.1 Introduction to the family of exponential function
   4.2 Comparing exponential and linear functions
   4.3 Graphs of exponential functions
   4.4 Applications to compound interest
   4.5 The number e

Chapter 5: Logarithmic functions
   5.1 Logarithms and their properties
   5.2 Logarithms and exponential models
   5.3 The logarithmic function and its applications
   5.4 Logarithmic scales

Chapter 11: Polynomial and rational functions
   11.6 Comparing power, exponential, and log functions
   11.7 Fitting exponentials and polynomials to data

Chapter 7: Trigonometry and periodic functions
   7.1 Introduction to periodic functions
   7.2 The sine and cosine functions
   7.3 Radians and arc length
   7.4 Graphs of the sine and cosine
   7.5 Sinusoidal functions
   7.6 The tangent function
   7.7 Trigonometric functions and identities
   7.8 Inverse trigonometric functions

Chapter 8: Triangle trigonometry and polar coordinates
   8.1 Trig functions and right triangles
   8.2 Non-right triangles

Chapter 9: Trigonometric identities, models, and complex numbers
   9.1 Trigonometric equations
   9.2 Identities, expressions, and equations
   9.3 Sum and difference formulas for sine and cosine
   9.4 Polar Coordinates
   9.5 Complex numbers and De Moivre’s theorem

Chapter 10: Compositions, inverses, and combinations of functions
   10.1 Composition of functions
   10.2 Revisiting Inverse Functions
   10.3 The Graph, Domain, and Range of an Inverse Function
   10.4 Combinations of functions

Abbreviations:

S=Skills Review, E=Exercises, GTP=Go Tutorial, AQ=Additional Questions, RE=Review Exercises, CTQ=ConceptTest Question

 

Chapter 4: Exponential functions 

4.1 Introduction to the family of exponential functions 

S: S2, S4 

E:  2, 5, 7, 8, 10, 16, 18, 21, 24, 26, 33, 41, 42, 47, 52, 57, 63

4.2 Comparing exponential and linear functions 

S: S2, S5

E: 2, 6, 9, AQ1, GTP 18,  13,  20, 26, 34, 35,  39, 46 

4.3 Graphs of exponential functions 

E: 2 (or 1-4 in WP) , 8 11, 13, GT15, 20, 25, 27, 29 (or 29 - 30 in WP) , 31, 35, 47

4.4 Applications to compound interest 

E: 2, 4, 7-10, 11, 12,  16, 18, 21 

4.5 The number e 

S: S3, S7, S14 

E:  4, 8, 10, 16, 30, GT11, 39, 47,  GT47, 57  

 

Chapter 5: Logarithmic functions 

5.1 Logarithms and their properties 

S: S9, S17

E: 4, 5,  8, 13, 16, 18-21, 30-34,  37, 47, 48, AQ1, AQ2, AQ5, 57, 78, 81, 94, 95, 102, 107, 108, 110

5.2 Logarithms and exponential models 

S: S1, S7, S14 

E: 5, 8, 11, 17, 20, 21, 24, 27, 29ab, GTP 34, 36, 42, 51, 57 

5.3 The logarithmic function and its applications 

S: S2, S3, S5, S7

EE: 2, 3- 6, 8, RE 29, 22, 24, 25, 27, 29, 32, 37, 48, 50 

5.4 Logarithmic scales (optional)

S: S3, S9

E: 1- 2, 3-4, 6-11, 16, 18, 22

 

Chapter 11: Polynomial and rational functions 

11.6 Comparing power, exponential, and log functions 

E: 1, 6, 8, 10, 11, 13, 15, 18, GTP 28, 36, 38, 41, 42 

11.7 Fitting exponentials and polynomials to data (optional)

E: 1- 4 , 8, 18, 20, 22, 23

 

Chapter 7: Trigonometry and periodic functions  

7.1 Intro to periodic functions 

E: 1, 3, 8, 11 (or 13), 15, 16, 18-22, 31, 33, 34  

7.2 The sine and cosine functions 

E: 1, 4(x2), 10 - 14, 15-16, 19- 20, 21- 22, 23, 25, GTP 29, 33  

7.3 Radians and arc length 

E: 1-8(x4), 10, 14, GTP 6, 16, 17, 18, 21, 25, 26-27, 28-31, 49, 50, 56, 69

7.4  Graphs of sine and cosine 

E: 4, CT5, AQ1, 8, 13, 18, 25, 26, 27, 29, 37 

7.5 Sinusoidal functions 

E: 3, 7, 8,  14, 16,  20,  22, 23, GTP 38,  32, 45

7.6 The tangent function 

E: 2-7, 8, 11, 14, 29, 39  

7.7 The six trigonometric functions and relationships between them 

E: 2, 4, 6, 11, 13, 14, 20, 22, 23, 27, 29 

7.8 Inverse trigonometric functions 

E: 2, 3, 5, GT7, 10, 11, 18, 24, 29, 31, 38, 42, 44, 45 

 

Chapter 8: Trigonometry starting with triangles 

8.1 Trig functions and right triangles 

E: 2, 4, 8, 12, 16, 22, 24, 28, 40, 45, 49

8.2 Non-right triangles 

E: 8, 12, 13, GTP 12, 14, 15, 23, 30, 37, 40, 41 

 

Chapter 9: Trigonometric identities, models, and complex numbers 

9.1 Trigonometric equations 

E:  1, 4, 6, 8, 10, 13, 14, 19, 22, 27, 29, 32 37, 40 

9.2 Identities expressions, and equations 

E: 1-4, 5-8, GTP 9, 12, 15, 16, 17, 24, 37, 48, 51, 56, 56a

9.3 Sum and difference formulas for sine and cosine 

E:  1-4, 5-8, 12, 13-16, 23-24 

9.4 Polar Coordinates 

E:  1, 4, 9, 14, 16 , 20, 22, 25, 26, 31, 35

9.5 Complex numbers & De Moivre’s theorem (optional)

E: 9, 10, 16, 17, 19, 21, 22, 40, 45, 46

 

Chapter 10: Compositions, inverses, and combinations of functions 

10.1 Revisiting composition of functions 

E:  3, 6, 10, 12, 18, 22, 26, 30, 32, 41

10.2 Revisiting inverse functions

E:  5, 10, 13- 16, 17, 23, 39, 40, 41, 45 

10.3 The graph, doman, and range of an inverse function

E: 1, 10, 15, 17 

10.4 Combinations of functions 

E:  5, 9, 18, 31, 32, GTP 46, 42, 48

Math 118 Common Final Study Materials 

The Math 118 common final exam is scheduled for Thursday, May 5, 2022, 7:00 pm – 9:00 pm.  Calculators will be permitted on the exam, however devices with a CAS (computer algeabra system) will not be permitted during the exam.  We provide a sample exam and study materials here from the 2020-2021 academic year.  Please note that these exams were administered online.  We plan for the Spring 2022 final exam to be administered in person on the Loyola campus.   

We provide three pdf files: 

  1. MATH 118 Exam questions from Fall 2020
  2. MATH 118 Exam questions from Spring 2021
  3. MATH 118 Exam questions from Fall 2021
  4. MATH 118 Exam answers from Fall 2021
  5. MATH 118 Final exam practice problems

See Course Page for additional resources.