# 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 (optional)

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

Chapter 7: Trigonometry and periodic functions
7.1 Introduction to periodic functions
7.2 The sine and cosine functions
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 (optional)

Chapter 10: Compositions, inverses, and combinations of functions
10.1 Composition of functions
10.2 Revisiting Inverse 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

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

Calculators will be permitted on the exam, however devices with a CAS (computer algeabra system) will not be permitted during the exam. We provide sample exams and study materials here from previous academic years. We plan for the Spring 2023 final exam to be administered in person on the Loyola campus.

We provide three pdf files:

See Course Page for additional resources.