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: A Preparation for Calculus, 6th Edition, Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason packaged with WileyPlus.

 

Common Syllabus for MATH 118

Textbook:  Functions Modeling Change(5th 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 

8.3 Polar coordinates

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

9.6 Complex numbers and De Moivre’s theorem 

 

Chapter 10: Compositions, inverses, and combinations of functions 

10.1 Composition of functions

10.2 Invertibility and properties of inverse functions

10.3 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

See Course Page for additional resources.