Syllabus With Links to Videos

MAT 1375 Precalculus

Text: Precalculus by Thomas Tradler and Holly Carley, Third Edition, PDF available from: https://openlab.citytech.cuny.edu/mat1375coursehub/resources/textbook/

Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.

ClassTopicHomework WeBWorKVideo Resource
11. Numbers and functions1.1, 1.2, 1.3, 1.5, 1.6, 1.7Interval Notation

Functions - Introduction to Functions
Interval notation

Functions
22. Functions via formulas2.1 (a)-(b), 2.2, 2.4 (b), (f)-(h), 2.6 (a), (c), (d), (f)-(h)Functions - Difference Quotient

Functions - Function Notation
Difference quotient

Function notation
33. Functions via graphs3.1 (a)-(c), 3.2(a)-(c), 3.3 (a)-(g) and (m)-(t), 3.4, 3.5Functions - Linear Functions

Functions - Graphs
Linear functions

Graphs of functions
44. Basic functions and transformations

(4.2 Exploring Functions with Desmos is optional)
4.1 (a)-(b), 4.2 (a)-(c) and (e), 4.8, 4.9 (a)-(f), 4.10 (a)-(d), 4.12 (a)-(e)

(optional: 4.3 (a)-(d), 4.4 (c))
Functions - Graphing Calculator

Functions - Translations

Functions - Symmetries
Graphing with Desmos

Transformation of graphs
5 5. Operations on functions65.1 (a)-(c), 5.2 (a)-(b), 5.3 (a)-(d), 5.4 (a)-(c), 5.5 (a)-(b), 5.6, 5.7Functions - OperationsOperations on functions
66. The inverse of a function6.1 (a)-(c), 6.2 (a)-(f) and (l)-(p), 6.3 (a)-(c), 6.4 (a)-(c), 6.5 (a) and (d)Functions - Inverse FunctionsThe inverse of a function
77. Dividing polynomials

(7.3 Synthetic division is optional)
7.1 (a)-(c) and (j)-(k), 7.2, 7.3, 7.4 (a)-(d)

(optional: 7.5 (a)-(d))
Polynomials - DivisionLong division

The remainder theorem
88. Graphing polynomials

(8.3 Graphing polynomials by hand is optional)
8.1-8.4 all, 8.5 (a)-(c), 8.7 (b), (g), (i), (j)

(optional: 8.8)
Polynomials - GraphsGraphing polynomials
9First Examination
109. Roots of polynomials

(9.1 Rational root theorem is optional)
9.3 (a), (c), (d), (e), (g), 9.4 (a), (b), (e), 9.5 (a), (b), (d), 9.6 (a)-(c) and (f)-(i)

(optional: 9.1 (a)-(c))
Polynomials - Theory

(Polynomials - Rational Roots is optional)
Polynomials
1110. Rational functions

(10.2 Graphing rational functions by hand is optional)
10.1, 10.2, 10.3, 10.4 (a), (b)Rational Functions - Domains Rational

Functions - Asymptotes Rational

Functions - Intercepts Rational

Functions - Comprehensive
Rational functions
1211. Exploring discontinuities and asymptotes

(11.2 Limits is optional)
11.1, 11.2, 11.3 (a)-(d), 11.4 (a)

(optional: 11.5, 11.6 (a), (d)-(f))
Rational Functions - Graphs

(Limits is optional)
Graphs of rational functions and asymptotes

Limits from graph
1312. Solving inequalities12.1 (a), (b), 12.2 (a)-(c), (h), 12.4 (a)-(c), 12.5 (a), (c)-(g)Polynomials - Inequalities

Rational Functions - Inequalities
Polynomial and rational inequalities

The absolute value
1413. Exponential and logarithmic functions13.1 (a)-(f), 13.2 (a)-(e), 13.4, 13.5 (a)-(b), 13.6 (a)-(h)Exponential Functions - Graphs

Logarithmic Functions - Graphs
Exponentials and logarithms
1514. Properties of exp and log14.1 (a)-(e), 14.2 (a)-(f), 14.3 (a), (b), (e)-(h)Logarithmic Functions - Properties

Logarithmic Functions - Equations
Properties of logarithms


Logarithmic equations
16Midterm Examination
1715. Equations and applications of exp15.1 (a)-(c) and (e), 15.2 (a)-(e) 15.3 (a)-(b), 15.5-15.10 allExponential Functions - EquationsExponential equations

Applications of exponential and logarithmic functions
1816. Compound interest and half-life16.1-16.7 all, 16.9 (a)-(c), 16.10 (a)-(e)Exponential Functions - Growth and DecayHalf-life and compound interest
1917. Trigonometric functions reviewed17.1 (a)-(d), 17.2 (a)-(d) 17.3 (a)-(i) and (q)-(s) 17.4 (a)-(c), 17.5 (a), (b), and (d)Trigonometry - Unit Circle

Trigonometry - Sum Difference and Half Angle Formulas
Computing trigonometric function values

Addition of angles formulas
2018. Graphing trigonometric functions18.2, 18.3, 18.4 (a)-(d), 18.5 (c)-(j)Trigonometry - Graphing Amplitude

Trigonometry - Graphing Period

Trigonometry - Graphing Phase Shift

Trigonometry - Graphing Comprehensive
Graphing trigonometric functions
2119. Inverse trigonometric functions19.1, 19.2 (a)-(j), 19.3 (a)-(c) and (g)-(i)Trigonometry - InversesInverse trigonometric functions
2220. Trigonometric equations20.1 (a)-(d), 20.2 (a)-(c), 20.4 (a)-(c), 20.5 (a)-(f)Trigonometry - EquationsTrigonometric equations
2321. Trigonometric identities

(21.2 Further Identities Revisited is optional)
21.1 (a)-(b), 21.2 (a), 21.3 (c)-(g), 21.4 (a) and (e)-(f)

(optional: 21.5 (a)-(b), 21.6 (b)-(c))
Trigonometry - IdentitiesTrigonometric identities
24Third Examination
2522. Vectors in the plane22.1 (a) and (d), 22.2 (a)-(c) and (e)-(h), 22.3 (b)-(e) and (k)-(l), 22.4 (a)-(b)Vectors - Magnitude and Direction

Vectors - Operations
Vectors in the plane
2623. Complex numbers23.1 (a)-(c), 23.2 (b)-(e), 23.3 (a)-(c), 23.4 (a)-(d), 23.5 (a), 23.6 (a)-(d), 23.7 (a)-(d)Complex Numbers - Operations

Complex Numbers - Magnitude and Direction

Complex Numbers - Polar Form
Complex numbers
2724. Sequences and series 24.1 (a)-(c), 24.3 (a)-(d), 24.4 (a)-(d), 24.5 (a)-(b), 24.7 (a)-(b) and (e)-(i)Sequences - Intro

Series - Intro

Sequences - Arithmetic

Series - Finite Arithmetic
Arithmetic sequences and series
2825. The geometric series25.1 (a)-(d), 25.2 (a)-(c), 25.3 (a) and (h), 25.4 (a) and (f)-(j), 25.5 (a)Sequences - Geometric

Series - Geometric
The geometric series
29ReviewFinal Exam Review ProblemsSelected final exam review questions solved
30Final Exam