Syllabus With Links to Videos

MAT 1375 Precalculus

Text: Precalculus by Thomas Tradler and Holly Carley, Second Edition, available on www.lulu.com, PDF available from: http://websupport1.citytech.cuny.edu/faculty/ttradler/precalculus.html

Class  Topic Homework WeBWorK Video Resource
1

1. The absolute value

 

 

1.1, 1.2, 1.3 (a)-(e), 1.4 (a)-(f), 1.6, 1.7 (a)-(f)

Interval Notation

Absolute Value Inequalities

Interval notation

The absolute value

 2 2. Lines and functions

2.1 (a)-(c), 2.3 (a)-(c), 2.5-2.8 all

Functions – Notation

Functions
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3. Functions by formulas and graphs

3.1 (a)-(b), 3.2, 3.4 (a)-(f), 3.6 (a)-(f), 3.7 (a)-(g) and (m)-(t), 3.8, 3.9

 

Functions – Difference Quotient

The difference quotient
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4. Introduction to the TI-84

4.1, 4.2 (a), 4.3 (c)-(i), 4.6

 

 

5

5. Basic functions and transformations

5.1, 5.2 (a)-(f), 5.3 (a)-(d), 5.5 (a)-(e)

 

 Functions – Translations Transformation of graphs
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6. Operations on functions

6.1 (a)-(c), 6.2 (a)-(b), 6.3 (a)-(d), 6.4 (a)-(c), 6.5 (a)- (b), 6.6, 6.7

 

Functions – Operations

Operations on functions
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7. The inverse of a function

7.1 (a)-(c), 7.2 (a)-(f) and (l)-(p), 7.3 (a)-(c), 7.4 (a)- (c), 7.5 (a) and (d)

 

Functions – Inverse Functions

The inverse of a function
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First Examination

 

 

 9

8. Dividing polynomials

(8.3 Synthetic division is optional)

8.1 (a)-(c) and (j)-(k), 8.2, 8.3, 8.4 (a)-(d) (Optional: 8.5 (a)-(d)) Polynomials – Division Long division

The remainder theorem

 

 

10

9. Graphing polynomials

(9.3 Graphing polynomials by hand is optional)

9.1-9.3 all, 9.4 (a)-(c), 9.5 (a)-(c) (Optional: 9.6)

Polynomials – Graphs

Graphing polynomials
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10. Roots of polynomials

(10.1 Rational root theorem is optional)

10.2 (a)-(d), 10.3 (a)-(c), 10.4 (a)-(c) and (f)-(h), 10.5 (a)-(c) and (f)-(i)
(Optional: 10.1)

Polynomials – Theory

Polynomials-theory
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11. Rational functions

(11.2 Graphing rational functions by hand is optional)

11.1-11.4 all

 

Rational Functions – Domains

Rational Functions – Intercepts

Rational Functions
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12. Polynomial and rational inequalities

12.1 (a)-(c), 12.2 (g)-(j), 12.4 (a)-(f), 12.5

Polynomials – Inequalities

Rational Functions – Inequalities

Polynomial Inequalities

 

14

13. Exponential and logarithmic functions

13.1 (a)-(f), 13.2 (a)-(e), 13.4, 13.5 (a)-(b), 13.6 (a)- (h)

Exponential Functions – Graphs

Logarithmic Functions – Graphs

Exponential and Logarithms
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Midterm Examination

16

14. Properties of exp and log

14.1 (a)-(e), 14.2 (a)-(f), 14.3 (a)-(c) and (e), 14.4 (e)-(g), 14.5 (a)-(e)

 

Logarithmic Functions – Properties

Properties of logarithms

Exponential equations

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15. Applications of exp and log

15.1 (a)-(b), 15.3-15.8 all

Exponential Functions – Growth and Decay

Applications of exp and log
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16. Half-life and compound interest

16.1-16.7 all, 16.9 (a)-(c), 16.10 (a)-(e)   Half-life

Compound interest

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17. Trigonometric functions

17.1 (a)-(d) and (g)-(h), 17.3, 17.4, 17.5 (a)-(d), 17.6 (a)-(g)

Trigonometry – Graphing Comprehensive

Graphing trigonometric functions
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18. Addition of angles and multiple angle formulas

18.1 (a)-(e), 18.2 (a)-(b), 18.3 (a)-(d), 18.4 (a)-(d)

Trigonometry – Sum and Difference Formulas

Trigonometry – Double and Half Angle Formulas

Addition of angles and multiple angle formulas
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19. Inverse trigonometric functions

19.1, 19.2 (a)-(j), 19.3 (a)-(c) and (g)-(i)

 

Inverse trigonometric functions
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20. Trigonometric equations

20.1 (a)-(f), 20.2 (b)-(c), 20.4 (a)-(k), 20.5 (a)

Trigonometry – Equations

Trigonometric equations
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Third Examination

24

21. Complex numbers

21.1 (a)-(c), 21.2 (b)-(e), 21.3 (a)-(c), 21.4 (a)-(d), 21.5 (c)-(d), 21.6 (a)-(d), 21.7 (a)-(d)

Complex Numbers – Direction

Complex Numbers – Magnitude

Complex Numbers – Polar Form

Complex numbers
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22. Vectors in the plane

22.1 (a) and (d), 22.2 (a)-(d), 22.3 (b)-(f) and (k)- (m), 22.4 (a)-(b)

Vectors – Components

Vectors – Magnitude and Direction

Vectors – Unit Vectors

Vectors in the plane
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23. Sequences and series

23.1 (a)-(c), 23.3 (a)-(d), 23.4 (a)-(d), 23.5 (a)-(b), 23.7 (a)-(b) and (e)-(i)  Sequences – Arithmetic

Series – Finite Arithmetic

Sequences and series
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24. The geometric series

24.1 (a)-(d), 24.2 (a)-(c), 24.3 (a)-(b) and (e)-(i), 24.4 (c) and (f)-(i), 24.5 (a)

Sequences – Geometric

Series – Geometric

The geometric series
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25. The binomial theorem

25.1 (a) and (i)-(l), 25.2 (b), 25.3 (a)-(d), 25.4 (a)- (d), 25.5 (a)-(d), 25.6 (a)-(d)

Sequences – Binomial Theorem

 

The binomial theorem

 

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Review

Selected final exam review questions
30 Final Examination