**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.*

Class | Topic | Homework | WeBWorK | Video Resource |
---|---|---|---|---|

1 | 1. Numbers and functions | 1.1, 1.2, 1.3, 1.5, 1.6, 1.7 | Interval Notation Functions - Introduction to Functions | Interval notation Functions |

2 | 2. Functions via formulas | 2.1 (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 |

3 | 3. Functions via graphs | 3.1 (a)-(c), 3.2(a)-(c), 3.3 (a)-(g) and (m)-(t), 3.4, 3.5 | Functions - Linear Functions Functions - Graphs | Linear functions Graphs of functions |

4 | 4. 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 functions | 65.1 (a)-(c), 5.2 (a)-(b), 5.3 (a)-(d), 5.4 (a)-(c), 5.5 (a)-(b), 5.6, 5.7 | Functions - Operations | Operations on functions |

6 | 6. The inverse of a function | 6.1 (a)-(c), 6.2 (a)-(f) and (l)-(p), 6.3 (a)-(c), 6.4 (a)-(c), 6.5 (a) and (d) | Functions - Inverse Functions | The inverse of a function |

7 | 7. 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 - Division | Long division The remainder theorem |

8 | 8. 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 - Graphs | Graphing polynomials |

9 | First Examination | |||

10 | 9. 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 |

11 | 10. 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 |

12 | 11. 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 |

13 | 12. Solving inequalities | 12.1 (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 |

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 | Exponentials and logarithms |

15 | 14. Properties of exp and log | 14.1 (a)-(e), 14.2 (a)-(f), 14.3 (a), (b), (e)-(h) | Logarithmic Functions - Properties Logarithmic Functions - Equations | Properties of logarithms Logarithmic equations |

16 | Midterm Examination | |||

17 | 15. Equations and applications of exp | 15.1 (a)-(c) and (e), 15.2 (a)-(e) 15.3 (a)-(b), 15.5-15.10 all | Exponential Functions - Equations | Exponential equations Applications of exponential and logarithmic functions |

18 | 16. Compound interest and half-life | 16.1-16.7 all, 16.9 (a)-(c), 16.10 (a)-(e) | Exponential Functions - Growth and Decay | Half-life and compound interest |

19 | 17. Trigonometric functions reviewed | 17.1 (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 |

20 | 18. Graphing trigonometric functions | 18.2, 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 |

21 | 19. Inverse trigonometric functions | 19.1, 19.2 (a)-(j), 19.3 (a)-(c) and (g)-(i) | Trigonometry - Inverses | Inverse trigonometric functions |

22 | 20. Trigonometric equations | 20.1 (a)-(d), 20.2 (a)-(c), 20.4 (a)-(c), 20.5 (a)-(f) | Trigonometry - Equations | Trigonometric equations |

23 | 21. 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 - Identities | Trigonometric identities |

24 | Third Examination | |||

25 | 22. Vectors in the plane | 22.1 (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 |

26 | 23. Complex numbers | 23.1 (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 |

27 | 24. 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 |

28 | 25. The geometric series | 25.1 (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 |

29 | Review | Final Exam Review Problems | Selected final exam review questions solved | |

30 | Final Exam |

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