Pre-Calculus with Limits

Pre-Calculus with Limits John Gomm jgomm@sanroque.net Pre-Calculus mathematics extends algebra and geometry into advanced trigonometry, matrix math, series, alternative graphing coordinate systems, limits, logarithms and exponential functions. We will build a thorough conceptual understanding of the topics and then apply them to a wide variety of sample problems including some from physics, engineering, economics, population studies and biology. Showing all your work in a clear manner is crucial for communication and we will be peer reviewing selected assignments, so make sure your classmates can understand your processes. All efforts will be made to return handed in assignments with comments by the following session and clarity in your presentation of the processes will help enormously. Assignments will consist of pre-reading text, completion of problem sets, tests and section projects as set out below. Grading weighting will be determined in consultation with students and will include consideration of participation. Assignments may be changed during the semester to reflect progress or newly discovered material in completing daily assignments. Please note there is the expectation that all students will be prepared to discuss assignments in class, and will be proactive in asking for assistance if that becomes challenging. Generally students should be prepared to at anytime make up for lost ground due to class periods where discussions and/or other circumstances hinder progress required by the outline in the syllabus. Topic Section 1.1 Rectangular Coordinates Section 1.2 Graphs of Equations Set for 9/11: Practice problems 1.1-1.2 Section 1.3 Linear Equations in Two Variables Section 1.4 Functions Section 1.5 Analyzing Graphs of Functions Set for 9/18: Practice problems 1.3-1.5 Due 9/11: Practice problems 1.1-1.2 Section 1.6 A Library of Parent Functions Section 1.7 Transformations of Functions Section 1.8 Combinations of Functions: Composite Functions Set for 9/25: Practice problems 1.6-1.8 Due 9/18: Practice problems 1.3-1.5 Section 1.9 Inverse Functions Section 1.10 Mathematical Modeling and Variation Section 2.1 Quadratic Functions and Models Set for 10/2: Practice problems 1.9-2.1 Due 9/25: Practice problems 1.6-1.8 Week Date / Notes 1 9/3 9/7 No school Monday 2 9/10 9/14 3 9/17 9/21 4 9/24 9/28

Section 2.2 Polynomial Functions of Higher Degree Section 2.3 Polynomial and Synthetic Division Chapter 1 Test Set for 10/9: Practice problems 2.2-2.3 Due 10/2: Practice problems 1.9-2.1 Section 2.4 Complex Numbers Section 2.5 Zeros of Polynomial Functions Section 2.6 Rational Functions Set for 10/16: Practice problems 2.4-2.6 Due 10/9: Practice problems 2.2-2.3 Section 2.7 Nonlinear Inequalities Section 3.1 Exponential Functions and Their Graphs Section 3.2 Logarithmic Functions and Their Graphs Set for 10/23: Practice problems 2.7-3.2 Due 10/16: Practice problems 2.4-2.6 Chapter 2 Test Section 3.3 Properties of Logarithms Section 3.4 Exponential and Logarithmic Equations Section 3.5 Exponential and Logarithmic Models Set for 10/30: Practice problems 3.3-3.5 Due 10/23: Practice problems 2.7-3.2 Section 4.1 Radian and Degree Measure Section 4.2 Trigonometric Functions: The Unit Circle Set for 11/6: Practice problems 4.1-4.2 Due 10/30: Practice problems 3.3-3.5 Section 4.3 Right Angle Trigonometry Chapter 3 Test Section 4.4 Trigonometric Functions of Any Angle Set for 11/13: Practice problems 4.3-4.4 Due 11/6: Practice problems 4.1-4.2 Section 4.5 Graphs of Sine and Cosine Functions Section 4.6 Graphs of Other Trigonometric Functions Section 4.7 Inverse Trigonometric Functions Set for 11/27: Practice problems 4.4-4.7 Due 11/13: Practice problems 4.3-4.4 5 10/1 10/5 6 10/8 10/12 7 10/15 10-19 8 10/22 10/26 9 10/29 11/2 No School Thurs or Fri 10 11/5 11/9 Howlings Wed, Thur, Fri 11 11/12 11/16 Thanksgiving 12 11/19 11/23 No school Section 4.8 Applications and Models Section 5.1 Using Fundamental Identities Section 5.2 Verifying Trigonometric Identities Set for 12/4: Practice problems 4.8-5.2 Due 11/27: Practice problems 4.4-4.7 13 11/26 11/30

Section 5.3 Solving Trigonometric Equations 14 12/3 12/7 Chapter 4 Test Section 5.4 Sum and Difference Formulas Set for 12/11: Practice problems 5.3-5.4 Due 12/4: Practice problems 4.8-5.2 Section 5.5 Multiple-Angle and Product-to-Sum 15 12/10 12/14 Formulas Section 6.1 Law of Sines Section 6.2 Law of Cosines Set for 12/18: Practice problems 5.5-6.2 Due 12/11: Practice problems 5.3-5.4 Section 6.3 Vectors in the Plane 16 12/17 12/21 Section 6.4 Vectors and Dot Products Section 6.5 Trigonometric Form of a Complex Number Chapter 5 Test Set for 1/8: Practice problems 6.3-6.5 Due 12/18: Practice problems 5.5-6.2 No school 17 12/24 12/28 Winter Break No school 18 12/31-1/4 Winter Break Section 7.1 Linear and Nonlinear Systems of Equations Section 7.2 Two-Variable Linear Systems Chapter 6 Test Section 7.3 Multivariable Linear Systems Set for 1/15: Practice problems 7.1-7.3 Due 1/8: Practice problems 6.3-6.5 19 1/7-1/11 Section 7.4 Partial Fractions Section 7.5 Systems of Inequalities Section 7.6 Linear Programming Set for 1/22: Practice problems 7.4-7.6 Due 1/15: Practice problems 7.1-7.3 20 1/14-1/18 End of semester

Topic Week Date / Notes Section 8.1 Matrices and Systems of Equations Section 8.2 Operations with Matrices Chapter 7 Test Section 8.3 The Inverse of a Square Matrix Section 8.4 The Determinant of a Square Matrix Section 8.5 Applications of Matrices and Determinants Chapter 8 Test Section 9.1 Sequences and Series Section 9.2 Arithmetic Sequences and Partial Sums Section 9.3 Geometric Sequences and Series 21 1/21 1/25 No school Monday MLK 22 1/28 2/1 23 2/ 4 2/8 24 2/11 2/15 No School 25 2/18 2/22 Section 9.4 Mathematical Induction 26 2/25 2/29 Section 9.5 The Binomial Theorem Section 9.6 Counting Principles 27 3/3 3/7 Section 9.7 Probability Chapter 9 Test Section 10.1 Lines 28 3/10 3/14 Section 10.2 Introduction to Conics: Parabolas Section 10.3 Ellipses Section 10.4 Hyperbolas 30 3/17 3/21 Conferences Wed, Thur Fri No School 31 3/24 3/28 Spring break No School 32 3/31 4/4 Spring break Section 10.5 Rotation of Conics 33 4/7 4/11 Section 10.6 Parametric Equations Section 10.7 Polar Coordinates Section 10.8 Graphs of Polar Equations 34 4/14 4/18 Section 10.9 Polar Equations of Conics 35 4/21 4/25 Chapter 10 Test Section 11.1 The Three-Dimensional Coordinate System Section 11.2 Vectors in Space 36 4/28 5/2 Section 11.3 The Cross Product of Two Vectors New Horizons 37 5/5 5/9 New Horizons 38 5/12 5/16 Section 11.4 Lines and Planes in Space 5/19 5/23

Chapter 11 Test Section 12.1 Introduction to Limits Section 12.2 Techniques for Evaluating Limits Section 12.3 The Tangent Line Problem Section 12.4 Limits at Infinity and Limits of Sequences Section 12.5 The Area Problem 39 5/26 5/30 No School Mon, Tue 40 6/2 6/6 Chapter 12 Test Wrap up year 41 6/9 6/13 Last week of school 42 6/16 6/18 End Of Year