Supplementary Materials : C30 Burt Thiessen

Precalculus this year will be taught in a ‘flipped’ classroom format which means that you will watch videos and write notes for homework and we will work on the assignments during class time. We will be using the local Moodle and Schoology.com to answer discussion questions and to ask questions.

Precalculus is often thought of as an advanced form of algebra. This course is intended to prepare students for the study of calculus. Precalculus can be seen as a bridge joining arithmetic, algebra, geometry, and trigonometry to Calculus. The prerequisite classes to join this class are Algebra II and Geometry.

Textbook: Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis Brown Richard G. Houghton Mifflen Company © 1997

Supplementary Materials: C30 Burt Thiessen

Topics covered:

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I. Functions (Ch 1, 2, 4, 5)

• Linear, quadratic
• Polynomial
• Operations on…
• Rational, radical
• Exponential, Logarithmic.

1. Trigonometry (Ch 7, 8, 9, 10)

• Circles
• Trigonometric functions and their graphs
• Identities and Equations
• Triangles

1. Analytical Geometry;Conics (Ch 6)

• Coordinate proofs
• Circles
• Ellipses
• Hyperbolas
• Parabola

1. Vectors (Ch 12)

• Geometric representation
• Algebraic representation
• Equations
• Planes

1. Matrices (Ch 14)

• Addition and scalar multiplication
• Application to linear systems

1. Sequence, Series (Ch 13)

• Arithmetic/Geometric
• Limits
• Sum of infinite series
• Sigma notation

1. Limits (Ch 19)
2. Calculus (Ch 20)

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Goals of this course:

Trigonometry

1. Students understand the notion of angle and how to measure it, in both radians and degrees. They can convert between degrees and radians.
2. Students know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
3. Students know the identity .
4. Students prove that this identity is equivalent to the Pythagorean theorem.
5. Students prove other trigonometric identities and simplify others by using the identity .
6. Students graph functions of the form .
7. Students know the definitions of the tangent and cotangent functions and can graph them.
8. Students know the definitions of the secant and cosecant functions and can graph them.
9. Students know the definitions of the inverse trigonometric functions and can graph them.
10. Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.
11. Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/or simplify other trigonometric identities.
12. Students demonstrate an understanding of the half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities.
13. Students use trigonometry to determine unknown sides or angles in a right triangle.
14. Students know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.
15. Students know the law of sines and the law of cosines and apply those laws to solve problems.
16. Students determine the area of a triangle, given one angle and the two adjacent sides.
17. Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.
18. Students represent equations given in rectangular coordinates in terms of polar coordinates.
19. Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in polar form.
20. Students know the DeMoivre’s theorem and can give nth roots of a complex number given in polar form.
21. Students are adept at using trigonometry in a variety of applications and word problems.

Linear Algebra

1. Students reduce rectangular matrices in row echelon form.
2. Students perform addition on matrices and vectors.
3. Students perform matrix multiplication and multiply vectors by matrices and by scalars.
4. Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions.
5. Students demonstrate an understanding of the geometric interpretation of vectors and vector addition in the plane and in three-dimensional space.
6. Students interpret geometrically the solution sets of systems of equations.
7. Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations.
8. Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse and matrices using row reduction methods or Cramer’s rule.
9. Students compute the scalar product of two vectors in n-dimensional space and know that perpendicular vectors have zero dot product.

Mathematical Analysis

1. Students are familiar with, and can apply, polar coordinates and vectors in the plane. In particular, they can translate between polar and rectangular coordinates and can interpret polar coordinates and vectors graphically.
2. Students are adept at the arithmetic of complex numbers. They can use the trigonometric form of complex numbers and understand that a function of a complex variable can be viewed as a function of two real variables.
3. Students know the statement of, and can apply, the fundamental theorem of algebra.
4. Students are familiar with conic sections, both analytically and geometrically:
5. Students can take a quadratic equation in two variables; put it in standard form by completing the square and using rotations and translations, if necessary; determine what type of conic section the equation represents; and determine its geometric components.
6. Students can take a geometric description of a conic section and derive a quadratic equation representing it.
7. Students find the roots of a rational function and can graph the function and locate its asymptotes.
8. Students demonstrate an understanding of functions and equations defined parametrically and can graph them.
9. Students are familiar with the notion of the limit of a sequence and the limit of a function as the independent variable approaches a number or infinity. They determine whether the sequence converges or diverges.
10. Students can give proofs of various formulas by using the technique of mathematical induction.

Grades:

First Semester

Tests/quizzes 40%

Homework 40%

Final 20%

Second Semester

Tests/quizzes 40%

Homework 40%

Final 20%

A graphing calculator is required for this course. If you do not have one you need to rent one from the school.

I am requiring that you have a separate notebook for your assignments. You will write the notes in one book and your assignments in one book. The assignment book is to be labeled with the date and the section from the text that the assignment is from.

All work done in the assignment book will be done in pencil.

There will be no food allowed during class time. Come to class on time and prepared to be engaged in the material.

If absent, it is expected that you work through the assignment and be prepared for class the next day. If the absence is unexcused you will be given a zero for that days work.

This course is one that will require the student to work hard and keep on top of the topics covered. Please feel free to ask questions.

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