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Description

This sequence is our version of Algebra II/ Trigonometry/ Pre-Calculus, and is for those students who have completed geometry.

Algebra and Geometry combine into an amazing mathematical dance that these courses beautifully demonstrate.

Despite the high level of mathematics that these courses represent, students continue to work in within the QED™ framework that is focused on context, concept, discovery, and application.

Through the study of:
• conic sections
• polynomial theory
• trigonometry
• transcendental functions
Students have the opportunity to not just memorize the "formula" but to actually understand its very existence through the activities they do in class.
Sequence

The Conics™
Through an exploration of the methods of conic section construction, students will learn polynomial theory and advanced function theory. This will help students gain full mastery of these crucial Algebra II standards.

topics include: conic sections, circles, ellipses, parabolas, hyperbolas, transformations, graphing techniques, ruler and compass construction methods

The Polynomials™
This course completes a student's study of advanced algebra by having them analyze and understand the mathematics of polynomials, an important part of the Algebra II standards.

topics include: quadratics, cubics, quartics, roots, completing the square, factors, product and sum of roots, degree n polynomials, synthetic division, remainder theorem, asymptotes

The Transcendentals™
This is our version of trigonometry. This course, however, covers a wider range of functions that are collectively referred to as the transcendental functions, which include the trigonometric and exponential functions and are unified by theory of complex numbers.

topics include: periodicity, radians, arc length, universality, inverse trig functions, pythagorean identities, sum and difference formulae, double and half angle formulae, Law of Sines and Cosines, logarithms, exponentials, compound interest, natural logarithm, imaginary numbers, Euler's formula, polar representation, complex functions
Information

The Advanced Mathematics sequence consists of three 30-hour workshops for a total of 90 hours of in-class material. Academic year sequences are held in 10 week classes each 3 hours long.

Classes consist of hands-on activities, practice problems, and concept synthesis. Academic year students are required to complete a minimal amount of practice problems.

#### Prerequisites

Students should have completed both Algebra and Geometry before taking any of the Advanced Math courses.

#### CDE standards covered

Algebra II

1. absolute value equations
2. systems of linear equations via substitution, graphs, matrices
3. polynomial division
4. difference of squares, perfect square trinomial, sum and difference of cubes
5. complex number plane
6. complex number arithmetic
7. evaluate rational expressions
8. quadratic equations and complex numbers
9. quadratic equation and coefficient analysis
10. maximum, minimum, zeros of quadratic functions
11. laws of logarithms
12. exponential growth and decay
13. logarithm base
14. logarithmic expression evaluation
17. graphs of circle, ellipse, parabola, hyperbola
20. binomial theorem
21. mathematical induction
22. arithmetic and geometric series
23. arithmetic and geometric series summation formula
24. composite and inverse function
25. number system properties in functions

Trigonometry

2. sine and cosine
3. sin2 + cos2 = 1 identity
4. amplitude, frequency, period, and phase shift
5. tangent and cotangent
6. secant and cosecant
7. tangent and slope
8. inverse trigonometric functions
9. common trigonometric values
10. sine and cosine addition formulas
11. half-angle and double-angle formulas
12. right triangle trigonometry
13. law of sines and cosines
14. triangle area using trigonometry
15. polar coordinates
16. polar coordinate equations
17.  complex number plane
18. DeMoivre's theorem
19. trigonometry word problems

Analysis

1. polar coordinates and vectors
2. complex number arithmetic
3. proof by induction
4. fundamental theorem of algebra
5. conic sections
6. roots and poles of rational functions
7. parametric functions
8. limits and convergence