6. Pre-Calculus
Course Description:
In an effort to develop skills in patient problem solving, responsibility, and the will to face any challenge, Pre-Calculus focuses on broadening conceptual understanding, applying of knowledge, and refining previous skills while learning new material from four broad categories as identified by the California State Standards: mathematical analysis, linear algebra, trigonometry, and probability and statistics.
The textbooks are:
Glencoe Pre-Calculus 2014 Edition
(Plus a focus on extensive teacher-created resources)
The teacher is:
Detailed Course Topic List:
FIRST SEMESTER
Linear Algebra
1. Students perform matrix multiplication.
2. Students multiply vectors by scalars and combine vectors in n-dimensions using arithmetic.
3. Students can find the resulting vector of the cross product of two vectors
4. Students compute the scalar (dot) product of two vectors in n- dimensional space.
5. Students can find the angle between two vectors using the dot product and know that perpendicular vectors have zero dot product.
Mathematical Analysis
6. Students can identify graphically and numerically different types of functions including transformed functions.
7. Students find the roots and poles of a rational function.
8. Students can graph a rational function and locate its asymptotes.
9. Parametric equations
10. Limits of a sequence as the independent variable approaches a number or infinity
SECOND SEMESTER
Probability and Statistics
11. Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
12. Students know the definition of conditional probability.
13. Students solve for probabilities in finite sample spaces.
14. Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.
Trigonometry
15. Understand angles in both degrees and radians.
16. Convert between degrees and radians.
17. Definition of sine and cosine as y- and x- coordinates of points on the unit circle.
18. Know the identity cos2 (x) + sin2 (x) = 1.
· Students prove that cos2 (x) + sin2 (x) = 1 is equivalent to the Pythagorean theorem
· Students prove and simplify other trigonometric identities using this one
19. Graph functions of the form f(t) = A sin ( Bt + C ) or f(t) = A cos ( Bt + C).
· Students interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.
20. Know the definitions of the six trigonometric function functions.
21. Graph the tangent and cotangent functions.
22. Know that tangent can be interpreted as = delta(y)/delta(x) = slope
23. Students know the definitions of the inverse trigonometric functions.
24. Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.
25. Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs
· Use those formulas to prove and/ or simplify other trigonometric identities.
26. Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines.
· Use those formulas to prove and/ or simplify other trigonometric identities.
27. Understand and apply the Law of Sines and Law of Cosines to solve for missing values in triangle.
Mathematical Analysis
28. Know polar coordinates and vectors
· Convert between polar and rectangular cords
· Can interpret it all graphically
29. Students are adept at the arithmetic of complex numbers, and can write them in trigonometric form
30. Students understand that a function of a complex variable can be viewed as a function of two real variables.
Bonus Topics (time permitting)
31. Graphing parametric equations
32. Determine whether sequences converge or diverge