Mr. Stanley Teitel
Mr. Daniel Jaye
Principal
A.P.S. Mathematics
MQ6 Syllabus: Spring 2003
| Students should be required to MEMORIZE the trig angle formulas to better prepare them for calculus. |
QUADRATIC RELATIONS AND
TRANSFORMATIONS
UNIFIED III
1. Review: equations
of a line, distance and MP
formulas
Dol. 90
2. Line reflections and composite
reflections
174, 184, 189
3. Review derivation of equation of
circle,
dilations
Dol. 306, 208
4. Translations, point reflections,
and symmetries of the
circle
192, 203
5. Derive equation of parabola V(0,0)
given its directrix &
focus
Dol. 309*
6. Transformations, symmetries of
graph of y =
x2
Dol. 309
7. Equations of ellipse, hyperbola
and symmetries of their graphs
C(0,0)
Dol. 312, 315
8. Rotations and rotational
symmetry
197
9. Inverse variations and their
graphs
Dol. 217, 319
INTRO TO RELATIONS AND FUNCTIONS
10.
Definition of a
relation
134
11. Using graphs and quad.
inequalities to determine domain,
range
134
12. Identifying and classifying
functions by their
graphs
138
13. Function notation and function
types
141
14. Composition of
functions
150
15. The inverse of a function and its
graph
153
GRAPHING TRIG FUNCTIONS AND THEIR INVERSES
16. The
graphs of y = sin x and y = cos
x
298-303
17. The graph of y = a sin bx:
amplitude, period,
frequency
426-433
18. The graph of y = tan
x
317-318
19. The graphs of y = csc x and y =
sec
x
318
20. The graphs of y = arcsin x and y
= Arcsin
x
449
21. The graphs of y = arccos x and y
= Arccos
x
449
22. The graphs of y = arctan x and y
= Arctan
x
449
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
23.
Rational
exponents
345
24. Solving exponential and
irrational
equations
345
25. Exponential functions and their
graphs
350
26. The inverse of an exponential
function and its
graph
353
27. The log product and quotient
rules
357
28. The log power rule and log
problems
357, 364 #29-43
29. Using scientific
notation
361, 364 #29-43
30. Finding common logs with
calculators (and log
tables?)
366
31. The antilog of x, x ³ 0;
products and
quotients
366, 370
32. The antilog of x, x < 0; the
kth root of N, N >
1
370
33. Finding the kth root of N, 0 <
N <
1
370
34. Solving logarithmic
equations
374
35. Log applications: change of base
formula
378
TRIG ANGLE FORMULAS AND RIGHT TRIANGLE TRIG
36. Solving
right and oblique
triangles
394
37. Derive Law of
Sines
398
38. The ambiguous
case
403
39. Derive the Law of
Cosines
407
40. Triangle and parallelogram area
formulas
412
41. Vectors and the parallelogram of
forces
416
42. Vector
problems
416
43. Derive formulas for cos(A - B)
and cos (A +
B)
434
44. Derive the other sum and
difference
formulas
434
45. Derive double angle
formulas
439
46. Derive half-angle
formulas
443
47. Applications: proving trig
identities
438, 442, 447
48. Applications: solving trig
equations
448
PROBABILITY AND STATISTICS
49. Review:
the counting principle and
factorials
492, Dol. 583
50. Review: permutations (with
repetition,
circular)
492, Dol. 586
51. Review: combinations and
formulas
492, Dol. 591
52. Combination applications
(optional)
Dol. 594
53. Probability review, mutually
exclusive
events
476, 481
54. Probability trees, sampling and
replacement
481, 486
55. Bernoulli
experiments
498
56. The Binomial Theorem and Pascal's
Triangle
503
57. Binomial expansion
problems
503
58. The summation
symbol
522
59. The mean, median, mode, and
range
533, 537
60. Standard deviation and
variance
537
61. Standard deviation and normal
distribution
543
TEXTBOOKS:
Rising, Unified Mathematics: Book 3, Houghton Mifflin,
1989.
Dolciani, Modern Algebra and Trigonometry: Book 2, rev. ed., H-M, 1970.
Cohen, Precalculus, West.