Mr. Stanley Teitel Mr. Danny Jaye 09/04/02
Principal Assistant Principal
Scientific calculators: The use of scientific calculators should be introduced in the first unit, immediately after the order of
operations has been covered. Thereafter, students should understand that preparation for every class includes bringing a scientific
calculator.
Texts: Gerald Rising et al, Unified Mathematics: Book 3, Houghton Mifflin, 1989.
Mary Dolciani et al, Modern Algebra and Trigonometry: Book 2, Houghton Mifflin, 1970.
INTRO TO THE REAL NUMBER SYSTEM UNIFIED III
1. Sets: union and intersection
2. The sets N, W, Z and the Î operator 1
3. The sets of rational and irrational numbers 1
4. Real numbers and order of operations 6, 10
5. Using a scientific calculator
6. The properties of inequalities and compound inequalities 21, 25
7. Absolute value equations 32
8. Absolute value inequalities 32
POLYNOMIALS AND QUADRATIC EQUATIONS
9. The laws of exponents: lesson 1 45
10. The laws of exponents: lesson 2 45
11. The algebra of polynomials 50
12. Factoring: the GCF and special products 54
13. Factoring: quadratic trinomials 54
14. Factoring: grouping and special techniques 54
15. Solving quadratic equation by factoring and by the quadratic equation 60
16. Division by monomials and binomials 64
17. Multiplying rational expressions 68
18. Finding the LCM and the LCD 72
19. Combining rational expressions 72
20. Simplifying complex fractions 75
21. Fractional equations: lesson 1: algebraic strategies 78
lesson 2: verbal problems
22. Solving quadratic inequalities by factoring 82
RADICAL AND COMPLEX NUMBERS
23. Introduction to radical expressions 93
24. Simplifying radicals 93, 98
25. Simplifying radical expressions; radical conjugates 98
26. Solving radical equations 102
27. The imaginary unit 105
28. Complex numbers: +, -, ·, and equality 108
29. Division by complex numbers 112
30. The Argand (Gaussian) plane 459
31. Quadratic equations: number and nature of the roots 115
32. Quadratic equations: relation between roots and coefficients 121
33. Optional: solving quadratic inequalities with quadratic equations
INTRODUCTION TO TRIGONOMETRY
34. Relevant circle definitions and derivation of equation x2 + y2 = r2 222, Dol. 306
35. The angle in standard position, coterminal angles 275
36. Radian measure 278
37. Two equations of unit circle C(0, 0), evaluating sinq & cosq at quadrantal angles 281
38. Finding trigq given: 1. (x, y) on terminal side 2. Data concerning trigq 281
39. Evaluating trigq at special angles 285
40. Determining and using special reference angle 285
TRIGONOMETRIC IDENTITIES AND EQUATIONS
41. The reciprocal ratios 315
42. The quotient and Pythagorean identities 315, 323
43. Using identities to simplify expressions 323
44. Proving that an equation is an identity 323, 327
45. Rules and guidelines for identity proofs 327
46. The cofunction relation (for effective use of trig tables) 337 #41-50
47. Solving trig equations in a single function using trig tables 331
48. Solving quadratic trig equations 331
49. Solving trig equations in two functions 334
THE GEOMETRY of THE CIRCLE and EQUATIONS of PARABOLA & INVERSE VARIATION
50. Circle definitions and the measure of an inscribed angle 222,227
51. Measure of angles formed on the circle 227,232
52. Measure of angles formed inside the circle 239
53. Measure of angles formed outside the circle 239
54. Measure of chords: intersecting, perpendicular, equidistant 244
55. Measure of secant and tangent segments 250
56. Derive equation of parabola V(0,0) given its directrix & focus Dol. 309*
57. Inverse variations: their asymptotes, graphs, and symmetries Dol. 217, 319
58. Optional: derive equation of quadratic hyperbola and its asymptotes & graph it Dol. 315*
|