Academics at Champion
The purpose of this course is to develop thinking and reasoning skills, provide general knowledge of basic mathematical concepts including number systems, operations, geometry, and functions, to develop problem-solving abilities as well as speed and accuracy in computation and to promote an interest in and an enjoyment of mathematics.
The importance of this course is the development of the reasoning and problem-solving skills essential throughout life. Also important is the general knowledge and computational skills necessary for placement and aptitude testing. Such general goals require both content and process. Certain content topics must be covered to prepare students for standardized tests but all the goals require teachers to employ appropriate processes. Skill development requires the process of regular review. Developing reasoning ability requires regular challenges to students’ thinking processes.
It is the purpose of this course to meet the needs of various teachers and students. Since every class is unique and students have varying abilities, the course will adapt the materials to the students. The teacher is the key to the students’ learning with an attitude that will set the tone for the class. This fact will be considered when assigning homework with three alternatives available: (1) minimum, (2) standard, and (3) extended. Efforts to improve student attitudes will bring greater success. A sense of success in solving challenging problems, a recognition of the power of mathematics, and an interest in further development of mathematical skills will impart students with attitudes for success.
This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas. Students will solve problems in these areas which include: operations of number systems (real and complex), linear equations and inequalities, (functions and graphing), solving quadratic equations by factoring, completing the square, and by use of the Quadratic Formula. Students add, subtract, multiply, divide, and evaluate radical and exponential expressions, graph functions, and solve equations. Students solve systems of equations and inequalities using various methods and simplify rational expressions and equations.
Trigonometry is introduced by right, special, and reciprocal triangular ratios along with functions, radian measure, amplitude, and period. Students prove simple laws of logarithms and understand and use the properties of logarithms to simplify logarithmic expressions. Students use fundamental counting principles to compute combinations and permutations and use these principles to compute probabilities. They know the binomial theorem and demonstrate and explain how geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.
(1 year - 10 credits - grades 9-12)
PREREQUISITE: Successful Completion of Algebra 1
To develop a student’s problem solving ability. To provide a background and preparation for Trigonometry and Pre-calculus.
COURSE OBJECTIVES: Students will be able to:
1. Understand angle relationships.
2. Understand absolute value.
3. Understand perimeter, area, volume surface area and sectors of circles.
4. Recognize types of triangles and polygons.
5. Understand proportional segments.
6. Understand negative exponents and conversion.
7. Understand and apply product and power theorems for exponents.
8. Solve relationships between circle area and circumferences.
9. Evaluate expressions.
10. Recognize and add like terms.
11. Use distributive property.
12. Solve equations with one variable.
13. Convert word problems to algebraic equations and solve.
14. Understand fractional parts of a number and solve fractional equations.
15. Solve equations with decimal numbers.
16. Solve word problems for consecutive integers.
17. Understand and apply percent.
18. Understand polynomials.
19. Graph linear equations using intercept-slope method.
20. Solve word problems using percent.
21. Understand and apply Pythagorean theorem to solve for the distance between two points on a graph.
22. Addition of fractions.
23. Understand the equation of a line.
24. Understand the relationship between the measure of central angles, inscribed angles and sectors of circles.
25. Use substitution to solve for equations with two variables.
26. Use Pythagorean theorem to solve for the area of an isosceles triangle.
27. Find the equation of a line when given two points lying on that line or when given the slope and a single point on that line.
28. Use elimination to solve for equations with two variables.
29. Multiply and divide polynomials.
30. Solve word problems using ratios.
31. Solve for sides of similar triangles, overlapping triangles and proportions. Understand AA means AAA.
32. Solve word problems using value of items.
33. Simplify radicals.
34. Understand negative reciprocals.
35. Find the line parallel and perpendicular to a given line that passes through the given point.
36. Understand scientific notation and be able to use it with estimation.
37. Use two statements of equality to solve an equation.
38. Solve uniform motion problems with equal distances,(RlT1=~T2) two distances that equal a total (R1Tl + ~T2 k) and D1+k--D2. (R1Tl+k=~T2)
39. Find solutions of two equations by graphing.
40. Understand monomial and trinomial factoring.
41. Add, multiply and divide rational expressions.
42. Simplify complex fractions.
43. Rationalize the denominator.
44. Understand the measure of vertical angles, corresponding interior and exterior angles, remote interior angles, triangles, congruent triangles and their relationships.
45. 45. Understand the quotient theorem for square roots.
46. 46. Understand angles in polygons and inscribed quadrilaterals.
47. Understand and simplify fractional exponents.
48. Solve contrived problems.
49. Solve for weight of chemicals in given compounds and solve for weight combination by percent.
50. Solve powers of sums.
51. Solve equations by factoring.
52. Understand and apply difference of two squares theorem.
53. Understand the relationship of the length of parallelogram and rhombus transversals.
54. Solve abstract fractional equations.
55. Use unit multipliers to convert rates, English to metric and metric to English.
56. Understand trigonometry functions and inverse functions and use to solve right triangles.
57. Simplify radical expressions and understand the product of square roots theorem.
58. Convert from radical to fractional exponents and fractional to radical.
59. Solve for the intercept of a line when not shown on the graph.
60. Solve for measure of transversals.
61. Solve quadratic equations using completing the square.
62. Understand and simplify imaginary numbers using Euler’s notation.
63. Solve word problems for chemical mixtures and strengths by percent.
64. 64. Use quadratic equations to solve word problems.
65. 65. Understand polar coordinates and convert from polar to rectangular and back.
66. 66. Use ideal gas laws to solve for missing components.
67. 67. Identify and manipulate lead coefficients.
68. 68. Form an equation based on experimental data results.
69. Solve simultaneous equations with fractions and decimals.
70. Use direct and inverse variation to solve for unknowns.
71. Solve quadratic equations with complex roots.
72. Understand how to add vectors and apply to force vectors at a point.
73. Multiply and simplify complex numbers.
74. Understand the three signs in a fraction.
75. Know and apply the ratios pertaining to 30-60-90 and 45-45-90 triangles.
76. Simplify radical denominators.
77. Understand how to use the scientific calculator, especially to find powers and roots.
78. Understand and apply the quadratic formula.
79. Understand negative angles.
80. Solve for the missing variables of uniform motion problems with both distances given.
81. Understand negative vectors.
82. Solve variable exponents.
83. Solve systems of nonlinear equations.
84. Understand and apply the slope formula.
85. Understand and apply the distance formula.
86. Solve for irrational roots.
87. Understand the relationship PV=nRT.
88. Solve for systems of three equations.
89. Solve for systems of linear and nonlinear inequalities.
90. Solve ‘boat-in-the-river problems.
91. Understand the discriminant.
92. Understand dependent and independent variables.
93. Understand functions and functional notation.
94. Solve absolute value inequalities.
95. Graph parabolas.
96. Understand sums and products of functions.
97. Understand sum and difference of two cubes.
98. Solve quadratic inequalities.
99. Understand and apply logarithms and antilogarithms.
100. Understand exponential equations and functions.
1. Lecture and Notes.
2. Class discussion of problems and applications.
MAJOR RESOURCE MATERIALS:
Algebra 2: An Incremental Development by John Saxon, Saxon Publishers, Inc., 1991
MEANS OF STUDENT EVALUATION:
1. Daily assignments.
2. Assessment of student participation in class discussions.
3. Quizzes and Tests.