Academics at Champion

Cover state standards for Algebra ll. 

ALGEBRA II

(1 year - 10 credits - grades 9-12)

PREREQUISITE:  Successful Completion of Algebra 1

PURPOSE:

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.

MAJOR ACTIVITIES:

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.