Algebra II

Standard 1.

Students solve equations and inequalities involving absolute value

Standard 2. 

Students solve systems of linear equations and inequalities (in two or three variables) simultaneously, by substitution, graphically, or with matrices

Standard 3.

Students are adept at operations on polynomials, including long division

Standard 4.

Students factor polynomials representing the difference of squares, perfect squares, trinomials, and the sum and difference of two cubes

Standard 5.

Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically, and in particular, they can plot complex numbers as points in the plane

Standard 6.

Students add, subtract, multiply, and divide complex numbers

Standard 7. 

Students add, subtract, multiply, divide, reduce and evaluate rational expressions with monomial and polynomial denominators, and simplify complicated fractions including fractions with negative exponents in the denominator

Standard 8.

Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula, and they apply these techniques in solving word problems, and they also solve quadratic equations in the complex number system

Standard 9.

Students demonstrate and explain the effect changing a coefficient has on the graph of quadratic functions, that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x - b)squared + c

Standard 10.

Students graph quadratic functions and determine the maxima, minima, and zeros of the function

Standard 11. 

Students prove simple laws of logarithms

Skills:

11.1 Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents

11.2 Students judge the validity of an argument based on whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step

Standard 12. 

Students know the laws of exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

Standard 13.

Students use the definition of logarithms and the product formula for logs to translate between logarithms using any base.

Standard 14.

Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and identify their approximate values.

Standard 15. 

Students determine if a specific algebraic statement involving rational expressions, radical expressions, logarithmic or exponential functions, is sometimes true, always true, or never true.

Standard 16. 

Students demonstrate and explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.

Standard 17.

Given a quadratic equation of the form ax(2) + by(2) + cx + dy + e = 0, students can use the method of completing the square to put the equation into standard from and can recognize whether its graph is a circle, ellipse, parabola, or hyperbola;

Standard 18. 

Students use fundamental counting principles to compute combinations and permutations

Standard 19.

Students use combinations and permutations to compute probabilities

Standard 20. 

Students know the Binomial Theorem and use it to expand binomial expressions which are raised to positive integer powers

Standard 21.

Students apply the method of mathematical induction to prove general statements about the positive integers

Standard 22.

Students find the general term and the sums of arithmetic series and both finite and infinite geometric series

Standard 23.

Students derive the summation formulas for arithmetic series and both finite and infinite geometric series

Standard 24. 

Students solve problems involving functional concepts such as composition, inverse, and arithmetic operations on functions

Standard 25. 

Students use properties from number systems to justify steps in combining and simplifying functions