ALGEBRA II 06/11
STRAND 1: NUMBERS AND OPERATIONS
S1.0 The student will demonstrate an understanding of numbers and operations.
B1.1 Comprehends the meaning of numbers and ways of representing numbers and number systems
CI 1 Recognizes and uses properties of rational exponents
Properties of Negative Exponent
o
o
Product of Powers Property
o
o
Quotient of Powers Property
o
o
Power of a Power Property
o
o
Power of a Product Property
o
o
Power of a Quotient Property
o
Writes radical expressions using rational exponents and vice versa
CI 2 Operations with radicals
Simplifies radicals
o
Adding radicals
o
Subtracting radicals
o
Multiplying radicals
o
Dividing radicals
o
Writes radical expressions using rational exponents and vice versa
CI 3 Uses operations of matrices (addition, subtraction, scalar multiplication)
Determines the dimensions of a matrix
Adding matrices
1 2 8 9
o
3 4 10 11
Subtracting matrices
1 2 8 9
o
3 4 10 11
Scalar multiplication
1 2 3
o 5
4 5 6
Know, understands, and applies properties of matrix operations
o Commutative Property of Addition: A + B = B + A
o Associative Property of Addition: (A + B) + C = A + (B + C)
o Left Scalar Distributive Property: k( A + B ) = kA + kB
o Right Scalar Distributive Property: ( A + B )k = kA + kB
CI 4 Multiplies matrices
Determine whether each matrix product is defined. If so, states the dimensions of the
product.
Multiplies matrices
Know, understands, and applies properties of matrix multiplication
o Associative Property of Scalar Multiplication: k(AB) = (kA)B = A(kB)
o Associative Property of Matrix Multiplication: (AB)C = A(BC)
o Left Scalar Distributive Property: C( A + B ) = CA + CB
o Right Scalar Distributive Property: ( A + B )C = AC + BC
CI 5 Calculates second and third order determinants
Calculates second order determinants
o Calculates the value of determinant given matrix
o Determines missing value in matrix given the value of determinant
Calculates third order determinants
CI 6 Applies the law of logarithms
CI 7 Uses an inverse matrix to solve a linear system
B1.2 Computes fluently with all sets of numbers
CI 1 Calculates with complex numbers
Adding complex numbers
o
Subtracting complex numbers
o
Multiplying complex numbers
o
Dividing complex numbers
8 2i
o
4i
STRAND 2: ALGEBRA
S2.0 The student will demonstrate an understanding of algebra.
B2.1 Recognizes and understands patterns, relations, and functions and their relationships
CI 1 Factors binomials
Difference of Squares (a 2 b 2 )
Difference of Cubes (a 3 b 3 )
Sum of Cubes (a 3 b 3 )
CI 2 Factors trinomials
Leading coefficient of 1 ( x 2 bx c)
Leading coefficient other than 1 (ax 2 bx c)
CI 3 Understands direct, inverse, and joint variations
B2.2 Represents and analyzes mathematical situations using algebraic symbols
CI Solves multi-step equations and inequalities
CI 2 Solves systems of equations with three variables
CI 3 Solves systems of equations with two variables
Solves system algebraically (method of choosing)
Graphs system of equations on coordinate plane
Identifies the graph of system given system of equations
Identifies a possible solution(s) given a graph of a system of equations
Identifies a possible solution(s) given a system of equations
CI 4 Solves systems of inequalities with two variables
Graphs system of inequalities on coordinate plane
Identifies the graph of system given system of inequalities
Identifies a possible solution(s) given a graph of a system of inequalities
Identifies a possible solution(s) given a system of inequalities
CI 5 Divides with polynomials
CI 6 Solves quadratic equations and inequalities by factoring, quadratic
formula, completing the square, or analyzing graphs
CI 7 Graphs, applies, and solves equations of conic sections
CI 8 Analyzes and graphs polynomial functions
Determine degree of polynomial function
Determine end behaviors
Determine number of real zeros and/or imaginary zeros
Sketch a polynomial given degree, lead coefficient, and zeros (real & imaginary)
Graphs using a table of values
Identifies equation given graph
Identifies graph given equation
CI 9 Solves equations and inequalities involving absolute value
CI 10 Applies linear programming
CI 11 Solves radical equations
CI 12 Uses operations of rational expressions
CI 13 Solves rational equations
STRAND 3: GEOMETRY
S3.0 The student will demonstrate an understanding of geometry.
B3.1 Specifies locations and describes spatial relationships using coordinate geometry
CI 1 Graphs quadratic equations/functions and inequalities on a coordinate plane
Graphs using table of values
Identifies equation given graph
Identifies graph given equation
CI 2 Identifies special functions given graph or equation
Absolute value, Constant, Direct Variation, Identity, Piecewise, Quadratic, Rational,
Square Root, Step/Greatest integer
CI 3 Identifies equations of conic sections given graph or equation
Circle, Ellipse, Hyperbola, Parabola
CI 4 Graphs rational functions
Identifies vertical asymptote given function
Identifies point discontinuities given function
Sketches a rational function given vertical asymptote and/or point discontinuity
Graphs using table of values
Identifies equation given graph
Identifies graph given equation
STRAND 4: MEASUREMENT
S4.0 The student will demonstrate an understanding of measurement.
NA
STRAND 5: DATA ANALYSIS AND PROBABILITY
S5.0 The student will demonstrate an understanding of data analysis and probability.