Download Quality Standard #1: Understand Linear Equations and Inequalities

Quality Standard #1: Understand Linear Equations and Inequalities
1.1 The students will understand how to determine the equation of a line or inequality
• Recognize standard form point slope form slope intercept form of a linear
equation/inequality
• Write the equation of a line in various forms (given a graph of a line, given 2
points, given the point and slope)
• Use the relationship of perpendicular and parallel lines to write equations
• Using a set of data find the equation of the line of best fit
• Use the direct variation model to write equations
1.2 Students will understand how to graph linear equations and inequalities.
• Use a variety methods to graph linear equations and inequalities (may include
slope and y intercept, x and y intercept, point slope, table of values)
• Using direct variations
• Use of solid and dotted lines and regions
1.3 Students will understand how to solve linear equations and inequalities.
• Solve a linear compound inequality (3< x+2 < 7; AND; OR)
• From a graph
• Algebraically
• Solve for a specific variable
Quality Standard #2 – Understands quadratic equations.
2.1 Students will understand how to graph quadratic equations.
• Using table of values
• Standard form - Ax2 + Bx + C = y
• Vertex form - y = a(x-h)2 + k
• Basic understanding of the characteristics of a parabola (max, min, vertex, line of
symmetry)
2.2 Students will understand how to solve quadratic equations.
• Factoring and zero factor theorem
• Completing the square
• Square root method; extracting the square root (x2=9)
• Quadratic Formula
• Graphing
• Use the discriminant to determine the number and type of roots
Quality Standard #3: Understand patterns, relations, and functions.
3.1 Students will understand the language of functions.
• Definition
• Functional notation
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Recursion and Iteration
Domain and range
3.2 Students will understand the operations of functions.
• Add, Subtract, Multiply, and Divide
• Evaluate functions
• Composition
• Inverse of a relation/simple function
3.3 Students will understand how to graph functions and simple inverses.
• Understands and uses vertical and horizontal line test
• Transformations
Quality Standard #4: Understand polynomial equations and expressions.
4.1 Students will understand the operations of polynomials.
• Add, Subtract, Multiply and Divide
• Simplify by factoring
• Property of exponents
4.2 Students will understand the language of polynomials.
• Definition
• Identify the type of polynomial by the term and degrees
• Zeros, roots, and/or solutions
4.3 Students will understand how to solve polynomials.
• Factoring
• Graphing
4.4 Students will understand the nature of the graph of polynomials.
• Recognize the graph of y=x2 and y=x3
Quality Standard # 5: Understand special expressions/functions: Rational, Radical and
Absolute Value
5.1 Students will understand operations of rational and radical expressions.
• Add, Subtract, Multiply, and Divide
• Simplify expressions including complex fractions
• Definition and use of rational exponents
5.2 Students will understand the language of special expressions/functions.
• Definition/properties of a rational expressions/functions
• Definition/properties of a radical expressions/functions
• Definition/properties of an absolute value function ( x ≤ a ; x ≥ a )
5.3 Students will understand how to solve special functions.
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• Graphing (y= x ; y= ; y= x )
x
• Algebraically
Quality Standard #6: Understand systems of 2 linear equations and inequalities.
6.1 Students will understand the language of systems of equations and inequalities.
• Consistent, Inconsistent, Independent, Dependent
6.2 Students will understand how to solve systems of equations and inequalities.
• Graphically
• Algebraically
o Substitution
o Elimination
6.3 Students will understand how to solve systems of compound inequalities.
Quality Standard #7: Understand complex numbers.
7.1 Students will understand the language of complex numbers.
• Definition
• Imaginary
• Standard form
• Conjugate
7.2 Students will understand the basic operations of complex numbers.
• Add, Subtract, Multiply, and Divide
• Cyclic powers of i
NICE to Knows
• Power Function
• Conic Sections
• Logs/Exponential functions
• Basic trig functions
• Sequences/Series
• Matrices
• Set notation
• Graphs of complex numbers
• Discontinuous ties to asymptotes
• Factor Theorem
• Fundamental Theorem of Algebra
• Descarte’s rule
• Rational Root Theorem
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Probability and Statistics
Systems – 3 equations, 3 unknowns