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Algebra Curriculum Guide

PROFICIENCY 1: THE LEARNER WILL SOLVE, GRAPH, AND USE EQUATIONS AND
INEQUALITIES

1.1 Solve linear equations and formulas for a specified variable
1..2 Graph linear equations, linear inequalities, and absolute value equations and inequalities
1.3 Interpret the slope and intercepts of a line
1.4 Apply the concepts of parallel and perpendicular lines as determined by a comparison of
their slopes
1.5 Write and use an equation of a line which models a set of linear data
1.6 Fit a line to a set of linear data. Interpret the slope and intercepts

PROFICIENCY 2: THE LEARNER WILL DEMONSTRATE AN UNDERSTANDING OF
RELATIONS AND FUNCTION

2.1 Determine if a given relation is a function
2.2 Identify the domain and range of a relation
2.3 Use function notation
2.4 Graph relations and functions with and without graphing technology
2.5 Find the zeros of a function
2.6 Solve an inequality by examining the graph
2.7 Communicate graphically, algebraically, and verbally real world phenomena as functions
2.8 Find the composition of two functions
2.9 Use iterative definitions of functions
2.10 Draw a scatter plot and solve problems using its prediction equation

PROFICIENCY 3: THE LEARNER WILL OPERATE WITH MATRICES

3.1 Organize data into an array or a matrix
3.2 Add and subtract matrices
3.3 Use scalar multiplication and multiply matrices
3.4 Find identity and inverse matrices of the second order
3.5 Solve real world problems using matrices
3.6 Solve matrix equations of the form AX = B
3.7 Write and solve systems of linear equations in matrix form

PROFICIENCY 4: THE LEARNER WILL GRAPH AND SOLVE SYSTEMS OF
EQUATIONS AND INEQUALITIES

4.1 Solve systems of two equations graphically
4.2 Solve systems of two equations in two variables using substitution and/or elimination
4.3 Solve systems of three equations in three variables using elimination
4.4 Use systems of equations and inequalities to solve real world and “word” problems
through linear programming
4.5 Solve systems of inequalities by graphing

PROFICIENCY 5: THE LEARNER WILL PERFORM OPERATIONS AND SOLVE
PROBLEMS WITH POLYNOMIALS

5.1 Divide one polynomial by another of a lower degree
5.2 Use synthetic division to divide a polynomial by a linear polynomial
5.3 Factor polynomials completely
5.4 Use factoring to solve polynomial equations
5.5 Use polynomial equations to solve real world and “word” problems
5.6 Expand powers of binomials using Pascal’s Triangle or the binomial theorem
5.7 Write a polynomial equation given its solutions

PROFICIENCY 6: THE LEARNER WILL USE RATIONAL EXPRESSIONS TO SOLVE
PROBLEMS

6.1 Use expressions involving negative and fractional exponents
6.2 Find products and quotients of rational algebraic expressions
6.3 Simplify complex fractions
6.4 Solve fractional equations
6.5 Solve real world and “word” problems involving fractional equations
6.6 Solve problems of direct and inverse variation
6.7 Use joint and combined variation to solve real world and “word” problems

PROFICIENCY 7: THE LEARNER WILL SOLVE PROBLEMS INVOLVING IRRATIONAL
AND COMPLEX NUMBERS

7.1 Simplify radicals having various indices
7.2 Simplify radicals using multiplication and division
7.3 Rationalize the denominator of a fraction
7.4 Add, subtract, multiply, and divide radical expressions
7.5 Evaluate expressions in either exponential or radical form
7.6 Simplify expressions containing rational exponents
7.7 Solve equations containing radicals
7.8 Identify and simplify expressions containing pure imaginary numbers
7.9 Solve quadratic equations that have pure imaginary solutions
7.10 Add, subtract, multiply, and divide complex numbers

PROFICIENCY 8: THE LEARNER WILL SOLVE PROBLEMS WITH QUADRATIC
EQUATIONS AND INEQUALITIES

8.1 Complete the square to solve quadratic equations
8.2 Use the quadratic formula to solve quadratic equations
8.3 Define complex numbers and perform basic operations with them
8.4 Solve quadratic inequalities
8.5 Determine the solutions of quadratic and other polynomial equations using graphing
technology
8.6 Solve real world and “word” problems using quadratic equations and inequalities
8.7 Interpret maximum and minimum values of a quadratic function
8.8 Use the discriminant of a quadratic equation to determine the nature of the roots and the
number of x-intercepts of the graph

PROFICIENCY 9: THE LEARNER WILL USE ANALYTIC GEOMETRY TO SOLVE
PROBLEMS

9.1 Write the equations of and graph circles and parabolas given their geometric properties
9.2 Write the equations of and graph ellipses and hyperbolas given their geometric properties
9.3 Solve systems of quadratic equations algebraically
9.4 Solve systems of quadratic equations using graphing calculators and finding intersection
points

PROFICIENCY 10: THE LEARNER WILL SOLVE PROBLEMS WITH POLYNOMIAL
FUNCTIONS

10.1 Identify general shapes of the graphs of polynomial functions
10.2 Find factors of polynomials using the Factor Theorem and synthetic division
10.3 Find the number of positive real zeros, negative real zeros, and complex zeros for a
polynomial function
10.4 Identify all possible rational zeros of a polynomial function
10.5 Find the zeros of polynomial functions
10.6 Determine the inverse of a function or relation and use to solve real-life and “word”
problems

PROFICIENCY 11: THE LEARNER WILL SOLVE PROBLEMS INVOLVING
LOGARITHMIC AND EXPONENTIAL FUNCTIONS

11.1 Write an exponential function of the form f(x) = a · bx given the base and a point
11.2 Graph exponential functions of the form f (x) = a · bx
11.3 Use exponential equations of the form f (x) = (1 + r)x where r is given as a rate of growth
11.4 Apply the definition of logarithms
11.5 Use properties of logarithms and exponents
11.6 Use logarithms to solve expressions of the form a · bx = c for x

PROFICIENCY 12: THE LEARNER WILL SOLVE PROBLEMS INVOLVING SEQUENCES
AND SERIES

12.1 Generate the terms of an arithmetic series by iteration
12.2 Use a calculator or computer to generate the terms of a geometric series by iteration
12.3 Use summation notation to describe the sums in a series

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