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CURRICULUM GUIDE FOR ALGEBRA 12
PROFICIENCY 1:  THE LEARNER WILL USE THE LANGUAGE OF ALGEBRA 
1.1 Evaluate algebraic expressions
1.2 Use formulas to solve problems
1.3 Translate word phrases and sentences into expressions and equations and vice
versa
1.4 Recognize the appropriate use of the associative, commutative, and
distributive properties
1.5 Use the associative, commutative, and distributive properties to simplify
algebraic
expressions
PROFICIENCY 2: 
THE LEARNER WILL PERFORM OPERATIONS WITH REAL NUMBERS 
2.1 Simplify real number expressions
2.2 Determine the additive or multiplicative inverse of a number
2.3 Determine the absolute value of expressions
2.4 Use exponents with real numbers
2.5 Distinguish between rational and irrational numbers
2.6 Find approximations for square roots
2.7 Compare real number expressions
2.8 Write inequalities for number line graphs and vice versa
PROFICIENCY 3: 
THE LEARNER WILL SOLVE EQUATIONS AND INEQUALITIES WITH ONE VARIABLE 
3.1 Solve an equation by using the addition property of
equality and the idea of additive
inverse
3.2 Solve an equation by using the multiplication property of equality and the
idea of
multiplicative inverse
3.3 Solve an equation graphically and by using more than one property of
equality
3.4 Solve an equation which contains like terms
3.5 Solve an equation which has the variable in both members
3.6 Solve an equation in which the numerical coefficients and constant terms are
fractions or
decimals
3.7 Solve a formula for one of its variables or find the value of a variable
when values of the
other variables are given
3.8 Use problem solving skills to solve real world and “word” problems which
involve a linear
equation or formula
3.9 Solve an equation involving absolute value
3.10 Solve an equation containing a radical
3.11 Find the solution set for a linear inequality when replacement values are
given for the
variable
3.12 Solve a linear inequality by using properties of order
3.13 Use problem solving skills to solve real world or “word” problems which
involve
inequalities
3.14 Find the solution set of combined inequalities
PROFICIENCY 4: 
THE LEARNER WILL DEMONSTRATE AN UNDERSTANDING OF RELATIONSHIPS BETWEEN REPRESENTATIONS OF A FUNCTION 
4.1 Given a rule or function that demonstrates a linear
equation, generate ordered pairs and
graph the equation
4.2 Translate between tables and graphs of functions
4.3 Given a linear inequality, determine whether a given value is in the
solution set
4.4 Given a linear inequality in two variables, graph the solution set
PROFICIENCY 5: 
THE LEARNER WILL GRAPH AND USE LINEAR EQUATIONS AND INEQUALITIES 
5.1 Determine if data are behaving in a linear fashion
5.2 Find the solution set of open sentences in two variables when given
replacement sets for
the variables
5.3 Graph a linear equation in two variables
5.4 Graph a line given its slope and y intercept
5.5 Find the slope of a nonvertical line given the graph
of the line or an equation of the line or
two points on the line
5.6 Describe the slope in a real world linear relationship using real world
terms
5.7 Write the slope intercept form of an equation of a line. Find the slope and
yintercept of a
line
5.8 Write the equation of a line given the slope and one point on the line, or
two points on the
line
5.9 Write the equation of a line which models a set of real data
5.10 Use the line which models real data to make predictions
5.11 Foreshadow inequalities by describing the location of an ordered pair in
relation to a line
5.12 Graph a linear inequality in two variables
PROFICIENCY 6: 
THE LEARNER WILL GRAPH AND SOLVE SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES 
6.1 Use a graph to find the solution of a pair of linear
equations in two variables
6.2 Graph the system of linear inequalities in two variables and find the
solution set
6.3 Use graphing technology to solve systems of linear equations
6.4 Use the substitution method to find the solution of a pair of linear
equations in two
variables
6.5 Use the addition or subtraction method to find the solution of a pair of
linear equations in
two variables
6.6 Use multiplication with the addition or subtraction method to solve systems
of linear
equations
6.7 Use systems of linear equations to solve real world and “word” problems
PROFICIENCY 7: 
THE LEARNER WILL PERFORM OPERATIONS WITH POLYNOMIALS 
7.1 Add and subtract polynomials
7.2 Multiply monomials
7.3 Find an indicated power of a monomial
7.4 Multiply a polynomial by a monomial
7.5 Find the product of two binomials
7.6 Multiply two polynomials
7.7 Divide two polynomials
7.8 Divide a polynomial by a monomial
7.9 Find a common monomial factor in a polynomial
7.10 Factor the difference of two squares
7.11 Factor a simple quadratic trinomial
PROFICIENCY 8: 
THE LEARNER WILL WORK WITH RATIOS, PROPORTIONS, AND PERCENTS 
8.1 Simplify ratios involving algebraic expressions
8.2 Solve proportions
8.3 Solve equations involving percents
8.4 Use ratios and proportions to solve real world and “word” problems
8.5 Solve real world and “word” problems involving percents
PROFICIENCY 9: 
THE LEARNER WILL EXPLORE, GRAPH, AND INTERPRET NONLINEAR EQUATIONS 
9.1 Graph a quadratic equation
9.2 Use graphing technology to find the solution to a quadratic equation
9.3 Solve a quadratic equation when one member is in factored form and the other
member is
zero
9.4 Solve a simple second degree equation by factoring
9.5 Use graphing technology to relate the solutions of quadratic equations and
the xintercepts
9.6 Understand that the vertex provides the maximum or minimum value of a
quadratic
function
9.7 Solve a quadratic equation in which a perfect square equals a constant
9.8 Solve a quadratic equation by using the quadratic formula
9.9 Determine if a set of data represents an exponential function
9.10 Use formulas, calculators , and graphing technology to
explore and solve problems
involving exponentials
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