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1. Verify solutions to equations.
2. Solve linear equations using the addition principle.
3. Solve linear equations using the multiplication principle.
4. Solve equations using both the addition and multiplication principles.
1. Verify solutions to equations.
2. Solve linear equations using the addition principle.
3. Solve linear equations using the multiplication principle.
4. Solve equations using both the addition and multiplication principles.
1. Verify solutions to equations.
2. Solve linear equations using the addition principle.
3. Solve linear equations using the multiplication principle.
4. Solve equations using both the addition and multiplication principles.
1. Plot points in the coordinate plane.
2. Find solutions for equations in two unknowns.
3. Graph linear equations by plotting solutions.
4. Graph linear equations using intercepts.
5. Graph vertical and horizontal lines.
1. Plot points in the coordinate plane.
2. Find solutions for equations in two unknowns.
3. Graph linear equations by plotting solutions.
4. Graph linear equations using intercepts.
5. Graph vertical and horizontal lines.
1. Plot points in the coordinate plane.
2. Find solutions for equations in two unknowns.
3. Graph linear equations by plotting solutions.
4. Graph linear equations using intercepts.
5. Graph vertical and horizontal lines.
1. Plot points in the coordinate plane.
2. Find solutions for equations in two unknowns.
3. Graph linear equations by plotting solutions.
4. Graph linear equations using intercepts.
5. Graph vertical and horizontal lines.
1. Plot points in the coordinate plane.
2. Find solutions for equations in two unknowns.
3. Graph linear equations by plotting solutions.
4. Graph linear equations using intercepts.
5. Graph vertical and horizontal lines.
1. Represent solutions to inequalities graphically and using set notation.
2. Solve linear inequalities.
3. Solve problems involving linear inequalities.
1. Represent solutions to inequalities graphically and using set notation.
2. Solve linear inequalities.
3. Solve problems involving linear inequalities.
1. Identify the domain and range of a relation.
2. Identify functions and their domains and ranges.
3. Find the value of a function.
4. Graph linear functions.
1. Identify the domain and range of a relation.
2. Identify functions and their domains and ranges.
3. Find the value of a function.
4. Graph linear functions.
1. Determine whether an ordered pair is a solution for a system of equations.
2. Solve a system of linear equations graphically.
3. Classify systems of linear equations in two unknowns.
1. Determine whether an ordered triple is a solution for a system of equations.
2. Understand the types of solution sets for systems of three equations.
3. Solve a system of three linear equations using the elimination method.
4. Solve application problems that translate to a system of three linear equations.
1. Evaluate exponential forms with integer exponents.
2. Write scientific notation in standard form.
3. Write standard form numbers in scientific notation.
1. Multiply a polynomial by a monomial.
2. Multiply binomials.
3. Multiply polynomials.
4. Determine the product when given special polynomial factors.
1. Multiply a polynomial by a monomial.
2. Multiply binomials.
3. Multiply polynomials.
4. Determine the product when given special polynomial factors.
1. Divide exponential forms with the same base.
2. Divide numbers in scientific notation.
3. Divide monomials.
4. Divide a polynomial by a monomial.
5. Use long division to divide polynomials.
6. Simplify expressions using rules of exponents.
1. List all possible factors for a given number.
2. Find the greatest common factor of a set of numbers or monomials.
3. Write a polynomial as a product of a monomial GCF and a polynomial.
4. Factor by grouping.
1. Factor trinomials of the form ax2+bx+c, eh , x squared , plus b x plus c comma where aâ‰ 1, eh not equal to 1 comma by trial.
2. Factor trinomials of the form ax2+bx+c, eh , x squared , plus b x plus c comma where aâ‰ 1, eh not equal to 1 comma by grouping.
1. Use the zero-factor theorem to solve equations containing expressions in factored form.
2. Solve quadratic equations by factoring.
3. Solve problems involving quadratic equations.
4. Use the Pythagorean theorem to solve problems.
1. Use the zero-factor theorem to solve equations containing expressions in factored form.
2. Solve quadratic equations by factoring.
3. Solve problems involving quadratic equations.
4. Use the Pythagorean theorem to solve problems.
1. Evaluate rational expressions.
2. Find numbers that cause a rational expression to be undefined.
3. Simplify rational expressions containing only monomials.
4. Simplify rational expressions containing multiterm polynomials.
1. Find the LCD of two or more rational expressions.
2. Given two rational expressions, write equivalent rational expressions with their LCD.
3. Add or subtract rational expressions with different denominators.
1. Find the nth root of a number.
2. Approximate roots using a calculator.
3. Simplify radical expressions.
4. Evaluate radical functions.
5. Find the domain of radical functions.
6. Solve applications involving radical functions.
1. Evaluate rational exponents.
2. Write radicals as expressions raised to rational exponents.
3. Simplify expressions with rational number exponents using the rules of exponents.
4. Use rational exponents to simplify radical expressions.
1. Add or subtract like radicals.
2. Use the distributive property in expressions containing radicals.
3. Simplify radical expressions that contain mixed operations.
1. Solve quadratic equations using the quadratic formula.
2. Use the discriminant to determine the number of real solutions that a quadratic equation has.
3. Find the x- and y-intercepts of a quadratic function.
4. Solve applications using the quadratic formula.
1. Solve quadratic equations using the quadratic formula.
2. Use the discriminant to determine the number of real solutions that a quadratic equation has.
3. Find the x- and y-intercepts of a quadratic function.
4.Solve applications using the quadratic formula.
1. Solve quadratic equations using the quadratic formula.
2. Use the discriminant to determine the number of real solutions that a quadratic equation has.
3. Find the x- and y-intercepts of a quadratic function.
4. Solve applications using the quadratic formula.
1. Solve quadratic equations using the quadratic formula.
2. Use the discriminant to determine the number of real solutions that a quadratic equation has.
3. Find the x- and y-intercepts of a quadratic function.
4. Solve applications using the quadratic formula.
1. Define and graph exponential functions.
2. Solve equations of the form bx=by b to the x , equals , b to the y for x.
3. Use exponential functions to solve application problems.
1. Use vocabulary related to solving equations and identify types of equations
2. Solve linear equations
3. Solve rational equations
4. Solve formulas for a specific variable
1. Simplify imaginary numbers;
2. Perform operations on complex numbers
3. Find powers of i
4. Determine the absolute value of a complex number
5. Factor the sum of two squares
1. Solve quadratic equations using factoring and the Square Root Property
2. Solve quadratic equations using completing the square
3. Solve quadratic equations using the Quadratic Formula
4. Determine the easiest strategy to use to solve a quadratic equation
5. Solve formulas for a variable that is squared
6. Define and use the discriminant
7. Write rational equations in quadratic form and solve the equations
1. Solve polynomial equations by factoring
2. Solve other equations by factoring
3. Solve equations in quadratic form
4. Solve radical equations
5. Solve applications of radical equations
1. Use the properties of inequalities
2. Solve linear inequalities and applications
3. Solve compound inequalities
4. Solve quadratic inequalities
5. Solve rational inequalities
1. Use the properties of inequalities
2. Solve linear inequalities and applications
3. Solve compound inequalities
4. Solve quadratic inequalities
5. Solve rational inequalities"
1. Use the properties of inequalities
2. Solve linear inequalities and applications
3. Solve compound inequalities
4. Solve quadratic inequalities
5. Solve rational inequalities
1. Define and use absolute value
2. Solve equations of the form |x|=k
3. Solve equations with two absolute values
4. Solve inequalities of the forms |x|
5. Solve inequalities of the forms |x|>k and |x|â‰¥k
6. Solve compound inequalities with absolute value
7. Solve inequalities with two absolute values
1. Define relation, domain, and range
2. Understand the concept of a function
3. Determine whether an equation represents a function
4. Find the domain of a function
5. Evaluate a function
6. Evaluate the difference quotient for a function
7. Solve applications involving functions
1. Plot points in the rectangular coordinate system
2. Graph linear equations
3. Graph vertical and horizontal lines
4. Solve applications using linear functions
5. Find the distance between two points
6. Find the midpoint of a line segment
1. Plot points in the rectangular coordinate system
2. Graph linear equations
3. Graph vertical and horizontal lines
4. Solve applications using linear functions
5. Find the distance between two points
6. Find the midpoint of a line segment
1. Find the slope of a line
2. Interpret slope as a rate of change
3. Find slopes of horizontal and vertical lines
4. Find slopes of parallel and perpendicular lines
1. Use slope-intercept form to write an equation of a line
2. Graph linear equations using the slope and y-intercept
3. Determine whether linear equations represent lines that are parallel, perpendicular, or neither
4. Use point-slope form to write an equation of a line
5. Write equations of parallel and perpendicular lines
6. Write an equation of a line that models a real-life problem
7. Use linear curve fitting to solve problems
1. Graph a function by plotting points
2. Use the Vertical Line Test to identify functions
3. Determine function values graphically
4. Determine the domain and range of a function from its graph
5. Recognize the graphs of common functions
1. Use vertical translations to graph functions
2. Use horizontal translations to graph functions
3. Graph functions using two translations
4. Use reflections about the x- and y-axes to graph functions
5. Use vertical stretching and shrinking to graph functions
6. Use horizontal stretching and shrinking to graph functions
7. Graph functions using a combination of transformations
1. Determine whether a function is even, odd, or neither
2. Identify the open intervals on which a function is increasing, decreasing, or constant
3. Identify local maxima and local minima on the graph of a function
4. Evaluate and graph piecewise-defined functions
5. Evaluate and graph the greatest integer function
1. Determine whether a function is even, odd, or neither
2. Identify the open intervals on which a function is increasing, decreasing, or constant
3. Identify local maxima and local minima on the graph of a function
4. Evaluate and graph piecewise-defined functions
5. Evaluate and graph the greatest integer function
1. Add, subtract, multiply, and divide functions, specifying domains
2. Write functions as sums, differences, products, or quotients of other functions
3. Evaluate composite functions
4. Determine domains for composite functions
5. Write functions as compositions
6. Use operations on functions to solve problems
1. Understand the definition of a one-to-one function
2. Determine whether a function is one-to-one
3. Verify inverse functions
4. Find the inverse of a one-to-one function
5. Understand the relationship between the graphs of f and f^{-1}
1. Recognize the characteristics of a quadratic functions
2. Find the vertex of a parabola whose equation is in standard form
3. Graph a quadratic function
4. Find the vertex of a parabola whose equation is in general form
5. Use a quadratic function to solve maximum and minimum problems
1. Recognize polynomial functions
2. understand characteristics of the graphs of polynomial functions
3. Find zeros of polynomial functions by factoring
4. Determine end behavior
5. Graph polynomial functions
6. Use the Intermediate Value Theorem
1. Understand the definition of a zero polynomial function
2. Use the Remainder Theorem
3. Use the Factor Theorem
4. Use synthetic division to divide polynomials
5. Use synthetic division to evaluate polynomial functions
6. Use synthetic division to solve polynomial equations
1. Find possible rational zeros of polynomial functions
2. Find rational zeros of polynomial functions
3. Find real and nonreal zeros of polynomial functions
4. Solve applications
1. Find the domain of a rational functions
2. Understand the characteristics of rational functions and their graphs
3. Find vertical asymptotes of rational functions
4. Find horizontal asymptotes of rational functions
5. Identify slant asymptotes of rational functions
6. Graph rational functions
7. Understand when a graph has a missing point
8. Solve problems modeled by rational functions
1. Find the domain of a rational functions
2. Understand the characteristics of rational functions and their graphs
3. Find vertical asymptotes of rational functions
4. Find horizontal asymptotes of rational functions
5. Identify slant asymptotes of rational functions
6. Graph rational functions
7. Understand when a graph has a missing point
8. Solve problems modeled by rational functions
1. Use properties of logarithms to simplify expressions
2. Use the Change-of-Base Formula
3. Use logarithms to solve pH problems
4. Use logarithms to solve problems in electronics
5. Use logarithms to solve physiology problems
1. Use like bases to solve exponential equations
2. Use logarithms to solve exponential equations
3. Solve logarithmic equations
4. Solve carbon-14 dating problems
5. Solve population growth problems
1. Solve systems using the graphing method
2. Solve systems using the substitution method
3. Solve systems using the elimination method
4. Solve systems with infinitely many solutions
5. Solve inconsistent systems
6. Solve systems involving three equations in three variables
7. Solve applications involving systems of equations
1. Write an equation of a circle
2. Graph circles
3. Write an equation of a parabola in standard form
4. Graph parabolas
5. Solve applied problems involving parabolas
1. Write an equation of a circle
2. Graph circles
3. Write an equation of a parabola in standard form
4. Graph parabolas
5. Solve applied problems involving parabolas
1. Use Pascal's Triangle to expand a binomial
2. Define and use factorial notation
3. Use the Binomial Theorem to expand binomials
4. Find a specific term of a binomial expansion
1. Define and use arithmetic sequences
2. Find arithmetic means
3. Find the sum of the first n terms of an arithmetic sequence
4. Solve problems involving sequences and series
1. Define and use gemeometric sequences
2. Find geometric means
3. Find the sum of the first n terms of a geometric series
4. Define and find the sum of infinite geometric series
5. Solve problems involving geometric sequences and series