# Florida Math Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper

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1 Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic expressions, including those with parentheses and exponents Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Order of operations with whole numbers and exponents: Basic Order of operations with whole numbers and exponents: Advanced Evaluating an algebraic expression: Whole number operations and exponents Absolute value of a number Operations with absolute value Exponents and integers: Problem type 1 Exponents and integers: Problem type 2 Exponents and signed fractions Order of operations with integers and exponents Evaluating a linear expression: Integer multiplication with addition or subtraction Evaluating a quadratic expression: Integers Evaluating a linear expression: Signed fraction multiplication with addition or subtraction Evaluating a linear expression: Signed decimal addition and subtraction Evaluating a linear expression: Signed decimal multiplication with addition or subtraction Combining like terms: Whole number coefficients Combining like terms: Integer coefficients Multiplying a constant and a linear monomial Distributive property: Whole number coefficients Distributive property: Integer coefficients Using distribution and combining like terms to simplify: Univariate Using distribution with double negation and combining like terms to simplify: Multivariate Combining like terms in a quadratic expression MDECU2: Simplifies an expression with integer exponents Understanding the product rule of exponents Introduction to the product rule of exponents Product rule with positive exponents: Univariate Product rule with positive exponents: Multivariate Understanding the power rules of exponents (FF4)Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/9

2 Introduction to the power of a power rule of exponents Introduction to the power of a product rule of exponents Power rules with positive exponents: Multivariate products Power rules with positive exponents: Multivariate quotients Power and product rules with positive exponents Simplifying a ratio of multivariate monomials: Basic Introduction to the quotient rule of exponents Simplifying a ratio of univariate monomials Quotient of expressions involving exponents Simplifying a ratio of multivariate monomials: Advanced Power and quotient rules with positive exponents Evaluating expressions with exponents of zero Evaluating an expression with a negative exponent: Whole number base Evaluating an expression with a negative exponent: Positive fraction base Evaluating an expression with a negative exponent: Negative integer base Rewriting an algebraic expression without a negative exponent Introduction to the product rule with negative exponents Product rule with negative exponents Quotient rule with negative exponents: Problem type 1 Quotient rule with negative exponents: Problem type 2 Power of a power rule with negative exponents Power rules with negative exponents Power and quotient rules with negative exponents: Problem type 1 Power and quotient rules with negative exponents: Problem type 2 Power, product, and quotient rules with negative exponents MDECU3: Add, subtract, multiply, and divide polynomials. Division by monomials only. Simplifying a sum or difference of two univariate polynomials Simplifying a sum or difference of three univariate polynomials Simplifying a sum or difference of multivariate polynomials Multiplying a univariate polynomial by a monomial with a positive coefficient Multiplying a univariate polynomial by a monomial with a negative coefficient Multiplying a multivariate polynomial by a monomial Multiplying binomials with leading coefficients of 1 Multiplying binomials with leading coefficients greater than 1 Multiplying binomials in two variables Multiplying conjugate binomials: Univariate Multiplying conjugate binomials: Multivariate Squaring a binomial: Univariate Squaring a binomial: Multivariate Multiplying binomials with negative coefficients Multiplication involving binomials and trinomials in one variable Multiplication involving binomials and trinomials in two variables Dividing a polynomial by a monomial: Univariate (FF4)Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/9

5 Classifying slopes given graphs of lines Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding the slope of horizontal and vertical lines Finding the slope and y-intercept of a line given its equation in the form y = mx + b Finding the slope and y-intercept of a line given its equation in the form Ax + By = C Graphing a line by first finding its slope and y-intercept Linear Equations MDECU7: Solve linear equations in one variable using manipulations guided by the rules of arithmetic and the properties of equality Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with integers Additive property of equality with signed fractions Multiplicative property of equality with whole numbers Multiplicative property of equality with fractions Multiplicative property of equality with decimals Multiplicative property of equality with integers Multiplicative property of equality with signed fractions Using two steps to solve an equation with whole numbers Additive property of equality with a negative coefficient Solving a two-step equation with integers Introduction to solving an equation with parentheses Solving a multi-step equation given in fractional form Solving a two-step equation with signed decimals Introduction to solving a linear equation with several occurrences of the variable Solving a linear equation with several occurrences of the variable: Variables on the same side Solving a linear equation with several occurrences of the variable: Variables on both sides Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions Solving a linear equation with several occurrences of the variable: Fractional forms with monomial numerators Solving a two-step equation with signed fractions Solving a linear equation with several occurrences of the variable: Variables on both sides and fractional coefficients Solving a linear equation with several occurrences of the variable: Fractional forms with (FF4)Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/9

6 binomial numerators Solving equations with zero, one, or infinitely many solutions MDECU8: Solve literal equations for a given variable with applications (geometry, motion [d=rt], simple interest [i=prt]) Solving for a variable in terms of other variables using addition or subtraction: Basic Solving for a variable in terms of other variables using addition or subtraction: Advanced Solving for a variable in terms of other variables using multiplication or division: Basic Solving for a variable in terms of other variables using multiplication or division: Advanced Solving for a variable in terms of other variables using addition or subtraction with division Solving for a variable inside parentheses in terms of other variables Solving for a variable in terms of other variables in a linear equation with fractions MDECU15: Solve multi-step problems involving fractions and percentages (Include situations such as simple interest, tax, markups/markdowns, gratuities and commissions, fees, percent increase or decrease, percent error, expressing rent as a percentage of take home pay) Translating a phrase into a two-step expression Translating a sentence into a one-step equation Translating a sentence into a multi-step equation Solving a fraction word problem using a linear equation of the form Ax = B Solving a fraction word problem using a linear equation with the variable on both sides Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Writing a ratio as a percentage without a calculator Computing a percentage from a table of values Finding the rate of a tax or commission Finding the total amount given the percentage of a partial amount Finding the multiplier to give a final amount after a percentage increase or decrease Finding the final amount given the original amount and a percentage increase or decrease Finding the sale price given the original price and percent discount Finding the sale price without a calculator given the original price and percent discount Finding the total cost including tax or markup Finding the original amount given the result of a percentage increase or decrease Finding the original price given the sale price and percent discount Finding the percentage increase or decrease: Basic Finding the percentage increase or decrease: Advanced Computations from a circle graph Finding simple interest without a calculator MDECU16: Solve linear inequalities in one variable and graph the solution set on a number line Translating a sentence into a one-step inequality Writing a one-step inequality for a real-world situation Graphing a linear inequality on the number line Identifying solutions to a linear inequality in one variable (FF4)Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/9

8 Simplifying a product of radical expressions: Univariate Simplifying a product of radical expressions: Multivariate Introduction to simplifying a product involving square roots using the distributive property Simplifying a product involving square roots using the distributive property: Basic MDECU17: Rationalize the denominator (monomials only) Simplifying a quotient of square roots Rationalizing a denominator: Quotient involving square roots Rationalizing a denominator: Square root of a fraction Rationalizing a denominator: Quotient involving a monomial MDECU18: Solve application problems involving geometry (Pythagorean Theorem) Introduction to the Pythagorean Theorem Pythagorean Theorem Word problem involving the Pythagorean Theorem Rationals MDECU19: Recognize proportional relationships and solve problems involving rates and ratios Solving a word problem on proportions using a unit rate Solving a proportion of the form x/a = b/c Solving a proportion of the form (x+a)/b = c/d Solving a one-step word problem using the formula d = rt Solving a word problem involving rates and time conversion Solving a proportion of the form a/(x+b) = c/x Finding a unit price Computing unit prices to find the better buy Finding unit rates Word problem on proportions: Problem type 1 Word problem on proportions: Problem type 2 Similar polygons Indirect measurement Word problem involving multiple rates MDECU20: Simplify, multiply, and divide rational expressions Simplifying a ratio of factored polynomials: Linear factors Simplifying a ratio of factored polynomials: Factors with exponents Simplifying a ratio of polynomials using GCF factoring Simplifying a ratio of linear polynomials: 1, -1, and no simplification Simplifying a ratio of polynomials by factoring a quadratic with leading coefficient 1 Simplifying a ratio of polynomials: Problem type 1 (FF4)Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/9

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