Florida Math 0028 Correlation of the ALEKS course Florida Math

Florida Math 0028

Correlation of the ALEKS course Florida Math 0028 to the Florida

Mathematics Competencies - Upper

Exponents & Polynomials

= ALEKS course topic that addresses the standard

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

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

Dividing a polynomial by a monomial: Multivariate

MDECU11: Convert between scientific notation and standard notation

Scientific notation with positive exponent

Scientific notation with negative exponent

Converting between scientific notation and standard form in a real-world situation

Multiplying numbers written in scientific notation: Basic

Multiplying numbers written in scientific notation: Advanced

Dividing numbers written in scientific notation: Basic

Dividing numbers written in scientific notation: Advanced

MDECU12: Solve application problems involving geometry (perimeter and area with

algebraic expressions)

Finding the side length of a rectangle given its perimeter or area

Finding a side length given the perimeter and side lengths with variables

Finding the perimeter or area of a rectangle given one of these values

Solving a word problem using a quadratic equation with rational roots

Using the Pythagorean Theorem and a quadratic equation to find side lengths of a right

triangle

Factoring

= ALEKS course topic that addresses the standard

MDECU4: Solve quadratic equations in one variable by factoring

Finding the roots of a quadratic equation of the form ax

+ bx = 0

Finding the roots of a quadratic equation with leading coefficient 1

Finding the roots of a quadratic equation with leading coefficient greater than 1

Solving a quadratic equation needing simplification

MDECU5: Factor polynomial expressions (GCF, grouping, trinomials, difference of

squares)

Factoring a linear binomial

Introduction to the GCF of two monomials

Greatest common factor of three univariate monomials

Greatest common factor of two multivariate monomials

Factoring out a monomial from a polynomial: Univariate

Factoring out a monomial from a polynomial: Multivariate

Factoring out a binomial from a polynomial: Basic

Factoring a univariate polynomial by grouping: Problem type 1

Factoring a univariate polynomial by grouping: Problem type 2

Factoring a multivariate polynomial by grouping: Problem type 1

Factoring a multivariate polynomial by grouping: Problem type 2

Factoring a quadratic with leading coefficient 1

Factoring a quadratic in two variables with leading coefficient 1

Factoring out a constant before factoring a quadratic

Factoring a quadratic with leading coefficient greater than 1: Problem type 1

Factoring a quadratic with leading coefficient greater than 1: Problem type 2

Factoring a quadratic with leading coefficient greater than 1: Problem type 3

Factoring a quadratic by the ac-method

Factoring a quadratic in two variables with leading coefficient greater than 1

Factoring a quadratic with a negative leading coefficient

Factoring a perfect square trinomial with leading coefficient 1

Factoring a perfect square trinomial with leading coefficient greater than 1

Factoring a perfect square trinomial in two variables

Factoring a difference of squares in one variable: Basic

Factoring a difference of squares in one variable: Advanced

Factoring a difference of squares in two variables

Factoring a polynomial involving a GCF and a difference of squares: Univariate

Factoring a polynomial involving a GCF and a difference of squares: Multivariate

Factoring a product of a quadratic trinomial and a monomial

Factoring with repeated use of the difference of squares formula

Graphing

= ALEKS course topic that addresses the standard

MDECU6: Graph linear equations using tables of values, intercepts, slope intercept

form

Graphing a linear equation of the form y = mx

Graphing a line given its equation in slope-intercept form: Integer slope

Graphing a line given its equation in slope-intercept form: Fractional slope

Graphing a line given its equation in standard form

Graphing a vertical or horizontal line

Graphing a line given its x- and y-intercepts

Graphing a line by first finding its x- and y-intercepts

Graphing a line given its slope and y-intercept

Graphing a line through a given point with a given slope

Graphing a line by first finding its slope and y-intercept

MDECU13: Identifies the intercepts of a linear equation

Finding x- and y-intercepts given the graph of a line on a grid

Finding x- and y-intercepts of a line given the equation: Basic

Finding x- and y-intercepts of a line given the equation: Advanced

Graphing a line given its x- and y-intercepts

Graphing a line by first finding its x- and y-intercepts

MDECU14: Identify the slope of a line (from slope formula, graph, and equation)

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

= ALEKS course topic that addresses the standard

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

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

Additive property of inequality with whole numbers

Additive property of inequality with integers

Additive property of inequality with signed fractions

Additive property of inequality with signed decimals

Multiplicative property of inequality with integers

Multiplicative property of inequality with signed fractions

Solving a two-step linear inequality: Problem type 1

Solving a two-step linear inequality: Problem type 2

Solving a two-step linear inequality with a fractional coefficient

Solving a linear inequality with multiple occurrences of the variable: Problem type 1

Solving a linear inequality with multiple occurrences of the variable: Problem type 2

Solving a linear inequality with multiple occurrences of the variable: Problem type 3

Word problem with linear inequalities: Problem type 1

Radicals

= ALEKS course topic that addresses the standard

MDECU9: Simplify radical expressions - square roots only

Square root of a perfect square

Using a calculator to approximate a square root

Finding all square roots of a number

Square root of a rational perfect square

Square roots of perfect squares with signs

Introduction to simplifying a radical expression with an even exponent

Square root of a perfect square monomial

Simplifying the square root of a whole number less than 100

Simplifying the square root of a whole number greater than 100

Simplifying a radical expression with an even exponent

Introduction to simplifying a radical expression with an odd exponent

Simplifying a radical expression with an odd exponent

Simplifying a radical expression with two variables

MDECU10: Adds, subtracts, and multiplies square roots of monomials

Introduction to square root addition or subtraction

Square root addition or subtraction

Square root addition or subtraction with three terms

Introduction to simplifying a sum or difference of radical expressions: Univariate

Simplifying a sum or difference of radical expressions: Univariate

Simplifying a sum or difference of radical expressions: Multivariate

Introduction to square root multiplication

Square root multiplication: Basic

Square root multiplication: Advanced

Introduction to simplifying a product of radical expressions: Univariate

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

= ALEKS course topic that addresses the standard

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

Simplifying a ratio of polynomials: Problem type 2

Simplifying a ratio of polynomials: Problem type 3

Simplifying a ratio of multivariate polynomials

Multiplying rational expressions involving multivariate monomials

Multiplying rational expressions made up of linear expressions

Multiplying rational expressions involving quadratics with leading coefficients of 1

Multiplying rational expressions involving quadratics with leading coefficients greater than 1

Dividing rational expressions involving multivariate monomials

Dividing rational expressions involving linear expressions

Dividing rational expressions involving quadratics with leading coefficients of 1

Dividing rational expressions involving quadratics with leading coefficients greater than 1

Complex fraction without variables: Problem type 1

Complex fraction involving univariate monomials

Complex fraction involving multivariate monomials

MDECU21: Add and subtract rational expressions with monomial denominators

Writing equivalent rational expressions with monomial denominators

Introduction to adding fractions with variables and common denominators

Adding rational expressions with common denominators and monomial numerators

Adding rational expressions with common denominators and binomial numerators

Adding rational expressions with different denominators and a single occurrence of a variable

Adding rational expressions with denominators ax and bx: Basic

Adding rational expressions with denominators ax and bx: Advanced

Adding rational expressions with denominators ax

and bx

Adding rational expressions with multivariate monomial denominators: Basic

Adding rational expressions with multivariate monomial denominators: Advanced

MDECU22: Convert units of measurements across measurement systems

Converting between temperatures in Fahrenheit and Celsius

Converting between metric and U.S. Customary unit systems

Converting between compound units: Basic

Converting between compound units: Advanced