# algebra regents review

##### SETS

Linear Functions | Algebra Study Guide

The Slope Formula | Algebra Study Guide

Variable

Coefficient

Equation

Expression

a letter or symbol representing a varying quantity

a number which multiplies a variable

a mathematical statement containing an equal sign

one or a group of terms and maybe include variables, constants…

Variable

a letter or symbol representing a varying quantity

Coefficient

a number which multiplies a variable

Polynomials

Multiplying Polynomials

Steps for Double Distributive

Box Method

An expression with more than 1 term.

Double Distributive, Box Method, FOIL

Rewrite the problem with one parentheses broken up, and the 2n…

Similar to Punnett Squares. Used to multiply polynomials.

Polynomials

An expression with more than 1 term.

Multiplying Polynomials

Double Distributive, Box Method, FOIL

rational

continuous graph

maximum turning point

absolute value

number that can be expressed as an integer or fraction; a numb…

allows the x-values to be ANY points in the interval, includin…

a relative maximum value in a polynomial function; the y value…

value or distance away from zero

rational

number that can be expressed as an integer or fraction; a numb…

continuous graph

allows the x-values to be ANY points in the interval, includin…

The Additive Property of Equality

The Multiplicative Property of Equality

The Commutative Property

The Associative Property

If a=b, then a+c=b+c... You can add or subtract the same quantit…

If a = b, then ac = bc... You can multiply (or divide) both side…

The order that you add or multiply doesn't matter... a+b = b+a…

The way in which numbers are grouped does not change their sum…

The Additive Property of Equality

If a=b, then a+c=b+c... You can add or subtract the same quantit…

The Multiplicative Property of Equality

If a = b, then ac = bc... You can multiply (or divide) both side…

Raising a negative number to a power

Factoring ax²+bx+c

Factoring by grouping

Canceling out opposites

When raising a negative number to a power always put the negat…

If both terms are opposite signs they can be crossed out and r…

Raising a negative number to a power

When raising a negative number to a power always put the negat…

Factoring ax²+bx+c

Quadratic formula (Find the Roots)

Completing the square

Discriminant (describe the roots)

Sum and product of roots

the quadratic formula is x equals negative b plus or minus the…

if the discriminant is 0, the roots are real, rational and equ…

The sum of the roots is negative b divided by a.... The product o…

Quadratic formula (Find the Roots)

the quadratic formula is x equals negative b plus or minus the…

Completing the square

Raising a negative number to a power

Factoring by grouping

Canceling out opposites

Factoring out a -1

When raising a negative number to a power always put the negat…

If both terms are opposite signs they can be crossed out and r…

To factor out a -1, remove the negative and change the signs o…

Raising a negative number to a power

When raising a negative number to a power always put the negat…

Factoring by grouping

Rational Number

Irrational Number

Expression

Equation

- Any number that can be represented as a fraction... - Terminati…

- Any number that cannot be represented as a fraction... - Non Te…

A mathematical phrase that contains operations, numbers, and/o…

A mathematical sentence that contains an equals sign.

Rational Number

- Any number that can be represented as a fraction... - Terminati…

Irrational Number

- Any number that cannot be represented as a fraction... - Non Te…

rational number

irrational number

commutative property

associative property

a number that can be written as a fraction

a number that cannot be written as a fraction

numbers can be added or multiplied in any way and the answer s…

the way in which numbers are grouped does not change their sum…

rational number

a number that can be written as a fraction

irrational number

a number that cannot be written as a fraction

Irrational Numbers

Rational Number

Integers

Whole numbers

*decimals do not end or repeat... *square roots that are not perf…

*Decimals end or repeat... *fractions that do not have a denomina…

positive or negative, and 0

{0,1,2,3,4,...}

Irrational Numbers

*decimals do not end or repeat... *square roots that are not perf…

Rational Number

*Decimals end or repeat... *fractions that do not have a denomina…

Linear Regression

Exponential Regression

Mean

Median

Stat- Edit- L1 and L2 ... Stat- Calc- LinReg (#4)

Stat- Edit- L1 and L2... Stat- Calc- ExpReg (#0)

Only a good measure of center for symmetric data

(middle) Better measure of center for skewed data or data with…

Linear Regression

Stat- Edit- L1 and L2 ... Stat- Calc- LinReg (#4)

Exponential Regression

Stat- Edit- L1 and L2... Stat- Calc- ExpReg (#0)

"a" in y = a•b^x

"b" in y = a•b^x

"b" in y = mx + b

"m" in y = mx + b

the variable used to represent the initial amount in an expone…

the variable used to represent the growth rate in an exponenti…

the variable used to represent the y-intercept in a linear fun…

the variable used to represent the slope of a line

"a" in y = a•b^x

the variable used to represent the initial amount in an expone…

"b" in y = a•b^x

the variable used to represent the growth rate in an exponenti…

Irrational Numbers

Rational Number

Integers

Whole numbers

*decimals do not end or repeat... *square roots that are not perf…

*Decimals end or repeat... *fractions that do not have a denomina…

positive or negative, and 0

{0,1,2,3,4,...}

Irrational Numbers

*decimals do not end or repeat... *square roots that are not perf…

Rational Number

*Decimals end or repeat... *fractions that do not have a denomina…

"a" in y = a•b^x

"b" in y = a•b^x

"b" in y = mx + b

"m" in y = mx + b

the variable used to represent the initial amount in an expone…

the variable used to represent the growth rate in an exponenti…

the variable used to represent the y-intercept in a linear fun…

the variable used to represent the slope of a line

"a" in y = a•b^x

the variable used to represent the initial amount in an expone…

"b" in y = a•b^x

the variable used to represent the growth rate in an exponenti…

rational

continuous graph

maximum turning point

absolute value

number that can be expressed as an integer or fraction; a numb…

allows the x-values to be ANY points in the interval, includin…

a relative maximum value in a polynomial function; the y value…

value or distance away from zero

rational

number that can be expressed as an integer or fraction; a numb…

continuous graph

allows the x-values to be ANY points in the interval, includin…

rational

continuous graph

maximum turning point

absolute value

number that can be expressed as an integer or fraction; a numb…

allows the x-values to be ANY points in the interval, includin…

a relative maximum value in a polynomial function; the y value…

value or distance away from zero

rational

number that can be expressed as an integer or fraction; a numb…

continuous graph

allows the x-values to be ANY points in the interval, includin…

term

variable

coefficient

constant term

A number, a variable, or a combination of a number and a varia…

A letter that represents a value that can change or vary

A number multiplied by a variable in an algebraic expression.

A value that does not change; an integer without a variable in…

term

A number, a variable, or a combination of a number and a varia…

variable

A letter that represents a value that can change or vary

Sequence

f(1) or a₁

previous term

recursive formulas

an ordered list of numbers... Formally defined as a function tha…

1st term

terms of a sequence are found by performing operations on prev…

Sequence

an ordered list of numbers... Formally defined as a function tha…

f(1) or a₁

1st term

"a" in y = a•b^x

"b" in y = a•b^x

"b" in y = mx + b

"m" in y = mx + b

the variable used to represent the initial amount in an expone…

the variable used to represent the growth rate in an exponenti…

the variable used to represent the y-intercept in a linear fun…

the variable used to represent the slope of a line

"a" in y = a•b^x

the variable used to represent the initial amount in an expone…

"b" in y = a•b^x

the variable used to represent the growth rate in an exponenti…

Linear Regression

Exponential Regression

Standard Deviation

Shape: Symmetric

Stat- Edit- L1 and L2 ... Stat- Calc- LinReg (#4)

Stat- Edit- L1 and L2... Stat- Calc- ExpReg (#0)

small- data close together... large- data spread out

The data on the graph is evenly spaced out.

Linear Regression

Stat- Edit- L1 and L2 ... Stat- Calc- LinReg (#4)

Exponential Regression

Stat- Edit- L1 and L2... Stat- Calc- ExpReg (#0)