Algebra One Math Vocabulary

Absolute ValueA number’s distance from zero on a number line.

Examples:

3

3 33 3

8 8 8

4 4 4

Algebraic expressionA mathematical phrase that can include numbers,

variables, and operation symbolsExamples:

3x2 + 2y + 7xy + 53x + 12 – x + 2

or 2x + 14

Evaluate the algebraic expression if x = 2:23 2x

23 2 3( 2 12 4) 0

Write an algebraic expression For the sum of six and a number:

6 + x

1 3 1

2 2 3

x

x

CoefficientThe numerical factor of a variable term

A number that multiplies a variable in a term

Examples:The coefficients are in red

3 4 2x y z

1a a

25x

1

2cd

4 .6m n

32x

coefficient

variable

exponent

CombinationsAn arrangement of the elements of a set

without regard to order

Examples

In how many different ways can three letters be chosen from the letters A, B, C, D, and E?

( The order of the three letters is not important:so, {A,B,C} and {C,B,A} are the same)

{A, B, C} {A, B, E} {A, C, E} {B, C, D} {B, D, E}

{A, B, D} {A, C, D} {A, D, E} {B, C, E} {C, D, E}

ConstantA term that has no variable factor

Examples

2 5x Coefficient

VariableConstant

22 3 5x x Constant12

Constant

3a

Constant

Coordinate PlaneA plane formed by

a horizontal number line (x-axis) and a vertical number line (y-axis)

Example:

Distance Formula

Examples

The distance between (-3,2) and (0,-2) is:

2 2

2 2

( ) ( )

2 ( 2)

4

1

(

( )

25

3 0

3

5

6

)

9

d

(-3,2)

(0,-2)

4

3

5

1 1,x y 2 2,x y

2 2

2 1 2 1d x x y y

The distance d between any two points and is

Domain and Range Domain: The set of all x-coordinates in the ordered

pairs (x,y) of a relationRange: The set of all the y-coordinates in the

ordered pairs (x,y) of a relation

Examples

{( , ), ( , ), ( , ), (21 2 3 44 6 ,8)}

Domain: {1,2,3,4}

Range: {2.4,6,8}

x y

1 1

0 0

-1

1

Domain:{1,0,-1}

Range:{1,0}

Equations(solving)

An equation is a mathematical sentence containing an equal sign

To solve an equation, find a value for the variable that makes the sentence true

Examples

2 3 17

2 20

10

x

x

x

3( 1) 15

3 3 15

3 12

4

x

x

x

x

5 2 18

3 18

6

x x

x

x

Equations(graphing)

The graph of an equation contains ordered pairs that make the equation true

Examples

2x y

3y x x Y=2-x

0 2

1 1

-2 4

x y=x-3

0 -3

3 0

-2 -5

The slope-intercept form of an equation is y = mx + b Where m is the slope of the line and b is its y-intercept

Equations(slope-intercept)

2y x 3y x 2 3y x Examples

slope = -1y-int = 2

slope = 1y-int = -3

slope = 2y-int = -3

FactoringTo write an expression (or number) as a product of

two or more expressions (or numbers )

Examples

Factor tree

Factor

3x+6 = 3(x+2)

x2-2x-15 =(x-5)(x+3)

2 2 ( )( )a b a b a b

Factor x2 + 3x + 2

(x + 1)

(x + 2)

(x + 1)(x + 2)

Function notationA way to write an equation or rule that is a function,

use the symbol f (x) in place of yf(x) is read “f of x” and means that the value of the

function depends on the value of xf(x) is the output of the function with input x

(Given an x, you get f(x) or y)

Examplesf(x) = x+3f(2) = 2+3= 5

when x=2, y=5(2,5)

f(x) = x2

f(-3)=(-3)2 = 9

3 ( ) 3y x f x x

Inequalities(number line)

The graph of a mathematical sentence showing the relationship between quantities that are not equal,

using <, >, <, >, or

Examples

2x

4x

2x

2x

Inverse Operations that undo each other

ExamplesAddition and subtraction are inverse operations

(undo adding 3 by subtracting 3) Multiplication and division are inverse operations

(undo multiplying by 2 by dividing by 2)

To solve an equation:x + 3 = 5

x + 3 – 3 = 5 – 3x = 2

1 and ( 0) are multiplicative inversesx x

x

and - are additive inversesx x

Irrational NumbersA number that cannot be written

as a ratio of two integers Numbers in decimal form that

are non-terminating and non-repeating

Examples

Real Numbers

Rational NumbersIrrational numbers

Integers

Whole numbers

Natural numbers

3.14159265358979323846264338327950288419716939937510582...

2 1.414213562...

.01011011101111...

Line of best fit A straight line that best fits the data on a scatter

plot(This line may pass through some, none,

or all of the points)

Examples

Linear systems:Elimination

A method of solving a system of equations with two variables to reduce it to an equation

with only one variable by eliminating one of the variables

by addition/multiplication Examples

2 3 2

2 13x

x y

y

2 3 2

2 4 26x

x y

y

7 28

2 3 2

2 4 2

6

4

x y

y

x y

y

2 4( ) 26

2 16 26

2 1

4

0

5

x

x

x

x

5,4

}

Linear systems:Substitution

Example12 3

(12

3 12

2 3 1

2 3 1

2 36 9 1

7 35

3 )

5

y x

y

x

x y

x

x

x x

x x

12 3( )

12 15 3

( , )

12 3

(5, 3)

5

5

x

y

y

y

y x

x

To solve a system by substitution, solve one equation for one variable in terms of the other,

Substitute into the other equation to obtain an equation with only one variable

Midpoint formulaThe midpoint of a line segment with endpoints

and

is

Examples

11 , yxA ),( 22 yxB

1 2 1 2,2 2

x x y yM

A

B

A: (-4,3) and B(2,-5)

3 ( 5),

2 2

2 2 ,

2 2

= 1,

2

1

4M

PermutationsAn arrangement of elements in which

order is important

ExamplesMATH: how many ways can two letters be arranged from the four letters M, A, T, and H?

12 possible permutations:MA, AM, MT, TM, MH, HM, AT, TA, AH, HA, TH, HT

CAT: How many permutations are there of the letters C A T ?

6 possible permutations:CAT, CTA, ATC, ACT, TAC, TCA

Polynomial An expression that is the sum (or difference) of

more than one term, each of these having variables with whole number exponents

(A quotient with a variable in the denominator is not a polynomial)

Some polynomials have special namesExamples

2: 3 , 2Monomials x a2: 3 2, 4Binomials x a a

2: 3 2 6 , 2 1Trinomials x y z a a 4 3 2: 3 4 2 6 , - 2 1Polynomials x w y z a a a a

2 3x

x

Not a polynomial

Pythagorean Theorem

2 2 2a b c

In a right triangle, the sum of the squares of the length of the legs is equal to the square of the length

of the hypotenuse:

12

513

2 2 2 5 12 13

25 144 169

15

8

172 2 2 8 15 17

64 225 289

53

42 2 2 3 4 5

9 16 25

Quadratic EquationAn equation of degree two: ax2 + bx + c = 0

Example

2 0ax bx c 2 4

2

b b acx

a

2

2

: 2 5 0 1, 2, 5

2 2 4(1)( 5) 2 4 ( 20)

2(1) 2

2 24 2 2 6 1 6

2 2

Solve x x a b c

x

To solve:

Quadratic formulaDiscriminant

Examples

2 4

2

b b acx

a

2: 4Discriminant b ac

The part of the quadratic formula that is under the radical:

It tells the nature of the roots: how many and whether they are real (D>0) or not (D<0)

2

2

2 5 0

2 4(1)(5)

16

16 0, so 2 non-real roots

x x

D

D

2

2

2 5 0

2 4(1)( 5)

24

24 0, so 2 real roots

x x

D

D

Ratio, ProportionRatio: A comparison of two numbers by

division.Proportion: An equation stating

that two ratios are equal.If the cross products of the two ratios are

equal, then the pair forms a proportion

Examples

2 7 and

5 15

1 4

3 12 is a proportion because 12x1 = 3x4

do not form a proportion because 15x2 5x7

Scale FactorThe ratio used to enlarge or reduce

similar figures

Examples

1

1000

Drawings: if the Eiffel Tower is 1000 feet tall and the drawing of it was 1 foot tall, the scale factor would be

Models: if a car is 204” in length and the length of a model of the car is 12” long,the scale factor would be 12 1

204 17

Real NumberA number that is either rational or irrational. Real numbers include natural numbers, whole

numbers, integers, rational numbers and irrational numbers

ExamplesReal Numbers

Rational NumbersIrrational numbers

Integers

Whole numbers

Natural numbers

3

2

4

0

2

3 1.5

SlopeA measure of the steepness of a line

The ratio of the vertical change (rise) to the horizontal change (run)

The change in y over the change in x

(-2,3)

rise = -2

run= 4

The symbol for slope is m

2 1

4 2

risem

run

2 1

2 1

3 1 2 1

2 2 4 2

y ym

x x

change horizontal

change vertical

12

12

xx

yy

1 2x xrise

runSlope = = = where

SubsetA set whose elements are all elements of another

setA set contained within a another set

The symbol for subset is Examples

The set {a,b,c} has subsets:{a}, {b}, {c}, {ab}, {ac},

{bc},{a,b,c} and { }

The set of Rational numbersis a subset of the set of Real numbers,All Rational numbers are Real numbers

{ } {Reals}Rationals

{ } { }Whole numbers Integers