algebra one math vocabulary. absolute value a number’s distance from zero on a number line....
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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