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Algebra One
Math Vocabulary
Absolute Value
A number’s distance from zero on a number line.
Examples:
4  4  4
3 3
3  3
3
8  8  8
Algebraic expression
A mathematical phrase that can include numbers, variables,
and operation symbols
Examples:
1 3 1 x
  
2 x 2 3
3x2 + 2y + 7xy + 5
Evaluate the algebraic expression
3x 2  2 if x = 2:
3  2   2  3(4)  2  10
2
3x + 12 – x + 2
or 2x + 14
Write an algebraic expression
For the sum of six and a number:
6+x
Coefficient
The numerical factor of a variable term
A number that multiplies a variable in a term
1
cd
2
3x  4 y  2 z
a  1a
Examples:
The coefficients are in red
coefficient
5x
2
4m  .6n
exponent
2x
3
variable
Combinations
An 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, B, D} {A, C, D}
{A, C, E}
{A, D, E}
{B, C, D}
{B, C, E}
{B, D, E}
{C, D, E}
Constant
A term that has no variable factor
Constant
a3
Examples
12
2 x  3x  5
2
Constant
Constant
2x  5
Coefficient
Variable
Constant
Coordinate Plane
A plane formed by
a horizontal number line (x-axis)
and a vertical number line (y-axis)
Example:
Distance Formula
The distance d between any two points  x1 , y1  and  x2 , y2 
is
2
2
d   x2  x1    y2  y1 
Examples
The distance between
(-3,2) and (0,-2) is:
d  ((3)  0)2  (2  (2))2
 32  (4) 2
(-3,2)
 9  16
5
 25
4
3
(0,-2)
5
Domain and Range
Domain: The set of all x-coordinates in the ordered
pairs (x,y) of a relation
Range: The set of all the y-coordinates in the ordered
pairs (x,y) of a relation
Examples
Range: {2.4,6,8}
{(1, 2), (2, 4), (3, 6), (4,8)}
Domain: {1,2,3,4}
Domain:
{1,0,-1}
x
y
1
1
0
0
-1
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 x  3  17
2 x  20
x  10
5 x  2 x  18
3x  18
x  6
3( x  1)  15
3x  3  15
3x  12
x4
Equations
(graphing)
The graph of an equation contains ordered pairs
that make the equation true
Examples
x y 2
y  x3
x
y=x-3
2
0
-3
1
1
3
0
-2
4
-2
-5
x
Y=2-x
0
Equations
(slope-intercept)
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
Examples
y  x3
y  2x  3
y  x  2
slope = -1
y-int = 2
slope = 1
y-int = -3
slope = 2
y-int = -3
Factoring
To write an expression (or number) as a product of two
or more expressions (or numbers )
a 2  b2  (a  b)(a  b)
Factor tree
Examples
Factor x2 + 3x + 2
Factor
3x+6 = 3(x+2)
x2-2x-15 =
(x-5)(x+3)
(x + 1)
(x + 2)
(x + 1)(x + 2)
Function notation
A way to write an equation or rule that is a function,
use the symbol f (x) in place of y
f(x) is read “f of x” and means that the value of the
function depends on the value of x
f(x) is the output of the function with input x
(Given an x, you get f(x) or y)
f(x) = x+3
f(2) = 2+3= 5
when x=2, y=5
(2,5)
Examples
y  3 x  f ( x)  3 x
f(x) = x2
f(-3)=(-3)2
=9
Inequalities
(number line)
The graph of a mathematical sentence showing the
relationship between quantities that are not equal,
using <, >, <, >, or 
Examples
x2
x2
x4
x  2
Inverse
Operations that undo each other
x and - x are additive inverses
x and
1
(x  0) are multiplicative inverses
x
Examples
Addition 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=5–3
x=2
Irrational Numbers
A 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
2  1.414213562...
Rational Numbers
Irrational
numbers
Integers
.01011011101111...
Whole
numbers
Natural
numbers
 3.14159265358979323846264338327950288419716939937510582...
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
x  2y  5
by eliminating one of the variables
x  2y  3
by addition/multiplication
2x
8
Examples
x4
4  2y  5
2y 1
1
y
2
 1
 4, 
 2
2 x  3 y  2
x  2 y  13
2 x  3 y  2
2 x  4 y  26
}
2 x  3 y  2
2 x  4 y  26
7 y  28
y4
 5, 4 
2 x  4(4)  26
2 x  16  26
2 x  10
x5
Linear systems:
Substitution
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
Example
3 x  y  12  y  12  3 x
2x  3y  1
2 x  3(12  3 x)  1
2 x  36  9 x  1
7 x  35  x  5
y  12  3 x
x5
y  12  3(5)
y  12  15  3
( x, y )  (5, 3)
Midpoint formula
The midpoint of a line segment with endpoints
Ax1 , y1  and B( x2 , y2 )
is
 x  x y  y2 
M  1 2 , 1

2 
 2
Examples
A: (-4,3) and B(2,-5)
A
B
 4  2 3  (5) 
M 
,

2
2


 2 2 
 ,

2
2


=  1, 1
Permutations
An arrangement of elements in which
order is important
Examples
MATH: 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 names
Examples
Not a polynomial
2  3x
x
Monomials :  3x, 2a 2
Binomials : 3x  2,  a 2  4a
Trinomials :  3x  2 y  6 z, 2a 2  a  1
Polynomials :  3x  4w  2 y  6 z, - a 4  a3  2a 2  a  1
Pythagorean Theorem
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:
a 2  b2  c2
5
3
13
5
4
32  42  52
9  16  25
12
52  122  132
25  144  169
15
17
8
82  152  17 2
64  225  289
Quadratic Equation
An equation of degree two: ax2 + bx + c = 0
To solve:
ax 2  bx  c  0
Example Solve : x 2  2 x  5  0
b  b2  4ac
x
2a
a  1, b  2, c  5
2  22  4(1)(5) 2  4  (20)
x


2(1)
2
2  24 2  2 6

 1  6
2
2
Quadratic formula
Discriminant
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
b  b  4ac
x
2a
Discriminant: b  4ac
Examples
x2  2 x  5  0
x2  2 x  5  0
D  22  4(1)(5)
D  24
24  0, so 2 real roots
D  22  4(1)(5)
D   16
16  0, so 2 non-real roots
Ratio, Proportion
Ratio: 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
1 4

3 12
is a proportion because 12x1 = 3x4
2
7 do not form a proportion
and
5
15
because 15x2  5x7
Scale Factor
The ratio used to enlarge or reduce
similar figures
Examples
Drawings: if the Eiffel Tower
is 1000 feet tall and the drawing of it
was 1 foot tall, the scale factor would be
1
1000
Models: if a car is 204” in length and
the length of a model of the car is 12” long,
1
the scale factor would be 12

204 17
Real Number
A number that is either rational or irrational.
Real numbers include natural numbers, whole numbers,
integers, rational numbers and irrational numbers
Examples
Real Numbers
Rational Numbers
Integers
4
Whole
numbers
Natural
numbers
2
3
1.5
0
2
Irrational
numbers
3
Slope
A 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
Slope = rise
run
(-2,3)
=
vertical change =
horizontal change
y 2  y1
x2  x1
The symbol for slope is m
m
rise = -2
run
=4
where x1  x2
rise 2
1


run
4
2
y2  y1
3  1 2
1
m



x2  x1 2  2 4
2
Subset
A set whose elements are all elements of another set
A set contained within a another set
The symbol for subset is 
Examples
The set {a,b,c} has subsets:
{a}, {b}, {c}, {ab}, {ac}, {Whole numbers}  {Integers}
{bc},{a,b,c} and { }
The set of Rational numbers
is a subset of the set of Real numbers,
All Rational numbers are Real numbers
{Rationals}  {Reals}