Algebra Defs, Formulas, & Properties

Front 1

Names/meanings for: X

Back 1

Domain, Independent Variable, Time, Input

Hint 1

Women have X chromosomes

Front 2

Names/meanings for: Y

Back 2

Range, Dependent Variable, Output

Hint 2

Men have Y chromosomes

Front 3

Functions

Back 3

Can't have repeating X values

Hint 3

Vertical line test (vertical line can only cross function once)

Front 4

Corrdinate values

Back 4

(X,Y)

Hint 4

X comes before Y in the alphabet

Front 5

Axis labels

Back 5

X axis-horizontal axis
Y axis-vertical axis

Hint 5

X goes left to right
Y goes up and down

Front 6

Slope/Rate of Change

Back 6

Change in Y's/change in X's
Vertical change/Horizontal change
(Y2-Y1)/(X2-X1)

Hint 6

Leans to right/goes up-Positive;
Leans to left/goes down-Negative;
Straight up and down-No slope;
Goes left to right-zero slope

Front 7

Linear Function

Back 7

y=mx+b;
m is slope;
b is y-intercept;
graph is a straight line

Hint 7

Line is first four letters of Linear

Front 8

Quadratic Function

Back 8

y=ax²+bx+c;
+a=U shaped;
-a=n shaped;
a=big whole #-U gets more narrow;
a=small fraction #-U gets wider

Hint 8

U in qUadratic describes the shape of the graph

Front 9

Absolute Value

Back 9

y=|x|;
any # for x - or + comes out positive;
ex: y=|-4| =4

Hint 9

V in Value describes the shape of the graph

Front 10

Y Intercept

Back 10

Where the function crosses the y-axis.
(0,#);
x is always 0

Hint 10

called "b" in slope intercept form

Front 11

X Intercept

Back 11

Where the function crosses the x-axis.
(#,0);
y is always 0

Hint 11

Also known as roots or solutions

Front 12

≥

Back 12

Greater than or Equal to:
denoted by a solid point & arrow going right on # line
--or--
denoted by a solid line & shading above the line on a graph

Hint 12

left side is bigger than or = to the right side

Front 13

Percents

Back 13

Part/Whole= %/100

Hint 13

move decimal 2 places to the left

Front 14

>

Back 14

Greater than:
denoted by an open circle & arrow going right on # line
--or--
denoted by dotted line and shading above line on graph

Hint 14

left side has to be bigger than the right side

Front 15

<

Back 15

Less than:
denoted by an open circle & arrow goin left on # line
--or--
denoted by dotted line and shading below line on graph

Hint 15

Left side has to be smaller than the right side

Front 16

≤

Back 16

Less than or Equal to:
denoted by solid point & arrow going left on # line
--or--
denoted by solid line and shading below line on graph

Hint 16

Left side has to be smaller than or = to the right

Front 17

X^a * X^b

Back 17

X^a+b

Hint 17

When you x your letters
you + your exponents.

Front 18

(X^a)/(X^b)

Back 18

X^(a-b)

Hint 18

When you / your letters
you - your exponents.

Front 19

(X^a)^b

Back 19

X^(a*b)

Hint 19

When you ^ a power to another power
you x your exponents.

Front 20

a less than b

Back 20

b-a

Hint 20

Less than=taken away from;
you have to have b before you can take a away from it

Front 21

Associative property

Back 21

(a+b)+c=a+(b+c)
(a*b)*c=a*(b*c)

Hint 21

You can associate with people around you without moving.

Front 22

Commutative property

Back 22

a+b=b+a
a*b=b*a

Hint 22

You commute to and from school.

Front 23

Distributive property

Back 23

a(b+c)=a*b+a*c

Hint 23

You have to distribute the a to everything in the parenthesis.
"Share the Love"

Front 24

When you are given a table with info. & you have functions as answer choices
(Also works when given any two points or coordinates.)

Back 24

1. Put table in STAT function & calculate either linear regression or quadratic regression
2. Put each function in y= and push 2nd Table and compare. (Equations must be in y=format)

Hint 24

STAT-EDIT-put x's under L1 & y's under L2-STAT-→-CALC-4 Linear Regress. or 5 Quadratic Regress.

Front 25

a²+b²=c²

Back 25

Pythagorean Thereom;
Can be used anytime you have a right △ and are missing only one side;
(Area of □ with side length a + Area of □ with side length b=Area of □ with side length c)

Hint 25

c=hypotenuse (always the longest side);
a+b>c;
a<c & b<c

Front 26

Prefixes implying numerical values

Back 26

mono-1;
bi-2;
tri-3;
quad-4;
penta-5;
hexa-6;
hepta-7;
octa-8;
nona-9;
deca-10

Front 27

Parent Function

Back 27

Linear y=x;
Quadratic y=x²;
Absolute Value y=|x|;
Square Root y=√x

Hint 27

The most basic forms of the function. Has no additional numbers to change the shapes and directions. It is your "starting point" for each type of function.

Front 28

Point of Intersection

Back 28

(x,y) where the x and y value solve each equation. They both make each equation true when the are plugged in and the equations are solved.

Hint 28

Where two lines touch.
Put each equation in Y=--
Graph--2nd--Trace--5 Intersect--Enter--Enter--Enter

Front 29

Volume of a Cube

Back 29

V=s³

Hint 29

V=l*w*h, but since all the side are the same for a cube then it is
V=s*s*s

Front 30

Parallel Lines

Back 30

The slopes are equal.
Ex:y=2x+5 and y=2x-7;
The slope is m=2 for both equations.
Both lines are leaning in the same direction.
# of Solutions: None

Hint 30

Two lines that never touch.
Ex: railroad tracks

Front 31

Perpendicular Lines

Back 31

Two lines that intersect at one point so that they form 90 degree angles where they cross. Looking like this: +;
The slopes are negative reciprocals of each other.
Ex: y=2/3x+5 & y=-3/2x+5;
The slopes are m=2/3 & m=-3/2
# of Solutions: 1

Hint 31

Take the first slope, flip it, and make it negative.
They form a "cross" when they intersect.

Front 32

Identical Lines

Back 32

Two lines that look the same.
Ex: y=3x-4 & y=3x-4;
These lines touch everywhere.
# of Solutions: infinitely many

Hint 32

When they are graphed you can only see one of them because they are on top of each other.

Front 33

Scale Factor

Back 33

Where you are going/
Where you are coming from

A # in fraction form comparing the same sides of 2 similar shapes expressing the amount of dilation that occured.

Hint 33

How much a shape shrinks or blows up.
If it shrinks, the small # is on top. ex: 1/2, 2/7, 3/8;
If it blows up, the big # is on top. ex: 2/1, 7/2, 8/3

Front 34

Transformation

Back 34

Sliding a shape on the coordinate grid or graph.

Hint 34

Translate=slide
(up ▲, down ▼, left ◀, or right ▶)

Front 35

Rotation

Back 35

Rotate a shape on the coordinate grid or graph.

Hint 35

To turn clockwise or couterclockwise. Spin

Front 36

Dilation

Back 36

Dilate a shape from it's original size.
* the coordinates by a scale factor.
Ex: Δ with points (1,1),(4,6),(8,-8);
Dilation by scale factor of 2:
2*{(1,1),(4,6),(8,-8)}=
{(2,2),((8,12),(16,-16)};
Dilation by a scale factor of 1/2:
(1/2)*{(1,1),(4,6),(8,-8)}=
{(1/2,1/2),(2,3),(4,-4)}

Hint 36

Reduce or enlarge a shape by a given scale factor.

Front 37

Reflection

Back 37

Reflect a shape on a coordinate grid or graph across a given axis.
The points must cross the axis of reflection no matter which side of the axis it is on.

Hint 37

Flip across the y-axis=like turn the page of a book.
Flip across the x-axis=like fliping over the page of a roladex.(upside down or right side up)

Front 38

Surface Area of a Prism

Back 38

Find the Area of all the surfaces in the prism and add them up.
Rectangular prism:
contains 6 ∓'s
2 (left & right sides)+
2 (front & back sides)+
2 (top & bottom sides);
Triangular prism:
contains 2 ∆'s & 3 ∓'s

Hint 38

Prisms have two eqaul bases. The shape of those bases determine the name of the prism. The lateral faces are all made up of rectangles.
Rectangular Prism=2 ∓ bases;
Triangular Prism=2 ∆ bases;
Cylindrical Prism=2 o bases

Front 39

Multiplying Polynomials

Back 39

When multipying polynomials: the # of terms in the 1st polynomial times the # of terms in the 2nd polynomial will give you the # of terms in your answer.
Ex: (2x+3)(5x-1)=10x²-2x+15x-3;
*This helps you not to forget a step.
Remember to distribute and then collect like terms.
(Always keep negatives with the # that it's in front of)

Hint 39

(1 term)(1 term)=1 term;
(1 term)(2 terms)=2 terms;
(1 term)(3 terms)=3 terms;
(2 terms)(2 terms)=4 terms;
(2 terms)(3 terms)=6 terms;
etc.

Front 40

Exponents

Back 40

x² is the same as x²/1;
x^-2 is the same as 1/(x²);
or
1/(x^-2)is the same as x²;
The negative exponent means that term must be moved to the opposite side of the fraction.

Hint 40

Negative exponent on top means it goes on the bottom.
Negative exponent on the bottom means it goes on the top.

Front 41

Measuring using centimeters:

Back 41

There are 3 different sized lines.
The longest lines are the whole # centimeter marks.
The middle length lines are the 1/2 centimeter marks.
The shortest lines are the 1/10 centimeter marks.

Hint 41

The # of the same sized lines in between each whole centimeter is the # of piece each centimeter is cut into.
Ex: 1/10 centimeters=there are 10 little lines in between each whole centimeter.

Front 42

Measuring using inches:

Back 42

There are 4 different sized marks.
The longest lines are the whole # inch marks.
The 2nd longest lines are the 1/2 inch marks (in the middle, between each inch).
The 3rd longest lines are the 1/4 inch marks.
The shortest lines are the 1/8 inch marks.

Hint 42

The # of same sized lines in between each inch are the # of pieces each inch is cut into.
Ex: 1/4 inch=there are 4 lines cutting each inch into 4 equal pieces.