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Flashcards in memorize Deck (77)
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1

if your system of equations has no solution...,

it will graph as two parallel lines because parallel lines never intersect

2

if your system of equations has one solution...,

the two equations will graph as two lines intersecting at a single point because two straight lines have only one intersection

3

if your system of equations has infinitely many solutions...,

it will graph as a single line because their graphs are the same line

4

integers

whole numbers (negative or positive)

5

rationals

fractions, anything expressable as a ratio of integers

6

real #s

integers plus rationals plus special numbers like roots and pi

7

arithmetic sequence

each term equal to previous term PLUS x

8

geometric sequence

each term equal to previous term TIMES x

9

factor

the factors of a number divide into that number without a remainder

10

multiples

the multiples of a number are divisible by that number without a remainder

11

how to find part of a percent of something

part = (percent/100) * whole

12

average of numbers(mean)

sum of terms/number of terms

13

average speed

total distance/total time

14

sum

average * number of terms

15

mode

value in the list that appears most often

16

median

middle value in the list (must be sorted)

17

Fundamental Counting Principle

If an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N*M ways.

18

Probability

probability= # desired outcomes / #total outcomes

19

x^a*x^b =

x^(a+b)

20

(x^a)^b =

x^(a*b)

21

x^0 =

1

22

x^a / x^b =

x^(a-b)

23

(xy)^a =

x^a * y^a

24

rootxy =

rootx * rooty

25

1 / x^b =

x^(-b)

26

(-1)^n =

1 is positive if 'n' is even
1 is negative if 'n' is odd

27

Difference of two squares

a^2 - b^2 = (a+b)(a-b)

28

Distance formula

root[ (x2-x1)^2 + (y2-y2)^1 ]

29

Mid point formula

(x,y) = ( x1+x2 / 2 , y1+y2/2 )

30

slope

y2-y1 / x2-x1 = rise/run

31

Intersecting Lines

Opposite angles are equal. Each pair of angles along the same line add to 180 degrees.

\ a /
\ /
\ /
\ /
b \ / b
/ \
/ \
/ \
/ a \

32

Parallel Lines

Eight angles are formed when a line crosses two parallel lines. The four big angles (a) are equal, and the four smaller angles (b) are equal.

/
___ a_/_ b____
b /a
/
/
___ a_ /_b____
b / a
/

33

pythagorean theorem

a^2 + b^2 = c^2

34

30-60-90 triangles

Hypotenuse (90 degrees): 2x
side across from 60 degrees: x root 3
side across from 30 degrees: x

35

45-45-90 triangles

hypotenuse (90 degrees): x root 2
side across from 45 degrees: x

36

area of a triangle

A = 1/2 * b * h
*works for all triangles

37

equilateral triangles

triangle with three EQUAL sides, all three angles measure 60 degrees each

38

Isosceles Triangle

Has two equal sides, the angles opposite these two equal sides are equal. (To find the third angle, add these two and subtract from 180 degrees, because a triangle is always 180 degrees).

39

Similar Traingle

Two or more triangles are similar if they have the same shape. The corresponding angles are equal, and the corresponding sides are in proportion. For example, if the sides of one triangle are 3-4-5 and the other are 6-8-10 the ratio is 2 to 1 but the angle measurements would remain the same.

40

Area of a circle

A = pi * r^2

41

Circumference of a circle

C = 2 * pi * r

42

How many degrees in a circle?

360

43

How to find Length of Arc

(n degrees/360 degrees) * (2*pi*r)

44

How to find area of a sector

(n degrees/360 degrees) * (pi*r^2)

45

Area of a square

A = bh

46

Area of a rectangle

A = bh

47

Area of a parallelogram

A = length * HEIGHT - not width ************************** the line going through the middle is the height.
____
/ l /
/ l h / w
/_ l__/
L
You do not use the length to figure out the area of a parallelogram.

48

Volume of a rectangular solid

V = length * width * height

49

Volume of a right cylinder

V = pi * radius^2 * height

50

less or greater than or equal to uses a ___________ dot on a number line and a __________ line on a graph

shaded in, solid

51

less or greater than used a _________ dot on number line and a _______ line on graph

open circle (not shaded in), dotted

52

only time a system of inequalities has no solution is when...,

the boundary lines are parallel and the shading is in opposite directions

53

1 cup = _____ oz

8 fl oz

54

1 pint = ____ cups

2 cups

55

1 quart = ____ pints

2

56

1 quart = ____ cups

4

57

2 pints = _____ cups

4

58

1 gallon = _____ quarts

4

59

1 pound = ______ ounces

16

60

1 ton = _____ pounds

2000

61

1 yard = _____ feet

3

62

1 mile = _____ feet

5280

63

1 gallon = _____ quarts

4

64

1 gallon = ____ pints

8

65

1 quart = ____ pints

2

66

1 gallon = _____ cups

16

67

1 pint = ____ cups

2

68

Distance =

rate * time

69

68-95-99.7 Rule

If you take the mean and go one standard deviation above and below the mean you will get 68% of the data.
If you take the mean and go two standard deviations above and below the mean you will get 95% of the data.
If you take the mean and go three standard deviations above and below the mean you will get 99.7% of the data

70

parallel lines have _______ slope

the same

71

perpendicular lines have ____________ lines

opposite reciprocal
(flip the number and change the sign - positive or negative)

72

sine of an angle

opposite/hypotenuse

73

cosine of an angle

adjacent/hypotenuse

74

tangent of an angle

opposite/adjacent

75

cotangent of an angle

adjacent/opposite
goes with tangent

76

secant of an angle

hypotenuse/adjacent
goes with cosine

77

cosecant of an angle

hypotenuse/opposite
(goes with sine)