Math: Facts & Formulas Flashcards
to learn formulas for determining area and volume
1
Q
Area of a Regular Polygon
A
nx/2 (side length times apothem)/2
2
Q
(number of sides x length of one side x apothem)/2
A
Area of a Regular Polygon
3
Q
6.4
diameter
A
d = 2r (radius)
4
Q
6.3
2 x radius =
A
diameter
5
Q
6.4
circumference
A
2 x π x radius
6
Q
6.4
2 x π x r
A
circumference
7
Q
6.4
How to get radius if you know circumference
A
C/2π = r
8
Q
Area of a Parallelogram
A
base x height
9
Q
Area of a Triangle
A
(base x height)/2 or 1/2(base x height)
10
Q
6.7
(base x height)/2 or 1/2(base x height)
A
Area of a Triangle
11
Q
6
Area of a Square
A
side squared
12
Q
6
side times side
A
Area of a square
13
Q
Area of a Trapezoid
A
1/2 (Top base + bottom base) x height
14
Q
1/2 (Top base + bottom base) x height
A
Area of a Trapezoid
15
Q
Another way to say 1/2 (anything)
A
Divide (anything) by 2
16
Q
Area of a Rectangle
A
Length x width
17
Q
Length x width
A
Area of a Rectangle
18
Q
The area is always written by the measurement__________
A
squared
19
Q
Area of an Ellipse
A
π x radius of major axis x radius of minor axis
20
Q
π x radius of major axis x radius of minor axis
A
Area of an Ellipse
21
Q
π
A
3.14 or 22/7
22
Q
3.14 or 22/7
A
π
23
Q
Volume of a cube or rectangular box
A
length x width x height
24
Q
length x width x height
A
Volume of a cube or rectangular box
25
# 7
Volume of a sphere
V = 4/3π(radius cubed)
26
# 7
V = 4/3π(radius cubed)
Volume of a sphere
27
# 7
Volume of a cone
V = [π(radius squared)h)]/3
28
# 7
V = [π(radius squared)h)]/3
Volume of a cone
29
# 7
Volume of a Pyramid
Volume = (Area of the Base x Height)/3
30
# 7
Volume = 1/3 x Area of the Base x Height
Volume of a Pyramid
31
# 7.
Volume of a Rectangular Prism
(V) = l × w × h
32
# 7
(V) = l × w × h
Volume of a Rectangular Prism
33
# 7
Volume of a Cylinder
π × cylinder radius² × cylinder height
34
# 7
π × cylinder radius² × cylinder height
Volume of a Cylinder
35
# 7.
The volume of an object is always expressed as the measurement
______________
Cubed
36
# 7.6
How do you get the Surface Area of a Pyramid?
1. Compute the area of the base
2. Compute the perimeter of the base
3. Identify the Slat Height (no the pyramid height.)
4. Use this formula:
SA = Base Area + Half of (Perimeter of the base x Slant Length)
37
# 4.1
What are the rules for rounding decimals?
1. Identify the place value to be rounded.
2. Look to the digit to the RIGHT of the number being rounded.
3. If it is 4 or less then change it and all the numbers after it to 0.
4. If it is 5 or more, increase the number being rounded by 1 and then change all the numbers after it to 0.
## Footnote
?How do you round 362.715 to the nearest tenth and to the nearest tens?
38
# 4.2
Important rule before adding or subtracting Decimals:
Always line the numbers up vertically by the decimal points.
39
# 4.2
Where does the decimal point go in the product of numbers with decimals?
Product is the answer when the numbers were multiplied. The answer has the same number of decimal places counting all the decimal places in the multiplied numbers. Example: 4.567 x 75.21 has 5 decimals places so put the decimal count places from the right.
40
# 4.3
What kind of fraction is this? Label its parts.
The top number is the numerator. The bottom number is the denominator. If the numerator is smaller that the denominator the fraction is called a "Proper Fraction."
41
# 4.2
When dividing numbers with decimals, you must first clear all decimals from the divisor. How do you do this?
Move the decimal places in the divisor the number of places needed to make it a whole number. Go to the dividend and move the decimal the same number of places. Be sure the decimal point in the quotient is aligned with the new decimal position in the dividend.
42
# 4.3
What is an Improper fraction?
A fraction whose numerator is larger than the denominator.
43
# 4.3
What is the difference between Like fractions and Unlike fractions?
Like fractions have the same denominator. Unlike fractions have different denominators.
44
# 4.3
Before you can add or subtract Unlike fractions you must....
Find the Lowest Common Denominator for all the fractions. Divide the old denominator into the new denominator and multiply the numerator by that number to get a new but equal fraction. Then add or subtract the Like fractions.
45
# 4.3
What is the Inverse of a fraction?
The numerator becomes the denominator and the denominator becomes the numerator.
46
# 4.3
How do you multiply fractions?
Multiply all the numerators. Multiply all the denominators. Reduce your answer to its simplest form.
47
# 4.3
How do you divide fractions?
Invert the divisor and change the problem to multiplication.
48
# 4.7
How do you change a fraction to a decimal?
Example: what decimal is equal to 4/8?
Divide the numerator by the denominator and carry the answer to several decimal places, if necessary. Answer: .5
49
# 4.7
How do you change a decimal to a fraction?
Example: What fraction is equal to .682?
The numerator is the decimal number. The denominator is the place value name of the decimal. Answer .682 is 682 as the numerator and 1000 as the denominator 682/1000. Reduce this number to its simplest form. 341/500
50
# 4.8
On a number line, the numbers to the left of 0 are what kind of numbers?
Negative numbers
51
# 4.8
If a number increases in value which direction do you look for the number on a number line.
To the right
52
# 4.8
If you see a number on the number line at position -2 and you want to increase its value by three, which way do you go and what is the answer?
You move to the right, count up three, and the answer is 1
53
# 4.8
If you see a number on the number line at position -8 and you want to reduce it by three, which way do you go and what is the answer?
You move to the left, count down by three and the answer is -11.
54
# 5.1
What is a Unit Rate?
The ratio between two unit values.
55
# 5.2
How do you find Scale Factor
Example: the length in the original is 6 and the length in the new figure is 3. What is the scale factor?
Look at the two figures. Determine which sides correspond to each other. Select one side. Put the length of the original in the denominator of a fraction and put the length of the new figure in the numerator. Simplify the fraction. The answer is the scale factor. Answer: 1:2 Why isn't it 2:1?
56
# 5.3
If you are looking at a scale drawing of a life size item, where do you look to see the Scale Factor for the drawing?
The ratio is found in the Legend.
57
# 5.4
What is a ratio?
A ratio is a comparison between two things. It can be expressed as a fraction.
58
# 5.4
What is a proportion? When do we use proportions?
A proportion is a pair of ratios that equal each other. Word problems that have 3 of the 4 values in a proportion can be written as 2 fractions (ratios) equal to each other. Once you fill in the numbers you know, you can solve for the missing number.
59
# 5.5
What is percentage?
"Per" means part and "Cent" means 100. So percentage is how much of a hundred. (What part of a hundred.)
60
# 5.5
What is the algebraic formula for percentage?
% x Whole = Part
or % x W = P
or % =P/W
61
# 5.5
How do you turn a decimal into a %?
| Multiply the decimal by 100 and add the % sign.
62
# 5.6
What is the formula for Simple Interest?
Formula for Simple Interest:
Interest = principal (the starting amount) x rate (the percentage it will change) x time (duration of the transaction)
or I = prt
63
# 5.6
What is Percent Change?
Percent Change is the value amount something changes over time.
64
# 5.6
How do you compute Percent Change?
The formula for Percent change is:
The New Value minus the Old Value divided by the Absolute Value of OldValue times 100% or
(NV-OV)/|OV| x 100%
65
# 5.7
What is a discount?
A discount is a deduction from the cost of an item. It is usually expressed as "xx%off"
## Footnote
WARNING: Notice what cost the discount applies to. Is it the orginal or the sale price?
66
# 5.7
What is a sales tax?
A sales tax is an added fee on purchases. It is usually expressed as a %.
## Footnote
Note. This means your final cost is the whole purchase (1) and the percentage. So to find your cost after tax, multiply cost x 1.decimal value of tax. Tax is 5% Multiply original amount x 1.05
67
# 5.8
What is a tip?
A tip is a % added to the orginal cost as an expression of gratitude to the waiter.
68
# 5.8
How do you calculate a tip?
Actually, the tip applies to the original bill--not the total bill. Multiple the decimal value of the tip you want to give by the amount of the original bill. It will be added to the total and the waitress will receive it as your offer of appreciation for his/her services.
69
# 5.9
What is Commission?
Commission if money paid to a person based on how much they sell.
70
# 5.9
How do you calculate the commission called "the percent of sales method"?
The percent of sales method is best used when the product is a "want" not a "need". Compute it by taking the decimal equivalent of the Commission times the Amount sold.
71
# 5.9
What is the kind of commission called the "Stair Step Structure"?
Stair Step Structure Method works in situations with Big Cost Items of want not need. The commission is calculated in several steps using the Percent of Sales method for each step, which increases, and then adding them together.
72
# 5.9
What is a Fixed Commission structure? How does it compare to the Percent of Sales Method?
The Fixed Commission structure applies a certain amount to each item sold. It's a standard amount not a percentage and it's based on the number sold not on the amount of the sale. It's works best in situations where customers are buying needs not wants.
73
# 14.1
What is the highest variable exponent that can be in a Quadratic Equation? Is this variable a requirement?
x squared
Yes. The equation must have a squared variable.
74
# 14.1
The graph of every Quadratic Equation is what shape, known as a what?
It's a curve known as a parabola.
75
# 14.1
What is the point called where one side of the Quadratic Equation curve meets the other?
Vertex
76
# 14.1
What is the standard form of a quadratic equation?
77
# 14.1
Why are there usually two answers for y in a quadratic equation?
Squares of numbers equal negative times negative and positive times positive.
78
# 14.1
What are the roots of a quadratic equation?
The roots are where the curve made by the quadratic equation intersect the x-axis. (It can be once, twice, or not at all)
79
# 14.1
Factoring when possible can offer simple solutions to a Quadratic Equation. What two answers are necessary to factor simply?
What numbers multiplied together = c?
When the same numbers are added, do they = b?
80
# 14.1
What is the Quadratic Formula to use to solve any Quadratic Equation?
81
# 14.2
The Quadratic Formula will never work when "a" has the value of ___
zero 0
82
# 14.2
What is the discriminant?
The Quadratic Formula includes a square root portion. The value under the Square Root symbol is the discriminant.
## Footnote
If the discriminant is positive, there are two possible answers for x. (negative and positive) If the discriminant is 0 then the value of x = 0. If the discriminant is negative then there are two imaginary solutions for x.
83
# 14.4
How do you solve a quadratic equation with just two variables?
Take the square root of the equation.
84
# 13.1
What are the inequality signs?
What do they mean?
85
# 13.1
How do you solve One-Step Inequalities?
Treat the problem the way you would a typical equation and check your answer.
## Footnote
Example s + 40/8 > 15
Get the variable on one side of the equation.
40/8 =5 So s +5 > 15 Take the 5 away on the left side and take it away on the right side. s>15-5 which means s>10
Check your answer. Numbers greater than 10: 17 and 11. Numbers less than 10: 8 and 4
Is 17 + 5 greater than 15? Yes
Is 8 + 5 greater than 15? No
Is 11 + 5 greater than 15 Yes
Is 4 + 5 greater than 15 No
86
# 13.1
One Step Inequalities can be graphed on a number line using a line ending in an arrow. Which way does the arrow go if the inequality is negative?
to the left
87
# 13.1
One Step Inequalities can be graphed on a number line using a line ending in an arrow. Which way does the arrow go if the inequality is positive?
To the right
88
# 13.1
The starting place for an inequality graph is indicated by a circle. There are two kinds of circles. What are they and what do they mean?
Open circle and filled in circle. The open circle means the inequality is less than or more than. If the circle is **closed** it means the point circled is included because the inequality is less/more than or **equal** to.
89
# 13.2
When you have two inequalties using different variables, the answers that fit each equation can be graphed on a coordinate x,y plane. If the inequality has used the < symbol, should the area be shaded above or below the line graphed?
below because the numbers are less than.
90
# 13.2
When you have two inequalties using different variables, the answers that fit each equation can be graphed on a coordinate x,y plane. If the inequality has used the > symbol, should the area be shaded above or below the line graphed?
above because the numbers are greater than
91
# 13.2
If the inequality signs used to graph answers to a linear inequality includes the equal line, how will the graph differ from ones that don't include the equal line?
The line is dotted if the inequality is only greater than or less than. The line is solid if the symbol includes the equal line.
92
# 13.3
If you graph two variable inequalities, where is the answer to the problem?
The answer is the shaded area where both inequalities overlap.
93
# 13.4
When solving an inequality which includes multiplying or dividing by a negative number, what must you do?
Flip the inequality sign.
94
