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Math Formulas and Concepts Flashcards

1
Q

Special right triangle ratios

A

3:4:5 and 5:12:13

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2
Q

Equilateral triangle

A

Equal side, 60-60-60 degree

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3
Q

Isosceles triangle

A

2 equal sides corresponding to 2 equal angles

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4
Q

Special right triangle angles

A

45-45-90 1:1:sq. rt. 2; 30-60-90 1:sq. rt. 3:2 half an equilateral

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5
Q

Find common factor of 2 #’s

A

Find prime factors and all combinations of shared prime factors.

Ex: What factors do 135 & 225 have in common?
135=3335
225=3355
335 so 3, 5, 9, 15, 45

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6
Q

Find least common multiple (LCM)

A

Find prime factorization and determine the greatest number of times each factor is used between the two numbers.

Ex: LCM of 28 & 42?
28 = 227, 42 = 237
LCM = 223*7=84

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7
Q

Use average to find sum of terms

A

Sum = average x # of terms

Ex: 17.5 is the average of 24 #’s. What’s the sum of the terms?
Sum=17.5*24=420

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8
Q

Find average of evenly spaced #’s

A

Equal to the average of the smallest and largest #’s.

Ex: what’s the average of all the integers from 13 to 77?
(13+77)/2=90/2=45

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9
Q

Counting consecutive #’s

A

of integers from A to B inclusive is B-A+1

Ex: how many integers are there from 73 to 419 inclusive?
419-73+1 = 347

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10
Q

Solve an inequality

A

When multiplying or dividing by a negative, REVERSE THE INEQUALITY SIGN

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11
Q

Absolute values

A

Ex: If |x-3|<2 what is the range of possible values for x?

if |x-3|<2 then x-3<2 and x-3>-2, so x<5 and x>1, thus 1

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12
Q

Circumference of a circle

A

C=2rpi=d*pi

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13
Q

Area of a circle

A

A=pi*r^2

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14
Q

Determine combined % up or down

A

Start with 100 as a value

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15
Q

Solve a compound interest problem

A

Final balance = principal(1+(interest rate/C))^(timeC) where C= # of times compounded annually

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16
Q

Remainders problem

A

Pick a number that fits the given conditions

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17
Q

Combines work problem

A

(1/r)+(1/s)=(1/t) where r, s = different people’s work times and t = combined work time

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18
Q

Dilution/mixture problem

A

(% difference between weaker and desired)(amount of weaker)=(% difference between stronger and desired)(amount of stronger)

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19
Q

Group problem with both/neither

A

group1+group2+neither-both=total

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20
Q

Standard deviation

A
  1. Find average of set
  2. Find difference between mean and each value
  3. Square each difference
  4. Find average of squared differences
  5. Take the square root of average
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21
Q

Multiply/divide with exponents

A

(x^a)*(x^b)=x^(a+b)

x^c)/(x^d)=x^(c-d

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22
Q

Exponent to exponent

A

(x^a)^b) = x^ab

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23
Q

Bases with exponent 0

A

x^0=1 except 0^0 is undefined

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24
Q

Fractional exponents

A

x^(a/b)=b*sq. rt (x^a)

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25
Find max/min lengths for a side of a triangle
If a, b are two sides of a triangle, then |a-b|
26
Angles of a regular polygon (all angles =)
Sum of interior angles in polygon with n sides = (n-2)*180
27
Length of arc
length of arc=(n/360)*2*r*pi where n=interior angle
28
Area of sector of a circle
Area of sector=(n/360)*pi*r^2 where n=interior angle
29
Surface area of rectangle solid
Surface area=2*l*w+2*w*h+2*l*h
30
Volume of a cylinder
volume = area of base*height=h*pi*r^2
31
Surface area of cylinder
surface area = 2*pi*r^2 + 2*h*r*pi
32
Digit
Number that makes up another number
33
Number
One or a combination of digits
34
Integer
Numbers that have no fractional part
35
Properties of Zero
* even * added to any number equals that number * multiplied by any number equals 0 * cannot divide by 0
36
Properties of adding even/odd numbers
Even + even = even Odd + odd = even Even + odd = odd
37
Properties of multiplying even/odd numbers
Even*even=even Odd*odd=odd Even*odd=even
38
Consecutive integers
Integers listed in order of value without any missing integers between them
39
Absolute value
The distance from 0 to a number on the number line
40
Factor
A number that will divide evenly into another integer
41
Multiples
All the integers for which a number is a factor
42
Prime number
An integer with only two factors, itself and one. Starts with 2.
43
Divisibility tricks for each digit
* # divisible by 3 if sum of digits is divisible by 3 * # divisible by 4 if last two digits form a number divisible by 4 * # divisible by 5 if units digit is 0 or 5 * # divisible by 6 if divisible by both 2 and 3 * # divisible by 8 if last 3 digits form a number that's divisible by 8 * # divisible by 9 if sum of digits is divisible by 9
44
Remainder
An integer left over when one number is not evenly divisible by another
45
Sum
The result of addition
46
Difference
The result of subtraction
47
Product
The result of multiplication
48
Quotient
The result of division
49
Divisor
The number you divide by
50
Numerator
The top number of a fraction
51
Denominator
The bottom number of a fraction
52
Terms
The numbers and expressions used in an equation
53
Order of operations
PEMDAS or parenthesis, exponents, multiplication, division, addition, subtraction Multiplication and division as well as addition and subtraction are done in the same step going from left to right.
54
Properties of multiplying Positive/negative
Positive*positive=positive Negative*negative=positive Positive*negative=negative
55
Properties of dividing positive/negative numbers
Positive/positive=positive Negative/negative=positive Positive/negative OR negative/positive=negative
56
Fraction
Expresses the number of parts out of a whole. Consists of a integer numerator on top and an integer denominator on bottom.
57
Adding/subtracting fractions
* if common denominator exists just add or subtract numerator and put the result over the denominator * if there are different denominators, first find a common denominator. This entails finding a common multiple of both denominators and multiplying the numerator and denominator of each fraction by the respective factors of the multiple. Then proceed as above.
58
Multiplying fractions
Multiply numerators and then denominators together and reduce the resulting fraction
59
Dividing fractions
Flip the second fraction such that denominator is the numerator and the numerator is the denominator and then multiply the two resulting fractions.
60
Mixed number
A number that is represented as an integer and a fraction. Ex: 2 and 2/3 * convert to a fraction by multiplying the denominator by the integer and adding the numerator and putting the result over the denominator.
61
Decimal
A different form of expressing a fraction
62
Percentage
Type of fraction that always has 100 as the denominator
63
Percent increase/decrease
Percent change=(difference/original)*100 where difference is the lesser number is subtracted from the greater.
64
When to use Plug-in-a-number
When there are variables in the problem and answer choices. *Note: in quantitative comparison questions, plug in multiple times using Fractions, Repeats, One, Zero, Extremes, or Negatives to eliminate all answer choices.
65
When to use Plug-in-the-answer
1. If the problem has the phrase "how much...", "how many...", or "what is the value of...". 2. Specific numbers in the answer choices in ascending or descending order. 3. If you're tempted to write your own algebraic formulas *Note: start with answer choice C to do half the work.
66
Standard deviation percentages 0-1 SD = ? 1-2 SD = ? 2+ SD = ?
0-1 SD = 34% 1-2 SD = 14% 2+ SD = 2%

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