Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
39 Cards in this Set
- Front
- Back
|
Consecutive Integars are
|
integars listed in order of increasing value without any integars missing between them.
0, 1, 2, 3, 4, and can also be even numbers 2, 4, 6, 8, or consecutive multiples such as 4, 8, 12, 16 |
|
|
Absolute balue
|
is equal to a numbers distance from zero and is always positive.
.... |-5| would be an absolute value of 5 |
|
|
Factors are
|
numbers that can divide evenly into the number in question...
1, 2, 3, 4, 6 and 12 are all factors of 12 for instance. |
|
|
Multiples
|
example: 8 is a factor of - 8 , 16, 32, 40,
a multiple of a number is one that the number itself is a factor of. zero is a multiple of every number, but rarely shows on the GRE |
|
|
Prime #s
|
integars with only two factors: itself and one.
37 for instance b/c only 1 and 37 factor into it. |
|
|
Prime # exceptions
|
1 is not a prime number
2 is the only even prime number prime numbers are only positive integars |
|
|
prime numbers under 30
|
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
|
|
|
DIVISIBILITY RULES:
Divisible by 2 if: |
it's unit digit is divisible by 2.
598, 447, 896 - divisible by 2 because 6 is the unit digit. |
|
|
DIVISIBILITY RULES:
Divisible by 3 if: |
sum of numbers digits is divisible by 3.
2,145 - sums to 12. 12 is divisible by 3. |
|
|
DIVISIBILITY RULES:
Divisible by 4 if: |
last two digits form a number divisible by 4.
712 is divisible by 4 b/c, 12 is divisible by 4. |
|
|
DIVISIBILITY RULES:
Divisible by 5 if: |
units digit is either 5 or 0
|
|
|
DIVISIBILITY RULES:
Divisible by 6 if: |
if it's divisible by both 2 and 3.
4,290 is divisible by 6 b/c it's divisible by 2 (it's even) and by 3 (4+2+9+0 = 15, which is divisible by 3) |
|
|
DIVISIBILITY RULES:
Divisible by 8 if: |
last 3 digits form a # divisible by 8.
11,640 - divisible by 8 because 640 is divisible by 8. |
|
|
DIVISIBILITY RULES:
Divisible by 9 if: |
If the sum of its digits is divisible by 9.
1,881 would be 1 + 8 + 8 + 1 = 18, which is divisible by 9. |
|
|
DIVISIBILITY RULES:
Divisible by 10 if: |
it's unit digit is 0.
E.g. 1,590 is divisible by 10 due to the unit digit zero |
|
|
What'a a remainder
|
if an integar isn't divisible by another (it's not a factor) the integar is the leftover when dividing.
5 divided by 2 is 2 with 1 left over. 1 is the remainder. 13/8 is 1 with 5 leftover as the remainder. |
|
|
The difference is
|
the result of subtraction
|
|
|
quotient
|
result of division
|
|
|
divisor is
|
the number you divide by
|
|
|
consecutive
|
from least to greatest
|
|
|
terms
|
the #s and expressions used in an equation
|
|
|
ORDER OF OPERATIONS
PEMDAS |
Parantheses, Exponents, Multiplication, Division, Addition, Subtraction
|
|
|
Rules to remember:
When multiplying or dividing, the result will only be negative if: |
you:
multiply a positive x negative = negative divide a positive x negative = negative all other situations are positive. |
|
|
Distributive Law
|
a (b+c) = ab + ac
a(b-c+ ab - ac 12(66) + 12(24) = 12 (66+24) |
|
|
RULES FOR EXPONENTS:
When multiplying with exponents |
If base # the same, add exponents.
2 ^2 x 2 ^ 4 = 2 ^ 6 DON'T Do this for addition. There's no easy rule for addition |
|
|
RULES FOR EXPONENTS:
When dividing with exponents: |
IF base # is the same, subtract exponents.
2^6 / 2 ^ 2 = 2 ^ 4. Do not try to apply this for subtraction of #s, it will not work. |
|
|
RULES FOR EXPONENTS:
When there are exponents inside and outside ( ) |
Simply multiple the exponents.
(4 ^5)^2 = 4 ^ 10 |
|
|
Factoring with exponents
|
If you see something like this:
15^12 - 15^11 do this: 15^11(14) |
|
|
A number raised to a negative power is
|
equal to the reciprocal of the number raised to the positive power:
i.e. 2^-2 would equate to= 1/2^2 = 1/4 |
|
|
Raising a fraction that's between 0-1 to a power greater than 1
|
results in a smaller number. (1/2)^2 = 1/4
|
|
|
Give examples of perfect squares
|
√9 = 3
√16=4 |
|
|
When multiplying square roots
When dividing square roots |
√a x √b = √ab or √3 x √12 = √36 = 6
√a / √b = √a / √b or √16/4 = √16 / √4 = 16 / 14 = 4 |
|
|
To add or subtract square roots
|
The roots must be the same:
√2 + √2 = 2 √2 (pretending there is an invisible 1 in front of the root sign |
|
|
Know this value:
√1 = |
1
|
|
|
Know this value:
√2 |
approximately 1.4
|
|
|
Know this value:
√3 |
approximately 1.7
|
|
|
Know this value:
√4 |
equals 2
|
|
|
To estimate and simplify roots, look at relative perfect squares.
I.e. the √32 can be solved |
by looking at two perfect squares. √25 = 5 and √36 = 6. Thus, the √32 must be between 5 and 6.
B/c 32 is closer to 36, it's likely to be closer to 6 than it is to 5. Around 5.6-5.7 |
|
|
learn the other method for simplifying and estimating on page 189.
|
learn the other method for simplifying and estimating on page 189.
|
