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An integer is divisible by 2 if its last digit is divisible by 2

An integer is divisible by 3 if its digits add up to a multiple of 3

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An integer is divisible by 4 if its last two digits are a multiple of 4

An integer is divisible by 5 if its last digit is 0 or 5

An integer is divisible by 6 if it is divisible by 2 and 3

An integer is divisible by 9 if its digits add up to a multiple of 9

Odd + Odd

Even

Even + Even

Even

Odd + Even

Odd

Odd x Odd

Odd

Even x Even

Even

Odd x Even

Even

Least common multiple

least common multiple of two or more integers is the smallest number that is a multiple of each integers

To multiply two powers with the same base (2^3 x 2^4)

Keep the base and add the exponents (2^7)

To divide two powers with the same base (4^5 / 4^2)

keep the base and subtract the exponent of the denominator from the exponent of the numerator (4^3)

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To raise a power to another power (3^2)^4

Multiply the exponents (3^8)

Raising a fraction between zero and one to a power produces a smaller result

raising a negative number to an even power produces a positive or negative result?

positive

raising a negative number to an odd power creates a negative or positive result?

negative

Only like radicals can be added to or subtracted from one another

To multiply or divide one radical by another

ex: (6 (sqrt3))(2(sqrt5)=

multiply or divide the numbers outside the radical sign, then the numbers inside the radical side again

ex: 12(sqrt15)

Is the square of any fraction between 0 and one less or greater than the original fraction?

less

is the square of any fraction between 0 and -1 greater or less than the original fraction?

multiplying two negative numbers gives a positive product, and any positive number is greater than any negative number

does multiplying any positive number by a fraction between 0 and 1 give a product smalller or greater than the original number

smaller

does multiplying any negative number by a fraction between 0 and 1 give a product greater or less than the original number

greater than the original number

1/20

5%

5%

1/20

1/12

8 1/3%

8 1/3%

1/12

1/10

10%

10%

1/10

1/8

12 1/2%

12 1/2%

1/8

1/6

16 2/3%

16 2/3%

1/6

1/5

20%

20%

1/5

1/4

25%

25%

1/4

3/10

30%

30%

3/10

1/3

33 1/3%

33 1/3%

1/3

3/8

37 1/2%

37 1/2 %

3/8

2/5

40%

40%

2/5

1/2

50%

50%

1/2

3/5

60%

60%

3/5

5/8

62 1/2%

62 1/2%

5/8

2/3

66 2/3%

66 2/3%

2/3

7/10

70%

70%

7/10

3/4

75%

75%

3/4

4/5

80%

80%

4/5

5/6

83 1/3%

83 1/3%

5/6

7/8

87 1/2%

87 1/2%

7/8

9/10

90%

90%

9/10

11/12

91 2/3%

91 2/3%

11/12

Percent increase formula

Percent increase= (increase/original)

Percent Decrease

Decrease/ Original

the "original" is the base from which the change occurs

Speed formula:

speed=distance/time

If a and b are different people and it takes one person a units of time to complete the job, the second person b units of time to complete the job and the total time is T then the formula for work is:

T=(ab)/(a +b)

if there are three people then 1/T= 1/a + 1/b + 1/c

Combination formula

where n = (# in the larger group) and

k = (# you're choosing)

Permutations

where n = number of objects

Probability of dependent events

- dependent if the outcome of one event affects the probability of the other event
- P(A and B) = P(A) x P(B given A)

Sum of Angles around a point

360 degrees

Sum of Angles along a straight line

180 degrees

If a line a bisects an angle

Splits it into two equal angles

Sum of interior angles

(n-2)*180

n=number of sides

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Pythagorean Theorem

a^{2}+ b^{2 }=^{ }c^{2}^{}^{c is the hypotenuse in any right triangle}

Pythagorean Triples

3:4:5

5:12:13

Special Triangles

Triangles and Data Sufficiency

If you know two angles, you know the third

To find the area, you need the base and height

In a right triangle, if you have two sides you can find the third. If you have two sides, you can find the area

In isosceles right triangles and 30/60/90 triangles, if you know one side, you can find everything

Area of a parallelogram

Area =base x height

Chord

A line segment that joins two points on the circle

Arc length

(n/360)2πr, when n is the degree of the arc

area of sector of a circle

(n/360) · πr^2

Volume of a rectangular solid

lwh

Surface area of a rectangular solid

2lw+2lh+2hw

volume of a cylinder

Surface/Lateral Area of Cylinder

L = 2∏rh

A = 2∏rh + 2∏r²

Word Problem Tip

Don't try to combine several sentences into one equation; each sentence usually translates into a separate equation

Digit

integer 0 to 9

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