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72 Cards in this Set
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multiple

The product of a specified number and some integer.
For example, 3, 12 and 90 are all multiples of 3. 4 is not a multiple of 3 because there is no integer that can be multiplied by 3 and yield 4 

An integer is divisible by 2 if...

...if its last digit is divisible by 2


An integer is divisible by 3 if...

...if its digits sum to a multiple of 3
6,930 is a multiple of 3 because 6+9+3+0=18 which is a multiple of 3 

An integer is divisible by 4 if...

...if its last two digits are a multiple of 4
4,716/4 = 1179 

An integer is divisible by 5 if...

...if its last digit is 0 or 5


An integer is divisible by 6 if...

...if it divisible by 2 and 3


An integer is divisible by 9 if...

...if its digits sum to a multiple of 9
6,930...6+9+3+0=18, which is a multiple of 9 

factors (aka divisors)

The factors of an integer are the positive integers by which it is evenly divisible. 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36


5% as a decimal and fraction

0.05 and 1/20


12.5% as a decimal and fraction

0.125 and 1/8


20% as a decimal and fraction

0.2 and 1/5


33 1/3% as a decimal and fraction

.3333 and 1/3


10% as a decimal and fraction

.1 and 1/10


16 2/3 % as a decimal and fraction

0.16666 and 1/6


percent formula

PART/WHOLE x 100 = PERCENT


percent increase (or decrease)

amount of increase/original whole X 100


distance =

rate x time


to multiple powers with the same base...

add the exponents and keep the base
7^3 x 7^5 = 7^8 

to divide powers with the same base...

subtract the exponents and keep the base the same
4^5/4^2 = 4^3 

to multiple powers (or raise a power to a power)

multiply the exponents
7^2(^3) = 7^6 

a negative number raised to an even power...

...yields a positive result (1)^2 = 1


a negative number raised to an odd power...

...yields a negative result
(1)^57 = 1 

raising a fraction between zero and 1 to a power...

...yields a smaller result
(1/2)^2 = 1/4 

what happens when an exponent is negative?

Take the reciprocal of the base and change the sign of the exponent
(2)^2 = 1^2/2^2 = 1/4 

what happens when an exponent is negative?

Take the reciprocal of the base and change the sign of the exponent
(2)^2 = 1^2/2^2 = 1/4 

raising a fraction between zero and 1 to a power...

...yields a smaller result
(1/2)^2 = 1/4 

what happens when an exponent is negative?

Take the reciprocal of the base and change the sign of the exponent
(2)^2 = 1^2/2^2 = 1/4 

Express 9^1/2 as a radical

= the square root of 9 = 3


Express 8^1/3 as a radical

= the cube root of 8 = 2


to simplify a radical...

factor out the perfect squares and move them to the front of the radical sign. For example, the square root of 50 = 5 square root 2


when can radicals be added and subtracted?

only when the number under the radical is the same! 6radical7 + 2radical7 = 8radical7


to multiply radicals...

...multiply the numbers under the signs and then put a single radical sign over them the new number


to divide radicals...

...divide the two numbers in question and then put them under a single radical


if multiplying or dividing an inequality by a negative number...

REVERSE the inequality sign
3x < 6 = x > 2 

supplementary angles

two angles are supplementary if their measures sum to 180


complementary angles

two angles are complementary if their measures sum to 90


adjacent angles

angles that are adjacent (next to each other) are supplementary because they lie along a straight line


vertical angles

two angles that are not adjacent to each other are opposite, or vertical, and are equal in measure


perimeter of a triangle

the sum of the lengths of all three sides


area of a triangle

area of a triangle = 1/2(base)(height)


isosceles triangles

an isosceles triangle has two equal sides and the angles opposite these sides are equal as well


equilateral triangle

all three sides of an equilateral triangle are equal and the interior angles equal 60


right triangles

triangles with one interior angle of 90. The hypotenuse lies opposite the right angle. The other two sides are legs. leg^2 + leg^2 = hypotenuse^2


pythagorean triplets (2)

3:4:5 (leg:3 leg:4 hypotenuse:5)
and 5:12:13 

isosceles right triangles

angles = 45, 45, and 90
the ratio of sides is always 1:1:root2 

306090 right triangles

the ratio of sides is always 1:root3:2
paired as follows...the side opposite the 30 degree angle is 1, etc. 

define: quadrilateral

a four sided polygon where the four interior angles add up to 36, regardless of the quadrilateral's shape


define: parallelogram

a parallelogram has two pairs of equal sides. Opposite angles are equal. Consecutive angles add up to 180


define: rectangle

a quadrilateral with four right angles. Opposite sides are equal.


perimeter of a rectangle

perimeter = 2(length + width)


area of a rectangle

area = length x width


area of a square

area = (side)(side)


area of a parallelogram

area = base x height, but the height is NOT the length of the side. You must draw a line from the one base to the other to form a right angle  that line = the height.


volume of a rectangular solid

volume rectangle = length x width x height


volume of a cube

volume of a cube = (edge)^3


define: diameter of a circle

diameter: a line segment that connects two points on the circumference of a circle and passes through the center


define: radius of a circle

radius: 1/2 of a circle's diameter, it's a line segment that connects the center with a point on the circle


define: central angle of a circle

central angle: an angle formed by two radii


define: circumference

circumference: the distance around a circle = (2)(pi)(r)


define: arc length

arcs are the portion of a circle cut off by a particular central angle. The degree measure of an arc is equal to the central angle that cuts it off
arc length = n/360 x (2)(pi)(r) 

area of a circle

area of a circle = (pi)(r^2)


area of a sector

area of a sector: a slice of pie,
n/360(pi)(r^2) 

define: cylinder and give the formula for volume

cylinder: a solid whose horizontal cross section is a circle. The volume of a cylinder = (pi)(r^2)(h)


distance formula, used to define the distance between two points:

distance formula = square root of (x1x2)^2+(y1y2)^2


define: slope

change in y/change in x


what is the equation for a straight line?

y = mx + b
where, m = slope and b = yintercept 

which is bigger: 8/3 or the square root of 7?

to figure this out, square both sides. They compare 64/9 to 7 (or 63/9)...64/9 (or 8/3) is a little bigger


fractions get smaller as...

...their denominator gets bigger


when a positive fraction is less than 1 squared the result is...

...less than the original fraction


when a negative number is raised to an even power, the result is...

...positive


when a negative number is raised to an odd power, the result is...

...negative


the smaller the negative number...

...the larger its square
