GRE Math 2
Terms
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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 - 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 - 30-60-90 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 (x1-x2)^2+(y1-y2)^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 = y-intercept - 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