# GRE General Test Math Flashcards

## Terms

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What are the first 10 prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
5/6 + 2/3
-Find the LCM:
5/6 + 2/3 LCM of 6 and 3 is 6
5/6 * 1/1 + 2/3 * 2/2 equals:
5/6 + 4/6 = 9/6 or 3/2
Subtracting Fractions:
3/4 - 2/3
-Find the LCM:
3/4 - 2/3 LCM of 4 & 3 is 12
3/4 * 3/3 - 2/3 * 4/4 equals:
9/12 - 8/12 = 1/12
Dividing Fractions:
2/5 / 7/8
-flip the fraction you're dividing by, then multiply:
2/5 / 7/8 = 2/5 * 8/7= 16/35
Multiplying Fractions:
-10/4 * 3/5
Simply Multiply:
-10/4 * 3/5 = -30/20 = -3/2
How do you convert a mixed fraction into a pure fraction?
Ex: 3 2/7
* integer by denominator & add product to numerator:
3 2/7 = 23/7
How do you convert a fraction to a decimal?
Ex: 2/7
Divide the top by the bottom:
2/7 = 7 divided by 2 = .28
When can you add and subtract exponents?
When they share the same base and the same power:
3x to the 2nd & 2x to the 2nd = 5x to the 2
When can you multiply and divide exponents and roots?
When they share a base:
x to the 2nd * x to the 3rd = x to the 5th
x to the 2nd / x to the 3rd = x to the 1st
How do you raise the power of an exponent?
Ex: (x to the a)to the b
Ex: (x to the 2nd)to the 3rd
(x to the a) to the b =
x to the ab
(x to the 2nd) to the 3rd =
x to the 6th
What is the definition of a cube root?
a # divided by itself twice
EX: the cube root of 27 is 3 because 27 / 3 = 9 and 9 / 3 = 3
What is the square root of 9?
The square root of 9 is 3
Acute Angle
An angle with less than 90 degrees
Right Angle
An angle measuring 90 degres
Obtuse Angle
An angle measuring more than 90 and less than 180 degrees
Complementary Angles
Angles whose sums measure 90 degrees
Supplementary Angles
Angles whose sums measure 180 degrees
Angles who share a common side and a common vertex
Vertical Angles
Angles opposite each other when 2 straight lines intersect, forming 4 angles. They are always equal.
Perpendicular Lines
2 lines that meet to for right ngles.
Parallel Lines
Two or more lines that remain the same distance apart at all times.
Corresponding Angles
Identical angles
Polygon
Closed shape/figure in a plane with three or more sides
Regular Polygon
All sides have the same length and all angles have the same measure
Convex Polygon
All diagonals are within the figure
Concave Polygon
At least one diagonal is outside the figure
Diagonals of Polygons
Line segment connecting one vertex with another vertex. It isn't a side.
Scalene Triangle
A triangle with no equal sides
Right Triangle
A triangle with a right angle in its interior
Every triangle has 3 ____ and 3 _______
bases (bottom sides) and heights (altitudes), heights being the perpendicular distance from a vertext it its opposite side
Triangle Median
The line segment drawn from a vertext to the midpoint of the opposite side
Rule for angles that are opposite from equl sides
They are also equal
Rule for the location of large and small angles in any triangle
The longest side is always opposite from the largest angle. Same for the shortest.
Rule for the sum of the lengths of the sides of a triangle
The sum of the lengths of any 2 sides must be larger than the lengh of the 3rd side.
Exterior Angle
If 1 side of a triangle is extended, the exterior angle formed = the sum of the other 2 interior angles
Hypotenuse
The side opposite the right angle in a right triangle
Pythagorean Theorem for right triangles
the 3 lengths, a, b, and c will always be #'s such that:
a^2 + b^2 = c^2
Isoceles Right Triangle
Has characteristics of both isoceles/right triangles: 2 equal sides, 2 equal angles, and one right angle
Rule for ratio of the sides of an isoceles right triangle
The sides are always:
__
x, x, and X/2
Ratio of the sides of a 30, 60, 90 triangle
__
X, 2x, x/3
-Side opposite 30 is x, side opposite 60 is x/3, side opposite 90 is 2x
Polygon w/4 sides
Sum of angles: 360 degrees
Parallelogram
Opp. sides are equal/parallel
Angles equal
Consec. angles supplementary
Diagonals not always equal
Rhombus
-Parallelogram with 4 equal sides
-Diagonals not always equal
Trapezoid
-1 pair of parallel sides
Formula for Interior Angles of a polygon
(n-2)180, n = the # of sides
Formula for the perimeter of a polygon
The sum of the sides
Formula for the area of a triangle
A= 1/2bh
Formula for the area of a square/rectangle
A= lw
Formula for the area of a parallelogram
A= bh
Formula for the area of a trapezoid
A= 1/2(b1 + b2)h
Diameter
A straight line segment passing through the center of the circle. It is 2 times the length of the radius
Chord
Line segment whose endpoints lie on the circle
Arc
distance between any 2 points on the rim of the circle
Formula for circumference of a circle
C = 2(pi)(r), pi = 3.14
Formula for area of a circle
A = (pi)r^2
Central Angle
Angle formed by any 2 radii in a circle
c.a. = measure of intercepted arc
Inscribed Angle
the angle formed by any 2 chords that meet on the circle
i.a. = 1/2 measure of intercepted arc
Formula for Calculating Interest
principal * rate * time = Interest
How do you change a fraction to a percent?
Ex: 2/5
1. change to a decimal
2. Change the decimal to a percent
Ex: 2/5 = .4 = 40%
How do you change a percent to a fraction?
Ex: 60%
1. Drop the %
2. Write over 100
3. Reduce if necessary
Ex: 60% = 60/100 = 3/5
How do you determine the percent of a number?
Ex: 20% of 80
Change % to a fraction or decimal and multiply
20/100 * 80 = 1600/100 or 16
18 is what percent of 90?
18 = x(90)
18/90 = x
1/5 = x
20% = x
10 is 50% of what number?
10 = .50(x)
10/.50 = x
20 = x
Formula for finding Percent Increase/Decrease
Ex: % decrease of a \$500 item on sale for \$400?
change/starting point = % change
100/500 = 1/5 = 20%
Inscribed angles
angles formed by 2 chords of a circle that meet on the circle
They equal 1/2 measure of intercepted arc
Concentric Circles
Circles with the same center
Tangent
2 Tangents drawn from the same point on a circle are...
A line touching a circle at only 1 point
= in length and perpendic. to a radius meeting at that point
Congruent geometric figures
Identical in size and shape
Similar geometric shapes
Have the same shape but aren't identical in size
Volume of a solid figure
The # of cubic units of space the figure contains. AKA "cubic units".
Formula for finding the area of a solid figure
A = b * h
Formula for the volume of a cube
V = s * s * s = s^3
Formula for the volume of a rectangular solid
V = (lw)(h) = lwh
Formula for the volume of a right circular cylinder (circular bases)
V = (PIr^2)h = PIr^2h
Raising a fraction b/t 0 and 1 results in a...
(1/2)^2 =
Number smaller than 1:
(1/2)^2 = 1/4
Factor

Factors of 12:
A number that can be divided by another number without leaving a remainder:
2,3,3,4,6, 12
Shortcut for comparing
3/7 and 7/14
Multiply diagonally up from each denominator:
14 * 3 and 7 * 7
Permutation
Arrangement of things in a definite order:
4 factorial: 4 * 3 * 2 * 1
Probability
Equal to the outcome you're looking for divided by the total outcomes
Reciprocal

Reciprocal of 1/2
The inverse of something:

2/1

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