GRE General Test Math Flashcards
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 What are the first 10 prime numbers?
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Adding Fractions:
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
 Adjacent Angles
 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  Quadrilateral

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
 (n2)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