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
- (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