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GRE Math > Level 2 Intermediate > Flashcards

Level 2 Intermediate Flashcards

Intermediate level math that you should know, but may need some refreshing.

1
Q

What is the order of operations? For a complex arithmetic expression.

A 
PEMDAS:
Parentheses
Exponents (or radicals)
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
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2
Q

How to use a Percent Formula

A 
Identify the part, percent, and whole. 
Part = Percent x Whole
Ex Part: 12 percent of 25 is
Part = 12/100 x 25 = 300/100 = 3.
Ex Percent: 45 is what percent of 9?
45 = Percent/100 x 9 = 45/9 x 100% = 500%
Ex Whole: 15 is 3/5 of what number?
15 = 3/5(1/100) x Whole
15 = 3/500 x Whole
Whole = 15(500/3) = 7500/3 = 2500
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3
Q

How to use the Percent Increase/Decrease Formula

A

Identify the original whole and the amount of increase/decrease.
% Increase = Amount of Increase/Original Whole x 100%
% Decrease = Amount of Decrease/Original Whole x 100%

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4
Q

How to Predict whether a sum, difference, or product will be Odd or Even.

A

Take simple numbers like 2 for even numbers and 3 for odd numbers and see what happens. Don’t memorize rules.

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5
Q

How to Recognize multiples of 2, 3, 4, 5, 6, 9, 10, and 12

A

2: Last digit is even.
3: Sum of digits is a multiple of 3.
4: Last two digits are a multiple of 4.
5: Last digit is 5 or 0.
6: Sum of digits is a multiple of 3, and last digit is even.
9: Sum of digits is a multiple of 9.
10: Last digit is 0.
12: Sum of digits is a multiple of 3, and last two digits are a multiple of 4.

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6
Q

How to find a Common Factor of two numbers

A

Break both numbers down into their prime factors to see which they have in common. Then multiply the shared prime factors to find all common factors.

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7
Q

How to find a Common Multiple of two numbers

A

The product of two numbers is the easiest common multiple to find, but it is not always the least common multiple.
First find prime factors. Then multiply each factor the greatest number of times it appears in a prime factorization.
(Ex. What is the least common multiple of 28 and 42? 28 = 2 x 2 x 7; 42 = 2 x 3 x 7
LCM = 2 x 2 x 3 x 7 = 84)

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8
Q

How to find the Average or Arithmetic Mean

A

Average = Sum of terms/Number of terms

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9
Q

How to use the Average to find the Sum

A

Sum = (Average) x (Number of terms)

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10
Q

How to find the Average of Consecutive Numbers

A

It is simply the average of the smallest number and the largest number.
(ex. The average of all integers from 13 to 77 is the same as the average of 13 and 77:
(13 + 77)/2 = 45)

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11
Q

How to Count Consecutive Numbers

A

The number of integers from A to B inclusive is B - A + 1.
(ex. How many integers from 73 to 419?
419 - 73 +1 = 347 (inclusive))

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12
Q

How to Find the Sum of Consecutive Numbers

A 
Sum = (Average) x (Number of Terms)
(Ex. What is the sum of integers from 10 through 50, inclusive? 
Average = (10 + 50) / 2 = 30
Numbers of Terms = 50 - 10 + 1 = 41
Sum = 30 x 41 = 1230)
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13
Q

How to Find the Median

A

Put the numbers in numerical order and take the middle number.
If there is an even number of numbers, take the average of the two in the middle.

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14
Q

How to find the Mode

A

Take the number that appears most often. If there’s a tie, there is more than one mode. If each number in a set is used equally often, there is no mode.

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15
Q

How to find the Range

A

Take the positive difference between the greatest and least values.

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16
Q

How to use actual numbers to determine a Ratio

A

Put the number associated with “of” on top and the number associated with “to” on the bottom.
Ratio = of/to
Ratios should always be reduced to lowest terms.

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17
Q

How to use a ratio to determine an Actual Number

A

Set up a proportion using the given ratio.
(Ex. The ratio of boys to girls is 3 to 4. If there are 135 boys, how many girls are there?
3/4 = 135/g
3 x g = 4 x 135
g = 180

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18
Q

How to use actual numbers to determine a Rate

A

Identify the quantities and the units to be compared. Keep the units straight.
(Ex. Anders typed 9450 words in 3.5 hours. what is the rate in words per minute?
Convert hours to minutes, then divide with words on top and minutes on bottom.
9450 words / 210 minutes = 45 words/minute

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19
Q

How to deal with Tables, Graphs, and Charts

A

Read the question and all labels CAREFULLY. Approximate if necessary.

20
Q

How to count the Number of Possibilities

A

Use multiplication to find the number of possibilities when items can be arranged in various ways.
(ex. How many 3-digit numbers can be formed with the digits 1, 3, and 5 each used only once?
Look at each digit individually. The hundreds digit has three possible numbers (1, 3, or 5), the tens digit has two possible numbers (since one is already taken), the ones digit has only one remaining possible number. Multiply possibilities together: 3x2x1 = 6.

21
Q

How to calculate a simple Probability

A

Probability = Number of favorable outcomes/Total number of possible outcomes.
(Ex. What is the probability of throwing a 5 on a six-sided die?
Probability = 1/6)

22
Q

How to work with new Symbols

A

Everything you need to know is in the question. Just read CAREFULLY and follow instructions.

23
Q

How to Simplify Binomials

A 
A binomial is the sum or different of two terms. This is where to use the FOIL method. 
First, Outside, Inside, Last. 
(Ex. (3x + 5)(x - 1) = 
3xsquared - 3x + 5x - 5 =
3xsquared + 2x - 5)
24
Q

How to Factor certain Polynomials

A

A polynomial is an expression consisting of the sum of two or more terms, where at least one of the terms is a variable.

Learn to spot these classic equations:
ab + ac - a(b + c)
asquared + 2ab + bsquared = (a + b)squared
asquared - 2ab + bsquared = (a - b) squared
asquared - bsquared = (a - b)(a + b)

Think reverse FOIL.

25
Q

How to solve for one variable in Terms of Another

A

To find “x in terms of y,” isolate x on one side, leaving y as the only variable on the other.

26
Q

How to solve an Inequality

A

Treat it like an equation; do the same thing to both sides.

Remember to reverse the inequality sign if dividing or multiplying by a negative quantity.

27
Q

How to handle Absolute Values

A

The absolute value of n is denoted by |n|. It is defined as n being positive OR negative.

When using absolute values of a number or expression, it is always positive.

28
Q

How to Translate English into Algebra

A

Addition: sum, plus, and, added to, more than, increased by, combined with, exceeds, total, greater than.

Subtraction: difference between, minus, subtracted from, decreased by, diminished by, less than, reduced by.

Multiplication: of, product, times, multiplied by, twice, double, triple, half.

Division: quotient, divided by, per, out of, ratio of __ to __.

Equals: equals, is, was, will be, the result is, adds up to, costs, is the same as.

29
Q

How to find an Angle formed by Intersecting Lines

A

Vertical angles are equal.
Angles along a line add up to 180 degrees.
All angles add up to 360 degrees.

30
Q

How to find an angle formed by a Transversal across Parallel Lines.

A

All the acute angles are equal.
All the obtuse angles are equal.
An acute plus an obtuse equals 180 degrees.
All angles around one parallel line equal 360 degrees.
All angles around both parallel lines equal 720 degrees.

31
Q

How to find the Area of a Triangle

A

Area = 1/2 (base)(height)

Base and height must be perpendicular to each other.

32
Q

How to work with Isosceles Triangles

A

Isosceles triangles have two equal sides and two equal angles.
If a question states that a triangle is isosceles, then the equal sides or angles are important to solving the problem.

33
Q

How to work with Equilateral Triangles

A

Equilateral triangles have three equal sides and each angle is 60 degrees.
If a question states that a triangle is equilateral, it is important to solving the problem.

34
Q

How to work with Similar Triangles

A

In similar triangles, corresponding angles are equal, and corresponding sides are proportional.

35
Q

How to find the Hypotenuse or a Leg of a Right Triangle

A

For all right triangles, use the Pythagorean Theorem: Asquared + Bsquared = Csquared. A and B are legs and C is the hypotenuse.

36
Q

How to spot Special Right Triangles

A

3:4:5 and 5:12:13 represent the ratio of the side lengths of special right triangles.
30 - 60 - 90 degrees and 45 - 45 - 90 degrees are the possible angles of right triangles.
The ratios of the side lengths of special triangles is:
1, square root of 3, 2 and 1, 1, square root of 2.

37
Q

How to find the Perimeter of a Rectangle

A

Perimeter = 2 (length + width)

38
Q

How to find the Area of a Rectangle

A

Area = (length)(width)

39
Q

How to find the Area of a Square

A

Area = (side)squared or (length)(width)

40
Q

How to find the Area of a Parallelogram

A

Area = (base)(height)

41
Q

How to find the Area of a Trapezoid

A

A trapezoid is a quadrilateral having only two parallel sides.

  1. Drop a perpendicular line to divide it into a triangle and rectangle or two triangles and add the areas together.
  2. Area = (average of parallel sides) x (height)
42
Q

How to find the Circumference of a Circle.

A
  1. Circumference = 2(pi)r, r is the radius.

2. Circumference = (pi)d, d is the diameter.

43
Q

How to find the Area of a Circle

A

Area = (pi)r(squared), r is the radius.

44
Q

How to find the Distance Between Points on the coordinate plane

A
  1. If the points have the same x OR y coordinates, simply subtract the numbers that are different on the same line segment. Distance is always positive.
  2. If all coordinates are different, make a right triangle and use the Pythagorean Theorem or use the special right triangle attributes if applicable.
45
Q

How to find the Slope of a Line

A

Slope = rise/run = change in y/change in x.

GRE Math (4 decks)

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