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GRE > Math > Flashcards

Math Flashcards

1
Q

Digit

A

The numbers that make up other numbers (0-9)

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2
Q

Names of digits

A

Designated by a place value. Ones, tens, hundreds, thousands, and ten thousands place

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3
Q

Number

A

Made up of either a digit or a collection of digits. Includes basically any collection of digits, like 0, negative numbers, fractions and decimals, and radicals

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4
Q

Integers

A

Numbers that have no fractional or decimal part. Can be negative and includes zero. Fractions are not integers. Integers are the only numbers that can be classified as even or odd

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5
Q

Distinct element

A

A unique digit, number, or integer

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6
Q

Is zero positive or negative?

A

Neither, but all other numbers can be classified as positive or negative

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7
Q

Zero

A

An integer that is not positive or negative. You can’t divide by zero. Zero is considered even and is not a prime number

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8
Q

Consecutive integers

A

Integers listed in order of value without any integers missing in between them (-6, -5, -4, -3, -2,..)

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9
Q

Absolute value

A

Equal to the number’s distance from 0 on a number line- it’s always positive

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10
Q

An integer is divisible by

A

Its factors

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11
Q

Remainder

A

An integer left over after division if one integer is not divisible by another

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12
Q

Multiples of a number

A

The multiples of an integer are all the integers that are the product of that integer and another integer. That number times an integer (times 1, times 2, times 3, etc). The multiples of 20 are 20, 40, 60, etc.

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13
Q

Factor

A

The factor of an integer is a number that divides evenly into that integer. There is no remainder after division. Includes 1 and the number- the factors of 40 include 1 and 40

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14
Q

Prime number

A

An integer that only has 2 factors- itself and 1. Prime numbers are positive integers. 2 is the only even prime number. 1 and 0 are not prime numbers

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15
Q

Sum

A

The result of addition

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16
Q

Difference

A

The result of subtraction

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17
Q

Product

A

The result of multiplication

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18
Q

Quotient

A

The result of division

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19
Q

Divisor

A

The number you divide by

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20
Q

Terms

A

The numbers and expressions used in an equation

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21
Q

Inclusive

A

A range of numbers that includes the numbers at the ends of the range

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22
Q

Between

A

A range of numbers that does not include the numbers at the ends of the range

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23
Q

Order of operations

A

Parentheses, exponents, multiplication and division, addition and subtraction

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24
Q

Mixed number

A

A number that is represented as an integer and a fraction

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25
Q

Associative law

A

When you are adding or multiplying a series of numbers, you can regroup the numbers in any way you’d like

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26
Q

Distributive law

A

Multiplying a number by a group of numbers added together is the same as doing each multiplication separately

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27
Q

Terminating decimal

A

A decimal that ends- not repeating

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28
Q

Is 1 a prime number?

A

No

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29
Q

When does the direction of the inequality sign change?

A

When you multiply or divide both sides of the inequality by a negative number

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30
Q

Roots

A

The values of the variable that make the equation equal to zero

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31
Q

When you see exponents that have equal bases and are being multiplied, what do you do?

A

Add the exponents

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32
Q

When exponents have equal bases and are being divided, what do you do?

A

Subtract the exponents

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33
Q

When an exponent is raised to a power, what do you do?

A

Multiply the exponents

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34
Q

Negative powers

A

Any term raised to a negative power is equal to the reciprocal of that term raised to the positive power.

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35
Q

Zero exponents

A

Any nonzero number raised to a power of zero is equal to 1

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36
Q

You can add or subtract square roots if

A

The values under the radical sign are equal

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37
Q

How to multiply and divide square roots

A

There are no restrictions on this, you just have multiply the terms outside the radical together and multiply the terms inside the radical together

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38
Q

Fractions with radicals can be rewritten as

A

An entire fraction in a radical can be rewritten as the numerator under a radical and the denominator under another radical

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39
Q

Ratio

A

Expresses a part to part relationship- does not mention the whole

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40
Q

Proportion

A

An equivalent relationship between two fractions or ratios- two fractions could be proportionate if they form equal ratios

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41
Q

Average

A

Arithmetic mean- the sum of all the numbers in the list divided by the number of numbers in the list

42
Q

Median

A

The middle value in a list of numbers. There is an equal number of values above and below the median

43
Q

Mode

A

The number in a list of numbers that occurs most frequently

44
Q

Range

A

The difference between the greatest and least numbers in a list of numbers

45
Q

Standard deviation

A

A measure of the variation of a set of data values. A low standard deviation indicates that the data values tend to be close to the mean. With a high standard deviation, the data is spread out over a wide range. Standard deviation focuses on the distance of a point from the mean, and it can never be negative. The GRE will never ask you to calculate the standard deviation, but you would need to know the mean to make an estimation. 68% of individuals are within one standard deviation of the mean, and 94% are within 2 standard deviations

46
Q

FROZEN number

A

Fractions
Repeats
One
Zero
Extremes
Negatives
Good to use for plugging in

47
Q

How many degrees in a line?

A

180

48
Q

When two lines intersect, how many angles do they make?

A

4, they sum up to 360

49
Q

Vertical angles

A

Angles that are across from each other when two lines intersect. The angles are equal if they are directly across from each other. It is possible for all 4 angles to be equal, as long as they add to 360.

50
Q

Parallel lines

A

Lines that never intersect and have the same slope. When a pair of parallel lines is intersected by a third line, two types of angles are formed- big and small. Any big angle is equal to any other big angle and any small angle is equal to any other small angle. The sum of any big angle and any small angle is 180.

51
Q

Equilateral triangle

A

A triangle in which all 3 sides are equal and all 3 angles are 60 degrees

52
Q

Isosceles triangle

A

A triangle in which 2 of the 3 sides are equal and 2 of the 3 angles are also equal

53
Q

How to tell which side of a triangle is longest and which one is shortest

A

The longest side is opposite the largest interior angle, and the shortest side is opposite the smallest interior angle. Equal sides are opposite equal angles

54
Q

Third side rule

A

The length of any one side of a triangle must be less than the sum of the other two sides and greater than the difference between the two sides. If you know two sides of a right triangle, you can use the Pythagorean theorem to find the third. However, if the triangle is not a right triangle, it’s not possible to find the third side on the GRE. You can just estimate what it is

55
Q

Right triangles

A

Triangles in which one interior angle is 90 degrees. They can be easily identified because there will be a box in the right angle. The other two angles have to sum to 90 degrees

56
Q

Pythagorean triples (3)

A

Right triangles may have specific combinations of side measurements. The side lengths could also be the ratios of these numbers
3:4:5
6:8:10
5:12:13

57
Q

30:60:90 right triangles

A

You can create a 30:60:90 triangle by drawing in the height of an equilateral triangle, which cuts the triangle in half. The shortest side of the new right triangle is x, the hypotenuse is 2x, and the height of the equilateral triangle is x radical 3. The side that is half the length of the hypotenuse is opposite the 30 degree angle

58
Q

45:45:90 right triangles

A

If you take a square and cut it in half along its diagonal, you create an isosceles right triangle. Two sides of the square are the same and are the equal sides of the triangle. The two equal sides are x and the hypotenuse is x radical 2.

59
Q

Chord

A

A line that connects two points on the circumference of a circle. The diameter of a circle is the longest chord in the circle. The radius is not a chord because it only touches one end

60
Q

Arc

A

A section of the outside (circumference) of a circle

61
Q

Central angle

A

Any angle formed by two radii

62
Q

Regular figure

A

The figure has equal sides and angles

63
Q

Polygons

A

Figures with at least 3 straight sides and angles, typically 5 or more. Includes pentagons, hexagons, and octagons

64
Q

Trapezoid

A

A quadrilateral with only one set of parallel sides

65
Q

Quadrants

A

Quadrant 1 is the top right, quadrant 2 top left, 3 is bottom left, 4 is bottom right
Goes counterclockwise

66
Q

X intercept

A

The point where a line crosses the x axis. This is when y=0

67
Q

Y intercept

A

The point where a line crosses the y axis. This is when x=0

68
Q

Slope

A

The vertical change divided by the horizontal change

69
Q

Perpendicular lines

A

Lines with slopes that are negative reciprocals of each other. The lines intersect at a right angle

70
Q

Parallel lines

A

Lines with the same slope

71
Q

For a parallelogram, angles on the same side

A

Add up to 180

72
Q

Probability

A

Express the chance of a certain outcome occurring. The denominator is the total number of possible outcomes and the numerator is the number of outcomes that would satisfy the criteria

73
Q

Probability of two events occurring

A

Multiply probability A and probability B

74
Q

Probability of event A or event B occurring

A

Add probability A and probability B

75
Q

Given event probability formula

A

Probability A+ Probability of not A= 1

76
Q

Factorial

A

The factorial of a number is equal to that number times every positive whole number smaller than that number, down to 1. The factorial of 6 (6!) is 6x5x4x3x2x1= 720. On these problems, find a shortcut like canceling or factoring instead of doing a lot of multiplication

77
Q

Remainder patterns when dividing by integers

A

When dividing by an integer s, there are s possible remainders, 0 through s-1. The remainders cycle in an infinite loop.
17/5 has an R of 2
18/5 has an R of 3
19/5 has an R of 4
20/5 has an R of 0
21/5 has an R of 1
Then the pattern repeats. There are s-1 (4) remainders when dividing by 5

78
Q

Unit digit cycles

A

You might need to know the patterns of the ones digit when a number is raised to a power
9^1= 9
9^2= 81
9^3= 729
The pattern for 9 is 9, 1, 9. When 9 is raised to an even power, the digit is 1, when raised to an odd power, the digit is 9.

79
Q

Permutation

A

An arrangement of things in a particular order. If asked to determine how many ways you could arrange 5 statues on the shelf, the answer is 5x4x3x2x1= 120. Figure out how many slots you have, write down the number of options for each slot, and multiply them

80
Q

Combination

A

A group- different from a permutation because the order is irrelevant. Like if you have to bring home 3 different flavors of ice cream and there are 5 possible flavors to choose from. The order doesn’t matter in this case. Figure out how many slots you have and fill in the slots like you would with a permutation. Then, divide this number by the factorial of the number of slots

81
Q

Combination problem with extra conditions

A

Find the number of ways to create each of the possibilities and add the two of them together

82
Q

Divisibility rule for 3

A

Sum all of the digits for the number and then see whether the sum is divisible by 3

83
Q

Divisibility rule for 4

A

Determine whether the last 2 digits (tens and ones place) is divisible by 4. Ignore all other digits

84
Q

Divisibility rule for 6

A

The number has to be divisible by both 2 and 3- if it is, it is divisible by 6

85
Q

Divisibility rule for 9

A

Sum all of the digits for the number and then see whether the sum is divisible by 9

86
Q

Rational number

A

A terminating decimal- an integer is in the numerator and denominator. If the only prime factors of the denominator are 2 or 5, the decimal is terminating

87
Q

Irrational number

A

A decimal that continues- found in non perfect squares like radical 2

88
Q

Bowtie method

A

Cross multiply- whichever fraction has the greater number above it is the greatest fraction

89
Q

Absolute value inequalities

A

Set the expression inside the absolute value bar greater than the positive value on the right of the inequality sign. Then, set the expression as less than the negative value on the right of the inequality sign

90
Q

Absolute value inequality problems

A

Set up 2 equations. For example, if the absolute value of x is less than 3, the first equation is just x is less than 3- take away the absolute value symbol. For the second equation, the 3 becomes negative and you flip the inequality sign- x is greater than negative 3.

91
Q

Steps of solving geometry problems

A
  1. Draw the figure
  2. Label any information you have
  3. Write down any formulas you need, like area or volume
92
Q

Line segment

A

A line between 2 points without arrows on either end- it’s only considered a line if it has the arrows (lines go on forever)

93
Q

Quadrilateral

A

Has 4 sides, all angles add up to 360. A parallelogram is a type of quadrilateral, but both sets of sides are parallel to each other. A rectangle (and square) is a type of parallelogram, but it has 4 equal angles

94
Q

MADSPM exponents rules

A
  1. When you’re multiplying 2 exponents with the same base, you add the numbers
  2. When you’re dividing 2 exponents with the same base, you subtract the numbers
  3. When you have a power, you multiply the 2 exponent numbers together
95
Q

“At least” probability questions

A

To find the probability of there being at least one woman on a committee of 3 people, you would have to find the probability of one woman, two women, and three women to find the answer.

96
Q

Zero factorial

A

Equals 1

97
Q

“Different groups” phrasing

A

Order doesn’t matter- multiply the terms, but divide by the factorial of the number of terms

98
Q

Arithmetic sequence

A

Have a common difference (adding/subtracting a specific number)

99
Q

Geometric sequence

A

Multiplying/dividing by a certain number- have a common ratio

100
Q

Vertices

A

The corners of a solid

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