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Math Rules Flashcards

1
Q

If starting fraction is <1, adding same # to top and bottom does what to the fraction?

A

Increases

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2
Q

If starting fraction is >1, adding same # to top and bottom does what to the fraction?

A

Decreases

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3
Q

a5 * a3

6(6x)

A

a5 * a3 = a8

6(6x) = 61 * 6x = 61+x

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4
Q

a5/a3

A

a5/a3 = a2

Divide terms with the same base, subtract exponents

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5
Q

a0

00

A

a0 = 1

00 = undefined

Anything to the power of 0 = 1, except 0

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6
Q

(a2)4

x-3(x2)4 / x5

A

(a2)4 = a8

x-3(x2)4 / x5 = x8 / x5x3 = x8 / x8 = 1

Apply two exponents: multiply the exponents

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7
Q

(ab)3

(2-2y2)-3

A

(ab)3 = a3b3

(2-2y2)-3 = 26/y6 = 64/y6

Applying exponent to a product: apply exponent to each factor

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8
Q

a2/3

A

a2/3 = 3√a2

If you raise a number to a fractional power, apply two exponents: the numerator as a power, and the denominator as a fractional root

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9
Q

135 + 133

x5+x3

A

135 + 133 = 133132 + 133 = 133 (132 + 1)

x5+x3 = x3x2+x3 = x3(x2 + 1)

Add or subtract terms with the same base: pull out a common factor

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10
Q

√2

√3

A

√2 = 1.4

√3 = 1.7

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11
Q

Square root of a number between 0 and 1 is greater or less than the original number?

√0.5

√2/3

A

Greater than!

√0.5 > 0.5 –> approx. 0.7

√2/3 > 2/3 –> approx. 0.8

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12
Q

√8 * √2

√27/√3

√15 * √12 / √5

A

√8 * √2 = √8*2 = √16 = 4

√27/√3 = √27/3 = √9 = 3

√15 * √12 / √5 = √(15 * 12)/ 5 = √(3 * 12) = 6

Multiplying square roots: put everything under the root

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13
Q

√32+42

√310+311

A

√32+42 = √9+16 = √25 = 5

CANNOT BREAK INTO √32+√42, MUST FOLLOW PEMDAS

√310+311 = √310(1+3) = √310 *√4 = (310)1/2 * 2 = 35 * 2

CANNOT COMBINE FURTHER

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14
Q

Percent Change

A

x2 - x1 / x1

x2 = final value

x1 = initial value

F - O / O

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15
Q

How to multiply decimals

  1. 02 * 1.4
  2. 0003 * 40,000
A

Multiply as if whole #s and count digits to the right of the decimal:

0.02 * 1.4

  • Digits to the right of decimal: 3
  • 2 * 14 = 28
  • Move decimal three digital to the left: 0.028

Move the same # of places left and right and multiply whole numbers:

0.0003 * 40,000

  • Move 0.0003 to the right four places (3)
  • Move 40,000 to the left four places (4)
  • 3*4 = 12
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16
Q

How to divide decimals

0.0045/0.09

A

Shift decimal same # in numerator and denominator to make whole number:

0.0045/0.09 = 45/900 (and divide from there)

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17
Q

When should I test cases?

A

Data sufficiency “theory” problem

Problem solving with a must be or could be question

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18
Q

When should I use smart numbers?

A

Problem solving with variables, fractions or percents

Ratios

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19
Q

When should I work backwards?

A

Problem-solving with real values in the answers, answer choices represent a single variable in the problem.

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20
Q

(x+y)2

A

(x+y)2 = x2 + 2xy + y2

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21
Q

(x-y)2

A

(x-y)2 = x2 - 2xy + y2

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22
Q

(x+y)(x-y)

A

(x+y)(x-y) = x2-y2

1 +

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23
Q

Total Cost Formula

A

= Unit Price * Quantity

24
Q

Profit

A

Revenue - Cost

25
Q

Total Earnings

A

= Wage Rate * Hours Worked

26
Q

Miles

A

Miles per Hour * Hours

Miles per Gallon * Gallon

27
Q

Distance

Work

A

Rate * Time

28
Q

Average Rate

A

Total Distance / Total Time

Average will always be closer to the closer of the two rates than to the faster (because more time spent in the slower rate)

29
Q

Standard Deviation

A

How far from the average the data points typically fall

Small SD: set is clustered closely around the average

Large SD: set is spread out widely with some points appearing far from the mean

If every absolute difference from the mean is equal, the SD equals that difference

Set: 0,0,10,10

Mean: 5

Difference from mean: 5,5,5,5

SD: 5

30
Q

Weighted Average Formula

A

Only use if you have two data points and relatively easy #

(Component 1)(Weighting 1) + (Component 2)(Weighting 2)…

31
Q

Weighted Average

Teeter-Totter Method

32
Q

Consecutive Integers:

How many integers from 14 to 765, inclusive?

A

Last - First + 1

765-14 + 1 = 752

33
Q

Consecutive Multiples:

A

Last-First / Increment + 1

34
Q

How many multiples of 7 between 10 and 80?

A

7 is not a factor of 10 nor 80, so find least multiple and greatest multiple of 7 in that range, and use at 1 and last digit:

(14, 77)

Last-First/Increment + 1

77-14/7 + 1 = 10

35
Q

Properties of evenly spaced sets:

A

Average = Median

Average = (First + Last)/2

Total = Avg * # of terms

of terms = [(largest - smallest)/spacing] + 1

36
Q

Combinatorics

A

Order doesn’t matter:

Pool!/In!Out!

Order matters:

Pool!/Place!Place!Place!Out!

1st, 2nd, 3rd place, one each, 7 kids total

[7!/1!1!1!4! = 7!6!5!4!/1!1!1!4! = 210 arrangements]

37
Q

Factor Foundation Rule

A

If a is a factor of b, and b is a factor of c, then a is a factor of c.

–> If 72 is divisible by 12, then 72 is also divisibly by the factors of 12 (1,2,3,4,6 and 12)

38
Q

E ± E

O ± O

E ± O

E * E

E * O

O * O

A

All same, even. One diff, odd.

E ± E = E

O ± O = E

E ± O = O

Any even present, even.

E * E = E

E * O = E

O * O = O

39
Q

Sum of Two Primes

A
  • All primes are odd except 2
  • Prime + Prime will be even unless one of those primes 2 (because O + O, unless 2)
  • If problem tells you sum of two primes is odd, one of the primes must be 2, other must not be 2
  • If you know 2 cannot be one of the primes in the sum, sum must be even
40
Q

If one of the sides of a triangle inscribed in a circle is a diameter of the circle, then the triangle must be a ________.

A

If one of the sides of a triangle inscribed in a circle is a diameter of the circle, then the triangle must be a right triangle.

The angle opposite the diameter is the right angle.

41
Q

Pythagorean Theorem + Common Right Triangles

A

a2 + b2 = c2

3 - 4 -5 (32 + 42 = 52) –> 6 - 8 - 10; 9 - 12 - 15; 12 - 16 - 20

5 - 12 - 13 –> 10 - 24 - 26

8 - 15 - 17

42
Q

Sum of interior angles of a polygon

A

(n-2) * 180

Triangle (3) = 180

Quadrilateral (4) = 360

Pentagon (5) = 540

Hexagon (6) = 720

43
Q

Area of a Trapezoid

A

(base1 + base2)(height) / 2

44
Q

Area of a Parallelogram

A

base * height

45
Q

Triangle Theorem

A
  • Sum of angles = 180
  • Angles correspond to opposite sides
    • Largest angle is opposite longest side
    • Smallest angle is opposite shortest side
    • If two sides are equal, their opposite angles are also equal
  • Sum of any two sides of a triangle must be greater than the third side
46
Q

Isosceles Triangle

A

Two of three sides are equal

Leg: x

Leg: x

Hypotenuse: x√2

Angles: 45/45/90

47
Q

Equilateral Triangle

A

Leg opposite 30: x

Leg opposite 60: x√3

Hypotenuse: 2x

Angles: 30/60/90

48
Q

Exterior Angles of a Triangle

49
Q

Area of a Triangle

A

Base * Height / 2

50
Q

Circumference

Diameter

Area

A

Circumference: πd OR 2πr

Diameter: 2r

Area: πr2

51
Q

Area of a Sector

A
  1. Find area of entire circle: πr2
    1. ​π32 = 9π
  2. Use central angle to determine what fraction of the entire circle is represented by the sector
    1. Central angle: 60
    2. Whole circle: 360
    3. Fraction: 60/360 –> 1/6 of area –> 1/6 (9π) = 1.5π
52
Q

Inscribed v Central Angle

A

Central angle: vertex @ center point of circle

Inscribed angle: vertex on circle itself

An inscribed angle = 1/2 of equivalent central angle

53
Q

Volume of a Cylinder

54
Q

Slope of a line

A

rise/run = y2-y1/x2-x1

55
Q

Slope-Intercept Equation

A

y = mx+b

m = slope

b = y-intercept

Horizontal line: y = #

Verticle line: x = #

GMAT (6 decks)

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