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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
Total Earnings
= Wage Rate \* Hours Worked
26
Miles
Miles per Hour \* Hours Miles per Gallon \* Gallon
27
Distance Work
Rate \* Time
28
Average Rate
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
Standard Deviation
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
Weighted Average Formula
Only use if you have two data points and relatively easy # (Component 1)(Weighting 1) + (Component 2)(Weighting 2)...
31
Weighted Average Teeter-Totter Method
32
Consecutive Integers: How many integers from 14 to 765, inclusive?
Last - First + 1 765-14 + 1 = 752
33
Consecutive Multiples:
Last-First / Increment + 1
34
How many multiples of 7 between 10 and 80?
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
Properties of evenly spaced sets:
Average = Median Average = (First + Last)/2 Total = Avg \* # of terms of terms = [(largest - smallest)/spacing] + 1
36
Combinatorics
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
Factor Foundation Rule
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
E ± E O ± O E ± O E \* E E \* O O \* O
*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
Sum of Two Primes
* 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
If one of the sides of a triangle inscribed in a circle is a diameter of the circle, then the triangle must be 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
Pythagorean Theorem + Common Right Triangles
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
Sum of interior angles of a polygon
(n-2) \* 180 Triangle (3) = 180 Quadrilateral (4) = 360 Pentagon (5) = 540 Hexagon (6) = 720
43
Area of a Trapezoid
(base1 + base2)(height) / 2
44
Area of a Parallelogram
base \* height
45
Triangle Theorem
* 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
Isosceles Triangle
Two of three sides are equal Leg: x Leg: x Hypotenuse: x√2 Angles: 45/45/90
47
Equilateral Triangle
Leg opposite 30: x Leg opposite 60: x√3 Hypotenuse: 2x Angles: 30/60/90
48
Exterior Angles of a Triangle
49
Area of a Triangle
Base \* Height / 2
50
Circumference Diameter Area
Circumference: πd OR 2πr Diameter: 2r Area: πr2
51
Area of a Sector
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
Inscribed v Central Angle
Central angle: vertex @ center point of circle Inscribed angle: vertex on circle itself An inscribed angle = 1/2 of equivalent central angle
53
Volume of a Cylinder
V = πr2h
54
Slope of a line
rise/run = y2-y1/x2-x1
55
Slope-Intercept Equation
y = mx+b m = slope b = y-intercept Horizontal line: y = # Verticle line: x = #

GMAT (6 decks)

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