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Math Prep Flashcards

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1
Q

Formula for interior angles of a triangle.

A

x+y+z=180o

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2
Q

Formula for exterior angle of a triangle

A

a + b + c = 360o

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3
Q

What is the relationship between a, b, c, and x, y, z?

A

a = y + z

b = x + z

c = x + y

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4
Q

Formula for area of a triangle.

A

Area = ½ base x height

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5
Q

Relationship between any two sides of a triangle?

A

Sum of any 2 side > 3rd side

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6
Q

What are the angles in an equilateral triangle?

A

All angles = 60 degrees

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7
Q

What is an isosceles triangle?

A

Triangle where 2 sides and 2 angles are equal.

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8
Q

What is the Pythagorean Theorem?

A

a2 + b2 = c2

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9
Q

What are the ratios of the Pythagorean Triples?

A

3: 4:5
5: 12:13
7: 24:25
8: 15:27
9: 40:41

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10
Q

Fill in the blanks.

A
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11
Q

Fill in the blanks.

A
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12
Q

What is the relationship of angles a and b?

A

a + b = 180

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13
Q

What are the angles of l2 if lines l1 and l2 are parallel?

A

c2 = c1

d2 = d1

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14
Q

What is the forumla for the diameter of a circle?

A

d = 2r

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15
Q

What is the formula for the circumference of a circle?

A

C = 2πR or πD

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16
Q

What is the formula for the area of a circle?

A

A = πR2

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17
Q

What is the relationship of A, B, C, 0, and no?

A
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18
Q

What is the order of operations?

A

PEMDAS = Parentheses, Exponents, Multiplation and Division, Addition and Subtraction

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19
Q

Factor out the expression (a + b)(c + d).

A

FOIL - First, Outer, Inner, Last

( a + b) (c +d) = ac+ ad + bc + bd

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20
Q

What is the area of a square?

A

A = s2

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21
Q

What is the area of a rectangle?

A

A = lw

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22
Q

What is the area of a parallelogram?

A

A = bh

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23
Q

What is the area of a trapezoid?

A

A = ½ (b1 + b2)h

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24
Q

What is the volume of a cylinder?

25
What is the surface area of a cylinder?
SA = 2πR2 + 2πRH
26
What is the volume of a cube?
V = lwh
27
What is the surface area of a cube?
SA = 2 (lw + lh + wh)
28
What is the relationship between rate, distance, and time?
Rate = Distance / Time Distance = Rate x Time Time = Distance / Rate
29
What is the relationship between average rate, total distance, and total time?
Average Rate = Total Distance / Total Time Total Distance = Average Rate x Total Time Total Time = Total Distance / Average Rate
30
What is the formula for rate?
Rate = Quantity of A / Quantity of B
31
What is the formula for % increase?
% Increase = _New Amount - Original Amount_ x 100% Original Amount
32
What is the forumla for % decrease?
% Decrease = _Original Amount - New Amount_ x 100% Original Amount
33
What are the exponent rules?
x-a = 1/xa x0 = 1 x1 = x x2 = x \* x (xa)b = xab xa / xb= xa - b xaxb = xa+b - xodd = -y - xeven = y
34
What are the radical rules?
35
What is the definition of a prime number and what are the first 5 prime numbers?
Primes are integers divisble by only 1 and itself. Ex: 2, 3, 5, 7, 11
36
What are the divisibility rules?
A number is divisible by... * 2, if the number is even * 3, if the sum of the digits is divisble by 3 * 4, if the 2-digit number formed by the last 2 digits is divisible by 4 * 5, if the last digit is 0 or 5 * 6, if the number is divisible by both 2 and 3 * 9, if the sum of the digits is divisible by 9 * 10, if the last digit is 0
37
How to convert a fraction into: 1. an equivalent fraction 2. a decimal
1. Equivalent Fraction: Multiple or divide the numerator and denominator by same number 2. Decimal: Divide numerator by denominator
38
How to convert a decimal into a fraction?
1. For numerator, move decimal to right until number is an integer 2. For denominator, add the same number of 0's as moved decimal after 1 3. Reduce fraction
39
How to convert a mixed fraction (ex. X y/z)
1. Multiple whole number by denominator, ex. X \* Z 2. Add numerator, ex. (X \* Z) + Y 3. Place total over denominator, ex. _(X \* Z) + Y _ .......Z
40
What is the ration forumla?
Quantity of A = (Ratio of A to total)(Total)
41
List the percent rules
x% = x / 100 x% of y = (x / 100) y Percent = Part / Whole x 100 Final as percent of original = Final / Original x 100 Percent Change = Difference / Original x 100
42
ab + ac = ?
ab + ac = a(b+c)
43
a(b+c) = ?
a(b+c) = ab + ac
44
(a + b) / c = ?
(a + b) / c = a/c + b/c
45
a/c + b/c = ?
a/c + b/c = (a + b)/c
46
x% of y = ?
x% of y = y% of x
47
|-x| = ?
|-x| = |x|
48
What is the general work formua?
_ 1 _ = _1_ + _1_ + _1_ + ... _1_ total time A B C N A, B, C = time for each individual to work alone
49
What yields odd numbers?
Only (odd) x (odd) and (odd) + (even)
50
What is the standard form of a line?
y = mx + b (where *m* is the slope and *b* is the *y*-intercept)
51
How do you calculate slope?
Slope = rise / run = (y2 - y1) / (x2 - x1)
52
What is the Kaplan Method for Problem Solving?
1. Analyze the question 2. State the task 3. Approach strategicaly 4. Confirm your answer
53
What is the Kaplan Method for Data Sufficiency?
1. Analyze the question stem * Determine if Value or Yes/No. * Simplify, if necessary * Identify what is needed to answer the question 2. Evaluate the statements using 12TEN.
54
What are the Kaplan Data Sufficiency Strategies?
For Value questions, seek to find a single answer. For Yes/No questions, seek to find a definite answer to the question. Keep track of your options as you go. · If (1) is sufficient, the answer must be (A) or (D) · If (1) is insufficient, the answer must be (B), (C), or (E) · If (2) is sufficient, the answer must be (B) or (D) · If (2) is insufficient, the answer must be (A), (C), or (E)
55
What are the rules for inequalities?
Inequalities should be treated exactly like fractions, except: 1. When multipling or dividing an inequality by a negative number, flip the direction of the inequality sign. Ex. (x \> y) \* -1 = (-x \< -y). 2. Inequalities can only be solved for a range of values.
56
What is simplified work formula?
Total time = _ AB _ A + B A, B = individual work times
57
What is the formula to calculate simple interest?
p + i = p (1+rt) P = Principal I = Interest t = time period r = interest rate per time period as a decimal
58
What is the formula to calculate compound interest?
p + i = p(1 + r)t p = principal i = interest r = interest per time period as a decimal, over number of times compounded per year (usually 1) t = time period times number of time compound per year (usually 1)

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