Volume 1 Flashcards
0
Q
Elevenths (1/11..2/11..3/11..) decimal equivalent pattern.
A
2 digit number repeating Numerator times 9 1/11 = .090909 2/11 = .181818 3/11 = .272727 4/11 = .363636 5/11 = .454545 6/11 = .545454 7/11 = .636363 8/11 = .727272 9/11 = .818181 10/11 = .909090
1
Q
Ninths (1/9..2/9..3/9..) decimal equivalent pattern.
A
1/9 = .11111 2/9 = .22222 3/9 = .33333 4/9 = .44444 5/9 = .55555 6/9 = .66666 7/9 = .77777 8/9 = .88888
2
Q
Eighths (1/8..3/8..) decimal equivalent pattern.
A
Nearest inferior quarter (.25, .5, .75) Plus .125 1/8 = .125 3/8 = .375 5/8 = .625 7/8 = .875
6
Q
Calculating circumference, diameter, and radius
A
c = πd c = 2πr
7
Q
Surface area of a sphere
A
4πr^2
8
Q
Remainder formula
A
Dividend/Divisor = decimal quotient = integer quotient + remainder/divisor
Dividend = (integer quotient)*(divisor) + remainder
*** DECIMAL PART OF DECIMAL QUOTIENT = REMAINDER/DIVISOR
9
Q
Divide small number by large number. Eg, 3/47
A
(100 * 3) / 47 {plus 2 positions}
= 300 / 47
= 6 + 42/47
= .06???
{420/47=8
= } ???
10
Q
Cancel BEFORE you multiply
Eg, 56/x = 24/27
A
56/x = 24/27 56 * 27 = 24x x = 56*27/24 x = 56*9/8 x = 7*9 x = 63
11
Q
Negative power
Eg (2)^-3
A
Base raised to a negative power is equal to the reciprocal of (ie 1 divided by) the base raised to the original power positive
= 1 / 2^3 = 1/8 = .125
12
Q
Area of a circle
A
Pi*r^2
13
Q
Exponential Equations
(X^n) * (X^m = ?
A
X^n+m
14
Q
Exponential Equations
(X^n) / (X^m) = ?
A
X^n-m
15
Q
Exponential Equations
(X/Y)^n = ?
A
(X^n) / (Y^n)
16
Q
Exponential Equations
(X^n) * (Y^n) = ?
A
(XY)^n
17
Q
Exponential Equations
(X^y)^z = ?
A
X^yz
18
Q
Exponential Equations
X^-n = ?
A
1/(X^n)
19
Q
Exponential Equations
1^n = ?
A
1
20
Q
Exponential Equations
X^0 = ?
A
1
21
Q
Exponential Equations
X^0 = ?
A
0, except 0^0 = 1 or undefined
22
Q
Exponential Equations
F(v) = ?
A
C(v) * (1+g)^T
23
Q
Distance formula
A
Rate*Time
24
Q
Wage formula
A
Rate*Time
25
Q
FOIL
A
First
Outside
Inside
Last
26
Q
Difference of squares
A
A^2 - B^2 = (A+B)(A-B)
27
Squares 11-20
```
11*11 = 121
12*12 = 144
13*13 = 169
14*14 = 196
15*15 = 225
16*16 = 256
17*17 = 289
18*18 = 324
19*19 = 361
20*20 = 400
```
28
Simple probability
(# of ways that fit the argument) / (# of total ways)
29
Common factors
What factors greater than 1 do 135 and 225 have in common?
```
5...
135=5*27=5*3*3*3
225=5*45{45=5*9}=5*5*9=5*5*3*3
...5s and 3s...
Strand in common: 5*3*3
3*3=9
5*3=15
5*3*3=45
Answer: 3, 5, 9, 15, 45
```
30
Gross profit
Selling price - Cost
31
Fast fractions
1/x + 1/y
Eg, 1/7 + 1/20
x+y / xy
1/7 + 1/20
= 27/140
32
Multiplying fractions
1) Multiply numerators
2) Multiply denominators
3) Simplify the fraction if necessary
33
Pythagorean theorem
Relationship of right triangle sides
A^2 + B^2 = C^2
Where C is hypotenuse
34
Area of a triangle
A = 1/2 * bh
| Half of a square/rectangle
35
Divide by 9 pattern
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999
Division by 9's causes the repeating pattern.
Number of numerator digits = number of denominator 9s
36
Divide by 9 pattern of 0
| Eg, 2/90
Answer: .022
Note the pattern if zeros preceed the repeating decimal:
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900
Adding zero's to the denominator adds zero's before the repeating decimal.
Number of numerator digits = number of denominator 9s
37
Sixths fraction-decimal equivalent
```
1/6 = .166...
5/6 = .833...
```
38
Sevenths fraction-decimal pattern
```
Remember 14 28 42 57 71 85 with varying combinations.
* These 6 integers are the first 2 decimal digits for ascending sevenths beginning 1/7.
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142
```
39
Twelfths fraction-decimal pattern
```
1/12 = .0833...
5/12 = .4166...
7/12 = .5833...
11/12 = .9166...
```
40
TAKEAWAY
If you need a calculator, you're probably going about the problem wrong.
41
Prime numbers
| Single digits
2, 3, 5, 7
42
Prime numbers
| 1's
11, 31, 41, 61, 71
43
Prime numbers
| 3's
13, 23, 43, 53, 73, 83
44
Prime numbers
| 7's
17, 37, 47, 67, 97
45
Prime numbers
| 9s
19, 29, 59, 79, 89
46
Common powers and roots
2
```
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024
```
47
Common powers and roots
3
```
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
```
48
Common powers and roots
4
```
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^5 = 1024
```
49
Common powers and roots
5
```
5^1 = 5
5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3125
```
50
Remainder formula
Dividend/Divisor = decimal quotient = integer quotient + remainder/divisor
Dividend = (integer quotient)*(divisor) + remainder
*** DECIMAL PART OF DECIMAL QUOTIENT = REMAINDER/DIVISOR
51
Divide small number by large number. Eg, 3/47
```
(100 * 3) / 47 {plus 2 positions}
= 300 / 47
= 6 + 42/47
= .06???
{420/47=8
= } ???
```
52
Cancel BEFORE you multiply
Eg, 56/x = 24/27
```
56/x = 24/27
56 * 27 = 24x
x = 56*27/24
x = 56*9/8
x = 7*9
x = 63
```
53
Negative power
| Eg (2)^-3
Base raised to a negative power is equal to the reciprocal of (ie 1 divided by) the base raised to the original power positive
= 1 / 2^3 = 1/8 = .125
54
Area of a circle
Pi*r^2
55
Exponential Equations
| (X^n) * (X^m = ?
X^n+m
56
Exponential Equations
| (X^n) / (X^m) = ?
X^n-m
57
Exponential Equations
| (X/Y)^n = ?
(X^n) / (Y^n)
58
Exponential Equations
| (X^n) * (Y^n) = ?
(XY)^n
59
Exponential Equations
| (X^y)^z = ?
X^yz
60
Exponential Equations
| X^-n = ?
1/(X^n)
61
Exponential Equations
| 1^n = ?
1
62
Exponential Equations
| X^0 = ?
1
63
Exponential Equations
| X^0 = ?
0, except 0^0 = 1 or undefined
64
Exponential Equations
| F(v) = ?
C(v) * (1+g)^T
65
Distance formula
Rate*Time
66
Wage formula
Rate*Time
67
FOIL
First
Outside
Inside
Last
68
Difference of squares
A^2 - B^2 = (A+B)(A-B)
69
Squares 11-20
```
11*11 = 121
12*12 = 144
13*13 = 169
14*14 = 196
15*15 = 225
16*16 = 256
17*17 = 289
18*18 = 324
19*19 = 361
20*20 = 400
```
70
Simple probability
(# of ways that fit the argument) / (# of total ways)
71
Common factors
What factors greater than 1 do 135 and 225 have in common?
```
5...
135=5*27=5*3*3*3
225=5*45{45=5*9}=5*5*9=5*5*3*3
...5s and 3s...
Strand in common: 5*3*3
3*3=9
5*3=15
5*3*3=45
Answer: 3, 5, 9, 15, 45
```
72
Gross profit
Selling price - Cost
73
Fast fractions
1/x + 1/y
Eg, 1/7 + 1/20
x+y / xy
1/7 + 1/20
= 27/140
74
Multiplying fractions
1) Multiply numerators
2) Multiply denominators
3) Simplify the fraction if necessary
75
Pythagorean theorem
Relationship of right triangle sides
A^2 + B^2 = C^2
Where C is hypotenuse
76
Area of a triangle
A = 1/2 * bh
| Half of a square/rectangle
77
Divide by 9 pattern
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999
Division by 9's causes the repeating pattern.
Number of numerator digits = number of denominator 9s
78
Divide by 9 pattern of 0
| Eg, 2/90
Answer: .022
Note the pattern if zeros preceed the repeating decimal:
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900
Adding zero's to the denominator adds zero's before the repeating decimal.
Number of numerator digits = number of denominator 9s
79
Sixths fraction-decimal equivalent
```
1/6 = .166...
5/6 = .833...
```
80
Secenths fraction-decimal pattern
```
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142
```
81
Twelfths fraction-decimal pattern
```
1/12 = .0833...
5/12 = .4166...
7/12 = .5833...
11/12 = .9166...
```
82
Addition 'wording'
```
Increased by
More than
Combined
Together
Total of
Sum
Added to
And
Plus
```
83
Subtraction 'wording'
```
Decreased by
Minus
Less
Difference between/of
Less than
Fewer than
Minus
Subtracted from
```
84
Multiplication 'wording'
```
Of
Times
Multiplied by
Product of
Increased/Decreased by a factor of
```
85
Division 'wording'
```
Per
Out of
Ratio of
Quotient of
Percent (divide by 100)
Divided by
Each
```
86
Equals 'wording'
```
Is
Are
Was
Were
Will be
Gives
Yields
Sold for
Costs
Adds up to
The same as
As much as
```
87
Variable or Value 'wording'
A number
How much
How many
What
88
Dividing fractions
EG, (2/3) / (1/4)
Multiple numerator by reciprocal of denominator.
EG, (2/3) / (1/4) = (2/3) * (4/1) = 8/3
89
Reciprocals
2 numbers are reciprocals if and only if their product is equal to 1.
Tricks: square root of x = (square root if x) / x
