Volume 1 Flashcards
Elevenths (1/11..2/11..3/11..) decimal equivalent pattern.
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
Ninths (1/9..2/9..3/9..) decimal equivalent pattern.
1/9 = .11111 2/9 = .22222 3/9 = .33333 4/9 = .44444 5/9 = .55555 6/9 = .66666 7/9 = .77777 8/9 = .88888
Eighths (1/8..3/8..) decimal equivalent pattern.
Nearest inferior quarter (.25, .5, .75) Plus .125 1/8 = .125 3/8 = .375 5/8 = .625 7/8 = .875
Calculating circumference, diameter, and radius
c = πd c = 2πr
Surface area of a sphere
4πr^2
Remainder formula
Dividend/Divisor = decimal quotient = integer quotient + remainder/divisor
Dividend = (integer quotient)*(divisor) + remainder
*** DECIMAL PART OF DECIMAL QUOTIENT = REMAINDER/DIVISOR
Divide small number by large number. Eg, 3/47
(100 * 3) / 47 {plus 2 positions} = 300 / 47 = 6 + 42/47 = .06??? {420/47=8 = } ???
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
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
Area of a circle
Pi*r^2
Exponential Equations
(X^n) * (X^m = ?
X^n+m
Exponential Equations
(X^n) / (X^m) = ?
X^n-m
Exponential Equations
(X/Y)^n = ?
(X^n) / (Y^n)
Exponential Equations
(X^n) * (Y^n) = ?
(XY)^n
Exponential Equations
(X^y)^z = ?
X^yz
Exponential Equations
X^-n = ?
1/(X^n)
Exponential Equations
1^n = ?
1
Exponential Equations
X^0 = ?
1
Exponential Equations
X^0 = ?
0, except 0^0 = 1 or undefined
Exponential Equations
F(v) = ?
C(v) * (1+g)^T
Distance formula
Rate*Time
Wage formula
Rate*Time
FOIL
First
Outside
Inside
Last
Difference of squares
A^2 - B^2 = (A+B)(A-B)
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
Simple probability
(# of ways that fit the argument) / (# of total ways)
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
Gross profit
Selling price - Cost
Fast fractions
1/x + 1/y
Eg, 1/7 + 1/20
x+y / xy
1/7 + 1/20
= 27/140
Multiplying fractions
1) Multiply numerators
2) Multiply denominators
3) Simplify the fraction if necessary
Pythagorean theorem
Relationship of right triangle sides
A^2 + B^2 = C^2
Where C is hypotenuse
Area of a triangle
A = 1/2 * bh
Half of a square/rectangle
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
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
Sixths fraction-decimal equivalent
1/6 = .166... 5/6 = .833...
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
Twelfths fraction-decimal pattern
1/12 = .0833... 5/12 = .4166... 7/12 = .5833... 11/12 = .9166...
TAKEAWAY
If you need a calculator, you’re probably going about the problem wrong.
Prime numbers
Single digits
2, 3, 5, 7
Prime numbers
1’s
11, 31, 41, 61, 71
Prime numbers
3’s
13, 23, 43, 53, 73, 83
Prime numbers
7’s
17, 37, 47, 67, 97
Prime numbers
9s
19, 29, 59, 79, 89
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
Common powers and roots
3
3^1 = 3 3^2 = 9 3^3 = 27 3^4 = 81 3^5 = 243
Common powers and roots
4
4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024
Common powers and roots
5
5^1 = 5 5^2 = 25 5^3 = 125 5^4 = 625 5^5 = 3125
Remainder formula
Dividend/Divisor = decimal quotient = integer quotient + remainder/divisor
Dividend = (integer quotient)*(divisor) + remainder
*** DECIMAL PART OF DECIMAL QUOTIENT = REMAINDER/DIVISOR
Divide small number by large number. Eg, 3/47
(100 * 3) / 47 {plus 2 positions} = 300 / 47 = 6 + 42/47 = .06??? {420/47=8 = } ???
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
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
Area of a circle
Pi*r^2
Exponential Equations
(X^n) * (X^m = ?
X^n+m
Exponential Equations
(X^n) / (X^m) = ?
X^n-m
Exponential Equations
(X/Y)^n = ?
(X^n) / (Y^n)
Exponential Equations
(X^n) * (Y^n) = ?
(XY)^n
Exponential Equations
(X^y)^z = ?
X^yz
Exponential Equations
X^-n = ?
1/(X^n)
Exponential Equations
1^n = ?
1
Exponential Equations
X^0 = ?
1
Exponential Equations
X^0 = ?
0, except 0^0 = 1 or undefined
Exponential Equations
F(v) = ?
C(v) * (1+g)^T
Distance formula
Rate*Time
Wage formula
Rate*Time
FOIL
First
Outside
Inside
Last
Difference of squares
A^2 - B^2 = (A+B)(A-B)
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
Simple probability
(# of ways that fit the argument) / (# of total ways)
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
Gross profit
Selling price - Cost
Fast fractions
1/x + 1/y
Eg, 1/7 + 1/20
x+y / xy
1/7 + 1/20
= 27/140
Multiplying fractions
1) Multiply numerators
2) Multiply denominators
3) Simplify the fraction if necessary
Pythagorean theorem
Relationship of right triangle sides
A^2 + B^2 = C^2
Where C is hypotenuse
Area of a triangle
A = 1/2 * bh
Half of a square/rectangle
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
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
Sixths fraction-decimal equivalent
1/6 = .166... 5/6 = .833...
Secenths fraction-decimal pattern
1/7 = .142857 2/7 = .285714 3/7 = .428571 4/7 = .571428 5/7 = .714285 6/7 = .857142
Twelfths fraction-decimal pattern
1/12 = .0833... 5/12 = .4166... 7/12 = .5833... 11/12 = .9166...
Addition ‘wording’
Increased by More than Combined Together Total of Sum Added to And Plus
Subtraction ‘wording’
Decreased by Minus Less Difference between/of Less than Fewer than Minus Subtracted from
Multiplication ‘wording’
Of Times Multiplied by Product of Increased/Decreased by a factor of
Division ‘wording’
Per Out of Ratio of Quotient of Percent (divide by 100) Divided by Each
Equals ‘wording’
Is Are Was Were Will be Gives Yields Sold for Costs Adds up to The same as As much as
Variable or Value ‘wording’
A number
How much
How many
What
Dividing fractions
EG, (2/3) / (1/4)
Multiple numerator by reciprocal of denominator.
EG, (2/3) / (1/4) = (2/3) * (4/1) = 8/3
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