Math final

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Author:
regishouse
ID:
120457
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Math final
Updated:
2011-12-05 05:42:46
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Math 35
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Math 35
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  1. area of square
    A = s2
  2. Perimeter of a square
    P = 4s
  3. Area of a rectangle
    A = L x W
  4. Perimeter of a rectangle
    P = 2L + 2W
  5. Area of a Circle
    A=πr2
  6. Cirumference of a circle
    C=2πr or C=πd
  7. Diameter of a Circle
    D = 2r
  8. Area of a triangle
    A=1/2(b)(h)
  9. Pythagorean Theorem
    C2 = A2 + B2
  10. D
    R x T
  11. Volume of a Rectangle
    V = LWH
  12. Anything divided by zero is undefined
    #/0 = undefined
  13. Simple Fractions
    • divide out common factor
    • 15/3 (divide by 5)
  14. Prime Numbers
    • only divisable by 1 & itself
    • 2,3,5,7,11,13
  15. Composite Numbers
    • can be divided by several numbers(even numbers except 2)
    • 10,15,20,100,42,66....
  16. Improper Fraction to Mixed Number
    • Use long division to make into mixed #
    • 7/3 (3 ÷ 7 = 2 r1 = 2 1/3)
  17. Mixed Number to Improper Fraction
    • Divided demoninator by whole number , add numerator, use same demoniator
    • 5 2/3 = (3÷5 + 2= 17/3)
  18. Multiplying Fractions
    • multiply across (a/b * c/d)
    • 5/8 * 3/4 (5*3/8*4) = 15/32

    *Simplify when possible*
  19. Multiplying Mixed Fractions
    • Change to improper fraction, divide denominator by whole number, add numerator, use same denominator
    • 4 1/2 * 5 4/5 ( 9/2*29/5)

    • Cross multiply
    • 9*29/2*5 = 261/10

    • Convert to Mixed Fraction *if answer is improper
    • 10÷261 = 26r1 = 26 1/10
  20. Dividing Fractions
    • to divide, flip the reciprocal, multiply
    • (a/b÷c/d = a/b÷d/c)
    • 5/8 ÷1/4 (5/8*4/1 = 20/8) *simplfy*
    • 20/8 (divide by 4) = 5/2 *improper*
    • 2 ÷5 = 2r1 2 1/2
  21. Equivalent Fractions
    • divide by same fraction on top & bottom with the same number
    • 2/5 ( divide by 7) = 14/35
  22. Adding & Subtracting Fractions
    • need to have the same denominator before adding or subtracting (GCF)
    • a/b + c/d = a+c/b or a/b-c/d = a-c/b
    • 2/3 + 4/5 (divide all by 5) = 10/15 + 12/15 = 22/15*improper*
    • 15÷22 = 1 7/15
  23. Adding & Subtracting Mixed Fractions
    • find common denominatior, add fraction & whole numbers
    • 3 1/4 + 5 2/3 (3 3/12 + 5 8/12 = 8 11/12)

    * can change to improper fraction & add*
  24. Complex Fraction
    • convert to nomal division, flip reciprical and multiply
    • a/b/c/d = a/b ÷ c/d = a/b*d/c

    5/9/1/3 (5/9÷1/3 = 5/9*3/1 = 15/1

    *simplify when needed*
  25. Multiplying Fractions w/ unknown veriable
    • 1/4x = 3/4
    • divide both sides by 4/1 = 1x=3 x=3
  26. Fraction to Decimal
    • convert fraction to division
    • 1/3 (3÷1 = 0.333)
  27. Multiplying decimals
    • multiply, add number of decimal points & apply that to answer
    • 1.235(3 decimal places)
    • 0.4(1 decimal place)
    • 4940(move 4 decimal places)
    • = 0.494
  28. Dividing decimals
    • move decimal places from divisor to make a whole number, move the same number of place in the dividend
    • .03÷15.322(move 2 places) = 3÷532.2

    • move decimal to same place in the quotent
    • 3÷532.2 = 177.4
  29. Solving Equations (multiplying)
    • move decimals, divide out
    • 0.4x = 0.24 ( 40x = 24 / 40÷24 = .6)
    • or
    • .4x = 0.24 / .4÷0.24 = 4÷2.4 = .6

    • with like veriables
    • 2.5x + 1.5x = 5.24
    • 4.0x = 5.24
    • 4÷5.24 = 1.31
  30. Solving Equations
    • 4(2x-1.45) - 3(x + 8.02) = 24.9
    • 8x - 5.5 - 3x -24.06 = 24.9 (Distrubte veriable)
    • 5x - 29.86 = 24.9 (add like veriables)
    • 5x = 54.79 (29.86+24.9)
    • 5÷54.76
    • x = 10.952
  31. Ratios
    • write ratio as fraction
    • 19 to 42 = 19/42

    • if number is decimal, move decimal to make number whole, add number of zeros to number of moved spaces
    • 1.75/25 (2 places in num, add 2 in dem) = 175/2500

    * unit rate/ unit cost means divide*
  32. Proportion
    • 4 cups flour is to 12 muffins as 8 cups flour is to 24 muffins
    • 4/12 = 8/24
  33. True Proportion
    • cross multiply, compare answer
    • 1/3 - 7/21( 21*1 = 21 - 7*3= 21) True
  34. Solving Proportions
    • cross multiply, divide
    • 8/x = 12/9
    • 8*9
    • 72 / 72÷12
    • x = 6
  35. Percent as Decimal
    • Move decimal place 2 times from the right
    • 526% = 5.26

    • if already decimal, move two places from exsisting decimal
    • 0.78% = 0.078
  36. Decimal to Percent
    • move two spaces from the left
    • 705 = 70,500%

    • if already decimal, move two places from the exisiting decimal
    • 0.954 = 95.4%
  37. Percent as a fraction or mixed number
    • make percent a fraction over 100, simplify
    • 15% = 15/100(divide by 5) = 3/20
  38. Fraction to percent
    • long division to decimal, decimal to percent
    • 6/25 ( 25÷6 = 0.24, move decimal to places = 24%)

    • mixed number only change fraction portion
    • 1 4/5 ( 5/4 = 0.8 = 1.80%)
  39. Solving of equation or porportoion
    is/of x/100
  40. Simple Interest
    I = p*r*t

    • p = principle
    • r = rate of interest (write as decimal)
    • t = time in years
    • I = interest
  41. Tax
    • tax = tax rate * subtotal (write as decimal)
    • subtotal = cost + total
  42. Commission
    commission = total sales * commission rate (decimal)
  43. Discount
    • discount = price * discount rate (decimal)
    • sale price = original price - discount
  44. Graphing
    pick point to plug into equation, (stick w/ 0,1,2,3), plot points
  45. Complement
    • angle equaling to 90
    • 75o = 75+15 = 90
  46. Supplement
    • sum of angle is 180
    • 125o = 125 +75 = 180
  47. Triangle
    sum of all sides are equal to 180
  48. Acute angle
    less than 90o
  49. Obtuse angle
    greater than 90o
  50. Equations with exponents
    • add like terms with similar exponents
    • 11y2 - 3y + 7 + 3y2 - 7y -7
    • 14y2 (11y2 + 3y2) - 10y(-3y-7y)

    • if negative, distrubute negative
    • (9b + 2) - (3b2 - 4b + 6)
    • 9b + 2 - 3b2 + 4b - 6
  51. Exponents
    • add exponents with the same base, no exponent equals 1
    • a3 * a * a7 = a11

    • Multiply bases, add exponents
    • 2x * 3x2 * 4x3 = 24x6

    • exponent being raised is multiplied
    • (28)7 = 226

    • number with coeffeciant, raise coeff by exponent, multiply exponents
    • (2x5)3 = 8x15

    • distribute exponents and multiply
    • (2x2y)2 (y3y2)3
    • 4x4y2 * x9y6
    • 4x3y8
  52. F.O.I.L
    First, outside, inside, last

    -3x(2x4 - 2x2 + 5) = -6x5 + 6x5 -15x

    • (x+6) (x - 2)
    • x2 - 2x + 6x - 12
    • x2 + 4x - 12
  53. GCF
    smallest number in group or smallest multiple of the group

    12, 26, 60 = GCF 12

    • smallest of coeff first, then smallest of exponents
    • 6m2, 2m2, 12m5 = 2m2
  54. Factorization
    • find smallest or coeff and undo multiplication
    • 7y2 = 14y - 28 = 7(y2 + 2y - 4)

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