CSET 2: Math Summary

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hunnie_bebe
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CSET 2: Math Summary
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2013-02-13 17:17:18
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CSET Math Summary
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CSET 2: Math Summary
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  1. Natural Number
    Whole Number
    Integer
    Rational Number
    Irrational Number
  2. Prime Number
    Composite Number
    • Prime number: 2 positive integer factors
    • 2,3,5,7...
    • Composite number: other numbers
    • 4,6,8...

    1 is neither
  3. Rules of Divisibility
  4. Which expression below is incorrectly written in scientific notation?
    A. 58x105
    B. 5.333x10-9
    C. 1.8x10-6
    D. 4.92x1010
    Scientific notation is the product of a number between 1 and 10 multiplied by a power of 10.

    (a) should be 5.8x106

    • 5.8 is a number between 1 and 10 and 58 is not
  5. Zero Rule
    Any number to the zero power equals 1 and not zero. This is so because the base is multiplied the exponent number of times so you are left with is 1

    20 = 1
  6. Rule of 1
    any base raised to the power of 1 is itself

    21 = 2
  7. Negative exponents
    look at the inverse operation of multiplication, which is division:

    2-4 =
  8. Product rules for exponents
    when multiplying exponents w/ the same base, add the exponents and keep the same base

    24 x 23 = 2 (4+3) = 27 = 128
  9. Quotient rules for exponents
    when dividing exponents w/ the same base, subtract the exponents and keep the same base

    = 2 (4-3) = 2-1
  10. Power rules for exponents
    When an exponent is raised to another power,multiply the exponents and keep the same base

    (24)-3 = 2 (4x-3) = 2 -12
  11. multiplicative identity
    a number is multiplied by 1 equals itself

    365 x 1 = 365
  12. commutative property
    addition n multiplication stating the order in which 2 numbers are added or multiplied does not change their sum or product

    • a + b = b + a
    • 44 + 55 = 55 + 44

    • a x b = b x a
    • 25 x 5 = 5 x 25
  13. associate property
    addition n multiplication stating the grp of 3 numbers does not change their sum or product

    • (a + b) + c = a + (b+c)
    • (a x b) x c = a x (b x c)
  14. distributive property
    addition n multiplication stating that when multiplying a number by a sum or difference, you may either add/subtract first and then multiply, or multiply first then add/subtract

    • a x (b+c) =a(b) + a(c)
    • a x (b-c) =a(b) - a(c)
  15. diving fractions w/ mixed numbers
    • 1) write in fraction form
    • 2) multiply first term by the reciprocal of the second term
    • 3) write in simplest form

    divide x = =
  16. PERDMAS

    please excuse my dear aunt sally PEMDAS
    • left to right:
    • Parentheses
    • Exponents
    • Roots
    • Division
    • Multiplication
    • Addition
    • Subtraction
  17. Flipping the inequality sign
    occurs only when multiplying or dividing each side by a negative number; add/subtraction of terms from each side of an inequality does not change the direction of the inequality sign.

    • -3x + 3 ≥ 12
    • -3x ≥ 9
    • x ≥ -3 change to x ≤3
  18. Linear equations and their properties pg 274
  19. System of equations pge 276
  20. Linear equation y=mx+b pg 274
    makes lines
  21. quadratic equation ax2+bx+c=0 pg 280
    finds a parabola that opens up and down (never sideways)

    • x2 > 0 up
    • x2 < 0 down

    • x = -b/2a axis of symmetry of a parabola
    • input "x" into the equation to find "y" to get
    • coordinates (x,y)
  22. Quadratic formula pg 284
  23. Steps to graphing quadratic equation

    y=ax2 + bx + c
    1. Determine where the parabola opens upward/downward

    a > 0 (up) or a < 0 (down)

    2. Use the axis of symmetry formula to find "x"

    x = -b/2a

    3. Vertex of the parabola: substitute the x-coordinate into the equation to find the y-coordinate (x,y)

    4. Determine the y-intercept: substitute x=0 into the standard form of the quadratic equation (0,y)

    5. Determine the x-intercept: substitute y=0 into the standard form of the quadratic equation (x,0),(x,0) [zero property]

    6. Draw the graph w/ the coordinates. Symmetric to the vertical axis
  24. Pythagorean Theorem (right triangles only)
    a2+b2=c2

    the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse
  25. Isosceles Triangle
    Scalene Triangle
    • Isosceles - 2 sides of the same length
    • Scalene - no equal sides
  26. Area: Parallogram = rectangle
    • A=bxh
    • A=lxw
  27. mass and weight
    • mass - amt of matter an object has
    • weight - measure of how much gravitational pull is acting on it

    proportional to each other
  28. Temperature
    C = 5/9 (F-32)

    F = 9/5C + 32
  29. Metric system
    • Metric Prefix     Mathematical Value
    • Mega-              Million
    • Kilo-                Thousand
    • Hecto-             Hundred
    • Deka-              Ten
    • Deci-               One-tenth
    • Centi-              One-hundredth
    • Milli-                One-thousandth
    • Micro-              One-millionth
  30. Length (US to metric)
    • Length
    • 1 in = 2.54 cm
    • 1 ft = 30 cm
    • 1 yd = .9 m
    • 1 mile = 1.6 km
  31. Weight (US to metric)
    • 1 oz = 28 g
    • 1 lb = 45 kg
    • 1 T = .9 metric tonne (t)
  32. Area (US to metric)
    • 1 in2 = 6.5 sq cm
    • 1 ft2 = .09 sq m
    • 1 m2 = 2.6 sq km
  33. Volume (US to metric)
    • 1 fl oz = 30 mL
    • 1 qt = .95 L
    • 1 gal = 3.8 L
    • 1 ft3 =.03 m3
    • 1 yd3 =.76 m3
  34. Metric Units
    • Volume
    • 1000 mL = 1 L
    • 250 mL = 1 metric cup
    • 4 metric cups = 1 L
    • 1000 L = 1 kL

    • Mass
    • 1000 mg = 1 g
    • 1000 g = 1 kg

    • Linear Units
    • 10 mm = 1 cm
    • 100 cm = 1 m
    • 1000 m = 1 km
  35. US Units
    • Volume
    • 8 fl oz = 1 c
    • 2 c = 1 pt
    • 2 pt = 1 qt
    • 4 c = 1 qt
    • 4 qt = 1 gal

    • Weight
    • 16 oz = 1 lb
    • 2000 lb = 1 T

    • Linear Units
    • 12 in = 1 ft
    • 3 ft = 1 yd
    • 5280 ft = 1 mi
    • 1760 yd = 1 mi
  36. Formulas
    Perimeter
    Area
    • Perimeter (P)          Area (A)
    • Triangle    = a+b+c           =1/2bh

    Trapezoid  =s1+s2+b1+b   =1/2h(b1+b2)

    Parallelogram =2(a+b)         =bh

    Rectangle      =2(l+w)          =lw

    Square          =4s                 =s2

    Circle            =d or 2r         =r2
  37. Formulas
    Surface Area
    Prism     =+ areas of each face            

    • Pyramid =+ areas of the base + each face

    • Cylinder =
    • (1) area of the 2 bases  r2
    • (2) length (circumference value r) x height (width)
    • (3) add the two values
  38. Formulas
    Volume
    Prism     =Bh (area of the base x height)

    Pyramid =Bh (area of the base x height)

    Cylinder =r2h

    Cone =r2h

    Sphere =r3
  39. Distance
    d = rt
  40. Graphs
    • Line - show change over time
    • Circle - part to whole relationships
    • Bar - compare amts between grps
    • Tally tables - record amts in general way
  41. Mean, median, mode, range
    • mean - avg
    • median - middle number
    • mode - occurs frequently
    • range - difference between high and low number
  42. Probability
    Probability of an event =

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