TAP MATH BIG FINAL

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shockwave
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263242
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TAP MATH BIG FINAL
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2015-01-12 19:25:24
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TAP MATH BIG FINAL
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TAP MATH BIG FINAL
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  1. DEFINE THIS:
    A U B 

    A UNION

    EVERYTHING THAT IS IN EITHER OF THE SETS

    {1,2,3}
  2. VENN DIAGRAM. WHAT DOES "A U B" LOOK LIKE OR MEAN?
    U IS UNION.

    EVERYTHING THAT IS IN EITHER OF THE SETS.

    {1,2,3}

  3. DEFINE THIS:
    • A ^ B    ----OR----  A Π B
    • (Π UPSIDE DOWN U)

    A INTERSECT B 

    ONLY THINGS THAT ARE IN BOTH OF THE SETS.

    {2}
  4. WHAT DOES THIS LOOK LIKE AND MEAN:

    A ^ B    ----OR----  A Π B(Π UPSIDE DOWN U).
    A INTERSECT B

    ONLY THINGS THAT ARE IN BOTH OF THE SETS.

    {2} 

  5. DEFINE:
    • A  "A COMPLEMENT"    OR
    • ~A   "NOT A"

    EVERYTHING IN THE UNIVERSE OUTSIDE OF A.

    {3,4}
  6. WHAT DOES THIS LOOK LIKE AND MEAN?

    AC       OR     ~A
    • AC   "A COMPLEMENT"    
    • ~A   "NOT A"

    EVERYTHING IN THE UNIVERSE OUTSIDE OF A.

    {3,4}

  7. DEFINE:
    A  B

    • "A minus B", or
    • "A complement B"

    • everything in A 
    • except for anything
    • in its overlap with B

    • {1}
  8. WHAT WOULD THIS LOOK LIKE AND MEAN:

    A – B
    • "A minus B"  OR
    • "A complement B"

    everything in A except for anything in its overlap with B

    • {1}
  9. DEFINE:
    ~(A U  B)

    "not (A union B)"

    everything outside A and B

    {4}
  10. WHAT WOULD THIS LOOK LIKE AND MEAN? 

    ~(A U  B)
    ~(A U  B)

     "not (A union B)"

    • everything outside A and B
    •  {4}
  11. DEFINE:
    • ~(A ^ B)
    • or
    • ~(A intersect B)

    "not (A intersect B)"

    everything outside of the overlap of A and {1, 3, 4}
  12. WHAT DOES THIS LOOK LIKE AND MEAN?

    ~(A ^ B)
    or
    ~(A intersect B)
    "not (A intersect B)"

    everything outside of the overlap of A and B {1, 3, 4}

  13. Given the following Venn diagram, shade in A ^ C.

    The intersection of A and C is just the overlap between those two circles.

    • Note that unioning with A put some of C (that is, some of what I'd cut out when I did "B – C") back into the answer. This is okay. Just because we threw out C at one point, doesn't mean that it all has to stay out forever.
  14. DEFINE:



    A IS A SUBSET OF B

    a subset is a set which is entirely contained within another set. For instance, every set in a Venn diagram is a subset of that diagram's universe. 


  15. DEFINE DISJOINT IN A VENN DIAGRAM AND WHAT WOULD IT LOOK LIKE?


    disjoint sets have no overlap; their intersection is empty. There is a special notation for this "empty set", by the way: "
    Ø"
  16. WHAT IS THE OPPOSITE FUNCTION OF SQUARE ROOT?
  17. NAME AND GIVE EXAMPLES OF THE FOUR PROPERTIES OF MULTIPLICATION.
  18. CONVERT IN TO SCIENTIFIC NOTATION:
    0.000000786
    7.8 X 10-7

    • REMEMBER WHEN MOVING TO THE 
    • RIGHT IS NEGATIVE
  19. CONVERT IN TO SCIENTIFIC NOTATION:
    4.7
    4.7 X 100


    • YES ZERO!
    • 10 X 0 = 1
  20. CONVERT IN TO SCIENTIFIC NOTATION:
    0.06
    6.0 X 10-2

    GOING RIGHT MEANS GOING NEGATIVE!
  21. CONVERT IN TO SCIENTIFIC NOTATION:
    88.4 X 103
    8.84 X 104

    ADDED A DECIMAL SPACE TO THE ORIGINAL NUMBER.
  22. SIMPLIFY:
    (2 X 104) (3 X 102)
    6 X 106

    • THE TAKE HOME:
    • 1. WHEN MULTIPLYING EXPONENTS ADD THEM. 
    • 2.THE BASES MUST BE THE SAME!
  23. SIMPLIFY:
    (7 X 104) (9 X 105)
    6.3 X 1010

    YOU ORIGINALLY GET 63 X 109 IN ORDER TO GET INTO SCI NOTE, MOVE THE DECIMAL ONE SPACE TO THE LEFT. THIS WILL MAKE 63 INTO 6.3. IT IS NOW SMALLER BY A FACTOR OF 10. SO NOW ADJUST THE EXPONENT BY ADDING ONE TO IT AND KEEPING THE CORRECT VALUE.
  24. SIMPLIFY: 
    (2.6 × 105) (9.2 × 10–13)
    •     = (2.6)(9.2)(10–8) 
    •     =2.6 × 9.2 = 23.92 = 2.392 × 10 = 2.392 × 101
    •     = (2.392 × 101)(10–8) 
    •     = (2.392)(101)(10–8) 
    •     = (2.392)(101–8) (ADD)
    •     = 2.392 × 10–7
  25. DEFINE PROBABILITY OF "AND"
    • AND = MULTIPLY
  26. DEFINE PROBABILITY OF "OR"
    • OR = ADD
  27. WHAT IS THE NEGATION FOR "SOME ARE"?
    • Quadrilateral just means "four sides" (quad means four, lateral means side).
    • Any four-sided shape is a Quadrilateral.
    • But the sides have to be straight, and it has to be 2-dimensional.
  28. DEFINE RHOMBUS
    • A 4-sided flat shape with straight sides where all sides have equal length. 
    • Also opposite sides are parallel and opposite angles are equal.
    • It is a type of parallelogram.

    • BOTH ARE EXAMPLES OF A RHOMBUS:
    •  
  29. DEFINE PERIMETER OF A CIRCLE OF A TRIANGLE OR A CIRCLE.
    The distance around a two-dimensional shape.

    The perimeter of a circle is called the circumference.

    The total distance around the outside of a triangle. A+B+C= PERIMETER OF TRIANGLE.
  30. WHAT DO YOU DO WHEN QUESTION STATE:
    ESTIMATE
    APPROXIMATELY
    • ESTIMATE= ROUND FIRST
    • APPROXIMATELY = ROUND @ END
  31. A $600 PC WAS SOLD FOR $360. THE REDUCTION WAS $240. 
    THE REDUCTION IN PRICE IS WHAT PERCENT OF THE ORIGINAL PRICE?
    PART/WHOLE. 240/600 = 2/5 = 40%

    • THE $300 HAS NOTHING TO DO WITH IT. 
    • THE QUESTION IS ASKING ABOUT REDUCTION!
    • PART = REDUCTION = 240 AND WHOLE = 600.
    • THE TAKEAWAY FOR THIS IS THAT YOU HAVE TO MULTIPLY A FRACTION TIMES A WHOLE NUMBER TO GET THE AMOUNT OF THE FRACTION OF THE WHOLE NUMBER.
  32. WHAT IS THE NEGATION OF THE FORM 
    ALL P ARE Q.
    SOME P ARE NOT Q
  33. WHAT IS THE NEGATION OF 
    "ALL OWLS FLY?"
    • SOME OWLS DO NOT FLY
  34. NEGATIONS FOR
    OR B
    AND B
    IF A THEN B

    FOR ALL x, A(x)

    THERE EXISTS X SUCH THAT A(x)"
    • "A or B"      "not and not B"
    • "A and B"    "not A or not B"
    • "if A, then B"      "A and not B"

    • "For all x, A(x)"
    • "There exist x such that not A(x)"

    • "There exists x such that A(x)"
    • "For every x, not A(x)"
  35. A CIRCLE HAS A CIRCUMFERENCE OF 72 FEET. IT HAS A ARC. (THINK PIE SLICE) 
    THE ANGLE OF THE ARC IS 20 DEGREES. 
    WHAT IS THE LENGTH OF THE ARC?
    • 1. A CIRCLE IS 360
    • 2. ARC = 20
    • 3 SO, WHAT IS 20 /360= 1/18
    • 4. WHATS 1/18 OF 72? 1/18 * 72/1= 4

    CIRCUMFERENCE IS THE DISTANCE AROUND THE CIRCLE, NOT THE AREA OF THE CIRCLE.
  36. A 20L SAMPLE OF WATER CONTAINS 1L OF POLLUTION. WHAT PERCENT OF THE SAMPLE IS POLLUTION?
    1 / 20 = .05 = 5%DIVIDE THE WHOLE INTO THE PART TO GET PERCENT. YOUR SAMPLE IS 20. THE 1L IS WHAT YOUR PERCENTAGE IS COMING FROM. 20 IS THE WHOLE AND 1 IS THE PART. WHEN YOU DIVIDE 1 BY 20 YOU ARE GETTING A DECIMAL OR PART OF THE 20. THEN JUST CONVERT DECIMAL INTO PERCENT.
  37. (-5) - (+8) =?
    (-3) - (-4) = ?
    • (-5) + (-8) = -13
    • (-3) + (+4) = +1
    • remember to change the sign and the 2nd integers property.

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