# TAP MATH BIG FINAL

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 Author: shockwave ID: 263242 Filename: TAP MATH BIG FINAL Updated: 2015-01-12 19:25:24 Tags: TAP MATH BIG FINAL Folders: TAP MATH BIG FINAL Description: TAP MATH BIG FINAL Show Answers:

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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
• ~()

"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
~()
"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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