Transcript Review for the Final

Mathemania for Teachers!
Problem
Solving
Sets and
Functions
Numeration Number
Systems
Theory
5
5
5
5
5
10
10
10
10
10
25
25
25
25
25
50
50
50
50
50
100
100
100
100
100
Final Question
Fractions
Problem Solving
Problem Solving: 5 Points
True or False: Problem Solving for
some may be an exercise for others.
True
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Problem Solving: 10 Points
Find a pattern in the following
sequence and write the next term:
3, 5, 11, 21, 35
53
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Problem Solving: 25 Points
What is the fifth number in the set of
triangular numbers?
15
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Problem Solving: 50 Points
There are 78 people around a
table. Each person shakes hands with
the person to his or her immediate
right and left. How many handshakes
take place? Write an algebraic
expression for the number of
handshakes.
78 handshakes and n handshakes.
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Problem Solving: 100 Points
Two men and two boys want to cross a
river, using a small canoe. The canoe
can carry two boys or one man. What
is the least number of times the canoe
must cross the river to get everyone to
the other side?
9 crossings
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Sets and Functions
Sets and Functions: 5 Points
Given the universal set U= {0, 1, 2,
3, 4, 5, 6,} and sets A = {2, 4, 6} and B
= {1, 2, 3, 4} determine the set A  B
and A B.
A  B = {1,2,3,4,6} and A  B = {2, 4}
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Sets and Functions: 10 Points
Sketch a Venn diagram to illustrate the
following set: A B
A
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Sets and Functions: 25 Points
Consider the function that relates the
length x of each line segment to f(x),
which is half of the length of the
segment. Determine the range value
f(x) for each of the following domain
values: 1, 2, 3, 4, and 5.
For the domain values 1, 2, 3, 4, 5, the
corresponding range values are .5, 1,
1.5, 2, and 2.5.
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Sets and Functions: 50 Points
In a certain town there live 150 men.
85 are married, 70 have a telephone, 75
own a car, 55 are married and have a
telephone, 35 have a telephone and a car,
40 are married and have a car, and 30 are
married, have a car, and have a telephone.
How many men are single and do not have
either a car or a telephone?
20 men
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Sets and Functions: 100 Points
Which of the following sets of numbers is
closed under division?
Natural (counting) numbers, Whole numbers,
Fractions, Even numbers, Odd numbers or all
multiples of 5.
Just the set of all Fractions.
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Numeration Systems
Numeration Systems: 5 Points
Round 6,281,497 to the nearest
hundred thousand.
6,300,000
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Numeration Systems: 10 Points
Use equal products to find a
replacement for each number that is
more convenient for mental
calculation. Show the new numbers
and determine the answer for 25 x 28.
25 x 4 x 7 = 100 x 7 = 700
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Numeration Systems: 25 Points
True or False: The set of whole
numbers is closed for subtraction.
False
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Numeration Systems: 50 Points
Calculate: 4325 x 225
21,1045
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Numeration Systems:
100 Points
If the number 652 is expanded and
written in positional numeration, what
is the digit in the units place?
6 is the digit in the units place.
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Number Theory
Number Theory: 5 Points
Determine if the following is true
or false:
348,025
False
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Number Theory: 10 Points
Is 371 a prime number?
No-it is a composite number.
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Number Theory: 25 Points
Find the GCF (280, 165) and the
LCM(12, 210) .
GCF is 5 and LCM is 420
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Number Theory: 50 Points
Shane has 72 inches of copper wire
and 42 inches of steel wire. He wants
to cut them into pieces, but wants all
the pieces to be the same length.
What is the largest length he can cut
these wires into so that each piece is
the same length? How many pieces of
wire will he have?
6 inches and he will have 19 pieces of
wire (12 copper and 7 steel).
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Number Theory: 100 Points
Suppose that Douglas the Decimal Dictator changed our calendar
so that there were now ten days in a week (Onesday, Twosday,
Threesday, Foursday, etc.) Also, since Douglas was born on
February 29th, he declares that every year is a leap year.
Furthermore, suppose that January 1st was a Onesday. How
many years will it take for January 1st to land on a Onesday
again? Assume that there are 366 days in a year. ?
5 years, or 183 weeks or 1830 days
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Integers/Fractions
Integers/Fractions: 5 Points
True or False? The set of fractions is
closed for multiplication?
True
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Integers/Fractions: 10 Points
Use equal quotients to calculate the
answer to 800  16.
800  16 = 200  4 = 100  2 = 50
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Integers/Fractions: 25 Points
Use Fraction Bars to illustrate 2/3 X
1/5 .
2/15
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Integers/Fractions: 50 Points
A school’s new pump can fill the
swimming pool in 5 hours, the old
pump takes 10 hours. How long will it
take to fill the pool if both pumps are
used together?
3 1/3 hours
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Integers/Fractions: 100 Points
Paula removed 4/5 of the disks from a
new box of computer disks, and Sam
removed 7/10 of the disks that
remained in the box. If Sam removed
28 disks from the box, how many
disks did Paula remove?
160 disks – not that anyone uses
computer disks anymore…
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Final Question
What are Polya’s 4 steps to problem
solving?
1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back
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