Transcript NIT FINALS - The Math Forum @ Drexel

Quiz Bowl
All eight students will solve problems as part of a quiz
bowl.
Students will work together to answer questions
and compete head to head against other teams.
Teams will be seated at tables.
A moderator will ask a question using a
microphone.
Each team will write an answer to each question on
the paper provided.
Team captains will hand one answer to the table
runner.
The team captain should be seated in middle of
the team.
Teams should write answers clearly and neatly so that
judges can read answers. Teams with unclear
answers will not receive points.
Time will begin once the moderator finishes
reading the question.
Teams should NOT include computational or scratch
work on the paper; only answers should be written on
the paper.
Once a team turns in their paper, the team may
NOT change their answer.
Teams will be provided with scratch paper and pencils
as well as their answer sheets.
NO books, notes, calculators, or electronic
devices, such as cell phones, may be used.
Cell phones must be turned off.
Quiz Bowl
Round 1: Solve the Problem
at Your Table
Round 1 will consist of 10
questions.
All teams will have 20 minutes to
complete their packets. Each
correct answer at the end of the 20
minutes earns 5 points.
Find a two-digit number such that if
you reverse its digits to get another
two-digit number, then add this to the
original number, you get 143.
Step 1
Step 2
Step 3
There are 5 squares in Step One, 10 squares in Step Two,
and 17 squares in Step Three.
How many squares will be in Step 25?
D
The hypotenuse of
Triangle ABD is 1 inch
longer than the
hypotenuse of Triangle
CBD. Find x.
x inches
A
5 inches
B
C
3 inches
Two linear functions are plotted
above. Find all x and y intercepts of
the graph of their product.
Tennis balls have a diameter of
2.7 inches. They are sold in a
cylindrical can whose height is
8.1 inches (the exact height of 3
tennis balls) and whose diameter
is 2.7 inches.
Which is bigger, the height of the can
or the circumference of the can?
The following five statements apply to a line in
the coordinate plane:
1.
2.
3.
4.
5.
The line is perpendicular to the line 5x + 6y = -18.
The line has a negative y-intercept.
The line passes through the point (6,8).
The line has a positive slope.
The line is parallel to the line 5x - 3y = -12.
Four of the statements are true and one is false.
Find an equation of the line.
If
value of:
, find the
The peak of Goose Bay Mountain is 400 meters
higher than the local GBT airstrip. The horizontal
distance from the end of the runway to a point
directly below the mountain peak is 2025 meters.
A plane takes off at the end of a runway in the
direction of the mountain at an angle that is kept
constant until the peak has been cleared. If the
pilot wants to clear the mountain by 50 meters,
what should she punch into her calculator to
calculate the angle of takeoff?
Juanita has a great job working as a mail
messenger in a skyscraper downtown.
When she is delivering packages to the 38th
floor, she is required to take a freight elevator up,
but she can return in an express passenger
elevator. The freight elevator travels at a speed
of one foot in three seconds; the express
passenger elevator, at three feet per second.
Find the average speed for the entire trip in feet
per second.
You are working on the election campaign of
Governor Calliope “Cal” Culus. The Governor is
known for her environmentally friendly
philosophy, and she would like you to develop an
environmentally friendly handbill encouraging
voters to vote for her in the upcoming election.
The handbill is to contain 50 square inches of
printed material, with 4-inch top and bottom
margins and 2-inch margins on each side. What
dimensions for the page would use the least
paper and thus be the most environmentally
friendly?
Quiz Bowl
Round 2: Multiple Answers
Round 2 will consist of 3 questions
that each have multiple answers.
Each team will earn 1 point for
each correct answer and 1 bonus
point if the team provides all of the
possible answers or the number of
possible answers.
4 plastic beads
are arranged to
make a bracelet.
Here you see 3 different
views of the same bracelet.
List all the different
bracelets that could be
made with these 4 beads
(including the bracelet in
the picture).
Solution
• RBYG or BRGY (this is the given bracelet)
– or BYGR or YBRG
– or YGRB or GYBR
– or GRBY or RGYB
• RYBG or YRGB
– or YBGR or BYRG
– or BGRY or GBYR
– or GRYB or RGBY
• RBGY or BRYG
– or BGYR or GBRY
– or GYRB or YGBR
– or YRBG or RYGB
The factors of 12 are 1, 2, 3, 4, 6,
and 12. The factors of 8 are 1, 2, 4,
and 8.
List all the numbers, from 1 to 30
(including 1 and 30) that have an
odd number of factors.
Solution
•
•
•
•
•
1: 1
4: 1, 2, 4
9: 1, 3, 9
16: 1, 2, 4, 8, 16
25: 1, 5, 25
Maurice has a bag of marbles.
• When he counts them by 2s he has 1
left over.
• When he counts them by 3s he has 2
left over.
• When he counts them by 4s he has 3
left over.
• He has fewer than 60 marbles.
How many marbles could he have. List
all the possibilities.
Solution
• If he had one more marble, his number of
marbles would be a multiple of 2, 3, and 4
• Multiples of 2, 3, and 4 under 60:
– 12, 24, 36, 48
• One less than each:
– 11
– 23
– 35
– 47
Quiz Bowl
Round 3: Speed Round with
Follow Up Questions
Round 3 will consist of 5 questions.
The first team to give a correct answer
to the runner will get 3 points.
The first team with the correct answer
will then receive a follow-up question
for 2 bonus points.
Q: Find the product:
-9 * -8 * -7 * -6 * -5 * -4 * -3 *
-2 * -1 * 0 * 1 * 2 * 3 * 4 * 5 *
6*7*8*9
Solution
• Anything multiplied by 0
is 0, so the answer is 0.
F: Find the sum:
-9 + -8 + -7 + -6 + -5 + 4 + -3 + -2 + -1 + 0 + 1
+2+3+4+5+6+7
+8+9
Solution
•Still zero… just make
pairs of the positive
and negative
numbers.
Q: Solve for x
3(x + 10) = 5(x + 10)
Solution
• 3 (___) = 5 (___) can only be true when
both sides equal 0
• Therefore, x + 10 must equal 0
• So x = -10
F: Solve for x
3(x + 10) + 2 = 5(x + 10)
Solution
•
•
•
•
3 somethings is 2 less than 5 somethings
3 ones is 2 less than 5 ones
The statement will be true if (x + 10) = 1
x = -9
Q: One fourth of the vehicles at Danielle’s
Cycle Shop are tricycles. The rest are
bicycles. Danielle counted a total of 45
wheels in her shop.
How many bicycles does she have?
Solution
• Every 4 vehicles has 9 wheels: 6 bike wheels
and 3 trike wheels
• There are 5 sets of 9 wheels in 45 wheels
• She has 4 * 5 = 20 vehicles all together, 15 of
which are bikes (3/4 of 20 is 15).
F: An outbreak of hoof-and-mouth disease is
spreading through the land of Narnia. A vet
examines each creature’s mouth and examines
each hoof (4 per centaur and 2 per faun). At the
end of the day the assistant says, “I need to
record how many fauns and how many
centaurs we checked.”
Faun
The vet replies, “I didn’t write that down, but
I do know I checked 47 mouths and 122
hooves.”
How many centaurs were checked?
Centaur
Solution
• If she checked all fauns (2 legs each) she
would have checked 47 * 2 = 94 hooves
• She checked 122 – 94 = 28 extra hooves
• That’s 14 extra pairs of hooves
• Therefore she checked 14 animals with 4
hooves (centaurs).
• 14 centaurs were checked.
Q: Find the product of
0.5 * 0.25 * 0.125
Your answer can be
given as a fraction or
decimal
Solution
• 0.5 * 0.25 * 0.125 = ½ * ¼ * 1/8
• ½ * ¼ * 1/8 = 1/(2*4*8)
• 1/(2*4*8) = 1/(8*8) = 1/64
• 1/64 = 0.15625
F: Evaluate
0.1 +
+ 0.25 +
0.1 +
Solution
+ 0.25 +
=
0.1 + 0.5 + 0.25 + 0.05 =
0.9
Q: A jacket is on sale for
25% off. The sale price is
$150.00.
How much money do you
save by buying the jacket on
sale?
Solution
• $150 is 75% of the jacket’s original price
• $50 is 25% of the jacket’s original price
• Therefore, you save $50.
F: Monica contributes 1/3 of
the total cost of a mother’s day
present. Nahim contributes ½
of the total cost. Their dad
pitches in $9 so they have
exactly enough money. How
much was Monica’s
contribution?
Solution
•
•
•
•
Total – ½(Total) – 1/3(Total) = 1/6(Total)
$9 was 1/6 of the price.
The total price was $54
1/3 of $54 = $18
• Or, $9 was 1/6 of the price, so 1/3 of the
price is 2 * $9 = $18