Fox Valley Math League
Kaukauna High School
2/13/2017
Round
1
Score
Name:
Team:
School:
The number of the problem is the value of the problem. Calculators are not allowed. Exact simplified answers.
1.
All edges of the figure meet at right angles as shown.
Find the area of the unshaded region.
1.
2.
Define A@B to be A/B + A x B. What is the value of
20 @ (4@2)?
2.
3.
Simplify
3.
6 4
( √ √𝜋 )
4.
−9
3 8
( √ √𝜋19 )
3
A laser is located at point A that is 4cm above the left-hand end
4.
of a 14-cm-long mirrored surface. The laser is directed to a spot
on the surface that is 5 cm from the left end. Moving in a plane,
the laser beam reflects off the first surface and then reflects off a
second mirrored surface that is perpendicular to the first (see diagram).
When the beam is at point B that is 11 cm above the first mirrored
surface, find the distance x (in cm) to the second surface.
Fox Valley Math League
Kaukauna High School
2/13/2017
Name:
Round
2
Score
Team:
School:
The number of the problem is the value of the problem. Calculators are not allowed. Exact simplified answers.
1.
A group of people, cats, and birds have 70 legs, 30 heads,
and 20 tails. How many cats are in the group?
(Assume all birds have 2 legs and a tail, all cats have 4 legs
and a tail, and that people have 2 legs, and no tail)
1.
2.
King John and his many children have 16 gold coins that appear
2.
identical. However, 15 of them are genuine coins all having the same
weight and one is a fake that weighs less than each genuine coin. By
using a pan balance to compare weights of stacks of coins, he can tell
which stack of coins weighs more. What is the fewest number of times
that King John needs to use the pan balance to guarantee that he has identified
the fake coin?
3.
Write as a fraction in lowest terms.
3.
26342 −26345
3173
64 3
4.
𝑥 2 + 4𝑥 − 5 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑥 4 + 𝑝𝑥 + 𝑞.
𝐹𝑖𝑛𝑑 𝑝 + 𝑞
4.__________
Fox Valley Math League
Kaukauna High School
2/13/2017
Name:
Round
3
Score
Team:
School:
The number of the problem is the value of the problem. Calculators are not allowed. Exact simplified answers.
1.
Margi has a mason jar of coins containing the same
number of nickels, dimes, and quarters. The total value of the
coins in the jar is $13.20. How many nickels does she have?
1.
2.
Mitch throws a dart at a circular dartboard with a radius of 2 feet. 2.
He is not very skilled at throwing darts, so the dart is equally likely
to land anywhere on the dartboard. However, he is skilled enough
so the dart always hits the dartboard. What is the probability that the dart lands
closer to the center of the dartboard, then to the edge?
3.
Karla participated in a math competition in which 20 problems
3.__________
were given. For each problem answered correctly, she received 8
points, but 5 points were deducted for each incorrect answer. For
unanswered problems, she received 0 points. Given that her final
point total was 13, how many problems did she answer correctly?
4.
What are the last four digits of the product of
5,544,332,211 x 9,999,999,999? The digits must be in the
correct order.
4.
Fox Valley Math League
Kaukauna High School
2/13/2017
Name:
Round
4
Score
Team:
School:
The number of the problem is the value of the problem. Calculators ARE allowed. Exact answer or round to the
nearest hundredth unless otherwise specified.
1.
Nine woodchucks can chuck eight pieces of wood in three
1.__________
hours. How much wood can Dan, the woodchuck, chuck in one hour?
2.
A wire of length x is cut into two pieces with lengths x/3
and 2x/3. Each piece is bent into a square. The sum of the areas
of the squares is 1. Rounded to the nearest hundredth,
what is the value of x?
2.__________
3.
Two numbers are such that their difference, their sum, and their
product are in the ratio of 1:7:24, respectively. What is their
product?
3.__________
4.
Laura and Catherine run along a flat, dry lake bed. They run
4.
one mile due west, then one mile due southwest, and finally another
mile due west. Find the distance between their initial and final positions.
Fox Valley Math League
Kaukauna High School
2/13/2017
Name:
Team
Round
Score
Team:
School:
Each problem is worth 10 points. Turn in one paper per team. Calculators ARE allowed. Exact answer or round to the
nearest hundredth unless otherwise specified.
1.
Stacy goes to a casino that requires a one-dollar entry
1.
fee and a one-dollar exit fee. Each day for three days, she goes
to the casino, pays the entry fee, loses half of the money with
which she has left to play, and pays the dollar to leave. After
paying her final dollar to leave the casino at the end of the third day,
she goes home broke. How much money did she start with?
2.
Mandy looked at the clock in her class, anxiously ready to leave 2.__________
so that she can go to her math class next hour. She knows the minute
hand on the clock is 5.5 inches long from the pivot point to the base.
It is 1:45 pm right now, and she gets to leave at 2:14 pm. How far
will the tip of the minute hand travel before she gets to leave class?
3.
The winner of an election with six candidates received half
3.
of the 200 votes cast. The candidate with the least number of votes
received only 9 votes. If each candidate received a different number
of votes, what is the minimum number of votes the second place
candidate could have received?
4.
A quadrilateral is inscribed in a circle. Calculate the area of the
circle if the squares of four consecutive sides of the quadrilateral
are 23, 50, 58, and 85.
4.__________
5.
A six-digit number can be written as 2abcde with digits, a,b,c,d, 5.
and e. If the digits are changed so that the number reads abcde2,
the result is a new number equal to three times the original number.
Find the original number.
6.
Dana gave a test to her math class. The test had a maximum
possible score of 76 points and all scores were integers in the
range from 15 to 76. As she was converting the raw scores to
percentage scores, she noticed that Nancy’s raw score and
percentage score had the same two digits but in reverse order.
What was Nancy’s raw score?
6.__________