MOCK MATHCOUNTS
STATE SPRINT ROUND
NO CALCULATORS! IF YOU USE A
CALCULATOR, THAT MAKES YOU A
CHEATING CHEATER. You have 40 minutes.
Score:_____________________
Grader: ___________________
Initials: ____________________
Name: _______________________
YOU HAVE 40 minutes. YOU WANT TO
MAKE NATS, SO GOOD LUCK!!!!!!!
WHEN YOU ARE DONE, PM answers to ME
MAYBACH!
You may begin.
1. A butcher is slicing deli. He slices 100 cuts on Monday, 200 cuts on Tuesday, and twice as many
cuts on Wednesday as Monday and Tuesday combined. How many cuts of deli did he slice on Monday,
Tuesday, and Wednesday combined? ____________
2. Roger and Tyler are on Algebra Network's hit game show "Complete the Sequence". As the 1
million dollar question, they are required to find the 1 millionth term of the following sequence:
2,5,8,11,........................
What number must the two say to win all the cash? ______________
3. An old man said "Reverse the 2 digits of my age and subtract 9 and you get my age". What's the
maximum possible age of the man? ________
4. In the currency of Giodorno City, 2 shuckles equals 5 knuckles and 3 knuckles equals 12 suckles.
Max has a certain number of one of these types of bills, but does not know which one. Unfortunately,
shuckles, knuckles, and suckles cannot be told apart by eye. A bystander said to Max "If these were
shuckles, we'd be 315 suckles richer than if these were suckles." Max then found out from a bank that
he had knuckles. If he wanted to convert his knuckles into shuckles, how many fewer bills would he
have? ________________
5. Two friends are mowing a lawn together. One friend can mow the lawn in 10 minutes. The other
can mow the lawn in 15 minutes. They then split their pay based on how much of the lawn each
mowed. If the slower friend received $5, how much did the two get paid altogether? Express your
answer as a decimal to the nearest tenth. ________________
6. A convex decagon said to a regular x-sided polygon "The number of diagonals I have is 135 less than
a measure of one of your interior angles". What is the value of x? ______
7. A serial murderer is at a hot pursuit with the police. If the crook is 150 miles away from the police
and is going at 75 miles per hour, how fast must the police go to catch the crook in exactly 3 hours?
Express your answer in miles per hour. ___________
8. A trapezoid has coordinates at (-2,3), (5,3), (2,5), and (3,5). What is the area of the trapezoid?
___________
9. Let x@y equal (2x)(x^y) If y=2x, and x@y equals 64, what is the value of x? ___________
10. Carly wants a new GameBoy game called "Alay". She shows her parents this equation about how
much the game costs(in pennies), where each letter is a different number from 0-9
GAME
+BOY
ALAY
If A equals 3, E equals 0, Y equals 9, and M equals 5, how much does the game(ALAY) cost in
dollars? Express your answer as a decimal to the nearest hundredth. ________
11. Mrs. Pauls is baking a cake. She has 2 cake mixes: one with 5% butter and one with 25% butter,
as well as an unlimited supply of pure butter. She adds 2 cups of the 5% butter cake mix and 3 cups of
the 25% butter cake mix. If she wants a 50% butter mix, how many cups of pure butter must she add?
Express your answer as a decimal to the nearest tenth. ________________
12. How many factors does 336 have? _____________
13. According to a recent political survey, 36 out of 255 voters disagree with Obama. If this data was
turned into a pie chart, what would the central angle be of those who agree with Obama?(Assume you
can only agree or disagree). Round your answer to the nearest whole number. __________
14. How many triangles are there in the figure below? ________________
15. Bob, Sally, Tonya, Shirley, Robert, and Grady have a lot of money. They have a total of $405
altogether. Sally has $5 less than Bob, Shirley has $5 less than twice as much as Sally, Tonya has $25
more than Tonya, Robert has $30 less than twice as much as Tonya, and Grady has 1/6 the amount of
money as Robert. How much money do Bob, Shirley, Robert, and Grady have together? _________
16. Let $x$ be the absolute value of the number, which is then subtracted by 2(eg $0$ is -2).
Let %x% be the absolute value of x-2(eg: %2% is 0). Find the mean of the following data set:
{$-1$, %-1%, $0$, %0%, $3$, %4%, $5$, %7%}. Express your answer as a common fraction.
____________
17. In an icoseles trapezoid, the measure of the short leg is 20, with the two sides with the same
measure are 10 units. Additionally, the height of the trapezoid is 8 units. What is the area of the
trapezoid? ________
18. A monkey followed a very interesting pattern each day when trying to catch bananas from a tree.
The first day, the monkey only attempted once and received one banana. The second day the monkey
attempted twice, and received 1 banana on the first attempt and 1 banana on the second attempt. On
the third day the monkey attempted 3 times, getting 1 banana on the 1st attempt, 2 bananas on the 2nd
attempt, and 1 banana on the third attempt. On the fourth day, the monkey attempted 4 times, getting 1
banana on the 1st attempt, 3 bananas on the second and third attempts, and 1 banana again on the 4th
attempt. If this pattern continues, how many bananas will the monkey get on the 3rd attempt of the
20th day? _______
19. Let the number of faces an octahedron has be x, the number of vertices be y, and the number of
edges be z. What is the value of x+y+z? ________
20. Bob is calculated the sum of the infinite geometric sequence 1/2 + 1/4 + 1/8 ...............................
Sally is calculating the sum of the infinite geomtetric sequence 1/3 + 1/9 + 1/27............................
What is the value of Bob's result minus Sally's result? Express your answer as a common fraction.
___________
21. Compute the product of these 2 base 7 numbers and express your result in base 2: 147 * 157.
__________
22. John got 44/46 on this test and now made national mathcounts! However, the mathcountss people
forgot to buy him an airfare ticket so now he has to shop around for a flight to Orlando. He has 2 bags
and will buy 3 snacks and 1 drink on flight over the total round trip. Find the difference(of the total
cost) of the least and most expensive airline for John. All bag costs are for the entire round trip unless
specified otherwise. Do calculations from left to right(eg calculate taxes before snack costs, discount
after service fee). Round to the nearest cent. _________
Airline
Round trip Bag costs Tax
Snack
Drink
Service Fee Discount
starting
Costs
Costs
cost
Skyjet
$550.00
Free
10.00%
Free
Free
None
25.00%
Budget
$50.00
Free
150.00%
$10 each
$45.00
$150.00
None
Premium
$500.00
$100 per
bag per
way
None
Free
Free
$100.00
None
Value Air
$150.00
First bag
free, $25
per
additional
bag
$25.00
Free
Free
Free
None
Swiss Air
$2,500.00
Free
50.00%
Free
Free
12.00%
None
Free
None
Free
Free
Free
None
Cheapskate $62.55
Air
23. After taking this test, Mississippi's Mathcounts competitiors were sureveyed. They could describe
the test in one or more of these terms: extremely difficult, made me sick, and " made me want my
mommy".(All people sureveyed said the test was at least one of these things. Here are the results:
55 kids considered the test "extremely difficult"
33 kids said the test "made them sick"
40 kids said the test made them "want their mommy"
8 kids said the test made them sick and made them want their mommy
13 kids said the test was extemely difficult and made them sick.
10 kids said the test was extremely difficult and made them want their mommy.
3 kids said the test made them sick, was extremely difficult, and made them want their mommy
How many kids were surveyed?(Hint: You can't just add up all the numbers to get the answer).
__________
24. How many zeros are at the end of 354! when it is multiplied out? _________
25. Detective Bob is looking for the "secret number". The "secret number" is the first three digit
number that meets these requirements:
-The number is a palindrome
-The number is divisible by 13
-The number is even.
What is the "secret number"? __________
26. Rob promised his Mom he'd be home by 6:00. However, he knew that his mom would come home
at a random time between 8 and 10. Therefore, Rob decided to come home between 8 and 9. If Rob
comes home AFTER his mom comes home, Rob is grounded. What is the probability Rob will be
grounded? _________
27. Rob's Mom is also in some trouble with her boss. She was caught stealing. As a deal, she made a
bet with the boss. The boss would choose any real number between 1 and 10 and so would Rob's
Mom. If the Mom was 2.0 or less away from the boss's number, she will be fired. If the boss chooses
the best possible strategy so the Mom would be fired, what's the probability the Mom will be fired?
________
28. How many divisors of 250 are odd? __________
29. A tetrahedron has a height of 7 feet and its base has an area of 25 square inches. What is the
figure's volume in cubic inches? _________
30. If r is the greater root of the equation x^2-x-6, what is the value of r^2+r^3+r^4? ____