Mount Rainier Math Invitational
Mount Rainier Math Invitational
February 17 2012
Mental Math Test
The mental math test contains 20 questions to be done in 10 minutes. All problems must be done mentally. Only answers may be recorded on the test. If work is present, or an answer is changed, even if correct, the problem will be marked wrong. Scratch paper will not be provided. All questions will be worth 1 point. Any area of math may be covered on this test. All non-integer answers must be recorded as improper fractions and in terms of π where appropriate, unless the question specifically asks for a different form. Please record your answers in the boxes of the column labeled Answers. Do not write anything in the column labeled Score. Be sure to record name, team #, and school on the test form. When your proctor says to, turn the paper over and begin working.
Mental Math / Answers / Score1. What is 12+19?
2. What is ?
3. What is4! ?
4. What is the area of a square whose perimeter is 12?
5. What is the greatest common factor of 20 and 44?
6. What is the least common multiple of 4, 5, and 6?
7. What is the absolute value of the sum of -47 and 13?
8. Simplify
9. What is ?
10. What is the perimeter of a regular nonagon with side length 2.5? Answer as a decimal.
11. What is ?
12. What is the sum of all prime numbers between 1 and 10?
13. What is 0.4+7 ? Answer as a decimal.
14. What is the area of a triangle with a base length of 18 and a height of 4?
15. The product of two numbers is 20. When the smaller number is divided into the larger, the quotient is 5. What is the sum of the two numbers?
16. Express . as a fraction.
17. What is the probability of drawing two hearts, without replacement, from a standard deck of 52 cards?
18. What is the mean of this set of numbers?
19. What is ?
20. Find the range of the following set:
Total Score:
Mental Math / Answers / Score
1. What is 12+19? / 31
2. What is ? / 110
3. What is4! ? / 24
4. What is the area of a square whose perimeter is 12? / 9
5. What is the greatest common factor of 20 and 44? / 4
6. What is the least common multiple of 4, 5, and 6? / 60
7. What is the absolute value of the sum of -47 and 13? / 34
8. Simplify / 5
9. What is ? / 216
10. What is the perimeter of a regular nonagon with side length 2.5? Answer as a decimal. / 22.5
11. What is ? / 36
12. What is the sum of all prime numbers between 1 and 10? / 17
13. What is 0.4+7 ? Answer as a decimal. / .47
14. What is the area of a triangle with a base length of 18 and a height of 4? / 36
15. The product of two numbers is 20. When the smaller number is divided into the larger, the quotient is 5. What is the sum of the two numbers? / 12
16. Express . as a fraction. / 10/33
17. What is the probability of drawing two hearts, without replacement, from a standard deck of 52 cards? / 1/17
18. What is the mean of this set of numbers? / 17
19. What is ? / 1/2
20. Find the range of the following set: / 26/63
Total Score:
Individual
The individual test contains 30 questions to be done in 30 minutes. The first 20 questions are worth 2 points each and the last 10 are worth 3 points each. Any area of math may be covered on this test. All non-integers answers must be recorded as improper fractions and in terms of π where appropriate, unless the question specifically asks for a different form. Please record your answers in the boxes of the column labeled Answers. Do not write anything in the column labeled Score. Be sure to record name, team #, and school on the test form. When your proctor says to, remove this cover sheet and begin working.
BE SURE TO WRITE YOUR NAME, SCHOOL and TEAM NUMBER ON THE ANSWER SIDE OF THIS PAPER.
Individual Answer Sheet KEYScore / Score
(2 or 0)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Score / Score
(3 or 0)
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Subtotal Questions 1-20
Subtotal Questions 21-40
Total Score
Individual
1. What is the remainder when 9865 is divided by 3?
2. If Vlad can eat 2 apples in 45 seconds, how many apples can he eat in one day?
3. James has 96 calculators. Dr. Tosch takes half of them, and then Mr. Roths borrows a third of the remaining calculators. How many calculators does James have left?
4. If the dividend is 4511 and the divisor is 13, what is the quotient?
5. What is the length of the hypotenuse of a right triangle with side lengths 5 and 12?
6. What is ?
7. What is the radius of a circle with a diameter of 10?
8. Solve for x if:
9. Find the degree of angle x:
10. Find the volume of a cylinder with base radius 50 and height 13.
11. John has 5 brothers and each of his brothers has a wife and 4 kids. How many people are there?
12. Solve for x if y=6 and
13. What is the slope of the line including the points (2,12) and (5,6)?
14. What is ?
15. A circle has the area of 169. What is the diameter of the circle?
16. Sally bought a pie. If she ate 1/8 of it one day, 1/7 of what remained the next day, and 1/6 of what remained the day after that, how much of the pie is left?
17. There are 5 black marbles, 7 green marbles and 3 orange marbles. What is the probability of taking an orange marble, keeping it, and then taking a green marble, in that order?
18. In the land of Boogabo their money is in boods, loods, and soods. 1 bood is worth 17 loods and 1 lood is worth 8 soods. If you have 11 boods, how many soods do you have?
19. What is 7% of 7? Answer as a decimal.
20. When 9,999 is squared, what is the sum of its digits?
The following questions are worth 3 points:
21. Find the area of the circle that circumscribes the square:
22. I roll a fair four-sided die, labeled 1 through 4, 4 times. What is the probability that I get the numbers 1, 2, 3 and 4 in some order?
23. I write down every number between 0 and 200. How many times will I write the number 1?
24. Write these numbers in order from smallest to largest:
2, , 2.5, ,
25. Candace went to the store to buy some fruit. Apples cost $1.55 each and oranges cost $0.95 each. She paid $42.90 for 30 pieces of fruit. How many apples did she buy?
26. An isosceles triangle has a height of 16, and a base, which has the unique side length, of 24. What is the sum of the other two side lengths?
27. Two friends have 54 apples. The friend with more apples ate 3 apples, and the friend with fewer apples ate 1 apple. The friend with more apples then had 4 times as many apples as the friend with fewer apples. How many apples did the friend with fewer apples have in the beginning?
28. Fill in the blank in this sequence:
1, 2, 5, 10, 17, 26, ____, 50
29. Steven collects trading cards. He already has 35 cards and he plans to start buying 3 cards every week. Later, he sells 19 and still has 58, how many weeks has it been since he started buying more cards?
30. What is the surface area of a rectangular prism with a length of 2 units, a width of 4 units, and a height of 4 units?
Individual Answer Sheet KEY
Score / Score
(2 or 0)
1. 1
2. 3840
3. 32
4. 347
5. 13
6. 100
7. 5
8. 179
9. 38
10. 32500π
11. 31
12. 7
13. -2
14. 300763
15. 26
16. 5/8
17. 1/10
18. 1496
19. .49
20. 36
Score / Score
(3 or 0)
21. 50π
22. 3 / 32
23. 140
24. 2, , , , 2.5
25. 24
26. 40
27. 11
28. 37
29. 14 [weeks]
30. 64 [sq units]
This answer sheet should be turned in after 8 minutes. Teams should copy answers they want to keep onto the second answer sheet. Each correct answer is worth 1 point.
Team Test Answer Sheet #1Answers / Score / Score
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12
13
14.
15.
16.
17.
18.
19.
20.
TOTAL
This answer sheet should be turned in after 20 minutes. These are the final answers for the team. Each correct answer is worth 2 points.
Team Test Answer Sheet #2Answers / Score / Score
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12
13
14.
15.
16.
17.
18.
19.
20.
TOTAL
Team Test
1. Find the product of x and y if: 3x+5y= 50
11y + 8x = 117
2. What is the maximum number of circles you can have where all the circles are tangent to all the other circles?
3. It’s raining cats and dogs. For every 11 dogs that rain, 17 cats rain. How many dogs rained if 3179 cats rained?
4. Chowder runs twice as fast as Stewbeaf, Stewbeaf runs 6/5 times as fast as Porridge and Mealoats runs 10 times as fast as Stewbeaf. They are running a one-mile relay. Chowder runs at 12 mph. How long, in minutes will it take their team to finish if they each run a quarter mile?
5. Evaluate .
6. What is the area of a triangle which has vertices at (1,3) (4,5) and (7,12)?
7. Evaluate
8. What is the volume of this rectangular prism in m3?
9. What is the next number in this sequence: 1, 3, 9, 21, 41....
10. What is the product of the mean, mode, and median of this set of numbers?
5, 7, 34, 4, 28, 12, 5, 5, 7, 3, 0
11. Gandalf the Grey can kill a mountain troll in 1 hour. Gandalf the White can kill a mountain troll in 45 minutes. How long will it take Gandalf the Grey and Gandalf the White to kill a mountain troll together, in hours?
12. What is ?
13. What is the area of an equilateral triangle with side length 4?
14. What is the sum of the digits of ?
15. How many prime numbers are there between 20 and 60?
16. Harry, Ron, Hermione, Dumbledore, Snape, and Voldemort must be paired up so they can compete in the greatest flaming quidditch hippogriff duel of all time. How many different pairs can be formed if Harry and Voldemort cannot be paired together?
17. For 30 minutes, Tyson rode his scooter at a rate of 30 mph. He then rode his segway for 40 minutes at a rate of 45 mph. Lastly he decides to jog for 90 minutes at a rate of 8 miles an hour. What is the total distance Tyson travelled?
18. How many sides does a heptagon have?
19. Matt was born on a Wednesday in January in the year 2006. What day of the week will his birthday be on in 2011 (2008 was a leap year)?
20. James has 7 math shirts and Mr. Roths has 10. If they only have one math shirt that is the same what is the probability that they will both be wearing the same math shirt?
Team Test Answer Sheet
Answers / Score / Score
1. 35
2. 4
3. 2057
4. 7 [minutes]
5. 999951
6. 15
7. -40058
8. 2400
9. 71
10. 250
11. 3/7 [hours]
12. 749
13. 4 [sq un]
14. 54
15. 9
16. 14
17. 57 [miles]
18. 7
19. Tuesday
20. 1/70
Medley Test
The medley contains a total 20 questions to be done in 16 minutes. Each team will receive four medley tests, one for each subject. Subjects are: number sense, algebraic sense, geometric sense, and probability/statistics. Each team member will receive one test. At the start of the test, each team member will work on their own test only. After four minutes, team members must pass their test to the next person. During the course of the test, each member will see each test. Teams of three will require that one person start with two tests. All questions will be worth 3 points. All answers must be recorded as improper fractions and in terms of π where appropriate, unless the question specifically asks for a different form. Please record your answers in the boxes of the column labeled Answers. Do not write anything in the column labeled Score. Be sure to record name, team #, and school on each test form. When your proctor says to, remove this cover sheet and begin working.
Number Sense #1 / Answer / Score1. How many numbers between 100 and 500 contain the number 3?
2. Which is larger ?
3. Jack and Jill went up a hill to fetch some pails of water, along with a Nerd from Mathland. Jill skips once every 3 seconds, Jack skips once every 5 seconds and the Nerd skips every 2 seconds. They start at the same time. How long will it take them in minutes, to all skip at the same time 12 times (not including when they started)?
4. What is the smallest positive integer (whole number) that has a remainder of 2 when divided by 3, a remainder 3 when divided by 5 and a remainder of 6 when divided by 7?
5.
The numbers 1, 2, 3, and 4 are placed into the four blanks of the following expression such that no number is repeated and no blank is left unfilled. What is the smallest possible value of the expression?
Algebra #2 / Answer / Score
- If X= 17 Y=12 and Z=13 what is ?
2. I am thinking of a number that is 12 times the size of Jinkins number. Jinkins number is the square root of (186-17). What I my number?
3. George is mixing up a salt solution to put on the sidewalks in front of his business. He has 10 liters of a 20% salt solution. How many liters of a 60% salt solution should he add to make a 30% salt solution?
4. In the Hogwarts library There are X book shelves that can each hold Y books. There are 20 books scattered around on tables and the total number of books is 200. If the ratio of X to Y is 1 to 30 and presuming that each shelf is full, what is the total number of book shelves?
5. There are 36 young whippersnappers on an old man’s lawn 10% are pestering the old man, 45% are playing tag and 20% are climbing a tree if every whippersnapper is only doing one activity how many are doing nothing ?
Geometry #3 / Answer / Score
1. The lengths of two sides of a triangle are 11 and 15. If the third side also has an integer length, how many possible values can it be?
2. What is the area of the square, if the lengths of the 2 legs of the triangle are 6?
3. Put the following in order from largest to smallest. Your answer should give the letters in the proper order.
A = The perimeter of a square who’s area is 36
B = The area of a equilateral triangle which has a side length of 6
C = The area of a circle with a diameter of 6
4. How many diagonals can be drawn in a 12-sided regular polygon (dodecagon)?
5. What is the measure in degrees of the interior angle of a regular octagon?
Probability/Statistics #4 / Answer / Score
1. An old candy stash contains 3 chocolate spheres, 14 pieces of bubble gum, 9 cherry lollipops, and 13 mini-chocolate bars. What is the probability of drawing a piece of candy that contains chocolate?
2. Tom got back his math test and it had a score of 18. When he checked over the paper, he discovered it should have been 81. The teacher then corrected the score in the gradebook and it raised the class average by 3. How many students (including Tom) are in the class?
3. Browsing through Finn’s board game collection, he found two fair six-sided dice. What is the probability that, when rolled, the numbers showing will total to 8 or more?
4. Finn brought home two spinners. One spinner contains five colors: red, yellow, blue, brown, and purple. The other spinner contains four colors: white, green, blue, and purple. From all the possible color combinations, if both spinners are spun at the same time, what is the probability that both will land on the same color?
5. At a local library, two books are borrowed often – a black one, and a blue one. The library conducted research into the frequency of these books and realized that every patron has checked out either one or both of these books. 392 patrons borrowed the black book and 756 borrowed the blue one. If 1000 patrons were counted into the research, what is the probability that a randomly selected patron only borrowed a black book?
Number Sense
Answers / Score
1. 157
2.
3. 6 [min]
4.83
5.
Algebra
Answers / Score
1. 48
2. 156
3. 10/3 [liters]
4. 6
5. 9
Geometry
Answers / Score
1. 21
2. 72
3. C, A, B
4. 54
5. 135
Probability/Statistics
Answers / Score
1. 16/39
2. 21
3. 5/12
4. 1/10
5. 61/250
Puzzle Test / Check / Answers / Score
1. Mathmaster James has 3 sons Jayz, Tyson, and Matt. If the sons’ ages multiply to equal 72 and the sum of the numbers does not uniquely determine them, what are the sons’ ages if the oldest one likes ice cream? / 1 / 3, 3, 8 / 4
2 / 2
2. There is a two-mile stretch of road, if for the first mile you drive at 30 mph, how fast would you have to go for the last mile to average 60 mph? / 1 / Can’t be done, or infinite / 4
2 / 2
3. Create the number 24 using all of 1, 3, 4, and 6. You must use each digit only once. You may add, subtract, multiply, and divide, as well as use Parentheses. But you cannot use powers nor can you “glue” numbers together. Example does not work. / 1 / / 4
2 / 2
4. What is the most common digit that occurs when writing the numbers between 1 and 1000 inclusive? / 1 / 1 / 4
2 / 2
5. Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Person A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. When two people cross the bridge together, they must move at the slower person's pace. What is the fastest time that all four people can cross over the bridge? / 1 / 15 min / 4
2 / 2
Total Score:
Puzzle Test
The puzzle test contains 5 questions to be done in 15 minutes. During the course of the test, a team may have answers checked up to two times. If an answer is correct, the proctor will circle the corresponding number in the score column. If an answer is incorrect, it will be marked with an x. Answers are worth more points with fewer checks. Incorrect answers may be modified and resubmitted, correct answers need not be. Any area of math may be covered on this test. All answers must be recorded as improper fractions and in terms of π where appropriate, unless the question specifically asks for a different form. Please record your answers in the boxes of the column labeled Answers. Do not write anything in the column labeled Score. Be sure to record name, team #, and school on the test form. When your proctor says to, remove this cover sheet and begin working.
Puzzle Test / Check / Answers / Score1. Mathmaster James has 3 sons Jayz, Tyson, and Matt. If the sons’ ages multiply to equal 72 and the sum of the numbers does not uniquely determine them, what are the sons’ ages if the oldest one likes ice cream? / 1 / 4
2 / 2
2. There is a two-mile stretch of road, if for the first mile you drive at 30 mph, how fast would you have to go for the last mile to average 60 mph? / 1 / 4
2 / 2
3. Create the number 24 using all of 1, 3, 4, and 6. You must use each digit only once. You may add, subtract, multiply, and divide, as well as use Parentheses. But you cannot use powers nor can you “glue” numbers together. Example does not work. / 1 / 4