The Sixth Annual West Windsor-Plainsboro Mathematics Tournament

Transcription

1 The Sixth Annual West Windsor-Plainsboro Mathematics Tournament Saturday October 27th, 2018 Grade 7 Test RULES The test consists of 25 multiple choice problems and 5 short answer problems to be done in 40 minutes. All multiple choice answers should be marked on the Scantron mark sheet. No marks on this paper will be graded. All short answers you write should be in exact, simplified form, unless otherwise stated in the question, following the rules below: All fractions must be simplified. All fractional answers must be expressed in the form a b where a and b share no common factors other than 1. For example, if the answer is 9 5, then (mixed fraction) or 10 are NOT ACCEPTABLE. Any question that involves the number π in the answer must be written using the symbol π. In particular, decimal approximations of π are NOT ACCEPTABLE. All radicals must be simplified. Radicals in the denominator of a final answer, a perfect n th power under a n th root, or fractions/decimals under a radical are NOT ACCEPTABLE. You can ask your proctor a question, but if they think answering your question will give you an unfair advantage on the test over other contestants, they don t have to respond. After the testing has completed, please go to your selected mini-event rotation (directions will be given for this after the main contest is over). DO NOT FLIP THIS PAGE TO BEGIN THE TEST UNTIL INSTRUCTED TO DO SO BY YOUR PROCTOR(S).

2 Multiple-Choice Questions Answers to this section of the test should go on the scantron multiple-choice form given to you. NOTHING WRITTEN ON THIS TEST PAPER WILL BE SCORED. 1. What is ( )/9? A. 99 B. 100 C. 101 D. 111 E Today is Saturday, October 27th, What day of the week is Halloween (Oct. 31st)? A. Monday B. Tuesday C. Wednesday D. Friday E. Sunday 3. David and his dad were born on the same day of the year! David just turned 17, and his dad is now exactly 3 times David s age. How old was his dad when David was born? A. 17 B. 18 C. 34 D. 35 E Bessie the Cow escapes from the farm. She heads 5 miles north and 12 miles east. Farmer Joe then goes in a straight line from his farm to Bessie s current location. How much more distance did Bessie travel than farmer Joe? A. 3 miles B. 4 miles C. 5 miles D. 6 miles E. 7 miles 5. Which of the following is the average of the remaining 4 answer choices? A. 4 B. 10 C. 14 D. 16 E Bessie the Cow loves eating lemons and oranges. If eating a lemon increases her fullness by 6 and eating an orange increases her fullness by 5, then what is the largest amount of fullness she can never achieve just by eating oranges and lemons? A. 4 B. 7 C. 13 D. 17 E Bessie the Cow has invented a new operation, ℵ. For any two numbers, a ℵ b = (a + a b + b). What is 4 ℵ 9? A. 13 B. 49 C. 76 D. 81 E Which of the following is true? Only one answer choice is correct. The letters in each answer choice refer to the other answer choices. A. B & C are false B. C is true C. B is true D. E is true E. None of the above 9. A cube of play-doh is broken apart and formed into three new cubes of side lengths 3, 4 and 5. What was the original side length of the cube? A. 5 B. 5 2 C. 6 D E. 8

3 10. Jack and Jill are rounding numbers. They are given a number, 49.49, and decide to round it. Jack rounds it by first rounding to the hundredths place, then the tenths place, then the ones place, then the tens place, then the hundreds place. Jill rounds by rounding it to the nearest hundreds place. What is the difference between Jack s final number and Jill s final number? A. 0 B. 50 C. 100 D. 150 E The numbers on the opposite faces of a die add up to 7. What is the sum of the numbers on the 4 faces touching the face with the number 1? A. 12 B. 13 C. 14 D. 15 E Which of the following has the largest area? A. A square with side length 3 B. A rectangle with dimensions of 2 4 C. An equilateral triangle with side length 3 D. A triangle with side lengths 3, 4 and 5 E. A circle with radius of Triangle ABC is a triangle where AB = 24, BC = AC = 13. What is the area of ABC? A. 48 B. 60 C. 120 D. 180 E Adam wants to travel to Canada, but he only has USD and Canada uses CAD. In addition, the places to exchange currency were all broken except for a couple strange options. The following are the exchange rates: 1 USD = 4 CAD 3 USD = 5 GBP 3 GBP = 5 CAD 2 GBP = 5 HKD 3 HKD = 4 CAD (Note: These exchange rates are made up for this problem) Adam does not want too many exchanges so he will never exchange a CAD for another type of currency. If he starts with 900 USD, what is the greatest amount of CAD he can get? A B C D E An ant is standing on a cube with a side length of 3. The ant has to get from one corner to the opposite corner, but can only travel along the surface of the cube. What is the shortest distance the ant can travel? A. 3 2 B. 3 3 C. 3 5 D. 6 E Allen wishes to make some changes to the design of the cylindrical Catfood containers. He forgot the radius of the cylinder, but he knows that the height of the cylinder is 2 units. When the height is quadrupled, the volume increases by the same amount as when the radius is increased by 6 units. What is the radius of the cylinder? A. 2 B. 3 C. 4 D. 6 E. 9

4 17. I have a dysfunctional calculator that can only divide by 3 or subtract 1. What is the minimum amount of steps it takes to get from 2018 to 0? A. 14 B. 16 C. 18 D. 20 E Determine the number of digits that 10! = has. A. 3 B. 4 C. 7 D. 10 E Al is taking a test he did not study for. He can only correctly answer 10% of the problems, and will guess the answer for the rest. If the test is 120 multiple choice with four choices per answer, how many problems is he expected to get right? A. 12 B. 30 C. 36 D. 39 E What is the area of the triangle with vertices A(5, 4, 3), B(5, 0, 0), C(17, 0, 0)? A. 30 B. 36 C. 45 D. 48 E Anna and Elsa are tour guides. They want to split 8 tourists into two groups. How many ways can they split up the tourists if each group has at least 1 person? A. 84 B. 126 C. 196 D. 216 E When Adam is asked to create a random number, he first checks the clock and takes note of the two digits in the minute s portion(ex. if the time is 4:23, he notes down 2 and 3). If the numbers are noted as a and b, his random number will be a b + a + b. Which of the following answers cannot be his random number at any given time? A. 34 B. 40 C. 41 D. 44 E Let S = What is the sum of the digits of S? A. 10 B. 15 C. 27 D. 30 E Let n = Find the units digit of n 3. A. 1 B. 3 C. 5 D. 7 E Adam and Allen are two ants who start on adjacent corners of a square. After a minute passes, they both randomly walk to an adjacent corner of the square. If Adam or Allen happen to ever cross each other on their path to the next corner, they fall off the square, ending their journey. What is the probability that Adam and Allen will not encounter each other for 4 minutes? A. 1 2 B. 4 9 C D E

5 Short Answer Questions Answers to this section of the test should go on the short answer questions answer form given to you. NOTHING WRITTEN ON THIS TEST PAPER WILL BE SCORED. 1. What is ? 2. A set of numbers is formed by taking the product of two integers which are 6 apart from each other. What is the minimum possible value of a number in the set? 3. The number 201 can be written as the sum of two primes. What is the difference between these two primes? 4. Bessie the Cow loves going for car rides. Bessie first travels at 28km/hr for 30 minutes, then 35km/hr for a distance of 7km. What is her average speed the entire ride? 5. What is the tens digit of 5! + 6! + 7! !? (The! is a factorial, and n! = n (n 1) (n 2) 2 1. For example, 4! = = 24)