2018 Mathcounts Practice Problems - Mrs. Chiera - Home
This Year’sHandbookProblemsYou and your students might notice something specialabout some of the problems in this year’sWarm-Ups and Workouts.Throughout this handbook are names—first and/or last—of people who donated to the MATHCOUNTS Foundation’s Giving Tuesday campaign last year to help us cover half the cost of registering for the CompetitionSeries for Mathletes from low-income schools. These donors help make this program possible for studentsacross the country, so we decided it was fitting to include them in the primary preparation resource for participants in this program.To all of our 2016 Giving Tuesday Donors(whether or not you chose to be featured in this handbook)Thank You!MATHCOUNTS 2017-201811
Probability Stretch% Petra randomly selects a card from a standard deck of 52 playing cards. What is the1.percent probability that the card shows a red number greater than 6? Express your answerto the nearest hundredth.2. Max has eight identical cups. Each cup contains a different combination of nickels, dimesand quarters, each totaling 45 cents. Max randomly selects a cup. What is the probabilitythat the cup he selects contains at least three dimes? Express your answer as a commonfraction.3. A bag contains five chips numbered 2 through 6. Danya draws chips from the bag one at atime and sets them aside. After each draw, she totals the numbers on all the chips she hasalready drawn. What is the probability that at any point in this process her total will equal10? Express your answer as a decimal to the nearest tenth.4. A drawer contains five socks: two green and three blue. What is the probability that twosocks pulled out of the drawer at random will match? Express your answer as a commonfraction.5. A penny, a nickel and a dime are flipped. What is the probability that at least two coins landheads up and one of them is the nickel? Express your answer as a common fraction.% When the circuit containing blinking lights A and B is turned on, lights A and B blink6.together. Then A blinks once every 5 seconds and B blinks once every 11 seconds.Lindsey looks at the two lights just in time to see A blink alone. What is the percentprobability that the next light to blink will be A blinking alone?% What is the percent probability that a randomly selected multiple of 3 less than or equal to7.3000 is also a multiple of 5?8. Starting at the top and selecting paths randomly as you move downward, what is theprobability of ending at an odd number? Express your answer as a common fraction.312456789. A five-digit number is made by randomly ordering the digits 1, 2, 3, 4 and 5. What is theprobability that this number is divisible by 4? Express your answer as a common fraction.10. Pierre throws darts that land randomly in the dartboard shown here. Thedartboard is a circle of radius 2 units, with an inner circle of radius 1 unit. Bothcircles are divided into six congruent sectors. What is the probability that a dartPierre throws will land in one of the four inner numbered sectors? Express youranswer as a decimal to the nearest hundredth.121 23 4MATHCOUNTS 2017-2018
Patterns Stretchdots The first four stages of a dot pattern are shown. How many more dots are in the figure at11.Stage 47 than in the figure at Stage 27?Stage 1Stage 2Stage 3Stage 412. The first three terms of a sequence are 1, 2 and 3. Each subsequent term is the sum of thethree previous terms. What is the 11th term of this sequence?13. What is the sum of the terms in the arithmetic series 2 5 8 11 14 . 89 92?14. Three consecutive terms in an arithmetic sequence are x, 2x 11 and 4x 3. What is theconstant difference between consecutive terms in this sequence?15. What is the sum of the terms in the geometric series 1 4 16 . 1024?16. What is the sum of the first 51 consecutive odd positive integers?17. What is the sum of the terms in the infinite series 1 11111 . ?4832216111118. What is the sum of the terms in the infinite series 1 . ?41664256Express your answer as a common fraction.19. Let f (x) 2x 3 and f 2(x) f (f (x)) f (2x 3) 2(2x 3) 3 4x 9. If f 5(x) ax b,what is the value of a b?degrees The degree measures of the interior angles of a quadrilateral form a geometric sequence20.whose terms have integer values and are all integer multiples of the first term. What is thelargest possible degree measure of an angle in this quadrilateral?MATHCOUNTS 2017-201813
Travel Stretchmi/h Jack and Jill travel up a hill at a speed of 2 mi/h. They travel back down the hill at21.a speed of 4 mi/h. What is their average speed for the entire trip? Express youranswer as a mixed number.:p.m. At 2:20 p.m., Jack is at the top of the hill and starts walking down at the exact same time22.that Jill, who is at the bottom of the hill, starts walking up. If they maintain the same uphilland downhill speeds from the previous problem, and the distance from the bottom to thetop of the hill is 1.5 miles, at what time will Jack and Jill meet?yards When Jack and Jill meet, as described in the previous problem, how many yards will they23.be from the bottom of the hill?minutes Alysha’s average speed when walking from home to the market is 5 mi/h,24.and it takes her 21 minutes longer than when she drives to the market. IfAlysha drives to the market, along the same route, at an average speedthat is eight times her average walking speed, how many minutes does ittake her to drive from home to the market?MARKETmiles Based on problem 24, how many miles does Alysha travel to get from home to the market?25.minutes26.Jana begins jogging along a path and, 5 minutes later, Zhao begins riding hisbicycle along the same path, which has a length of 2 miles. Zhao rides hisbicycle at a speed of 10 mi/h, and Jana’s jogging speed is 6 mi/h. If they bothbegin at one end of the path and end at the other, how many minutes afterZhao reaches the end of the path will Jana reach the end of the path?minutes Based on problem 26, how many minutes after Zhao begins riding will he catch up with27.Jana? Express your answer as a mixed number.miles Again, based on problem 26, how many miles will Jana have traveled when Zhao catches28.up with her? Express your answer as a mixed number.29.Ansel left the dock in his motorboat, traveled 10 miles, and then returnedto the dock along the same route. On the return trip, Ansel was travelingagainst the current of the river, and his average speed relative to thewater was 20 mi/h. If the round-trip took Ansel 64 minutes, what is thespeed of the river’s current?30. Based on problem 29, what fraction of Ansel’s total travel time was spent travelingupstream? Express your answer as a common fraction.14MATHCOUNTS 2017-2018
10 MATHCOUNTS 2017-2018 MATHCOUNTS 2017-2018 11 This Year’s Handbook Problems You and your students might notice something special about some of the problems in this year’s . If the round-trip took Ansel 64 minutes, what is the speed of the river’s current? Based on problem 29, what fraction of Ansel’s total travel time was spent .File Size: 2MB
2018 AMC 8 Problem 2 exactly the same as 2012 3 is MathCounts State Sprint Problem 3, and very similar to the following 4 problems: 2017 MathCounts Chapter Countdown #49 2016 MathCounts National Sprint #11 2016 - 2017 MathCounts School
2018-2019 MATHCOUNTS Playbook 15 The 2018-2019 Playbook Problems Start here to choose a math problem to solve! We have reformatted the 2018-2019 MATHCOUNTS School Handbook exclusively for the Math Video Challenge. In this playbook, all 250 of the handbook problems are organized by math topic.
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