Math Challenge - Solve Four Questions within Three Minutes Each!
Test your mathematical skills with four challenging questions in this timed math competition. Solve each question within three minutes, without using a calculator. Be quick and accurate to score points based on the correctness of your answers. Fold and submit your answer sheet within five seconds after the timer ends to participate effectively.
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Presentation Transcript
Basic Rules Eight Questions; Three Minutes Each NO CALCULATORS on the First Four Questions! One Answer Submission Allowed Per Question; To Submit, Fold Answer Sheet and Hold Above Your Head for the Proctor; Answer must be submitted within 5 seconds of timer in order to count. Scoring (Each Problem) First Correct Answer = 7 points Second Correct Answer = 5 points All Other Correct Answers = 3 points
The Next Slide Begins The Competition. This is a timer example:
Question 1 (NO CALCULATORS) Question 1 (NO CALCULATORS) 1 1 ??+ 1 Let ? = ??+ ?? with ? + ? + ? = 15 and ??? = 5. ? ? ??+ ? ?? with ?2+ ?2+ ?2= 12 and ??? = 3. Let ? = ??+ Determine (? + ?).
Question 2 (NO CALCULATORS) Question 2 (NO CALCULATORS) Let ? ? = ???219? + ???2(19?) 2 ? 9. and ? ? = 1 If ? = ?(? 2 ) and ? = ?(? 2 ), then determine (? + ?).
Question 3 (NO CALCULATORS) Question 3 (NO CALCULATORS) Let log864 + log2? 2log48 = 4, and 3sin? 6+ 4tan?? + 7cos5? 3= 1 with 0 ? ?. Determine ? ?.
Question 4 (NO CALCULATORS) Question 4 (NO CALCULATORS) Let ? be the coefficient of ?4 in (? + 1)7 and t be the coefficient of ?3 in (? + 2)5. Determine (? ?).
Question 4 (Answer) 5 You may use calculators beginning with the next question.
Question 5 Question 5 (CALCULATORS ALLOWED) (CALCULATORS ALLOWED) Let ? be a positive integer number base so that 28?= 1325. Let 3? 2?=32? ? 81. Determine (? + ? + ?).
Question 6 Question 6 (CALCULATORS ALLOWED) (CALCULATORS ALLOWED) A circle ? has a diameter with endpoints ?(4, 1) and ?(2,5). If ? has center ( ,?) and radius ?, determine ( + ? + ?2).
Question 7 Question 7 (CALCULATORS ALLOWED) (CALCULATORS ALLOWED) Let ? be the probability of rolling at least one 6 on one roll of two fair, standard, cubical dice. Let ? be the probability of rolling a sum of 20 on one roll of two fair, standard, 20-sided dice. Determine (??). Provide your answer as a common reduced fraction.
Question 7 (Answer) 209 14400
Question 8 will be the final question. Proctors will keep and total your answer sheets after you submit this question. Please remain in your seats until totals have been verified, as ties among the top three positions would be broken with tie-breaker questions.
Question 8 Question 8 (CALCULATORS ALLOWED) (CALCULATORS ALLOWED) 1 1 1 1 Let ? = 1968+ 1969+ 1970+ + 2019. Let ? be 1 3 the length of the side of a cube whose surface area is 2019. Round (5? + ?) to the closest integer.
Question 8 (Answer) 12 This ends the competition unless there are ties; please remain while proctors total the scores.
Tie-Breakers Only teams involved in tie for any of the top three positions will participate. If tie is not broken after two rounds because no correct answers are submitted, then the result will remain a tie. Tie-breaking questions will not count toward a team s overall score.
Tiebreaker 1 Tiebreaker 1 (CALCULATORS ALLOWED) (CALCULATORS ALLOWED) ?2 ? 12 (?+2)(?2 2? 15) Let ? ? = where ? denotes the sum of all ? where ? ? = 0, and ? denotes the product of all ? where ? = ? is a vertical asymptote. Determine (? + ?).
Tiebreaker 2 Tiebreaker 2 (CALCULATORS ALLOWED) (CALCULATORS ALLOWED) Let ? be the value of the product 3? 3 3? 6 3? 9 3? 60 when ? = 15. Let ? be the sum of the zeros of ? ? = ?3 ?2 6?. Determine (? + ?).
