WELCOME TO THE 8 TH ANNUAL DAMIEN HIGH

  • Slides: 47
Download presentation
WELCOME TO THE 8 TH ANNUAL DAMIEN HIGH SCHOOL MATH COMPETITION Schedule 8: 00

WELCOME TO THE 8 TH ANNUAL DAMIEN HIGH SCHOOL MATH COMPETITION Schedule 8: 00 – 8: 30 – 8: 45 – 9: 15 – 9: 30 – 10: 00 – 10: 15 – 11: 45 – 12: 00 Check-In Greeting from the Principal Individual Subject Exams Break Math Medley Exam Break Super Quiz Bowl & Solutions Results and Awards If your school has not checked in, please make your way to the front of the Athletic Center.

WELCOME COMPETITORS 281 Competitors 157 - 8 th Graders 124 - 7 th Graders

WELCOME COMPETITORS 281 Competitors 157 - 8 th Graders 124 - 7 th Graders 23 Schools Represented • • • 23 Schools Represented • St. Joseph, Upland • St. Louise de Marillac, Covina • St. Luke, Temple City • St. Margaret Mary, Chino Holy Name of Mary, San Dimas • St. Mark’s Episcopal, Upland Loving Savior of the Hills, Chino Hills Our Lady of the Assumption, Claremont • St. Mark’s Lutheran, Hacienda Heights • St. Peter & St. Paul, Rancho Cucamonga Pomona Catholic, Pomona • St. Philip the Apostle, Pasadena Sacred Heart, Rancho Cucamonga • St. Rita, Sierra Madre Sacred Heart, West Covina • St. Thomas More, Alhambra St. Christopher Parish, West Covina • United Christian Academy, St. Dorothy, Glendora Rancho Cucamonga St. John the Baptist, Baldwin Park California Virtual Academy Christ Lutheran, West Covina Day Creek Intermediate, Etiwanda

INDIVIDUAL EXAM The first exam you will take is your Individual Exam. Some will

INDIVIDUAL EXAM The first exam you will take is your Individual Exam. Some will take their exam in this room, while others will move to classrooms. Be sure to bring ALL scantrons, pencils, and pens with you. If you are taking Logic & Reasoning please stand up. If you are taking Arithmetic please stand up.

MATH MEDLEY EXAM Now we will take the Math Medley exam. Some of you

MATH MEDLEY EXAM Now we will take the Math Medley exam. Some of you will be moving so be sure to bring your scantron, pencil, and pen with you. If you are taking ALGEBRA please stand up. If you are taking GEOMETRY please stand up.

15 MINUTE BREAK We will soon begin the SUPER QUIZ

15 MINUTE BREAK We will soon begin the SUPER QUIZ

SUPER QUIZ BOWL • Your group is about to challenged by questions from various

SUPER QUIZ BOWL • Your group is about to challenged by questions from various fields of mathematics. You’ll have to use wit, teamwork, and your knowledge of mathematics to do your best to solve as much of each question as possible in the time permitted. • Use the Eight Standards Practices of Mathematics to help guide you. • Questions have multiple parts, each worth a different amount of points. Do your best to answer as much of each question as possible. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. • Work together as a team to be efficient with your time and talents. 3. Construct viable arguments and critique the reasoning of others. Record your final answers on ONE of your answer sheet. When time is called, it will be collected by an ambassador. Once an answer has been 5. Use appropriate tools strategically. entered, it can not be changed. • 4. Model with mathematics. 6. Attend to precision. • The final solution must be true for all the given clues. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

LET’S GET THIS SUPER QUIZ BOWL STARTED!!!

LET’S GET THIS SUPER QUIZ BOWL STARTED!!!

Q 1: WHOLE NUMBERS- BACKGROUND INFORMATION 45, 12, 34 are examples of whole numbers.

Q 1: WHOLE NUMBERS- BACKGROUND INFORMATION 45, 12, 34 are examples of whole numbers. 4. 3, 7. 2, and 5. 6 are not whole numbers. Since 1 x 10 = 10 and 5 x 2 = 10, the numbers 1, 2, 5, and 10 are all considered positive whole number factors of 10.

Q 1: WHOLE NUMBERS- QUESTION Consider the whole numbers from 1 to 50. A.

Q 1: WHOLE NUMBERS- QUESTION Consider the whole numbers from 1 to 50. A. How many numbers are prime? B. How many numbers have only 3 unique factors? C. How many numbers have only 5 unique factors? D. How many numbers have only 6 unique factors? E. Which number has the most unique factors? Note: For this problem we are only considering

Q 1: WHOLE NUMBERS- SOLUTION Consider the whole numbers from 1 to 50. A.

Q 1: WHOLE NUMBERS- SOLUTION Consider the whole numbers from 1 to 50. A. How many numbers are prime? Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 Total: B. How many numbers have only 3 unique 15 factors? 4 1, 2, 4 9 1, 3, 9 25 1, 5, 25 49 1, 7, 49 Total: 4 Notice: These numbers are the squares of the first 4 primes C. How many numbers have only 5 unique None: This would require one prime factor to be repeated (squared) and two other prime factors to multiple to give use the squared term. 12 1, 2, 3, 4, 6, 12 factors? This is not possible. 18 1, 2, 3, 6, 9, 18 D. How many numbers have only 6 unique 20 1, 2, 4, 5, 10, 20 48 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 28 1, 2, 4, 14, 28 Total: 8 Has 10 factors? 32 1, 2, 4, 8, 16, 32 44 1, 2, 4, 11, 22, 44 E. Which number has the most unique factors? 45 1, 3, 5, 9, 15, 45 50 1, 2, 5, 10, 25, 5

Q 2: COUNTDOWN- BACKGROUND INFO The French show Des Chiffres et Des Lettres is

Q 2: COUNTDOWN- BACKGROUND INFO The French show Des Chiffres et Des Lettres is a game show that has been on TV since 1965 (over 53 years)! A British version Countdown has been on TV since 1982 (36 years). In the game show, contestants compete in 3 disciplines. One involves numbers, in which the contestants must use arithmetic to reach a random generated target number from six randomly generated numbers.

Q 2: COUNTDOWN- BACKGROUND INFO For example: In one round, the following random numbers

Q 2: COUNTDOWN- BACKGROUND INFO For example: In one round, the following random numbers were TARGET selected. 250 Using only addition, subtraction, multiplication, and/or division of these six numbers contestants needed to achieve a target score of 250. NUMBERS 25 , 4 , 3 , 5 , 9 , 8 Numbers can ONLY be used once and

Q 2: COUNTDOWN- BACKGROUND INFO So you might achieve this target using a variety

Q 2: COUNTDOWN- BACKGROUND INFO So you might achieve this target using a variety of combinations. TARGET 250 25 4 3 5 9 8 NUMBERS 25 , 4 , 3 , 5 , 9 , 8 – ((5– 3)+8) x 25 2 + Another way (((9+8) – 4) – 3) x 25 10 x On the game show they only have 30 seconds to determine a path to the target.

Q 2 A: COUNTDOWN- QUESTION ROUND 1 Following the Countdown rules achieve the target.

Q 2 A: COUNTDOWN- QUESTION ROUND 1 Following the Countdown rules achieve the target. You’ll only have 90 seconds. You’ll receive a bonus point if you use ALL the numbers. TARGET 301 NUMBERS 100, 50, 4 , 5 , 8 , 2 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 A: COUNTDOWN- SOLUTION ROUND 1 Here is one possible solution that happens

Q 2 A: COUNTDOWN- SOLUTION ROUND 1 Here is one possible solution that happens to use all the numbers. There are many more. A computer generated ____ different solutions TARGET 301 NUMBERS 100, 50, 4 , 5 , 8 , 2 ((50 x 8) – 100)+4+2 – 5 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 B: COUNTDOWN- QUESTION ROUND 2 Another try? Following the Countdown rules achieve

Q 2 B: COUNTDOWN- QUESTION ROUND 2 Another try? Following the Countdown rules achieve the target. You have 90 seconds. You’ll receive a bonus point if you use ALL the numbers. TARGET 436 NUMBERS 100, 75, 1 , 7 , 10 , 6 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 B: COUNTDOWN- SOLUTION ROUND 2 Here is one possible solution that happens

Q 2 B: COUNTDOWN- SOLUTION ROUND 2 Here is one possible solution that happens to use all the numbers. TARGET 436 NUMBERS 100, 75, 1 , 7 , 10 , 6 ((100 -75+1) x (10+7) – 6 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 C: COUNTDOWN- QUESTION ROUND 3 Another? Following the Countdown rules achieve the

Q 2 C: COUNTDOWN- QUESTION ROUND 3 Another? Following the Countdown rules achieve the target. You’ll only have 75 seconds this time. You’ll receive a bonus point if you use ALL the numbers. TARGET 923 NUMBERS 100, 75, 2 , 6 , 4 , 9 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 C: COUNTDOWN- QUESTION ROUND 3 Here is one possible solution that happens

Q 2 C: COUNTDOWN- QUESTION ROUND 3 Here is one possible solution that happens to use all the numbers. TARGET 923 NUMBERS 100, 75, 2 , 6 , 4 , 9 ((2+9)x 75+100+6– 4 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 D: COUNTDOWN- QUESTION ROUND 4 Can you do this faster? You’ll only

Q 2 D: COUNTDOWN- QUESTION ROUND 4 Can you do this faster? You’ll only have 50 seconds. You’ll receive 2 bonus points if you use ALL the numbers. TARGET 984 NUMBERS 25, 75, 1 , 9 , 3 , 5 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 D: COUNTDOWN- SOLUTION ROUND 4 Here is one possible solution that happens

Q 2 D: COUNTDOWN- SOLUTION ROUND 4 Here is one possible solution that happens to use all the numbers. TARGET 984 NUMBERS 25, 75, 1 , 9 , 3 , 5 ((75+5)x(9+3)+25 -1 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 E: COUNTDOWN- QUESTION ROUND 5 FINAL Last round. Achieve the target. You’ll

Q 2 E: COUNTDOWN- QUESTION ROUND 5 FINAL Last round. Achieve the target. You’ll only have 30 seconds. You’ll receive 2 bonus points if you use ALL the numbers. TARGET 234 NUMBERS 25, 50, 2 , 3 , 9 , 5 Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 2 E: COUNTDOWN- SOLUTION ROUND 5 FINAL Here is one possible solution that

Q 2 E: COUNTDOWN- SOLUTION ROUND 5 FINAL Here is one possible solution that happens to use all the numbers. . TARGET 234 NUMBERS 25, 50, 2 , 3 , 9 , 5 ((25 -9+2)x((50/5)+3) Rules: You can only use the operations of addition, subtraction, multiplication, and division only. Numbers can ONLY be used once and you DO NOT need to use all the numbers.

Q 3: WHICH DOESN’T BELONG- BACKGROUND In the 2 x 2 grid, you are

Q 3: WHICH DOESN’T BELONG- BACKGROUND In the 2 x 2 grid, you are given 4 items. One of them might seem out of place or is unique. You can make a MATHEMATICAL statement about each item and how it either doesn’t belong with the other three or is unique to the other three. For example: 9 is the only single digit number 16 is the only even number 43 is the only prime number

Q 3 A: WHICH DOESN’T BELONG- QUESTION RD 1 You are going to be

Q 3 A: WHICH DOESN’T BELONG- QUESTION RD 1 You are going to be given your own 2 x 2 grid. Make ONE MATHEMATICAL statement about EACH item and how it either doesn’t belong with the other three or is unique to the other three. One point per correct statement. No points will be given to trivial answer (example: it’s the only 9 or it the only number with a 3 in it). Non-mathematical statements receive no credit. The key: Use Math

Q 3 B: WHICH DOESN’T BELONG- QUESTION RD 2 Let’s try that again. Make

Q 3 B: WHICH DOESN’T BELONG- QUESTION RD 2 Let’s try that again. Make ONE MATHEMATICAL statement about EACH item and how it either doesn’t belong with the other three or is unique to the other three. One point per correct statement. Non-mathematical and trivial statements receive no credit.

Q 3: WHICH DOESN’T BELONG- QUESTION RD 3 Final Round. Make ONE MATHEMATICAL statement

Q 3: WHICH DOESN’T BELONG- QUESTION RD 3 Final Round. Make ONE MATHEMATICAL statement about EACH item and how it either doesn’t belong with the other three or is unique to the other three. One point per correct statement. Non-mathematical and trivial statements receive no credit.

Q 3 A: WHICH DOESN’T BELONG- SOLUTION RD 1 Answers vary. Here are some

Q 3 A: WHICH DOESN’T BELONG- SOLUTION RD 1 Answers vary. Here are some examples: Non-mathematical and trivial statements receive no credit.

Q 3 B: WHICH DOESN’T BELONG- SOLUTION RD 2 Answers vary. Here are some

Q 3 B: WHICH DOESN’T BELONG- SOLUTION RD 2 Answers vary. Here are some examples: Non-mathematical and trivial statements receive no credit.

Q 3 C: WHICH DOESN’T BELONG- SOLUTION RD 3 Answers vary. Here are some

Q 3 C: WHICH DOESN’T BELONG- SOLUTION RD 3 Answers vary. Here are some examples: Non-mathematical and trivial statements receive no credit.

Q 4: ADJACENT NUMBERS- BACKGROUND INFO 1 5 3 Sum is even (6) Sum

Q 4: ADJACENT NUMBERS- BACKGROUND INFO 1 5 3 Sum is even (6) Sum is even (8)

Q 4: ADJACENT NUMBERS- QUESTION Give an example of a two digit number whose

Q 4: ADJACENT NUMBERS- QUESTION Give an example of a two digit number whose adjacent digits sum is a square. How many two digit numbers have adjacent digits whose sum of squares? Give an example of a three digit number whose adjacent digits sum is a square. What is the largest number whose adjacent digits is the sum of a square? Note: For each no numeral {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} can be used more than once. Example: 22222 is forbidden.

Q 4: ADJACENT NUMBERS- SOLUTION Give an example of a two digit number whose

Q 4: ADJACENT NUMBERS- SOLUTION Give an example of a two digit number whose adjacent digit’s sum is a square 72 How many two digit numbers have 97 adjacent digits whose sum of squares? 17 90 10 88 13 Give an example of a three digit number 18 81 79 22 whose adjacent digit’s sum is a square. 27 72 318 31 36 63 40 What is the largest number whose 45 54

Q 5: BRILLIANT LOGIC- QUESTION As illustrated below, Alice needs to draw just 3

Q 5: BRILLIANT LOGIC- QUESTION As illustrated below, Alice needs to draw just 3 (red) squares to create 4 unit squares. What is the least number of squares she needs to draw to create 16 unit squares?

Q 5: BRILLIANT LOGIC- SOLUTION What is the least number of squares she needs

Q 5: BRILLIANT LOGIC- SOLUTION What is the least number of squares she needs to draw to create 16 unit squares? You need 6 total squares 51 2 3 46

Q 6: RACE- BACKGROUND INFORMATION Four people are going to run a race around

Q 6: RACE- BACKGROUND INFORMATION Four people are going to run a race around a uniquely shaped track. Each starts at the Northern most position of their lane and travels clockwise around their lane One lane of this track is a regular triangle. One is a circle that is inscribed in the triangle. One lane is a regular square circumscribed by the circle. North start

Q 6: RACE- BACKGROUND INFORMATION North Adam starts on the triangle and start completes

Q 6: RACE- BACKGROUND INFORMATION North Adam starts on the triangle and start completes a side of the triangle in 10 seconds. It take him then 2 start seconds to change direction before You’ll need to correct this on the question starting the next side. sheet Beth, on the circle, completes 2 and a quarter laps in a minute and half. Her pace never changes. Chuck starts on the square and completes half of a side in 4 seconds, but also take 1 second to turn a corner. Dominic starts on triangle, switches at his first chance to the circle lane, switches to the square as soon as he can before switching back to the circle again, before switching back to the triangle to finish. He travels the same rate as the other competitors do on their respective lanes.

North Q 6: RACE- QUESTION A. Rank who finishes 1 st , 2 nd

North Q 6: RACE- QUESTION A. Rank who finishes 1 st , 2 nd , and 3 rd between Adam, Beth, and Chuck if they only do one lap. B. Determine how long it takes Dominic to complete a lap. C. What is the total time (in seconds) is takes all 4 of them to finish one lap? Adam starts on the triangle and completes a side of the triangle in 10 seconds. It take him then 2 seconds to change direction before starting You’ll need to correct this on the question the next side. sheet Beth, on the circle, completes 2 and a quarter laps in a minute and half. Her pace never changes. Chuck starts on the square and completes half of a side in 4 seconds, but also take 1 second to turn a corner. Dominic starts on triangle, switches at his first chance to the circle lane, switches to the square as soon as he can before switching back to the circle again, before switching back to the triangle to finish. He travels the same rate as the other competitors do on their respective lanes.

Q 6: RACE- SOLUTION A. Rank who finishes first, second, and third between Adam,

Q 6: RACE- SOLUTION A. Rank who finishes first, second, and third between Adam, Beth, and Chuck if they N only do one lap. start start t s 1 Adam Beth d r 3 d n 2 Chuck ½ side 4 seconds corner 1 seconds ½ side 4 seconds corner 10 seconds 2. 25 laps = min + half corner 1 seconds turn 2 seconds ½ side 4 seconds corner 10 seconds 2. 25 laps = 90 seconds ½ side 4 seconds turn 2 seconds 9/4 laps = 90 seconds corner 10 seconds 1/4 lap = 10 seconds ½ side 4 seconds TOTAL 34 seconds 1 lap = 40 seconds TOTAL 36 seconds

C. Total Time: 34 + 36 + 38 + 40 = 148 seconds Q

C. Total Time: 34 + 36 + 38 + 40 = 148 seconds Q 6: RACE- SOLUTION B. Determine how long it takes Dominic to complete a N lap. Adam Chuck corner 10 seconds ½ side 4 seconds turn 2 seconds ½ side 4 seconds corner 10 seconds corner 1 seconds TOTAL 34 seconds ½ side 4 seconds Dominic Beth ½ side triangle side 5 seconds ½ side 4 seconds 2. 25 laps = min + half ¼ of a circle 10 seconds corner 1 seconds 2. 25 laps = 90 seconds ½ side 4 seconds 9/4 laps = 90 seconds ¼ of a circle 10 seconds corner 1 seconds ½ side triangle side 5 seconds ½ side 4 seconds TOTAL 38 TOTAL 36 seconds 1/4 lap = 10 seconds 1 lap = 40 seconds

Q 7: BRILLIANT LOGIC 2 - QUESTION A and B are digits. What is

Q 7: BRILLIANT LOGIC 2 - QUESTION A and B are digits. What is B? A A A x A 3 B B A

Q 7: BRILLIANT LOGIC 2 - SOLUTION A and B are digits. What is

Q 7: BRILLIANT LOGIC 2 - SOLUTION A and B are digits. What is B? AAA x A 3 BBA

Q 8: WHOLE NUMBERS 1 TO 100 - QUESTION Consider the whole numbers from

Q 8: WHOLE NUMBERS 1 TO 100 - QUESTION Consider the whole numbers from 1 to 100. A. How many numbers are prime? B. There are 5 numbers that have 12 unique factors. What are these 5 numbers? C. What is the Greatest Common Factor between the 5 numbers above? Note: For this problem we are only considering positive factors. A table of the numbers from 1 to 100 has been provided to help you.

Q 8: WHOLE NUMBERS 1 TO 100 - SOLUTION Consider the whole numbers from

Q 8: WHOLE NUMBERS 1 TO 100 - SOLUTION Consider the whole numbers from 1 to 100. A. How many numbers are prime? Primes 1 to 50: Total: 15 Primes 50 to 100: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 Total: 10 B. There are 5 numbers that have 12 unique factors. What are these 5 numbers? 60= 1, 60; 2, 30; 3, 20; 4, 15; 5, 12; 6, 10 72= 1, 72; 2, 36; 3, 24; 4, 18; 6, 12; 8, 9 84= 1, 84; 2, 42; 3, 28; 4, 21; 6, 14; 7, 12 90= 1, 90; 2, 45; 3, 30; 5, 18; 6, 16; 9, 10 96= 1, 96; 2, 50; 3, 32; 4, 24; 6, 16; 8, 12 C. What is the Greatest Common Factor between the 5 numbers above?

8 TH ANNUAL DAMIEN HIGH SCHOOL MATH COMPETITION Congratulations to all of our competitors

8 TH ANNUAL DAMIEN HIGH SCHOOL MATH COMPETITION Congratulations to all of our competitors !

Q 9: WHICH DOESN’T BELONG- QUESTION RD 3 Make ONE MATHEMATICAL statement about EACH

Q 9: WHICH DOESN’T BELONG- QUESTION RD 3 Make ONE MATHEMATICAL statement about EACH item and how it either doesn’t belong with the other three or is unique to the other three. None mathematical statements receive no credit.

Q 9: WHICH DOESN’T BELONG- SOLUTION RD 3 Make ONE MATHEMATICAL statement about EACH

Q 9: WHICH DOESN’T BELONG- SOLUTION RD 3 Make ONE MATHEMATICAL statement about EACH item and how it either doesn’t belong with the other three or is unique to the other three. None mathematical statements receive no credit.