High School Math Contests
High School Math ContestsBlake MadillUniversity of Toronto Mississaugab.madill@utoronto.caAugust 28, 2017Blake Madill (UTM)Math ContestsAugust 28, 20171 / 19
Outline1Benefits of ParticipationFor the StudentsFor the Teachers2Available Contests3Preparation4Other OpportunitiesBlake Madill (UTM)Math ContestsAugust 28, 20172 / 19
Benefits for the StudentsHigh school math contests.provide a fun, low-pressure atmosphere for students to practice theirmathematicsBlake Madill (UTM)Math ContestsAugust 28, 20173 / 19
Benefits for the StudentsHigh school math contests.provide a fun, low-pressure atmosphere for students to practice theirmathematicsexpose students to new mathematics not regularly covered in the highschool curriculumBlake Madill (UTM)Math ContestsAugust 28, 20173 / 19
Benefits for the StudentsHigh school math contests.provide a fun, low-pressure atmosphere for students to practice theirmathematicsexpose students to new mathematics not regularly covered in the highschool curriculumbetter prepare students for university proof-based courses (eg.MAT102 at UTM)Blake Madill (UTM)Math ContestsAugust 28, 20173 / 19
Benefits for the StudentsHigh school math contests.provide a fun, low-pressure atmosphere for students to practice theirmathematicsexpose students to new mathematics not regularly covered in the highschool curriculumbetter prepare students for university proof-based courses (eg.MAT102 at UTM)offer students scholarship opportunitiesBlake Madill (UTM)Math ContestsAugust 28, 20173 / 19
Benefits for the StudentsHigh school math contests.provide a fun, low-pressure atmosphere for students to practice theirmathematicsexpose students to new mathematics not regularly covered in the highschool curriculumbetter prepare students for university proof-based courses (eg.MAT102 at UTM)offer students scholarship opportunities(in special cases) increase competitiveness in a student’s universityapplicationBlake Madill (UTM)Math ContestsAugust 28, 20173 / 19
Benefits for the StudentsHigh school math contests.provide a fun, low-pressure atmosphere for students to practice theirmathematicsexpose students to new mathematics not regularly covered in the highschool curriculumbetter prepare students for university proof-based courses (eg.MAT102 at UTM)offer students scholarship opportunities(in special cases) increase competitiveness in a student’s universityapplicationrealize mathematics as both an individual and team sportBlake Madill (UTM)Math ContestsAugust 28, 20173 / 19
Benefits for the TeachersBesides the obvious benefits for your students.You get to solve the problems too! Many of the contests containhighly non-trivial problems.Blake Madill (UTM)Math ContestsAugust 28, 20174 / 19
Benefits for the TeachersBesides the obvious benefits for your students.You get to solve the problems too! Many of the contests containhighly non-trivial problems.I strongly recommend that you volunteer to mark some of thecontests. (If interested, please feel free to speak with me afterwards)Blake Madill (UTM)Math ContestsAugust 28, 20174 / 19
Benefits for the TeachersBesides the obvious benefits for your students.You get to solve the problems too! Many of the contests containhighly non-trivial problems.I strongly recommend that you volunteer to mark some of thecontests. (If interested, please feel free to speak with me afterwards)You may also wish to apply to be a part of the question committees.Blake Madill (UTM)Math ContestsAugust 28, 20174 / 19
I will not be speaking about:contests not available to Ontario studentsBlake Madill (UTM)Math ContestsAugust 28, 20175 / 19
I will not be speaking about:contests not available to Ontario studentsCanadian Mathematical Olympiad (CMO)Blake Madill (UTM)Math ContestsAugust 28, 20175 / 19
I will not be speaking about:contests not available to Ontario studentsCanadian Mathematical Olympiad (CMO)International Mathematical Olympiad (IMO)Blake Madill (UTM)Math ContestsAugust 28, 20175 / 19
I will not be speaking about:contests not available to Ontario studentsCanadian Mathematical Olympiad (CMO)International Mathematical Olympiad (IMO)the PutnamBlake Madill (UTM)Math ContestsAugust 28, 20175 / 19
Canadian Open Mathematics Challenge (COMC)“The COMC is Canada’s premier national mathematics competitionthat is open to any student with an interest in and grasp of highschool mathematics.”Blake Madill (UTM)Math ContestsAugust 28, 20176 / 19
Canadian Open Mathematics Challenge (COMC)“The COMC is Canada’s premier national mathematics competitionthat is open to any student with an interest in and grasp of highschool mathematics.”The top 50 students from the COMC will be invited to write theCMO.Blake Madill (UTM)Math ContestsAugust 28, 20176 / 19
Canadian Open Mathematics Challenge (COMC)“The COMC is Canada’s premier national mathematics competitionthat is open to any student with an interest in and grasp of highschool mathematics.”The top 50 students from the COMC will be invited to write theCMO.contest date: Thursday, November 2, 2017registration begins: September 1, 2017Blake Madill (UTM)Math ContestsAugust 28, 20176 / 19
Canadian Open Mathematics Challenge (COMC)“The COMC is Canada’s premier national mathematics competitionthat is open to any student with an interest in and grasp of highschool mathematics.”The top 50 students from the COMC will be invited to write theCMO.contest date: Thursday, November 2, 2017registration begins: September 1, 2017French or EnglishBlake Madill (UTM)Math ContestsAugust 28, 20176 / 19
Canadian Open Mathematics Challenge (COMC)“The COMC is Canada’s premier national mathematics competitionthat is open to any student with an interest in and grasp of highschool mathematics.”The top 50 students from the COMC will be invited to write theCMO.contest date: Thursday, November 2, 2017registration begins: September 1, 2017French or English2.5 hour on-paper contestBlake Madill (UTM)Math ContestsAugust 28, 20176 / 19
Canadian Open Mathematics Challenge (COMC)EligibilityA participating student must be under 19 years old as of June 30,2017.They must be attending school (elementary or secondary) full-timesince September 15, 2017.They must not have written the Putnam.Blake Madill (UTM)Math ContestsAugust 28, 20177 / 19
Canadian Open Mathematics Challenge (COMC)EligibilityA participating student must be under 19 years old as of June 30,2017.They must be attending school (elementary or secondary) full-timesince September 15, 2017.They must not have written the Putnam.Prizes etc.A prize pool of 2000 will be divided among the top students inCanada.A group of students in grade 8, 9, or 10 will be invited to the CMSNational Canada Math Camp at the University of Toronto.Competition results are shared with participating universities.Blake Madill (UTM)Math ContestsAugust 28, 20177 / 19
Canadian Senior/ Intermediate Mathematics Contests“The CSMC and CIMC are two contests designed to give students theopportunity to have fun and develop their mathematical problemsolving ability.”Blake Madill (UTM)Math ContestsAugust 28, 20178 / 19
Canadian Senior/ Intermediate Mathematics Contests“The CSMC and CIMC are two contests designed to give students theopportunity to have fun and develop their mathematical problemsolving ability.”made by the Centre for Education in Mathematics and Computing(CEMC) at the University of WaterlooBlake Madill (UTM)Math ContestsAugust 28, 20178 / 19
Canadian Senior/ Intermediate Mathematics Contests“The CSMC and CIMC are two contests designed to give students theopportunity to have fun and develop their mathematical problemsolving ability.”made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: November 22, 2017registration deadline: November 3, 2017Blake Madill (UTM)Math ContestsAugust 28, 20178 / 19
Canadian Senior/ Intermediate Mathematics Contests“The CSMC and CIMC are two contests designed to give students theopportunity to have fun and develop their mathematical problemsolving ability.”made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: November 22, 2017registration deadline: November 3, 2017French or EnglishBlake Madill (UTM)Math ContestsAugust 28, 20178 / 19
Canadian Senior/ Intermediate Mathematics Contests“The CSMC and CIMC are two contests designed to give students theopportunity to have fun and develop their mathematical problemsolving ability.”made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: November 22, 2017registration deadline: November 3, 2017French or English2 hour on-paper contestsBlake Madill (UTM)Math ContestsAugust 28, 20178 / 19
Canadian Senior/ Intermediate Mathematics Contests“The CSMC and CIMC are two contests designed to give students theopportunity to have fun and develop their mathematical problemsolving ability.”made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: November 22, 2017registration deadline: November 3, 2017French or English2 hour on-paper contestsThe CSMC is a great warm-up for Grade 12 students planning towrite the Euclid!Blake Madill (UTM)Math ContestsAugust 28, 20178 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Blake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Blake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Hypatia - Grade 11Blake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Hypatia - Grade 11made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloo.Blake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Hypatia - Grade 11made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloo.contest date: April 12, 2018registration deadline: March 23, 2018Blake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Hypatia - Grade 11made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloo.contest date: April 12, 2018registration deadline: March 23, 2018French or EnglishBlake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Hypatia - Grade 11made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloo.contest date: April 12, 2018registration deadline: March 23, 2018French or English75 minute on-paper contestsBlake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Fryer, Galois, and Hypatia ContestsFryer - Grade 9Galois - Grade 10Hypatia - Grade 11made by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloo.contest date: April 12, 2018registration deadline: March 23, 2018French or English75 minute on-paper contestsheld the day after the EuclidBlake Madill (UTM)Math ContestsAugust 28, 20179 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of WaterlooBlake Madill (UTM)Math ContestsAugust 28, 201710 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: April 11, 2018registration deadline: March 22, 2018Blake Madill (UTM)Math ContestsAugust 28, 201710 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: April 11, 2018registration deadline: March 22, 2018French or EnglishBlake Madill (UTM)Math ContestsAugust 28, 201710 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: April 11, 2018registration deadline: March 22, 2018French or English2.5 hour on-paper contestsBlake Madill (UTM)Math ContestsAugust 28, 201710 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: April 11, 2018registration deadline: March 22, 2018French or English2.5 hour on-paper conteststhe top five contestants receive a plaque and a prize of 500Blake Madill (UTM)Math ContestsAugust 28, 201710 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: April 11, 2018registration deadline: March 22, 2018French or English2.5 hour on-paper conteststhe top five contestants receive a plaque and a prize of 500the next top ten students receive a prize of 200Blake Madill (UTM)Math ContestsAugust 28, 201710 / 19
Euclid Contestusually written by grade 12 studentsmade by the Centre for Education in Mathematics and Computing(CEMC) at the University of Waterloocontest date: April 11, 2018registration deadline: March 22, 2018French or English2.5 hour on-paper conteststhe top five contestants receive a plaque and a prize of 500the next top ten students receive a prize of 200the Euclid score is considered for admission to the University ofWaterlooBlake Madill (UTM)Math ContestsAugust 28, 201710 / 19
PreparationWhen preparing for a Grade 12 contest (Euclid or COMC), the followingtopics should be studied and practiced.1counting and patterns2basic algebra3geometry4trigonometry5functions and graphs6logarithms and exponents7polynomials8divisibility and gcd’s9sequencesBlake Madill (UTM)Math ContestsAugust 28, 201711 / 19
Counting and PatternsExample (Easier, COMC 2015)What is the smallest palindrome larger than 2015?Blake Madill (UTM)Math ContestsAugust 28, 201712 / 19
Counting and PatternsExample (Easier, COMC 2015)What is the smallest palindrome larger than 2015?Example (Harder, COMC 2015)A polynomial x 2 px q, where p and q are real numbers, is said to be adouble-up polynomial if it has two real roots, one of which is twice theother one. Determine all double-up polynomials such that p q 6.Blake Madill (UTM)Math ContestsAugust 28, 201712 / 19
AlgebraExample (Easier, COMC 2016)Solve the following system of equations:11 1,xy23 4.xyBlake Madill (UTM)Math ContestsAugust 28, 201713 / 19
AlgebraExample (Easier, COMC 2016)Solve the following system of equations:11 1,xy23 4.xyExample (Easier, Euclid 2016)If x 2 2016 then what is the value of (x 2)(x 2)?Blake Madill (UTM)Math ContestsAugust 28, 201713 / 19
GeometryExample (Easier, COMC 2015)A rectangle has an area of 180 units2 and a perimeter of 54 units. If eachside of the rectangle is increased by 6 units, what is the area of the newrectangle?Blake Madill (UTM)Math ContestsAugust 28, 201714 / 19
GeometryExample (Easier, COMC 2015)A rectangle has an area of 180 units2 and a perimeter of 54 units. If eachside of the rectangle is increased by 6 units, what is the area of the newrectangle?Example (Harder, COMC 2016)Let A (0, a), C (c, 0), and B (c, b), where a, b, and c are positiveintegers. Suppose P (p, 0) is the point on OC that minimizes AP PB.Set X AP PB. If a, b, p, and X are positive integers, prove that thereexists a positive integer n 3 such that n divides both a and b.Blake Madill (UTM)Math ContestsAugust 28, 201714 / 19
OtherExample (Easier, Euclid 2017)If cos θ tan θ then what are the possible exact values for sin θ?Blake Madill (UTM)Math ContestsAugust 28, 201715 / 19
OtherExample (Easier, Euclid 2017)If cos θ tan θ then what are the possible exact values for sin θ?Example (Very Hard, Euclid 2014)Let f (n) denote the number of positive integers who have exactly n digitsand whose digits sum to 4. How many of f (1), f (x), . . . , f (2014) have aunits digit of 1?Blake Madill (UTM)Math ContestsAugust 28, 201715 / 19
OthersExample (Very Easy, COMC 2012)Which positive integer satisfies 84 4n ?Blake Madill (UTM)Math ContestsAugust 28, 201716 / 19
OthersExample (Very Easy, COMC 2012)Which positive integer satisfies 84 4n ?Example (Harder, Euclid 2013)Solve for x:log2 (2x 1 3x 1 ) 2x log2 (3x )Blake Madill (UTM)Math ContestsAugust 28, 201716 / 19
A Sample Year1COMC - Nov. 22CIMC/CSMC - Nov. 223Fryer, Galois, Hypatia - April 124Euclid - April 11Blake Madill (UTM)Math ContestsAugust 28, 201717 / 19
Math Circlesa high school enrichment program here at UTMBlake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Math Circlesa high school enrichment program here at UTMa fun way to practice problem solving skills and prepare for contestsBlake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Math Circlesa high school enrichment program here at UTMa fun way to practice problem solving skills and prepare for contestsgrades 10 to 12Blake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Math Circlesa high school enrichment program here at UTMa fun way to practice problem solving skills and prepare for contestsgrades 10 to 12math battlesBlake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Math Circlesa high school enrichment program here at UTMa fun way to practice problem solving skills and prepare for contestsgrades 10 to 12math battles“Fields trips”Blake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Math Circlesa high school enrichment program here at UTMa fun way to practice problem solving skills and prepare for contestsgrades 10 to 12math battles“Fields trips”registration is limited to 20 studentsBlake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Math Circlesa high school enrichment program here at UTMa fun way to practice problem solving skills and prepare for contestsgrades 10 to 12math battles“Fields trips”registration is limited to 20 studentscontact Marina Tvalavadze for details: marina.tvalavadze@utoronto.caBlake Madill (UTM)Math ContestsAugust 28, 201718 / 19
Thank You!Blake Madill (UTM)Math ContestsAugust 28, 201719 / 19
Canadian Senior/ Intermediate Mathematics Contests \The CSMC and CIMC are two contests designed to give students the opportunity to have fun and develop their mathematical problem solving ability." made by the Centre for Education in Mathematics and Computing (CEMC) at t
Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra 1/2 Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra ½ form a series of courses to move students from primary grades to algebra. Each course contains a series of daily lessons covering all areas of general math. Each lesson
2016 MCAS Results September 29, 2016 Page 4 8 Year Math CPI Results For State, District, and Schools Ranked by 2016 CPI School el 2009 Math MCAS 2010 Math MCAS 2011 Math MCAS 2012 Math MCAS 2013 Math MCAS 2014 Math MCAS 2015 Math MCAS 2016 Math PARCC Sewell-Anderson 1 80.0 78.7 76.7 84.2 88.3 89.0 89.3 92.5
age to improve math education in primary and secondary schools 5. . math competitions, contest formats, topics covered and type of questions appearing in each contest. Most contests covered three major areas, namely, . Washington State Math Council s Middle School Math Olympiad One hour-long, open ended question, team test Five, 15-minute .
MATH 110 College Algebra MATH 100 prepares students for MATH 103, and MATH 103 prepares students for MATH 110. To fulfil undergraduate General Education Core requirements, students must successfully complete either MATH 103 or the higher level MATH 110. Some academic programs, such as the BS in Business Administration, require MATH 110.
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from the previous competitions (Math Kangaroo, Abacus, Pythagorus contests, Waterloo contests). Older and more advanced children may tackle the problems of di erent mathematical olympiads (Tournament of Towns, CMO, USAMO, APMO, IMO). V. Ivrii, O. Zaitseva (Math., Toro
The paper then turns to an empirical study of logo design competitions, drawing on a sample of contests from a popular online platform.2 In these contests, a rm (\sponsor") solicits custom designs from freelance designers (\players"), who compete for a winner-take-all prize. The contests in the sample o er prizes of
Abrasive Jet Machining INTRODUCTION Abrasive water jet machine tools are suddenly being a hit in the market since they are quick to program and could make money on short runs. They are quick to set up, and offer quick turn-around on the machine. They complement existing tools used for either primary or secondary operations and could make parts quickly out of virtually out of any material. One .
