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Welcome to the 2 nd annual Math Contest Summer Mini-Camp!!!

Welcome to the 2 nd annual Math Contest Summer Mini-Camp!!!. Get a pocket folder a nd write your name o n it. Get a note card and m ake a “name tent” Feel free to sit where you want (we’ll be moving around seats in just a bit). Schedule for the week. Monday : Geometry

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Welcome to the 2 nd annual Math Contest Summer Mini-Camp!!!

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  1. Welcome to the 2nd annual Math Contest Summer Mini-Camp!!! • Get a pocket folder and write your name on it. • Get a note card and make a “name tent” • Feel free to sit where you want (we’ll be moving around seats in just a bit)

  2. Schedule for the week • Monday: Geometry • Tuesday: Counting and Algebra • Wednesday: Primes and Number Theory • Each day we’ll play some math/logic games, and have a snack sometime around 10:45. • Each day, if we have time we’ll end with a little team math competition, just for fun.

  3. Groundrules • Do your best at all times, whether the activity is a worksheet, a game, a contest, or anything else. • Keep all your materials (notes, worksheets, etc) and refer back to them whenever you want. • Participate, and listen to each other. • If we don’t have time to thoroughly answer your questions, don’t give up! (talk to me afterwards, or send me an email) • Try to minimize your “break time.”

  4. Major Math Contests • MathCounts • The AMC 8 and AMC 10 • Colorado Math League • The Purple Comet

  5. Math Contest Topics (a quick overview) • Arithmetic • Algebra • Geometry • Number Theory • Counting • Probability and Statistics • “Other”

  6. Why we do math contests • Discuss • “How Would You Move Mount Fuji” video

  7. Icebreaker “Naughts and Crosses” • 3 in a row = 1 point • 4 in a row = 2 points • 5 in a row = 3 points

  8. 1st Problem Set!! • This first problem set is from the 2008 AMC 8 (25 questions, no calculator). • Yes, THREE out of the last FIVE questions are geometry questions . . . that’s why we’re ONLY going to focus on geometry today.

  9. Geometry Essentials • Area/volume formulas • Basic Algebra 1 (equations, binomials) • Similar triangles • Diagonals of polygons • Interior angles of polygons • The Pythagorean Theorem!! For higher-level contests: • Special Right Triangles: • 45, 45, 90 • 30, 60, 90 • What it means when figures are “tangent”

  10. Area/Volume Formulas Area: • Triangles, rectangles, parallelograms, squares, circles, and trapezoids. • (optional) Equilateral Triangles: A = Volume: • Prisms and Cylinders: V = Bh (B is the area of the base) • Pyramids and Cones: V = (Bh)/3 (Again, B is the area of the base)

  11. Basic Algebra 1 Solving equations 2x + 4 = -5(x + 2) 2x + 4 = -5x – 10Distribute +5x +5xAdd 5x to both sides 7x + 4 = -10 -4 -4Subtract 4 from both sides 7x = -14 x = -2 Divide by 7 on both sides

  12. The Pythagorean Theorem • In right triangles, if a and b are the legs, and c is the hypotenuse, then a2+ b2 = c2 • Often, you have to work to find the hidden right triangles in diagrams. • Example: “If a bird flew directly from A to B, how far would it travel?” (all angles are right angles) A 3mi 8mi 3mi B

  13. Similarity/Diagonals/Angles • Similar Triangles • Look for ways to prove triangles similar, then use proportions to solve for missing sides If DE and BC are parallel, find the length of DE A 4cm Do we need those two angle measures? Which triangles are similar? How do you know? 50o D E 2cm 50o B C 6cm

  14. BONUS Geometry: Special Right Triangles • 45,45,90 • Sides in ratio of 1: • 30,60,90 • As easy as “1,2,3”!! 60o 2 6 1 90o 30o 90o 45o

  15. MORE Bonus: What it means to be “tangent” • When things are tangent, they touch at exactly one point • When lines are tangent to circles, right angles are formed  • When circles are tangent to each other, their centers connect in a line (and the shared tangent line is perpendicular to the radii) 90o 90o

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