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Upcoming Events

2012-2013

September

Practice starts!

October

More practice!

November

1st meet on 1st

2nd meet on 22nd

December

3rd meet on 13th

January

4th meet on 10th

February

5th meet on 14th

March

State tournament on 14th

math team logo and rollover image of a matrix pi

Practice Information

1) Practices are Tuesdays and Thursdays

from 2:45 to about 3:30 PM

2) Scoring team test days go till 4:30 PM

3) Mr. Haugh will teach you the subjects of the next event and give you practice exams at every practice.

Upcoming Practice

1A: Tuesday September 23

Practice Notes

1A Prealgebra Topics
• Fractions to add and express as the quotient of two relatively prime integers
• Complex fractions and continued fractions
• Decimals, repeating decimals
• Percentage, interest, and discount
• Least common multiple, greatest common divisor
• Number bases; change of base
• Challenge topic: the Euclidean algorithm

Haugh's Notes:

1B Measuring Angles
• Angle sums for triangles and polygons
• Complementary, supplementary, and vertical angles
• Interior and exterior angles of a triangle
• Angles formed by transversals cutting parallel lines
• Familiarity with isosceles, equilateral and 30°-60°-90° triangles

Haugh's Notes:

1C Elementary Trigonometry
• Definitions and solution of right triangles
• Elementary identities
• Radian measure and graphs of elementary functions
• Trigonometric functions of multiples of π/6, π/4, π/3, π/2.

Haugh's Notes:

1D Roots of Quadratic and Polynomial Equations
• Solution of quadratic equations by factoring, by completing the square, by formula
• Complex roots of quadratic equations; the discriminant and the character of the roots
• Relations between roots and coefficients
• Synthetic Division
• Challenge Topic: Rational functions and their graphs
• Function notation

Haugh's Notes:

2A Linear Equations in One Unknown
• Solving numeric equations (perhaps involving a second degree term which drops out)
• Solving literal equations
• Story problems leading to linear equations in one variable
• Linear inequalities

Haugh's Notes:

2B Familiar Geometric Figures, Congruence and Similarity
• Ratio and proportion
• Segments intercepted by parallel lines
• Medians, angle bisectors, and altitudes
• The Theorem of Pythagoras; familiar Pythagorean triples
• Relationships in 30°-60°-90° and 45°-45°-90° triangles
• Equilateral and isosceles triangles, associated terminology
• Challenge Topic: Number theoretic aspects of Pythagorean triples 10

Haugh's Notes:

2C Trigonometry
• Functions of sums of angles and sums of functions of angles
• Half and double angle formulas
• Reduction formulas
• (Not required: formulas for sin A + sin B, etc.)

Haugh's Notes:

2D Analytic Geometry of Straight Lines and Circles
• Slope, families of parallel, perpendicular, or coincident lines
• Point-slope, slope-intercept, intercept, normal forms of the straight line
• Intersections (solution of simultaneous systems)

Haugh's Notes:

3A Systems of Linear Equations in Two (or on occasion three) Variables
• Numeric and literal systems
• Relation to graphical procedures
• Word problems leading to such systems
• Systems of inequalities used to define a region in the plane
• Determinants

Haugh's Notes:

3B Quadrilaterals and Polygons
• Rectangles, parallelograms, the rhombus, and the trapezoid
• Intersecting diagonals
• Ptolemy's Theorem
• Regular polygons and inscribed or circumscribed circles

Haugh's Notes:

3C Trigonometry
• Law of sines, law of cosines
• Inverse functions and their graphs
• Solving trigonometric equations
• De Moivre's Theorem and the roots of unity

Haugh's Notes:

3D Exponents and Logarithms
• Use of fractional, negative exponents
• Simplifying expressions involving radicals
• Solving equations involving radicals
• Use of logarithms; identities involving logarithms
• Solving logarithmic equations
• Relationships between logarithms to different bases

Haugh's Notes:

4A Algebraic Manipulation
• Factoring
• Sums, products, quotients of rational expressions
• Solving equations (including radical equations) involving these skills, but
ultimately solvable by factoring or the quadratic formula (but no complex roots)
• Rational exponents
• Simplifying radical expressions
• Function notation and variational dependencies 11

Haugh's Notes:

4B Circles
• Inscribed angles
• Secants, intersecting chords
• Interior and exterior tangents of two circles
• The measurement of angles by intercepted arcs

Haugh's Notes:

4C Miscellaneous Topics
• Sequences: patterns and recursion formulas, arithmetic and geometric sequences
• Series: partial sums, formulas
• Function notation; factorial notation and Binomial Theorem

Haugh's Notes:

4D Analytic Geometry of the Conic Sections
• Using the standard forms of equations of the conic sections
• Graphs, including the location of foci, directrices, and asymptotes
• Use of properties of conics to solve applied problems, including max-min for
parabolas

Haugh's Notes:

5A Puzzle Problems (20 minutes)
• Word problems, one or more variables
• Max-min problems not requiring calculus
• Problems found in "brain-teaser" type books
• Logic puzzles, including the use of Venn Diagrams

Haugh's Notes:

5B Areas, Perimeters, and Volumes
• Triangles - including Heron's formula and ability to use ideas of elementary
trigonometry to find certain lengths
• Trapezoids and parallelograms
• Circles, sectors of circles
• Volumes of familiar 3-dimensional objects

Haugh's Notes:

5C Counting and Probability
• Permutations, with and without replacement
• Combinations, with and without replacement
• Using the principle of inclusion, exclusion
• Using the binomial and multinomial expansions
• Nonnegative integer solutions to x1+x2+...+xn = b.
• Definition, simple applications of probability (when to multiply, when to add)

Haugh's Notes:

5D Variations of previous AMC 12

Haugh's Notes:

I ate some pie and it tasted great joke

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