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:
