# State Tournament

### STATE TOURNAMENT IS ON MONDAY, MARCH 11, 2024

@ SPRING LAKE PARK HIGH SCHOOL

@ SPRING LAKE PARK HIGH SCHOOL

## event A

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

2A Linear Equations in One Unknown:

Solving numeric equations (perhaps involving a second degree term which drops out)

Story problems leading to linear equations in one variable

Linear inequalities

Absolute value equations and inequalities

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

4A Algebraic Manipulation:

Factoring (including x3 + y3, x3 – y3)

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

5A Puzzle Problems:

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

## event B

1B Angles and Special Triangles:

The Theorem of Pythagoras; familiar Pythagorean triples

Complementary, supplementary, and vertical angles

Interior and exterior angles for triangles and polygons

Angles formed by transversals cutting parallel lines

2B Triangular Figures and Solids:

Medians, angle bisectors, and altitudes

Ceva’s and Stewart’s Theorems (Stewart's Theorem Practice Problems)

Area of a triangle (including Hero’s Formula)

Triangular prisms & pyramids (including volume and surface area)

3B Polygonal Figures and Solids:

Special quadrilaterals and regular polygons (including area formulas)

Intersecting diagonals

Polygonal prisms & pyramids (including volume and surface area)

4B Circular Figures and Solids:

Central, inscribed, tangential, and exterior angles

Power of a point (chords, secants, tangents)

Interior and exterior tangents of two circles

Intercepted arcs

Area of circles, sectors, circular segments

Cylinders, cones, & spheres (including volume and surface area)

5B Congruence and Similarity:

Ratio and proportion

Segments intercepted by parallel lines

Identification of similar/congruent figures

Ratios of areas and volumes

Elementary trigonometric ratios

## event C

1C Elementary Trigonometry:

Radian measure and graphs of elementary functions

Trigonometric functions of multiples of π/6, π/4, π/3, π/2.

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.)

3C Trigonometry:

Solving trigonometric equations

De Moivre's Theorem and the roots of unity

4C Miscellaneous Topics:

Sequences: patterns and recursion formulas, arithmetic and geometric sequences

Series: partial sums, formulas for 1+2+…+n, 12 + 22 + … + n2, 13 + 23 + … + n3

Function notation; factorial notation and Binomial Theorem

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)

## event D

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

Synthetic Division, Synthetic Division example, Remainder Theorem

Function notation

2D Analytic Geometry of Straight Lines and Circles:

Slope, families of parallel, perpendicular, or coincident (lines that cross) lines

Point-slope, slope-intercept, intercept (scroll down to the intercept-intercept section), normal ("normal" means perpendicular) forms of the straight line

Intersections (solution of simultaneous systems)

3D Exponents and Logarithms:

Use of fractional, negative exponents

Simplifying expressions involving radicals (including denesting radical expressions... this is tough!)

Use of logarithms; identities involving logarithms

Relationships between logarithms to different bases

4D Analytic Geometry of the Conic Sections:

Using the standard forms of equations of the conic sections

Graphs, including the location of foci, directrices (plural of directrix), and asymptotes

Use of properties of conics to solve applied problems, including max-min for parabolas

5D Variations of Problems Appearing on the Previous Year's AMC 12 (Contest A and B):

Instructional Videos: #1-10 #11-15 A better response to 12B #11