Skills for November Rounds Math Team Skills for November Rounds Round 1 Round 2 Round 3 Round 4 Round 5 Round 6

Round 1 - Complex Numbers (No Trig.) Imaginary numbers Introduction Simplify imaginary numbers and radicals Complex Numbers Simplify Multiply (expand) Divide (rationalize) Conjugates Complex Fractions Simplify complex fractions

Imaginary Numbers

Simplify Radicals

Complex Numbers Standard form of a complex number z = a-bi is often denoted as the conjugate of z

Round 2 – Algebra Anything Vocabulary: consecutive, odd, even, integers, whole numbers, sum, product, mean Consecutive integer problems Solve equations with multiple answers Order of operations Percent (interest) problems

Consecutive Integers: x, (x+1), (x+2), (x+3) … Consecutive Odd Integers: x, (x+2), (x+4), (x+6) … (Where the initial x is odd.) Consecutive Even Integers: x, (x+2), (x+4), (x+6) … (Where the initial x is even.)

Round 3 – Plane Geometry: Areas of Rectilinear Figures Vocabulary: diagonal, altitude, base Triangles: equilateral, isosceles, scalene, right Formulas Area of a Triangle Area of a Square Area of a Rectangle Area of a Trapezoid Area of a shaded region Ratios: You will often be asked the ratio of two areas

Altitude (a): height Base (b), (b1), or (b2): Diagonal (d): d d

Equilateral: All sides equal, All angles equal 60o or Isosceles: Two sides equal, Two angles equal Scalene: No equal sides, No equal angles Right One right angle 90o or

Area Formulas:

Round 4 – Algebra 1: Factoring and Its Applications All Factoring Greatest Common Factor Factor by Grouping Quadratic Type Polynomials (reverse FOIL) Special Cases Perfect Square Trinomials Difference of Two Perfect Squares Solving Proportions: Cross multiply Other equations: Descending order set equal to zero

Greatest Common Factor GCF of coefficients Lowest powered common variable Factor by Grouping Group first two and last two GCF from each Factor out binomial GCF Quadratic trinomials Reverse FOIL

Special Cases Quadratic Type Perfect Square Trinomials Difference of Two Perfect Squares Quadratic Type Reverse FOIL with higher powers

Round 5 – Trigonometry: Functions of Special Angles Radian Measures: Unit Circle (any angle) Values of Trig. Functions on an Axis Special Triangle 30o-60o-90o 45o-45o-90o Reciprocal Identities

Unit Circle

Special Right Triangles

Use reference angles ( )for angles that are not between 0o and 90o.

Round 6 – Plane Geometry: Angles, Triangles, and Parallels Vocabulary: vertex angle, base angle, isosceles triangle, regular polygon, exterior angle, interior angle, bisector, intersect, angle bisector, etc. Notation: Parallel Perpendicular Measure of an angle Length of a line segment Angle properties {polygons (especially triangles) and transversals} Sum of interior angles of a polygon = (n-2)180

The sum of interior angles for a polygon with n sides: Exterior angle Interior angle Exterior angle A B C D no

Vertical angles are equal Alternate interior angles are equal Alternate exterior angles are equal Corresponding angles are equal Same side interior angles are supplementary Same side exterior angles are supplementary