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

2. 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

3. Imaginary Numbers

4. Simplify Radicals

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

6. 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

7. 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.)

8. 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

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

10. 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

11. Area Formulas:

12. 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

13. 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

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

15. 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

16. Unit Circle

17. Special Right
Triangles

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

19. 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

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

21. 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