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

2. Round 1 – Trig: Right Angle Problems Law of Sines and Cosines
For right triangles:
Pythagorean Theorem

3. For oblique triangles:
(ASA, AAS, or SSA)

4. For oblique triangles:
(SAS or SSS)

5. Round 2 – Arithmetic/Number Theory
Percent of Change =
Positive percent of change  percent increase
Negative percent of change  percent decrease

6. Number of Factors Example: 90 has 12 positive integer factors
To find the number of positive integer factors of a number:
Find the number’s prime factorization (using exponents to describe repeating factors)
Add 1 to each of the exponents
Find the product of the numbers generated by adding 1 to each exponent
Example: has 12 positive integer factors

7. Base 10 Numbers
We use base 10 numbers all of the time. We have memorized the places of base 10 numbers since we were young children.
For Example, the number has a 2 in the one’s place, a 9 in the ten’s place and a 6 in the hundred’s place.
(The subscript of 10 simply means that it is a base 10 number. When there is no subscript, we always assume that the number is base 10)
To understand other bases, we need to know where the names of the place values come from.
So the number is really:
Six 100’s = 600
+ Nine 10’s = 90
+ Two 1’s = 2
= 692
Base 10 place values:
Evaluate to get the names:

8. Base 2 Numbers Base 2 numbers’ place values work the same as base 10:
Base 2 place values:
In base 2, each place
value is worth…
When we are in base 10, remember that we can only use the numbers from 0 to 9. In base 2, we can only use numbers from 0 to 1. So to evaluate :
Evaluating this base 2 number:
Using these place values:
One 16 + Zero 8’s + One 4 + One 2 + Zero 1’s
Yields:
=22
Which is:
= 2210
Therefore:

9. Base 3 Numbers
If you can figure out the base 10 equivalent to then you’ve got it.
Solution: = 46

10. Round 3 – Coordinate Geometry of lines and circles
Equation of a Circle: {with center (h,k) and radius r}
If given this form
Divide both sides by ac, then complete each square to change back to general form.

11. Ex) Circle with center (2, -1) and radius 4

12. Equations of lines: slope y-intercept Given Point (x1 , y1)
Typically A > 0
and A, B, C are Integers
Given Point (x1 , y1)

13. Center of a circle is the midpoint of a diameter
Slope of a line is constant.
If given slope, use to find additional points

14. Round 4 – Log and Exponential Functions
Logarithmic Form vs Exponential Form
exponent
base
base
exponent
Remember: Log is exponent

15. Properties
of Logs
Properties
of Exponents
Ex)
Ex)
Ex)
Ex)
Ex)
Ex)

16. Inverse Properties:
Ex)
Ex)
Special logs:
Special Values:

17. Round 5 – Alg 1: Ratio, Proportion or Variation
If the ratio of x to y is 3 : 4, then
Cross multiply to
solve proportions
Ratios can be reduced the same as fractions:
25 is to 100 as 1 is to 4.

18. Direct Variation Inverse Variation Joint Variation
“y varies directly as x”
Direct variation is a line that intersects the origin (0, 0) and has slope (or constant of variation), k.
Inverse Variation
“y varies inversely as x”
To solve variation problems, use the initial values of x and y to find the constant of variation, k. Then substitute k back into the equation.
Joint Variation
“z varies jointly with x and y”

19. Round 6 – Plane Geometry: Polygons (no areas)
Vocabulary: Midpoint, segment bisector, segment trisector, angle bisector, perpendicular, altitude, etc.
Sum of interior angles of a polygon with n sides:
For a regular polygon with n sides, each
Interior angle of the polygon would be:
Know your shapes and their properties: square, rhombus, rectangle, triangle, quadrilateral, etc.

20. Length of the sides of a Tangential (inscribed) polygon
(a polygon in which each side is tangent to a circle)
For a tangential polygon with an even number of sides, if you number the sides consecutively, the sum of the even sides is always equal to the sum of the odd sides. a
In this example,
a + c + e = b + d + f f b e c d