Math Team Skills for March Rounds

Round 1 – Alg 2: Simultaneous Equations and Determinants The determinant of a 2x2 matrix is determined using a formula The determinant of matrix Denoted: Alternatively, the negatively sloped diagonal product minus the positively sloped diagonal product

To find the determinant of a 3x3 or larger square matrix… The sum of the negatively sloped diagonal products minus the sum of the positively sloped diagonal products. Negatively sloped diagonal products Positively sloped diagonal products

Solving Simultaneous Equations – Reduce the number of variables then backfill. Example: (2 equations, 2 unknowns) Multiply both sides of the top equation by 3. Add the two equations and the y-terms will cancel. Solve for x. Substitute the known value into either of the first equation to find the other unknown.

Example: (3 equations, 3 unknowns) Backfill into previous equations to find y and z.

Round 2 – Alg 1: Exponents and Radicals Rules of Exponents If n is a positive integer and x is a nonnegative real number, then Therefore, rules for radicals are the same as the rules for exponents. If n is a positive integer and x is a nonnegative real number, then Therefore, rules for radicals are the same as the rules for exponents. Rational Exponents Power Root

Ex.) Simplify a) b) c) d)

Matching Bases Solving equations involving exponents often requires matching the bases of the terms. If the bases are matched, the exponents must be equal. Ex.)Solve All the terms can be expressed using base 3. Power to a power - Multiply (distribute) Product of powers - Add (comb. Like terms) Bases are matched, exponents are equal

Simplifying and Manipulating Radicals To simplify a radical, we basically take the perfect squares out. (Or perfect cubes for cube roots) Ex) But remember, if it is convenient, we can put numbers or variables back into the radical. Ex) Solve for a and b.

Round 3 – Trigonometry: Anything See Trigonometry Rounds and info from previous months

Round 4 – Alg 1: Anything Solving equations Proportions Percent and mixture problems The coordinate plane Factoring Solving rational equations … just to name a few topics

Round 5 – Plane Geometry: Anything Regular polygons and their properties Triangles Transversals Interior and exterior angle theorems Circles … just to name a few topics

Round 6 – Probability and the Binomial Theorem Using the Binomial Theorem for a binomial expansion. To expand, we use the n th row of Pascal’s triangle to find the coefficients. The powers of x start with n in the first term and decrease by one for each successive term. The powers of y start with zero and increase by one for each successive term. Row 0 Row 1 Row 2 Row 3 Row 4 Row 5 Pascal’s Triangle Ex)

Row 0 Row 1 Row 2 Row 3 Row 4 Row 5 Pascal’s Triangle Ex) Expand

Probability Independent events Dependent events Compound probability Combinatorics Counting principles Combinations Permutations