This section separates regional qualifiers from casual competitors. Systems of equations and operations with polynomials.
Convert repeating decimals to fractions instantly.
Week 5: Counting, Probability, Word Problems General Math Tmsca Study Guide
Weeks 1–2: Foundations
Solve every question you can answer in under 20 seconds. These are usually the first 20-25 questions. Week 5: Counting, Probability, Word Problems Weeks 1–2:
| Category | Formula / Concept | | :--- | :--- | | | Slope Formula: ( m = \fracy_2 - y_1x_2 - x_1 ) Point-Slope Form: ( y - y_1 = m(x - x_1) ) Slope-Intercept Form: ( y = mx + b ) Midpoint Formula: ( \left( \fracx_1+x_22, \fracy_1+y_22 \right) ) Distance Formula: ( \sqrt(x_2-x_1)^2 + (y_2-y_1)^2 ) Quadratic Formula: ( x = \frac-b \pm \sqrtb^2-4ac2a ) | | Geometry | Circle Area: ( A = \pi r^2 ) Circumference: ( C = 2\pi r ) or ( C = \pi d ) Sum of Interior Angles: ( (n-2) \times 180^\circ ) Each Interior Angle: ( \frac(n-2)180n ) Number of Diagonals: ( \fracn(n-3)2 ) Surface Area of a Cube: ( S = 6x^2 ) Surface Area of a Sphere: ( S = 4\pi r^2 ) | | Number Theory | Geometric Mean: ( \sqrtab ) Number of Subsets: ( 2^n ) (where n is the number of elements) Proper Subsets: ( 2^n - 1 ) Largest Unattainable Sum: ( mn - (m+n) ) (where m and n are two positive integers) | | Probability & Combinatorics | Permutations: ( _nP_r = \fracn!(n-r)! ) Combinations: ( _nC_r = \fracn!r!(n-r)! ) Sum of a Sequence: ( \fracn(\textfirst + \textlast)2 ) | | Triangles | 30-60-90 Triangle: Sides are in the ratio ( 1 : \sqrt3 : 2 ) 45-45-90 Triangle: Sides are in the ratio ( 1 : 1 : \sqrt2 ) Triangle Classification: Use the Pythagorean theorem (( c^2 = a^2 + b^2 )) to classify as right, acute, or obtuse | | Conversions | Time: Hours to minutes: Multiply by 60 Weight: Pounds to ounces: Multiply by 16 Percentages: Decimal to percent: Multiply by 100; Percent to decimal: Divide by 100 Area: Square miles to acres: Multiply by 640 Length: Miles to yards: Multiply by 1760 Volume: Gallons to cups: Multiply by 16 |
This public link is valid for 7 days and shares a thread, including any personal information you added. This link or copies made by others cannot be deleted. If you share with third parties, their policies apply. Can’t copy the link right now. Try again later. ) Combinations: ( _nC_r = \fracn
The Texas Math and Science Coaches Association (TMSCA) General Mathematics contest is one of Texas's most demanding academic competitions. It challenges students from middle school through high school to solve a wide range of mathematical problems in a high-pressure, 40-minute environment. This study guide is designed to help you navigate the test's format, master its scoring system, and implement a strategy to achieve a top score.
The exam covers elementary math through early high school algebra and geometry. Focus your preparation on these key buckets. 1. Number Theory and Properties Master rules for 2 through 12.
| Concept | Formula | | :--- | :--- | | Circumference of a circle | ( C = 2\pi r = \pi d ) | | Area of a circle | ( A = \pi r^2 ) | | Sum of interior angles (n-sided polygon) | ( 180(n-2) ) degrees | | Measure of each interior angle (regular n-gon) | ( \frac(n-2)180n ) | | Measure of each exterior angle (regular n-gon) | ( \frac360n ) | | Lateral surface area of a cylinder | ( A = 2\pi r h ) |
Practice finding these for three or more numbers.