Guide ((better)) — General Math Tmsca Study

Master direct and inverse variations. (e.g., "If 5 workers take 8 hours, how long do 4 workers take?").

Least Common Multiple (LCM) and Greatest Common Factor (GCF).

Begin by reviewing the fundamentals. This is not about speed; it's about ensuring you understand every concept that might appear on the test. Use your school textbooks, workbooks, and reliable online resources like Khan Academy to solidify your understanding of algebra, geometry, and number theory. The TMSCA test draws from pre-algebra to calculus, so a broad, deep foundation is essential. General Math Tmsca Study Guide

Due to the -2 penalty for wrong answers, only guess if you can eliminate at least two choices. 6. Recommended Resources

Efficiently calculate the Greatest Common Factor and Least Common Multiple using the Venn diagram or ladder method. Master direct and inverse variations

| 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 |

Geometry makes up a significant portion of the middle and late sections of the test. Focus heavily on: Don't calculate Begin by reviewing the fundamentals

Basic arithmetic and pre-algebra. Aim for 20–30 seconds each.

Practice squaring two-digit numbers mentally, multiplying by 11 or 25 quickly, and memorizing fractional equivalents of common percentages (e.g.,