General Math Tmsca Study Guide Jun 2026

TMSCA General Mathematics Study Guide Target: Middle School & High School Competitors Focus: Speed, Accuracy, and Problem-Solving Strategies

I. Understanding the Test

Format: 50 Multiple Choice Questions. Time Limit: 30 Minutes. Scoring: +5 points for correct answers; -2 points for incorrect answers; 0 points for skipped questions. The Goal: Score 200+ to medal at the state level (roughly 30–35 correct answers).

The "Three-Pass" Strategy Do not go question-by-question from 1 to 50. General Math Tmsca Study Guide

Pass One (2 minutes): Scan the test. Answer only the "one-step" problems (basic arithmetic, simple definitions) that you can solve in under 10 seconds. Pass Two (20 minutes): Go back to the start. Solve the standard multi-step problems. If a problem takes more than 60 seconds, star it and move on. Pass Three (Remaining time): Tackle the starred/difficult problems. Review skipped questions.

II. Essential Formulas & Concepts Memorize these. You should not have to derive these during the test. A. Number Theory & Sets

Order of Operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (L→R), Addition/Subtraction (L→R). Set Notation: TMSCA General Mathematics Study Guide Target: Middle School

$A \cup B$ (Union): Elements in A or B (combine them). $A \cap B$ (Intersection): Elements in A and B (overlap). $n(A)$: The number of elements in set A.

Types of Numbers:

Natural (Counting): ${1, 2, 3, ...}$ Whole: ${0, 1, 2, 3, ...}$ Integers: ${..., -2, -1, 0, 1, 2, ...}$ Rational: Can be written as a fraction ($p/q$ where $q \neq 0$). Includes terminating and repeating decimals. Irrational: Non-terminating, non-repeating decimals ($\pi, e, \sqrt{2}, \sqrt{3}$). Scoring: +5 points for correct answers; -2 points

B. Algebra

Distance Formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Midpoint Formula: $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ Slope Formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Slope-Intercept Form: $y = mx + b$ Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$