Overview
This lecture reviews key concepts and problem-solving strategies for the TSIA2 (formerly TSI) math test, covering algebra, geometry, probability, and test-taking tips relevant to the exam.
TSIA2 Math Test Structure
- The initial TSIA2 math test has 20 questions; passing this section means you pass the test.
- If not passed, a 48-question diagnostic test follows; passing this can still earn a passing score.
- Schools may use diagnostic results for class placement.
Algebra & Proportions
- Isolate variables by rearranging and solving equations (e.g., 3T - 7 = 5T).
- Direct proportion means y = kx (no y-intercept).
- The slope of a line = (change in y)/(change in x).
- Solve linear systems with substitution or by checking answer choices.
- Factoring uses patterns: difference of squares (a²-b² = (a+b)(a-b)); check exponents with power rules.
Quadratic Equations & Word Problems
- Vertex formula gives max/min of quadratic: vertex x = -b/(2a).
- Area/perimeter: rectangle area = length × width; perimeter = 2(length + width).
- Apply substitution in geometric problems using given relationships.
- Use quadratic formula: x = (-b ± √(b²-4ac))/(2a).
Probability & Statistics
- Probability = (favorable outcomes)/(total outcomes).
- Median: arrange numbers in order; median is middle value.
- Probability with marbles or dice: count specific outcomes, divide by total.
- For compound probability events, consider all distinct arrangements.
Functions & Graphs
- The y-intercept occurs where x = 0.
- For directly proportional variables, use ratios to set up equations.
Problem-Solving Strategies
- Plug in answer choices to check which one works, especially for equations.
- For expressions involving exponents or factoring, apply power and factoring rules stepwise.
- When given a function for height or distance problems, set the equation to match the scenario (e.g., height = 0 when object hits ground).
Key Terms & Definitions
- Direct Proportion — Relationship where y = kx, with k being a constant.
- Difference of Squares — Expression in the form a²-b²; factors as (a+b)(a-b).
- Vertex — The highest or lowest point on a parabola; found using x = -b/(2a).
- Zero Product Property — If ab = 0, then a = 0 or b = 0.
- Probability — Ratio of desired outcomes to total possible outcomes.
- Quadratic Formula — Formula to solve ax²+bx+c=0: x = [-b±√(b²-4ac)]/(2a).
Action Items / Next Steps
- Take the official College Board TSIA2 math practice test.
- Review concepts in algebra, geometry, and probability.
- Practice plugging in answer choices on multiple-choice questions.
- Memorize key formulas (vertex, quadratic formula, probability).
- Prepare a calculator for the test.