SAT Math Concepts Overview

Introduction

• Comprehensive review of every concept, process, and formula for the SAT Math.
• Content organized into five levels.

Level 1: Basics

Key Concepts:

• Algebra: Basic algebra including isolating variables, adding fractions, and order of operations.
• Desmos: Use for solving single variable equations.
• Linear Functions: Understanding the relationship between equations, tables, and graphs.
  • Equation form: ( y = mx + b )
  • Finding slope by determining rate of change.
  • Calculating y-intercept through slope and known points.

Level 2: Intermediate Challenges

Key Concepts:

• Variables and Constants: Understanding their roles in equations.
• Systems of Equations: Graphically solving through intersections.
  • Concepts include parallel lines (same slope) and perpendicular lines (negative reciprocal slopes).
• Exponent Rules: Memorizing key rules for simplifying expressions.
• Geometry Basics:
  • Angle sums in right angles, semicircles, triangles, and quadrilaterals.
  • Pythagorean theorem for triangle side lengths.

Level 3: Advanced Concepts

Key Concepts:

• Integers and Functions: Understanding translations and percentages in algebraic expressions.
• Circle Equation: Deriving and utilizing the equation from Pythagorean theorem.
• Triangles and Probability:
  • Similar and congruent triangles distinctions.
  • Conditional probability and interpreting box plots.
• Biased Samples: Recognizing sample bias and ensuring representative data.

Level 4: Pre-Expert Level

Key Concepts:

• Quadratics:
  • Forms of quadratic equations and their features (vertex, solutions).
  • Sum and product of solutions.
• Polynomial and Exponential Functions: Construction and application of exponential growth problems.
• Triangle Sine and Cosine Relationships: Complementary angle identities.
• Unit Conversions: Understanding area and volume conversions.

Level 5: Mastery

Key Concepts:

• Altitude in Triangles: Understanding triangle similarities through altitudes.
• Complex Quadratic Problems: Solving integer based quadratics through setup and logical reasoning.
• Surface Area Problems: Recognizing the complexity of surface area in 3-dimensional shapes.
• Manual Problem Solving: Importance of solving without Desmos for high-level problems.

Additional Insights

• Practice challenging problems in each category.
• Focus on understanding and solving problems manually.
• Concepts like mean, integer problems, and complex exponents need special attention.
• Strategy to predict possible harder variants of problems for SAT preparation.

Conclusion

• Emphasized importance of practice and prediction in excelling SAT Math section.
• Engagement with tutoring and further resources for personalized guidance.