SAT Math Lecture Notes

Introduction

• Presenter covers every concept, process, and formula relevant to the SAT Math test.
• Concepts are broken down into five levels of difficulty.

Level 1: Basic Algebra and Functions

1. Basic Algebra
   • Isolating variables, adding fractions, and order of operations.
2. Desmos
   • Useful for solving single-variable equations.
3. Linear Functions
   • Functions as machines: input (x) to output (y).
   • Graphing linear functions: straight lines.
   • Key concepts: slope (rate of change) and y-intercept.

Level 2: Intermediate Concepts

1. Variables and Constants
   • Variables (x, y) vary, while constants (m, b) remain unchanged.
   • Coefficients multiply variables.
2. Systems of Equations
   • Represent constraints with equations.
   • Solutions are points of intersection (graphically using Desmos).
   • Parallel lines have the same slope; perpendicular lines have negative reciprocal slopes.
3. Translation and Exponent Rules
   • Translate English sentences into mathematical equations.
   • Memorization of six exponent rules.
4. Geometry Basics
   • Angle sums: right angles (90°), semicircles (180°), circles (360°).
   • Triangles: Pythagorean theorem for missing sides.
   • Recognize shapes: isosceles, equilateral triangles.
5. Statistics Basics
   • Mean vs. median; understand conceptually using examples (e.g., wealth disparity).
   • Range: max - min.

Level 3: Advanced Algebra and Geometry

1. Integers and Functions
   • Understanding function translation.
   • Percentages: increase or decrease by a percentage.
   • Circle equations derived from Pythagorean theorem.
2. Triangles and Angles
   • Congruent vs. similar triangles.
   • Conversion between degrees and radians.
3. Advanced Triangle Knowledge
   • Understand properties of specific triangles (e.g., 3-4-5 triangle).
   • Convert units squared for area calculations.
4. Box Plots and Scatter Plots
   • Understand percentiles in box plots.
   • Sample bias in survey data.
5. Quadratics and Functions
   • Factoring quadratics; use Desmos for solutions and vertex location.

Level 4: Complex Concepts

1. Quadratic Equations
   • Standard and vertex forms; vertex calculation.
   • Sum and product of solutions.
2. Polynomial Functions
   • Understanding polynomial behavior graphically.
3. Exponential Functions
   • Create and manipulate exponential functions.
   • Practice with real-world applications.
4. Geometry and Area
   • Relationship between scaling and area/volume changes.
   • Surface area understanding without memorization.
5. Statistics and Probability
   • Read and analyze frequency tables.
   • Standard deviation as a measure of spread.
   • Margin of error and its implications.

Level 5: Mastery and Perfect Score

1. Altitude and Similar Triangles
   • Understand altitude in right triangles and its properties.
2. Complex Quadratic Problems
   • Solve problems involving mystery constants.
3. College Board's Favorite Problems
   • Pyramid surface area and constant-heavy problems.
4. Critical Formula Memorization
   • Quadratic formula and discriminant.
5. Advanced Problem Practice
   • Focus on weaknesses and anticipate harder variants.

Conclusion

• Final tips: focus on weaknesses, predict potential test problems, and seek tutoring if needed.
• Encouragement to like and share the video for further learning.