SAT Math Lecture Notes

Introduction

• Best SAT Math video on YouTube.
• Covers every concept, process, and formula on the SAT Math test.
• Organized into five levels from basic concepts to advanced problems.

Level 1: Basic Concepts

• Topics Covered:
  • Algebra: Isolating variables, adding fractions, order of operations.
  • Desmos: Use for solving single-variable equations.
  • Linear Functions: Understanding input-output relationships, graphing.
• Example Problem: Finding the slope and y-intercept from two points.

Level 2: Intermediate Concepts

• Topics Covered:
  • Variables and Constants: Understanding variable change and constant stability.
  • Systems of Equations: Using two constraints to solve problems.
  • Geometry Basics: Right angles, semicircles, full circles, parallel lines.
  • Exponent Rules: Memorizing six key rules.
  • Basic Geometry: Pythagorean theorem, isosceles/equilateral triangles.
  • Word Problem Translation: Converting English into mathematical equations.
• Tools and Resources: Use Desmos for graphically solving systems of equations.

Level 3: Intermediate to Advanced

• Topics Covered:
  • Integer Understanding: Positive/negative whole numbers.
  • Function Translation: Horizontal and vertical shifts.
  • Percentages: Practical applications like tips and total calculations.
  • Circle Equations: Understanding and deriving circle formulas.
  • Triangle Similarity and Congruence.
  • Conditional Probability and Box Plots.
• Example Problems: Various problems on percentages, circle equations, and probability.

Level 4: Advanced Concepts

• Quadratic Functions
  • Standard and Vertex Forms.
  • Relation between forms and the vertex.
  • Sum/Product of solutions.
• Polynomial Functions: Understanding deep-level function properties.
• Exponential Functions: Constructing and interpreting exponential growth problems.
• Advanced Geometry: Trigonometric identities, unit conversions, surface area/volume.
• Statistics: Frequency tables, standard deviation, and margin of error.

Level 5: Expert Level

• Altitude of a Triangle: Understanding triangle similarity through altitudes.
• Complex Quadratic Problems: Handling mysteries with integer constants.
• Pyramid Surface Area Problems: Differentiating between slant height and pyramid height.
• Advanced Problem Solving: Solving by hand without Desmos.
• Key Theorems and Tricks: Triangle inequality, integer mean problems.

Conclusion

• Mastery leads to understanding complex SAT problems.
• Emphasizes practicing specific problem types and reviewing missed problems.
• Encourages predicting potential SAT questions based on weaknesses.
• Suggestions for further study include personal tutoring and constant review of missed problems.