SAT Math Overview Lecture

Introduction

• Comprehensive review of SAT Math concepts, processes, and formulas.
• Organized into five levels, from basic to advanced.

Level 1: Basic Concepts

Algebra

• Isolating variables, adding fractions, order of operations.
• Drills available; foundational skills assumed.

Desmos

• Essential for solving single-variable equations.
• Graphing tool to find solutions.

Linear Functions

• Functions as input-output machines (e.g., f(x) = x + 7).
• Relations between equations, tables, and graphs.

Problem Example

• Finding equation of a line given two points.
• Calculate slope and y-intercept.

Level 2: Intermediate Concepts

Variables and Constants

• Variables change, constants remain the same.
• Coefficients multiply variables.

Systems of Equations

• Simultaneous equations representing constraints.
• Solutions found using graphical intersections.

Translation of Language to Math

• Understanding phrases like "X is half of 50".

Exponent Rules

• Memorization of six key rules.

Geometry Basics

• Sum of angles in various geometrical contexts (e.g., triangles, circles).
• Pythagorean theorem for right triangles.

Other Key Concepts

• Density, triangle types, formula sheet for area/volume.
• Example problem using Acy tool.

Basic Statistics

• Mean: sum divided by number of values.
• Median: middle value.
• Range: max minus min.

Level 3: Advancing Concepts

Integers and Function Translation

• Understanding and applying integer properties.

Percentages

• Calculations for increases and decreases.
• Example problem for practice.

Circles and Slopes

• Circle equation derivation.
• Calculating tangent line slopes.

Triangle Similarity and Probability

• Conditions for triangle similarity (angle, side rules).
• Understanding of conditional probability.

Data Interpretation

• Box plots, scatter plots, and biased samples.

Quadratic Functions

• Graphing solutions and finding vertices using Desmos.

Level 4: Advanced Concepts

Quadratic Forms

• Standard and vertex forms, relationships between them.
• Memorization of key formulas (e.g., sum/product of solutions).

Polynomial and Exponential Functions

• Constructing functions and understanding shifts and scales.
• Example problems provided.

Complex Algebra and Geometry

• Understanding trigonometric identities and conversions.
• Unit conversion concepts.
• Example problems.

Statistics and Probability

• Understanding frequency tables, standard deviation, margin of error.

Level 5: Expert Concepts

Triangle Altitudes

• Relation of altitudes and similarity in triangles.

Complex Algebra Problems

• Solving problems with unknown integer constants.

Surface Area and Advanced Geometry

• Understanding pyramids, surface area problems.

Miscellaneous Advanced Topics

• Discriminant of quadratics, completing the square.
• Key formulae and theorems.

Practice and Strategy

• Focus on weaknesses and hard problem categories.
• Predict potential SAT questions.

Conclusion

• Additional resources and tutoring offers.
• Encouragement to engage with the material thoroughly.