SAT

1. Heart of Algebra

• Linear Equations and Inequalities:

  • Solving linear equations and inequalities in one variable

  • Interpreting and solving linear equations and inequalities in two variables

  • Creating linear equations and inequalities to solve problems

• Systems of Linear Equations and Inequalities:

  • Solving systems of linear equations in two variables

  • Solving systems of linear inequalities in two variables

  • Interpreting solutions to systems of equations or inequalities

• Linear Functions:

  • Understanding the properties and behavior of linear functions

  • Analyzing and interpreting linear function graphs

  • Creating linear functions to model relationships between quantities

2. Problem Solving and Data Analysis

• Ratios, Proportions, and Percents:

  • Solving problems involving ratios, proportions, and percent changes

  • Analyzing proportional relationships in various contexts

• Rates and Units:

  • Working with unit conversions and dimensional analysis

  • Solving problems involving rates, such as speed, density, and other rates of change

• Descriptive Statistics:

  • Interpreting and analyzing data presented in various forms (tables, graphs, charts)

  • Understanding and calculating mean, median, mode, range, and standard deviation

  • Analyzing data distributions and recognizing patterns or trends

• Probability and Statistics:

  • Understanding basic probability principles and calculating simple probabilities

  • Analyzing statistical data and making inferences based on sample data

• Data Interpretation:

  • Interpreting categorical and quantitative data

  • Using data to make predictions and draw conclusions

• Representing and Analyzing Quantitative Data:

  • Creating and interpreting scatterplots and line graphs

  • Understanding and using lines of best fit to model data

3. Passport to Advanced Math

• Quadratic Equations:

  • Solving quadratic equations by factoring, completing the square, and using the quadratic formula

  • Understanding the properties of quadratic equations, including their graphs and key features (vertex, axis of symmetry, etc.)

• Non-Linear Functions:

  • Analyzing and interpreting non-linear functions, such as exponential and polynomial functions

  • Understanding the properties of exponential and logarithmic functions

  • Modeling real-world situations using non-linear functions

• Manipulating Expressions:

  • Simplifying and transforming algebraic expressions, including polynomial, rational, and radical expressions

  • Understanding the effects of operations on expressions and equations

• Solving Non-Linear Equations:

  • Solving systems of equations involving quadratic or other non-linear equations

  • Solving polynomial equations of higher degree

• Function Notation and Operations:

  • Understanding and using function notation

  • Performing operations on functions, including composition and transformation

4. Additional Topics in Math

• Geometry:

  • Understanding and applying properties of angles, triangles, and other polygons

  • Calculating areas, perimeters, and volumes of geometric shapes

  • Working with circles, including understanding the properties of arcs, chords, and sectors

  • Using coordinate geometry to solve problems, including finding the distance between points, the midpoint of a segment, and the equation of a circle

• Trigonometry:

  • Understanding and applying the basic trigonometric ratios (sine, cosine, and tangent)

  • Solving right triangle problems using trigonometry

  • Working with the unit circle and understanding the relationship between angle measures and trigonometric values

  • Applying trigonometric identities and equations to solve problems

• Complex Numbers:

  • Understanding the concept of imaginary and complex numbers

  • Performing arithmetic operations with complex numbers

  • Solving equations involving complex numbers

• Coordinate Geometry:

  • Analyzing and interpreting the graphs of various functions, including linear, quadratic, exponential, and trigonometric functions

  • Understanding the properties and behavior of conic sections (parabolas, circles, ellipses, and hyperbolas)

  • Solving problems involving the distance formula, midpoint formula, and slope

5. Math Test Structure

• Calculator and No-Calculator Sections:

  • The SAT Math section is divided into two parts: one that allows the use of a calculator and one that does not.

  • Understanding when and how to use the calculator effectively.

• Multiple Choice and Grid-In Questions:

  • The test includes both multiple-choice questions and grid-in questions (student-produced responses).

  • Strategies for answering grid-in questions where no answer choices are provided.

6. Test-Taking Strategies

• Time Management:

  • Tips for managing time effectively during the test.

  • Strategies for pacing yourself and ensuring that you have time to answer all questions.

• Process of Elimination:

  • Techniques for eliminating incorrect answer choices.

  • Identifying common traps and distractors in multiple-choice questions.

• Estimation and Approximation:

  • Using estimation and approximation to check the reasonableness of answers.

  • Applying quick mental math techniques to save time.

• This course is designed for students preparing to take the SAT exam. It includes a comprehensive explanation of all SAT Math topics