SAT Algebra - Detailed Syllabus

Digital SAT Math: A Comprehensive Guide

Algebra Syllabus

The Algebra section of the Digital SAT Math test covers a wide range of topics that build upon your foundational mathematical knowledge. Here's a detailed overview:

1. Linear Equations and Inequalities

• Solving Linear Equations:
  • Isolating variables using inverse operations.
  • Solving equations with variables on both sides.
  • Solving equations with fractions and decimals.
• Graphing Linear Equations:
  • Understanding slope-intercept form (y = mx + b).
  • Plotting points and drawing lines.
  • Interpreting the slope and y-intercept.
• Solving Linear Inequalities:
  • Graphing inequalities on a number line.
  • Solving inequalities with variables on both sides.
  • Writing inequalities from word problems.

2. Systems of Linear Equations

• Solving Systems Graphically:
  • Graphing two lines and finding the intersection point.
• Solving Systems Algebraically:
  • Elimination method.
  • Substitution method.
• Interpreting Solutions:
  • Determining if a system has one solution, no solution, or infinitely many solutions.

3. Linear Functions

• Understanding Function Notation:
  • Using f(x) to represent the output of a function.
  • Evaluating functions for given input values.
• Determining Domain and Range:
  • Identifying the possible input and output values for a function.
• Graphing Linear Functions:
  • Using slope-intercept form and point-slope form.
  • Interpreting the slope and y-intercept in context.
• Writing Linear Equations:
  • Given two points or a point and slope.

4. Functions

• Identifying Functions:
  • Using the vertical line test.
• Evaluating Functions:
  • Plugging in values for the input variable.
• Finding Domain and Range:
  • Determining the possible input and output values.
• Graphing Functions:
  • Understanding different types of functions (linear, quadratic, exponential).
  • Plotting points and sketching the graph.

5. Function Transformations

• Shifts:
  • Vertical and horizontal shifts.
• Stretches and Compressions:
  • Vertical and horizontal stretches and compressions.
• Reflections:
  • Reflections across the x-axis and y-axis.

Examples of Algebra Topics on the Digital SAT

Linear Equations and Inequalities

Example 1:

• Solve for x: 2x + 5 = 13

Example 2:

• Graph the inequality: y > 3x - 2

Systems of Linear Equations

Example 1:

• Solve the system of equations:
  • 2x + y = 7
  • x - 3y = 1

Example 2:

• Determine if the following system has one solution, no solution, or infinitely many solutions:
  • 3x + 4y = 12
  • 6x + 8y = 24

Linear Functions

Example 1:

• Evaluate f(x) = 2x - 3 for x = 5

Example 2:

• Write the equation of a line passing through the points (2, 4) and (5, 10)

Functions

Example 1:

• Determine if the following relation is a function: {(1, 2), (3, 2), (5, 4)}

Example 2:

• Graph the function f(x) = x^2 - 4

Function Transformations

Example 1:

• Describe the transformation of the function g(x) = (x - 3)^2 + 2 from the parent function f(x) = x^2

Example 2:

• Graph the function h(x) = -2f(x), where f(x) = |x|

By mastering these algebra concepts, you'll be well-prepared to tackle the Algebra section of the Digital SAT Math test. Remember to practice regularly and seek help from teachers, tutors, or online resources if you encounter difficulties