SAT Maths

What are the main content areas assessed in the SAT Math section?

The SAT Math section focuses on four key areas:

1. Heart of Algebra: Linear equations, inequalities, functions, and systems.

2. Problem Solving and Data Analysis: Ratios, proportions, percentages, statistics, and probability.

3. Passport to Advanced Math: Quadratic equations, polynomials, parabolas, and other non-linear expressions.

4. Additional Topics in Math: Geometry (area, volume, theorems), trigonometry, and complex numbers.

How do you solve a linear equation for a single variable?

To solve a linear equation for a single variable, isolate the variable on one side of the equation by performing inverse operations (addition/subtraction, multiplication/division) to both sides, maintaining equality.

What are common methods for solving systems of linear equations?

Common methods for solving systems of linear equations include:

• Substitution: Solve one equation for a variable, then substitute that expression into the other equation.
• Elimination: Multiply one or both equations by a constant to make the coefficients of one variable opposites, then add the equations to eliminate that variable.
• Graphing: Graph both equations and find their point of intersection.

How are linear inequalities typically represented on a number line?

Linear inequalities are represented on a number line using:

• Open circle (o) for strict inequalities (< ext{ or }> ext{}).
• Closed circle (•) for inclusive inequalities (\le\text{ or }\ge\text{}).
• A shaded region extending from the circle in the direction that satisfies the inequality.

What is the difference between a ratio and a proportion?

A ratio compares two quantities (e.g., a:b or a/b). A proportion is an equation stating that two ratios are equal (e.g., a/b = c/d).