Using Desmos on the SAT

Overview

• Desmos calculator: Essential and efficient tool for the SAT
• KH Academy's traditional approach: Solve by hand
• Desmos is fast, accurate, and should be utilized for multiple problem types

Key Features of Desmos

• Similar to SAT version, with minor limitations (no image uploads, no sound)

Solving Single Variable Equations

• Traditional method: Subtracting, factoring, splitting, rearranging, and solving
• Desmos method: Copy-paste equation and find where the vertical line intersects
• Applicable for various types of equations (square root, absolute value, rational, quadratic)

Systems of Equations

• Solution: Plug into Desmos
• Intersection points: Red line and blue line represent solutions to individual equations
• Works for quadratics and other systems

Conceptual Understanding

• Solutions for single variable equations can be rewritten as systems of equations
• Example: Convert quadratic to system for better insight into solutions
• Warnings: Be cautious when interpreting no solutions vs. infinite solutions

Systems of Inequalities

• Desmos shades regions satisfied by each inequality
• Find overlapping shaded regions for solutions
• Example: Solve by considering price and quantity constraints

General SAT Advice

• Desmos helps in solving problems quickly; focus on conceptual understanding
• Avoid misinterpreting graph constraints (e.g., buying negative apples)

Quadratics

• Graphical representation: Parabolas
• Use Desmos to find x/y intercepts and vertices easily
• Example: Finding the minimum/maximum by clicking on Desmos graph

Important Problems and Tips

• Quadratic and linear intersections: Understand vertex significance
• Horizontal line intersections: Locate vertex for single solution
• No real solutions: Adjust slider in Desmos, understand graphical representation
• Linear no solutions: Use paper-pencil, rely on slope to determine parallel lines

Further Functions

• Simple mean and median: Type functions in Desmos for quick results

Ambiguous Topics

• Functions: Treat them like single variable equations in Desmos for reliability
• Circle problems: Know the circle formula, use Desmos for x-value validations
• Equivalent expressions: Not suitable for Desmos, better to solve manually

Summary

Use Desmos For:

• Single variable equations
• Systems of equations and inequalities
• Number of solutions, intercepts, vertices for quadratics
• Mean and median computations
• Valid points on a circle

Avoid Desmos For:

• Linear systems with no solutions
• Complex mean/median problems
• Center or radius of a circle
• Equivalent expressions
• Any other SAT topics

Additional Resources

• Private tutoring available through learnsatmath.com