Overview
This lecture covers effective ways to use the Desmos calculator on the SAT Math section, highlighting when and how to use it for best results.
Desmos Calculator Basics
- The Desmos calculator on the SAT is almost identical to the online version, except you can't upload images or play sounds.
- Desmos allows fast and accurate solutions for many SAT math problems.
Solving Equations with Desmos
- Single variable equations (including square root, absolute value, rational, quadratic) can be solved by graphing and identifying intersections.
- For equations asking when there are no real solutions, substitute answer choices to see which graphs show no intersections.
Systems of Equations & Inequalities
- Graph both equations in Desmos; the intersection point(s) represent the solution(s).
- Every single variable equation can be rewritten as a system of equations.
- Infinite solutions can occur when two equations graph as the same line.
- For systems of inequalities, Desmos shades regions; overlap indicates valid solutions.
Contextual Problems
- When variables represent quantities (e.g., apples and bananas), use x and y in Desmos.
- Always consider the context; avoid impossible answers like negative quantities.
Quadratics & Graph Features
- Quadratics are parabolas; use Desmos to find x-intercepts, y-intercepts, and the vertex quickly.
- For transformations (e.g., f(x) + 5), Desmos automatically shows the result.
- If a line intersects a quadratic at one point, the intersection is the vertex.
- For questions about no real solutions, adjust the parameter in Desmos to see when the graph does not touch the x-axis.
Linear Equations with No Solution
- For two lines, no solution means they are parallel (same slope).
- Find the slopes algebraically, not in Desmos, for best accuracy.
Statistics: Mean & Median
- Calculate mean and median directly using Desmos functions (mean(), median()).
- Harder statistics problems still require conceptual understanding.
Functions, Tables, and Circles
- Functions can be solved in Desmos by creating tables or solving for variables.
- Use Desmos for circle problems only when identifying valid points; know the circle formula for center and radius problems.
Equivalent Expressions
- Do not use Desmos for factoring or identifying equivalent expressions—use algebraic manipulation.
Summary: When to Use Desmos
- Use Desmos for: single variable equations, systems, inequalities, intercepts, vertices, intersection points, mean/median, and circle points.
- Do NOT use Desmos for: linear systems with no solution, advanced statistics, finding circle centers/radii, or factoring/equivalent expressions.
Key Terms & Definitions
- Desmos — a graphing calculator tool available on the SAT.
- Quadratic Equation — an equation where the highest exponent of the variable is 2, forming a parabola.
- Vertex — the minimum or maximum point of a parabola.
- Intersection — a point where two graphs meet; a solution to both equations.
- System of Equations — a set of two or more equations with shared variables.
- Parallel Lines — lines with equal slopes that never intersect.
Action Items / Next Steps
- Practice solving sample SAT math problems using Desmos.
- Review and memorize key algebraic formulas (factoring, circle equations).
- Avoid relying solely on Desmos for problems better suited to conceptual or algebraic solutions.