Overview
The lecture explains how to use Desmos to solve a wide range of SAT math problems efficiently, covering both basic and advanced question types and highlighting key Desmos strategies.
Using Desmos for Calculations
- Use Desmos to quickly multiply numbers (e.g., 16 × 4 = 64).
- Graph equations and check which answer choices align with the given graph.
- Input complex expressions to see which matches the original function.
Solving Linear and Nonlinear Equations
- Identify slope (rise/run) and y-intercept from points or tables.
- Use linear regression in Desmos for equations like y = 4x + 6.
- For equations in the form ax + b = c, subtract c on both sides and find zeros.
Working with Systems and Proportions
- Set up systems in Desmos to solve for missing values (e.g., x + y = total).
- Use ratios to scale up survey results or solve proportion questions.
Handling Quadratic Equations and Roots
- Enter quadratic functions in Desmos and find x-intercepts for roots.
- Solutions occur where the graph crosses the x-axis; positive solutions are the positive roots.
Desmos in Geometry and Functions
- Calculate area and volume using basic formulas (area = side², volume = area × height).
- Use tables and sliders to explore function behavior, roots, or intercepts.
- For transformations, visualize how graphs shift up, down, or change radius.
Probability and Statistics with Desmos
- Find ranges by subtracting smallest from largest values in a data set.
- Calculate probabilities by dividing favorable outcomes by total outcomes.
Special Problem Types
- For percent increase, use the formula final = initial × (1 + percent/100).
- Use regression for word problems linking multiple equations or unknowns.
- For "no solution" system, find when lines are parallel (same slope, different y-intercept).
Key Terms & Definitions
- Slope — Change in y over change in x (rise/run).
- Linear Regression — Statistical method to model the relationship between variables; in Desmos, used to fit lines.
- Root/Zero — A value where the function equals zero; where the graph crosses the x-axis.
- Range (stats) — Difference between largest and smallest data values.
- Transformation — Shifting or scaling a graph.
Action Items / Next Steps
- Practice using Desmos for each SAT math module question type.
- Review SAT math topics: linear equations, proportions, quadratics, functions, statistics, geometry.
- Set up basic equations and try regression and table features in Desmos for familiarity.