1:52:05
The Last SAT Desmos Guide You'll Need
James Lu SAT
Overview
This video serves as a comprehensive guide to using Desmos, the graphing calculator integrated into the SAT testing software. It demonstrates how Desmos can be used to solve a significant portion of the SAT math questions, from basic graphing to advanced regression techniques. The guide covers fundamental Desmos features like graphing equations and inequalities, using sliders for constants, and understanding function notation. It then delves into more complex applications such as regression analysis for curve fitting and solving systems of equations, emphasizing practical strategies and common pitfalls to help students maximize their efficiency and accuracy on the SAT math section.
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Chapters
- Desmos is the built-in graphing calculator for the SAT, accessible during the test.
- The SAT version of Desmos has a 'table' function, unlike the standard version.
- Desmos can graph various functions, including absolute value and inequalities, and identify intersections and intercepts.
- Graphing inequalities shades the solution region; points on dashed lines are not solutions, while points on solid lines are.
- Single-variable equations graph as vertical lines, with the x-value of the line representing the solution.
Understanding these basic graphing capabilities is crucial because many SAT math problems can be solved visually or by directly inputting equations into Desmos, saving time and reducing the need for complex algebraic manipulation.
Graphing `x < y` shades the region above the line y=x, illustrating how Desmos visualizes inequality solutions.
- Letters not assigned as variables (like x, y, e) can be defined as constants.
- Setting a letter equal to a number (e.g., `a = 5`) creates a slider for that constant, allowing interactive adjustment.
- Sliders have adjustable ranges and steps, which can be customized beyond the default settings.
- Manually typing values for constants can often be faster than using sliders, especially for precise decimal values.
- Desmos can automatically add a slider for an undefined constant by clicking the 'add slider' button.
Constants and sliders allow for dynamic problem-solving, enabling you to test multiple scenarios or find specific values that satisfy given conditions without manual recalculation.
To find the value of 'a' that makes a graph pass through a specific point, you can create a slider for 'a' and adjust it until the graph intersects the point.
- Function notation (e.g., `f(x) = ...`) allows you to define and reuse complex equations easily.
- Desmos can evaluate functions for specific inputs (e.g., `f(2)`) and perform transformations (e.g., `f(x+2)`).
- Points can be graphed by directly typing coordinates or by using the table feature.
- The 'zoom fit' button adjusts the graph's view to encompass all plotted points.
- The table feature is useful for inputting multiple points and working with constants that represent coordinates.
Mastering function notation and tables streamlines the process of working with multiple related equations or data points, significantly speeding up problem-solving on the SAT.
Defining `f(x) = x^2 + 1` and then calculating `f(3)` directly in Desmos.
- Regression uses a tilde symbol (`~`) to find an equation that best fits a set of data points.
- Common regression types include linear and quadratic, useful for SAT problems.
- Desmos can automatically generate regression equations from a table of points or allow manual input for custom regressions.
- The 'zoom fit' and 'default viewpoint' buttons help manage graph scaling and orientation.
- The 'create table' option can convert equations into tables, useful for finding factors or converting equation forms.
Regression is a powerful tool for solving problems where you're given data points and need to find the underlying equation, or when you need to convert an equation into a different form.
Inputting two points into a table and using Desmos's linear regression to find the equation of the line passing through them.
- The 'edit list' mode allows duplicating, coloring, and deleting items, serving as a workaround for the SAT's lack of copy-paste.
- Built-in functions like `mean`, `median`, `stdev`, `distance`, `midpoint`, and `gcd` can solve specific math problems instantly.
- Desmos automatically converts decimals to fractions when possible.
- When working with angles, ensure Desmos is set to degrees or radians as required by the problem.
- Typing mathematical operations like square roots (`sqrt`), nth roots (`nthroot`), and powers (`^`) is efficient using keyboard shortcuts.
These advanced features and shortcuts provide significant time-saving advantages by automating complex calculations and offering alternative methods to solve problems that might otherwise require lengthy manual computation.
Using `distance((1,1), (4,5))` to find the distance between two points without needing to memorize or apply the distance formula.
- Regression with the tilde (`~`) estimates constant values to make both sides of an equation equal.
- Variables like lowercase 'x' and 'y' cannot be used directly in regression; they must be converted to constants (e.g., `x1`).
- When solving for a constant's value, not a variable's, you must ensure the constant remains constant across varying values of the variable.
- This is achieved by setting the variable equal to a list of numbers (e.g., `x1 = 1...10`) or using the `random()` function.
- For systems of equations, list regression is used by creating separate lists for the left and right sides of all equations.
This advanced regression technique is essential for solving complex equations and determining unknown constants, particularly in problems that appear algebraically challenging but are readily solvable with Desmos.
To find the value of 'b' in an equation, set up `(expression with b) ~ (another expression)` and replace 'x' with 'x1', then set `x1 = 1...10` to ensure 'b' is a true constant.
- When solving for constants in multi-equation systems, ensure constants remain constant by varying the input variables (e.g., using lists).
- Constraints (e.g., `P > 1`) can be applied using curly brackets `{}`.
- If a problem involves multiple equations, they must all be placed on a single regression line, using lists to separate left and right sides.
- Percentage problems are often solvable by directly translating the word problem into Desmos equations using 'is' as '='.
- For very difficult regression problems, simplifying the system into a single equation or checking constraints manually might be necessary.
Understanding these advanced strategies allows you to tackle the most complex SAT math problems, especially those involving systems of equations, constraints, and abstract constants, with confidence.
Translating 'Object X is 300% of Object Y' into `X = 300% * Y` in Desmos to solve for unknown values.
Key takeaways
- Desmos is a powerful tool that can solve a significant portion of SAT math questions, often much faster than traditional methods.
- Familiarity with Desmos's core functions (graphing, tables, sliders) is fundamental for efficient problem-solving.
- Regression analysis is key for problems involving data fitting, finding equations, and solving for unknown constants.
- Understanding how to handle variables, constants, and constraints within Desmos is crucial for advanced problem-solving.
- Keyboard shortcuts and built-in functions can dramatically speed up calculations and reduce the need to memorize formulas.
- Always verify that your Desmos setup meets all conditions stated in the problem, especially when dealing with inequalities or constraints.
- Practice is essential to internalize Desmos patterns and develop the intuition to apply them effectively during the SAT.
Key terms
DesmosGraphing CalculatorSlidersConstantsFunction NotationTable FeatureRegressionTilde Symbol (~)ConstraintsLists
Test your understanding
- How can Desmos be used to visually solve inequalities, and what is the significance of dashed versus solid lines?
- Explain the difference between a variable and a constant in Desmos and how sliders are created.
- What is regression in Desmos, and how does the tilde symbol facilitate it?
- Describe a scenario where using Desmos's built-in functions like `mean` or `distance` would be more efficient than manual calculation.
- How do you ensure that a constant remains constant when solving for it using regression with multiple variables or equations in Desmos?