# The only SAT Math DESMOS Guide you'll ever need

TLDRThis video guide teaches students how to effectively use Desmos calculator for SAT Math, emphasizing its speed and accuracy over traditional hand-solving methods. It covers solving single variable equations, systems of equations, inequalities, quadratic functions, and more, while also discussing when not to rely on Desmos. The guide is designed to boost SAT scores by leveraging Desmos for a variety of math problems, with a humorous and energetic presentation to keep viewers engaged.

### Takeaways

- 😎 Desmos is a powerful tool for solving various math problems on the SAT, but many people don't know how to use it effectively.
- 🔍 For single variable equations, Desmos can quickly show where the vertical line is, eliminating the need for manual algebraic manipulation.
- 📊 Systems of equations can be easily solved by graphing both equations in Desmos to find their intersection point.
- 🤔 Desmos can help identify when there are no real solutions to an equation by graphing and checking for intersections.
- 🟢 Systems of inequalities are solved by graphing them in Desmos, which shades the regions satisfying each inequality.
- 🍎 Desmos can be used to visualize price and quantity constraints in word problems, helping to find the maximum or minimum values as required.
- 📈 Desmos simplifies the process of finding x and y intercepts, vertices, and understanding transformations of quadratic functions.
- 🔢 Desmos can instantly calculate mean and median by inputting the data set, saving time on simple problems.
- 👀 When a quadratic intersects a horizontal line at exactly one point, it's typically at the vertex of the quadratic, a useful shortcut.
- ❌ Desmos should not be used for finding no solutions in systems of linear equations; instead, compare slopes to determine if lines are parallel.
- 📚 Learning algebraic manipulation and factoring is essential for equivalent expressions problems, where Desmos is not the optimal tool.

### Q & A

### What is the significance of the Desmos calculator in the context of the SAT Math section?

-The Desmos calculator is significant for the SAT Math section as it is a tool that can help students solve problems more quickly and accurately. It is almost the same version that students will use during the SAT, with the only differences being the inability to upload images or play sounds.

### How does Desmos simplify the process of solving single variable equations on the SAT?

-Desmos simplifies the process by allowing students to input the equation and visually identify where the vertical line intersects the x-axis, representing the solution, without having to manually solve the equation through traditional algebraic methods.

### What is the concept of 'sigma males' as mentioned in the script and how does it relate to using Desmos?

-'Sigma males' is a term used in the script to describe individuals who prefer efficiency and practicality, much like using Desmos for solving equations. It implies that even without a deep understanding of algebraic manipulations, one can still solve problems effectively using Desmos.

### How can Desmos be used to determine when there are no real solutions to an equation?

-Desmos can be used to determine when there are no real solutions by inputting the equation and observing the graph. If the graph does not intersect the x-axis, it indicates that there are no real solutions.

### What is the strategy for solving systems of equations using Desmos?

-The strategy involves inputting both equations into Desmos and observing their points of intersection. The red line represents all points satisfying the first equation, and the blue line represents the second. The intersection point(s) is where both equations are satisfied.

### Why is it important to understand the context of the problem when using Desmos?

-Understanding the context is crucial because the graph in Desmos might suggest a solution that doesn't make sense within the real-world scenario of the problem. For example, a solution might involve negative quantities, which are not feasible in a practical situation.

### How does Desmos assist in solving systems of inequalities?

-Desmos assists by shading the regions that satisfy each inequality. For a problem that requires finding a solution, one should look for any point where the shaded regions overlap, indicating a solution that satisfies all given inequalities.

### What is the advantage of using Desmos for quadratic equations, and how does it help in finding specific features like the vertex?

-Desmos is advantageous for quadratic equations as it allows students to easily find the x and y intercepts, as well as the vertex, which represents the minimum or maximum value of the parabola. By inputting the quadratic equation into Desmos and clicking on the respective features, students can quickly identify these points.

### Why might Desmos not be the best tool for solving certain types of problems on the SAT, such as equivalent expressions?

-Desmos might not be the best tool for equivalent expressions problems because these types of problems require a strong understanding of algebraic manipulation and factoring. Using Desmos could bypass the learning of these essential skills and is not as efficient as manually solving the problem.

### What is the recommendation for using Desmos in the context of the SAT Math section?

-The recommendation is to use Desmos for single variable equations, systems of equations, systems of inequalities, finding x and y intercepts, vertices of quadratics, and computing mean and median directly. However, for linear systems of equations with no solution, mean and median problems that aren't straightforward, and finding the center or radius of a circle or equivalent expressions, it is advised to use paper and pencil methods.

### Outlines

### 📚 Mastering Desmos for SAT Math

This paragraph introduces the importance of Desmos calculator for SAT math, emphasizing its efficiency and accuracy. The speaker critiques traditional methods and promises a fast-paced tutorial on leveraging Desmos for single variable equations, systems of equations, and inequalities. It highlights the need for conceptual understanding over rote memorization and introduces the idea of using Desmos for quick problem-solving without getting distracted by unnecessary details.

### 🔍 Desmos Strategies for Equations and Inequalities

The speaker provides a detailed explanation of how to use Desmos for solving single variable equations and systems of equations, including quadratics. They discuss the concept of intersection points and how Desmos can visualize these solutions. The paragraph also covers the use of Desmos for systems of inequalities and real-world application scenarios, such as budget constraints in purchasing fruits. The importance of context in problem-solving is stressed, as well as the pitfalls of misinterpreting graphical data.

### 📉 Desmos Applications in Quadratics and Data Analysis

This section delves into the use of Desmos for quadratic functions, including finding x and y intercepts, vertices, and intersections with lines. The speaker simplifies the process of solving complex problems by demonstrating Desmos' capabilities in graphing and analyzing quadratic equations. They also touch on the efficient calculation of mean and median using Desmos and the correct approach to identifying valid points on a circle's graph.

### 🚫 When Not to Use Desmos and Final Thoughts

The final paragraph addresses situations where Desmos may not be the best tool, such as with linear systems of equations that have no solution or when finding the center and radius of a circle. The speaker advises against using Desmos for equivalent expressions problems and encourages traditional algebraic methods for better understanding. They summarize the video by reiterating when Desmos is most beneficial and caution against over-reliance on it, ending with an offer for private tutoring and well-wishes for the viewers' studies.

### Mindmap

### Keywords

### 💡Desmos calculator

### 💡Single-variable equation

### 💡System of equations

### 💡Vertex of a quadratic

### 💡Systems of inequalities

### 💡Price and quantity constraints

### 💡Quadratic

### 💡Mean and median

### 💡Equivalent expressions

### 💡Circle formula

### 💡Conceptual understanding

### Highlights

Desmos calculator is a valuable tool on the SAT, simplifying complex math problems.

Most people, including Khan Academy, still solve problems by hand instead of using Desmos effectively.

Desmos is fast, accurate, and can significantly improve SAT scores when used correctly.

Desmos online calculator has the same functionality as the one used in the SAT, with minor differences.

Single variable equations can be easily solved on Desmos by observing the vertical line intersections.

Desmos can quickly determine when there are no real solutions to an equation by testing answer choices.

Systems of equations should be input into Desmos to find points of intersection efficiently.

Desmos can help conceptualize solutions in the context of both single variable equations and systems of equations.

Desmos can reveal infinite solutions where none seem apparent, by converting single variable equations into systems.

Systems of inequalities can be solved using Desmos by identifying overlapping regions that satisfy all conditions.

Desmos is useful for finding maximum or minimum values within the context of constraints, like budget and quantity.

Desmos can quickly solve quadratic equations by finding intercepts, vertices, and points of intersection with lines.

For quadratics intersecting a line at one point, Desmos can identify the vertex as the point of intersection.

Desmos should be used for finding no solutions in quadratic systems but not for linear systems with no solution.

Desmos can instantly calculate mean and median by inputting data directly into the calculator.

Desmos can be used to find valid points on a circle, but knowledge of circle formulas is essential.

Some tutors recommend Desmos for all problems, while others are more selective; the video provides guidance on when to use it.

The video emphasizes the importance of understanding when to use Desmos and when to rely on algebraic skills.

The presenter offers private tutoring for those interested in mastering SAT Math with Desmos.