How to use Desmos graphing calculator on Digital SAT

SAT Quantum
7 Feb 202306:36

TLDRThis video tutorial showcases how to utilize the Desmos graphing calculator for solving various math problems on the new digital SAT. It covers five examples, including solving quadratic equations, identifying solutions with radicals, determining the radius and center of circles, and dealing with linear equations and systems. The tutorial demonstrates the ease of graphing equations to find solutions without complex calculations, highlighting Desmos' power as a tool for SAT preparation.

Takeaways

  • 📊 The Desmos graphing calculator is a valuable tool for solving various types of math questions on the digital SAT.
  • 🔢 Quadratic equations can be easily solved by graphing them on Desmos, even when solutions are not obvious integers.
  • 🔍 For quadratic equations with radical solutions, Desmos can help identify which answer choice is closest to the actual solution.
  • ⭕ Desmos is useful for determining the radius and center of a circle when given its expanded form equation.
  • 🔄 When dealing with linear equations, including those with absolute values, Desmos can quickly show the solution by graphing.
  • 🤝 Systems of linear equations can be solved by finding the intersection point on Desmos, which represents the solution.
  • 🔎 Desmos allows for easy visualization and manipulation of graphs, which can be zoomed in or out for better clarity.
  • 📉 The video provides practical examples of how to use Desmos for different types of equations, enhancing understanding.
  • ❓ It's uncertain if the actual SAT will have questions easily solvable by Desmos, as this could affect the test's ability to differentiate between students.
  • 💡 The video serves as a guide to the potential of Desmos in the context of the SAT, encouraging strategic use of graphing calculators.

Q & A

  • What is the main purpose of the video?

    -The main purpose of the video is to demonstrate how to use the Desmos graphing calculator to solve various types of math questions for the new digital SAT.

  • What is the first type of math question discussed in the video?

    -The first type of math question discussed is solving quadratic equations, specifically finding the larger of two solutions to a given quadratic equation.

  • How does the video suggest finding the larger solution of a quadratic equation on Desmos?

    -The video suggests graphing the quadratic equation on Desmos, zooming out if necessary to visualize the solutions, and then selecting the larger of the two solutions.

  • What is the second variation of quadratic equations mentioned in the video?

    -The second variation of quadratic equations mentioned is when the solutions involve radicals and may require using the quadratic formula or identifying the correct answer from choices that include radicals.

  • How can Desmos be used to solve questions about circles?

    -Desmos can be used to solve questions about circles by graphing the equation of the circle and then identifying the radius by measuring the diameter or finding the center coordinates by calculating the midpoint of the diameter.

  • What is an example of a linear equation with absolute value discussed in the video?

    -An example of a linear equation with absolute value discussed is 3x + |x - 4| = 20, where the video demonstrates how to graph the equation and find the solution.

  • How does the video suggest solving a system of linear equations using Desmos?

    -The video suggests solving a system of linear equations by graphing both equations on Desmos and finding the point of intersection, which represents the solution to the system.

  • What is the concern raised about the use of Desmos for the digital SAT?

    -The concern raised is that if many questions can be easily solved using the calculator, it may not differentiate between students effectively, making the questions too easy.

  • What is the advice given regarding the potential over-reliance on Desmos for the SAT?

    -The advice is that while Desmos is a powerful tool for certain types of questions, it's important to be prepared for the possibility that not all questions will be easily solvable with the calculator.

  • What is the final message of the video regarding the use of Desmos on the digital SAT?

    -The final message is that Desmos can be a helpful tool for certain types of math questions on the digital SAT, but it's also important to be prepared for a variety of question types and not solely rely on the calculator.

Outlines

00:00

📊 Desmos Calculator for Solving Quadratics and Circles

The video introduces the use of Desmos calculator for solving problems related to quadratic equations and circles. It demonstrates how to input a quadratic equation into Desmos to find the larger of two solutions, and how to handle equations with radicals. The video also covers how to use Desmos to determine the radius and center of a circle from its expanded form equation. The presenter uses examples to show the process of graphing and finding the necessary values directly from the graph, highlighting the calculator's utility for these types of questions.

05:03

🔍 Desmos Calculator for Linear Equations and Systems

This part of the video script focuses on using the Desmos calculator for solving linear equations and systems of equations. It explains how to input linear equations with absolute values and find their solutions, as well as how to solve systems of linear equations by finding the point of intersection. The presenter emphasizes the importance of zooming in or out to accurately identify the solutions and points of intersection. The video concludes with a discussion on the potential limitations of using a calculator for SAT questions, suggesting that the College Board may need to adapt to ensure questions remain challenging and discriminating for test-takers.

Mindmap

Keywords

💡Desmos graphing calculator

The Desmos graphing calculator is an online tool that allows users to visually plot and analyze mathematical functions and equations. In the context of the video, it is highlighted as a powerful resource for solving various types of math problems on the new digital SAT. The video demonstrates how to use Desmos to graph quadratic equations, linear equations, and systems of equations, showcasing its utility in finding solutions and visualizing mathematical concepts.

💡Quadratic equations

A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0. The video uses the Desmos calculator to solve a specific quadratic equation (3(x - 50)^2 = 27) and identify the larger of its two solutions. Quadratic equations are a common topic in algebra and are often used in the SAT to test students' algebraic skills and problem-solving abilities.

💡Solutions

In the context of the video, 'solutions' refers to the values of the variable that make the equation true. For the quadratic equation example given, the solutions are the x-values where the graph of the equation intersects the x-axis. The video explains how to use Desmos to find these solutions, which is crucial for answering SAT questions that ask for the value of the larger solution.

💡Zoom out

This term is used in the video to describe the action of adjusting the view on the Desmos graph to see the entire graph or to find solutions that are not immediately visible. It's an important step when using graphing calculators to ensure that all relevant parts of the graph are visible and that no potential solutions are missed.

💡Quadratic formula

The quadratic formula is a method used to find the solutions of a quadratic equation. It is given by x = [-b ± sqrt(b^2 - 4ac)] / (2a). Although the video does not explicitly mention the formula, it implies that Desmos can be used as an alternative to directly applying the quadratic formula, especially when the solutions are not neat integers.

💡Circles

In the video, circles are discussed in the context of finding the radius and center of a circle given its equation in the expanded form. Desmos is used to graph the circle and identify its key characteristics, such as the endpoints of the diameter, which can be used to calculate the radius, and the midpoint, which gives the coordinates of the center.

💡Linear equations

Linear equations are equations that represent a straight line when graphed. The video demonstrates how to use Desmos to solve a linear equation with absolute value (3x + |x - 4| = 20) by graphing it and finding the point where the line intersects the x-axis. This is a practical example of how Desmos can simplify the process of solving linear equations.

💡Absolute value

Absolute value refers to the distance of a number from zero on the number line, regardless of direction. In the context of the video, absolute value is part of a linear equation that adds complexity to the graphing process. The video shows how Desmos can handle absolute values, which is important for solving SAT questions involving such equations.

💡System of linear equations

A system of linear equations consists of two or more linear equations that are solved simultaneously. The video uses Desmos to solve a system by graphing both equations and finding their point of intersection, which represents the solution to the system. This is a common type of problem on the SAT that tests students' ability to apply algebraic methods to find common solutions.

💡College Board

The College Board is the organization responsible for the SAT exam. The video mentions that the types of questions demonstrated using Desmos are based on practice questions or tests released by the College Board. This indicates that the strategies and examples provided in the video are relevant and practical for students preparing for the SAT.

Highlights

Desmos graphing calculator can simplify solving questions on the new digital SAT.

Quadratic equations can be solved by graphing them on Desmos to find the larger of two solutions.

For quadratic equations with radical solutions, Desmos can help identify the correct answer choice.

Desmos is useful for solving quadratic equations without needing to use the quadratic formula.

Circle questions on the SAT can be addressed by graphing and finding the radius or center coordinates on Desmos.

The radius of a circle can be determined by finding the diameter's endpoints on Desmos.

Desmos can help find the center of a circle by calculating the midpoint of the diameter.

Linear equations, including those with absolute values, can be solved using Desmos by graphing them.

Desmos allows for easy identification of solutions for linear equations with absolute values.

System of linear equations can be solved by finding the intersection point on Desmos.

Desmos is effective for solving classic system of linear equations questions on the SAT.

Desmos can be used to approach a variety of question types on the digital SAT.

The College Board has released practice questions and tests that include types of questions solvable with Desmos.

It remains to be seen how the College Board will balance the use of Desmos in official SAT exams.

Desmos can potentially make certain SAT questions easier, impacting the differentiation between students' abilities.

The video provides examples of how Desmos can be used to solve specific types of questions on the digital SAT.

Desmos is a powerful tool for visualizing and solving mathematical problems on the SAT.

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