Digital SAT Math - Desmos Lesson #1 Solve any Equation!

Tutorllini Test Prep
11 Nov 202205:54

TLDRIn this tutorial, the presenter from Tutorlini Test Prep demonstrates how to use Desmos for solving equations on the digital SAT Math section. The lesson covers how to graph the left and right sides of an equation to find their intersection points, which represent the solutions. The presenter guides viewers through several examples, showing how to use Desmos's features like zooming and graphing to solve for x values. The video emphasizes the importance of identifying the positive solution when asked. It concludes with a call to action for viewers to try the method themselves and to subscribe for more SAT Math content.

Takeaways

  • 📘 Desmos is a powerful tool for solving equations on the digital SAT Math.
  • 📐 To use Desmos, graph 'y =' the left-hand side and 'y =' the right-hand side of the equation.
  • 🔍 Intersection points of the graphs on Desmos indicate the solutions to the equation.
  • ⚙️ Use a mouse for easier navigation, clicking, and dragging on Desmos during the test.
  • 🔎 Zoom in and out to find intersection points more accurately.
  • 📊 Focus on the x-values of the intersection points, as these are the solutions for x.
  • 📈 For equations with no clear intersection, zoom out to better visualize the graphs.
  • 📝 Convert decimal solutions to fractions if necessary, using Desmos' fraction feature.
  • 🎯 Always consider the question's requirement, such as selecting the positive solution.
  • 💡 Desmos can assist with solving any equation, even those without multiple-choice answers, reducing the need for guesswork.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is how to use Desmos for solving equations on the digital SAT Math.

  • What is the first step in solving an equation using Desmos as per the video?

    -The first step is to graph y equals the left-hand side of the equation.

  • What is the second step in solving an equation using Desmos?

    -The second step is to graph y equals the right-hand side of the equation and find the points of intersection.

  • Why is it recommended to bring a mouse on test day according to the video?

    -It is recommended to bring a mouse on test day because it's easier to click, drag, and move around, and the scroll wheel can be used to zoom in and out.

  • What does the video suggest to do with the y-values of the points of intersection?

    -The video suggests not to care about the y-values, but only to look at the x-values to solve for x.

  • How does the video demonstrate solving the first equation?

    -The video demonstrates solving the first equation by graphing y = 55/x + 6 and y = x in Desmos and finding the x-values of the intersection points.

  • What is the positive solution to the first equation demonstrated in the video?

    -The positive solution to the first equation demonstrated is x = 5.

  • How does the video handle equations that are difficult to see intersections?

    -The video suggests zooming out using the scroll wheel to better see the intersections of the graphs.

  • What tool does the video mention for converting a decimal to a fraction in Desmos?

    -The video mentions using the fraction button on the left-hand side to convert a decimal to a fraction.

  • What is the significance of using Desmos for solving equations on the SAT as per the video?

    -Using Desmos is significant because it allows solving any equation on the test without needing to guess and check, even for free response questions without multiple-choice answers.

Outlines

00:00

📚 Introduction to Desmos for SAT Math

The video begins with a tutorial on using Desmos for solving equations on the digital SAT Math test. The instructor explains that Desmos can be used to graph and solve any equation by plotting the left and right sides of an equation. The example given involves solving for the intersection points of the equations '55/X + 6' and 'Y = X'. The instructor demonstrates how to use Desmos, emphasizing the use of a mouse for ease of navigation and the zoom feature to find intersection points. The solution to the first example is found to be X = -11 and X = 5, with the positive solution being X = 5. The video encourages viewers to practice using Desmos by pausing and attempting the next problem, which involves solving 'Y = -4X^2 - 7X' and 'Y = -36'. The instructor shows how to adjust the graph for better visibility and how to find and label the intersection points, resulting in the solutions X = -4 and X = 9/4, with the positive solution being 9/4.

05:04

🔍 Advanced Desmos Techniques for SAT Math

The second paragraph continues the tutorial with more complex equations. The instructor demonstrates how to use Desmos to solve equations involving absolute values, such as 'Y = |4 - X| + 3' and 'Y = 25'. The video shows the process of graphing these equations, zooming out to locate the intersection points, which are found to be X = -1 and X = 9. The focus is on finding the positive solution, which in this case is X = 9. The instructor highlights the utility of Desmos for solving any equation on the SAT, even those without multiple-choice answers, eliminating the need for guesswork. The video concludes with a call to action for viewers to like, subscribe, and consider the instructor's tutoring services for all SAT sections and math subjects. A link to the instructor's website is provided in the video description for those interested in further assistance.

Mindmap

Keywords

💡Desmos

Desmos is an online graphing calculator that is widely used for creating and analyzing graphs of mathematical functions. In the context of the video, Desmos is utilized as a tool to solve equations for the digital SAT Math section. The tutor demonstrates how to graph the left and right sides of an equation to find their intersection points, which represent the solutions to the equation.

💡Digital SAT Math

The digital SAT Math refers to the section of the SAT (Scholastic Assessment Test) that is administered in a digital format. This section tests students' mathematical problem-solving skills. The video specifically addresses how to use Desmos to solve equations within this digital testing environment, highlighting its utility for students preparing for the SAT.

💡Graphing

Graphing is the process of plotting the relationship between two variables, often in the form of a graph. In the video, graphing is central to solving equations using Desmos. By graphing 'y equals the left-hand side' and 'y equals the right-hand side' of an equation, the tutor shows how to visualize where the two graphs intersect, indicating the solutions.

💡Intersection Points

Intersection points are the values on the x-axis (or y-axis) where two graphs meet. These points are crucial for solving equations because they represent the solutions. The video illustrates how to identify these points on Desmos by zooming in and clicking on the points of intersection to find the x-values.

💡Mouse

A mouse is a pointing device that detects two-dimensional motion relative to a surface. In the video, the tutor suggests bringing a mouse to the test day for the digital SAT Math because it facilitates easier navigation and manipulation of the graph on Desmos, such as clicking, dragging, and zooming to find intersection points.

💡Zoom In/Out

Zooming in and out are actions used to magnify or reduce the scale of a graph on Desmos. The video demonstrates the importance of these actions for finding intersection points that might not be immediately visible on the screen. Zooming out helps to get a broader view, while zooming in allows for precise identification of the points.

💡Scroll Wheel

The scroll wheel is a feature on many computer mice that allows for scrolling up and down or zooming in and out on a digital document or application. In the context of the video, the tutor uses the scroll wheel to zoom in and out on the Desmos graph, which is essential for locating the intersection points of the equations being solved.

💡Positive Solution

The positive solution refers to the solution that is greater than zero. In the video, after finding the intersection points, the tutor often needs to determine the positive solution, as many math problems are specifically interested in solutions that are positive numbers. This is especially relevant in the context of the SAT, where certain questions may only require the positive solution.

💡Absolute Value

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars (e.g., |x|). In the video, the tutor uses the absolute value function in Desmos to graph equations involving absolute values, such as |4 - x| + 3, which is part of solving a particular equation.

💡Fraction Button

The fraction button in Desmos is a tool that allows users to convert decimal numbers into their fractional form. In the video, after identifying a solution like 2.25, the tutor uses the fraction button to convert this decimal into a fraction (9/4), which is necessary for providing the answer in a format that matches the question's requirements.

Highlights

Introduction to using Desmos for solving equations on the digital SAT Math.

Desmos can solve any equation by graphing y equals the left-hand side and the right-hand side of the equation.

Demonstration of solving the first problem using Desmos by graphing y = 55/x + 6 and y = x.

Advice on bringing a mouse for easier navigation on test day.

Using the scroll wheel to zoom in and out for better visibility of intersection points.

Identifying the x-values of intersection points as the solutions to the equation.

Solution to the first problem is x = -11 and x = 5, with the positive solution being x = 5.

Encouragement for viewers to practice using Desmos with a pause in the video.

Guidance on solving a quadratic equation using Desmos by graphing y = -4x^2 - 7x and y = -36.

Method for converting a decimal solution to a fraction in Desmos.

Solution to the second problem is x = -4 and x = 9/4, with the positive solution being x = 9/4.

Explanation of solving absolute value equations in Desmos using the absolute value function.

Solution to the third problem is x = -1 and x = 9, with the positive solution being x = 9.

Emphasis on Desmos' utility for solving any equation on the test, including free-response questions.

Invitation to like, subscribe, and check the description for tutoring services.

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