Part 1: Use Desmos to Ace the SAT

Method Learning
4 Mar 202318:46

TLDRThis tutorial video showcases how Desmos, a graphing calculator, can be effectively utilized to tackle questions on the digital SAT. The host demonstrates the tool's interface, highlighting its features such as graphing basic functions, adjusting axis scales, and modifying equation settings. Practical examples are provided to solve SAT problems involving quadratic equations, systems of equations, and finding intersection points. The video emphasizes Desmos's efficiency in solving complex problems quickly, offering an alternative to traditional algebraic methods.

Takeaways

  • 🌐 Desmos is a powerful graphing calculator that can be accessed online at desmos.com to assist with solving problems on the digital SAT.
  • 📈 To graph basic functions on Desmos, simply type the equation, and use the shift key for exponents.
  • 🎨 Desmos allows you to add new functions and change their colors to differentiate them on the graph.
  • 🔄 The 'home' button resets the graph to its default zoom, which is helpful when you've zoomed out too far.
  • ⚙️ The settings (wrench icon) let you customize the graph's appearance, such as turning grid lines on or off, and adjusting the axis steps for more precise viewing.
  • 🔢 Desmos can handle complex equations, but sometimes removing 'equals zero' can help graph equations that initially don't display correctly.
  • 🔍 Sliders are a useful feature in Desmos for finding the exact value that makes two graphs intersect at a single point.
  • 📉 Desmos can be used to solve for the value of constants in equations where graphs intersect, such as finding the value of 'C' in a line intersecting a parabola.
  • 🔄 For quadratic equations, adjusting the slider for 'B' can help determine when a graph will cross the x-axis twice, indicating more than one real solution.
  • 📝 Even simple algebraic equations can be solved quickly using Desmos by looking for the x-intercept where the graph crosses the x-axis.
  • 📚 Practice using Desmos with various SAT question types to become more efficient and accurate in solving problems.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is how to use Desmos, a graphing calculator, to help answer questions on the new digital SAT.

  • How can Desmos be accessed for personal use?

    -Desmos can be accessed for personal use by visiting desmos.com/calculator or by searching for 'Desmos graphing calculator' on Google.

  • What is one way to graph a basic function like 3x - 5 on Desmos?

    -To graph a basic function like 3x - 5 on Desmos, you can simply type it into the input field on the calculator.

  • How do you input an exponent in Desmos?

    -To input an exponent in Desmos, you hold down the shift key and then press the number key corresponding to the exponent.

  • How can you add a new function to the graph in Desmos?

    -You can add a new function to the graph in Desmos by clicking on an empty line and typing in the new function's equation.

  • What is the purpose of the home button in Desmos?

    -The home button in Desmos resets the graph to its default zoom level, which is useful for returning to the original view after zooming in or out.

  • How can you change the color of a graphed function in Desmos?

    -You can change the color of a graphed function in Desmos by clicking the gear icon (settings) and then selecting the color you want from the options provided.

  • What does Desmos suggest when you type an equation in the form of 'y = some expression'?

    -When you type an equation in the form of 'y = some expression', Desmos may suggest adding a slider for a variable in the expression, allowing you to adjust the value and see the graph update dynamically.

  • Why might Desmos not graph an equation when you type it as '64x^2 + BX + 25 = 0'?

    -Desmos might not graph an equation when typed as '64x^2 + BX + 25 = 0' because it may not recognize the format. It's suggested to remove the 'equals zero' part and instead graph '64x^2 + BX + 25' and then use a slider for B.

  • How can Desmos help in finding the value of a constant in an equation that intersects another graph at exactly one point?

    -Desmos can help find the value of a constant by graphing both equations and adjusting a slider for the constant until the two graphs intersect at exactly one point, indicating the correct value.

  • What is a feature of Desmos that allows for dynamic adjustment of a variable's value?

    -A feature of Desmos that allows for dynamic adjustment of a variable's value is the slider, which can be added to a variable in an equation to see how changes affect the graph.

Outlines

00:00

📊 Introduction to Desmos Graphing Calculator

The video begins with an introduction to Desmos, a graphing calculator, as a tool for solving questions on the digital SAT. The presenter demonstrates how to access Desmos and navigate its interface, including typing in functions like '3x - 5' or '3x^2'. The video also covers basic functionalities such as adding new functions, changing colors, zooming in and out, and resetting to default view. The presenter emphasizes the importance of understanding Desmos's features for solving SAT problems.

05:03

🔍 Using Desmos to Solve SAT Problems

The presenter discusses how to use Desmos to solve specific SAT problems, such as finding the value of a constant 'C' in an equation where a line intersects a parabola at exactly one point. The video shows how to input equations into Desmos, troubleshoot common issues like implicit equations, and use sliders to adjust variables and find the exact intersection point. The presenter also highlights the importance of understanding when to adjust the range and step of sliders for precise answers.

10:04

🎯 Desmos for Quadratics and Systems of Equations

This section focuses on using Desmos to solve problems involving quadratics and systems of equations, where the goal is to find values that result in graphs intersecting at specific conditions. The presenter provides examples, including adjusting the value of 'B' in a quadratic equation to find when it has more than one real solution, and finding the exact point of intersection between a parabola and a line with a certain slope. The video demonstrates how to use sliders effectively to pinpoint these values and emphasizes the importance of careful reading of the problem to answer correctly.

15:06

📘 Desmos for Equation Solving and Further Resources

The final part of the video showcases Desmos's capability to solve simple equations by graphing and finding the x-intercepts. The presenter solves an example equation and demonstrates how Desmos can quickly provide the solution without manual algebraic manipulation. The video concludes with recommendations for further study, including checking out resources on the presenter's blog, using their program 'Methodize', and taking practice tests from the SAT's official website. The presenter encourages viewers to engage with the content, ask questions, and subscribe for more educational content.

Mindmap

Keywords

💡Desmos

Desmos is an online graphing calculator that is used in the video to demonstrate how it can be utilized to solve problems on the digital SAT. It is a tool that allows users to graph equations and visualize their solutions, which is particularly useful for understanding complex mathematical concepts. In the video, Desmos is shown as an alternative to traditional algebraic methods for solving equations, with the added benefit of visualizing the solutions.

💡Graphing Calculator

A graphing calculator is a type of electronic calculator that is capable of plotting graphs of functions. In the context of the video, the Desmos platform serves as a graphing calculator, enabling the user to input mathematical functions and see their graphical representations. This tool is highlighted as a way to assist students in answering SAT questions that involve graphical analysis.

💡SAT

The SAT, or Scholastic Assessment Test, is a standardized test widely used for college admissions in the United States. The video focuses on how Desmos can be used as a tool to help students prepare for and answer questions on the new digital SAT, particularly those that involve graphing and algebra.

💡Exponent

In mathematics, an exponent is used to indicate the power to which a number, called the base, is raised. In the video, the script mentions how to input exponents into Desmos by using the shift key followed by the number key to raise a variable to a power, such as '3x^2' for '3x squared'.

💡Parabola

A parabola is a U-shaped curve that is defined by a quadratic equation. In the video, the concept of a parabola is used to demonstrate how Desmos can graph quadratic equations and how these graphs can be used to find the intersection points with other functions, which is a common type of problem on the SAT.

💡Vertex

The vertex of a parabola is the point where the curve changes direction. It is the highest or lowest point on the graph of a parabola. The video uses the term 'vertex' when discussing the minimum or maximum point of a parabola, which is an important concept when graphing and analyzing quadratic equations.

💡Slider

In Desmos, a slider is a user interface element that allows the user to adjust the value of a variable within a set range. The video demonstrates how to add a slider for a variable like 'C' in an equation, which can then be used to dynamically change the graph and find the exact point of intersection between two graphs.

💡X-intercept

An x-intercept is the point where a graph of a function or an equation crosses the x-axis. In the video, the term is used to discuss the conditions under which a quadratic equation will have more than one real solution, which corresponds to the graph crossing the x-axis at two different points.

💡Discriminant

The discriminant of a quadratic equation is the part under the square root when the equation is in the form 'ax^2 + bx + c = 0'. It determines the nature of the roots of the equation. The video briefly mentions the discriminant in the context of solving quadratic equations, although it focuses more on the graphical approach using Desmos.

💡Equation

An equation is a statement that asserts the equality of two expressions. In the video, equations are the core of the problems being solved, and the script explains how to input and manipulate these equations in Desmos to find solutions graphically. Equations are used to represent various mathematical relationships and are central to the SAT's mathematical section.

Highlights

Desmos is a graphing calculator that can be used to assist with the new digital SAT.

Access Desmos by visiting desmos.com or searching for it online.

Desmos allows you to graph equations by simply typing them in.

Use the shift key and a number key to input exponents in Desmos.

Desmos automatically graphs new functions in different colors for clarity.

Click the gear icon to change the color of a graphed function.

The home button resets the graph to its default zoom level.

Desmos settings can be adjusted to show or hide grid lines and to change the axis steps.

Some equations might not graph correctly with 'equals zero' at the end; try removing it.

Desmos can be used to find the value of a constant that makes two graphs intersect at exactly one point.

Adding a slider for a variable in Desmos can help visualize how changes affect the graph.

Desmos can be used to solve for x in linear equations by finding where the line crosses the x-axis.

For quadratic equations, Desmos can show when there is more than one real solution by graphing x-intercepts.

Desmos is a valuable tool for solving a variety of SAT数学题 types, including quadratics and systems of equations.

Practice using Desmos with SAT problems to become more efficient and accurate.

The video provides a summary of how Desmos can be applied to various SAT question types.

Desmos can simplify solving equations by visually representing where they intersect without manual calculation.

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