The only SAT Math DESMOS Guide you'll ever need

LearnSATMath
20 Jun 202417:04

TLDRThis video offers a comprehensive guide on utilizing Desmos calculator for SAT Math, emphasizing its efficiency and accuracy over manual problem-solving. It covers solving single variable equations, systems of equations, inequalities, and quadratics, while highlighting the importance of understanding Desmos' limitations, especially with no solution scenarios in linear systems. The tutorial also touches on Desmos' capabilities for geometric and statistical problems, advocating for a conceptual understanding alongside its use.

Takeaways

  • 📚 Desmos is a powerful tool for the SAT Math section, but many students are not fully utilizing its capabilities.
  • 🔍 For single variable equations, Desmos can quickly show you where the vertical line is, without manual calculations.
  • 📈 Systems of equations can be easily solved using Desmos by finding the point of intersection of the graphs.
  • 🤔 Desmos can handle complex equations, including those with no real solutions, by comparing graphs against answer choices.
  • 📊 Systems of inequalities are visualized in Desmos by shading the regions that satisfy each inequality.
  • 🍎 Desmos can be used to solve real-world problems, like maximizing the number of bananas within a budget constraint.
  • 📉 Quadratics are common on the SAT, and Desmos can help find x and y intercepts, vertices, and analyze transformations.
  • 📐 When a quadratic intersects a line at exactly one point, it's typically at the vertex of the parabola.
  • 🚫 Desmos should not be used for linear systems with no solution; instead, compare slopes for parallel lines.
  • 📈 Desmos can calculate mean and median directly, but understanding these concepts is crucial for more complex problems.
  • 🛑 Some problems, like equivalent expressions, are better solved with algebraic manipulation rather than relying on Desmos.

Q & A

  • What is the main purpose of the Desmos calculator on the SAT according to the video?

    -The Desmos calculator on the SAT is a tool that can help students solve math problems more quickly and accurately than solving them by hand.

  • Why does the video suggest using Desmos for single variable equations?

    -Desmos allows students to simply input the equation and visually identify where the vertical line is, making it easier to find solutions without needing to manually solve the equation.

  • How can Desmos be used to solve systems of equations on the SAT?

    -By inputting both equations into Desmos, students can visually identify the point of intersection, which is the solution to the system of equations.

  • What is the significance of understanding the context of the problem when using Desmos for inequalities?

    -Understanding the context is crucial because even if the graph indicates a solution, it must align with the real-world scenario described in the problem, such as not being able to buy a negative number of items.

  • How does the video suggest using Desmos to find the maximum number of bananas in a given scenario?

    -The video suggests graphing the inequality and looking for the greatest y-value within the overlapping region that satisfies both the price and quantity constraints.

  • What is the advantage of using Desmos for quadratic functions on the SAT?

    -Desmos can easily find x and y intercepts, vertices, and other characteristics of quadratic functions, making it easier to solve problems related to these functions.

  • Why does the video recommend against using Desmos for linear systems of equations with no solution?

    -For linear systems with no solution, it's more precise and less error-prone to use paper and pencil to determine that the lines are parallel by setting their slopes equal to each other.

  • What is the video's stance on using Desmos for finding the mean and median of a data set?

    -The video suggests that for simple mean and median problems, Desmos can be used directly by inputting the data set, but for more complex problems, a strong understanding of mean and median concepts is necessary.

  • How does the video describe the process of finding the vertex of a quadratic function using Desmos?

    -By inputting the quadratic function into Desmos and clicking on it, the vertex, which represents the minimum or maximum of the function, can be easily identified.

  • What is the video's advice on using Desmos for equivalent expressions problems on the SAT?

    -The video advises against using Desmos for equivalent expressions problems, suggesting that students should instead learn how to factor and apply algebraic skills to solve these types of problems.

Outlines

00:00

📚 Desmos Calculator Mastery for the SAT

This paragraph introduces the Desmos calculator as an essential tool for the SAT, emphasizing its speed and accuracy. The speaker criticizes Khan Academy for not utilizing Desmos effectively and promises to demonstrate Desmos' capabilities in solving various SAT math problems. The paragraph covers single-variable equations, systems of equations, and the importance of understanding solutions in different contexts. It also humorously addresses the limitations of Desmos on the SAT, such as the inability to upload images or play sounds.

05:00

🔍 Leveraging Desmos for Systems of Equations and Inequalities

The speaker explains how to use Desmos for solving systems of equations and inequalities, highlighting the visual representation of solutions as points of intersection or overlapping regions. The paragraph discusses the concept of rewriting single-variable equations as systems and vice versa, and the importance of understanding the context of the problem to avoid incorrect solutions. It also touches on the practical application of Desmos for solving real-world problems, such as budget constraints in purchasing fruits.

10:03

📉 Desmos in Action: Quadratics and Graph Analysis

This paragraph delves into the use of Desmos for analyzing quadratic functions and their graphs. The speaker demonstrates how to find x and y intercepts, vertices, and the minimum or maximum values of quadratics using Desmos. It also addresses the importance of understanding transformations of quadratics and how Desmos can simplify the process of finding the minimum value when the function is translated vertically. The paragraph concludes with a strategy for solving problems involving the intersection of a quadratic and a horizontal line, emphasizing the efficiency of using Desmos over manual calculations.

15:04

📈 Desmos for Statistical Problems and Cautionary Advice

The speaker discusses the use of Desmos for solving statistical problems, such as calculating mean and median directly from a dataset. The paragraph also provides cautionary advice on when not to use Desmos, such as for linear systems of equations with no solution, where paper and pencil are preferred for precision. It concludes with a humorous anecdote about the speaker's personal experience with a green t-shirt used as a failed green screen, serving as a light-hearted reminder that not all attempts at using tools will be successful.

📌 Desmos Usage Recommendations for SAT Math

The final paragraph summarizes the situations where Desmos should be used for SAT math problems, including single-variable equations, systems of equations, systems of inequalities, finding intercepts and vertices of quadratics, and computing mean and median directly. It also advises against using Desmos for problems that require a strong understanding of algebra and arithmetic, such as equivalent expressions or finding the center and radius of a circle. The speaker emphasizes the importance of practice and understanding of concepts for effective test preparation.

Mindmap

Keywords

💡Desmos calculator

The Desmos calculator is an online graphing calculator that is permitted for use during the SAT Math section. It is praised in the video for its ability to simplify complex mathematical problems, making it easier for students to visualize and solve equations. The video emphasizes its importance and usefulness, especially for those who may not be adept at manual calculations.

💡Single variable equations

Single variable equations are algebraic expressions with one unknown variable. The video demonstrates how Desmos can be used to solve these equations by graphing and identifying where the equation equals zero, thus finding the value of the variable. This method is presented as a time-saving alternative to traditional algebraic manipulation.

💡Systems of equations

Systems of equations refer to multiple equations that need to be solved simultaneously. The script explains that Desmos can graph these equations and visually identify their intersection points, which are the solutions to the system. This is particularly useful for quadratic equations, where finding the intersection can be complex.

💡Vertex

The vertex of a quadratic equation is the point at which the parabola turns, representing either the maximum or minimum value of the function. The video mentions that Desmos can easily identify the vertex of a parabola, which is crucial for solving certain types of SAT Math problems.

💡Quadratics

Quadratics are polynomial equations of degree two, often graphed as a parabola. The script discusses how Desmos can be used to find the x and y intercepts of a quadratic, as well as its vertex, which are key steps in solving SAT Math problems involving quadratics.

💡Systems of inequalities

Systems of inequalities involve multiple inequalities that need to be solved together to find the common solutions. The video explains that Desmos can shade the regions that satisfy each inequality, allowing students to visually identify the area of overlap where all conditions are met.

💡Price and quantity constraints

Price and quantity constraints are part of word problems on the SAT that involve budget limitations and the number of items that can be purchased. The script uses an example to illustrate how Desmos can graph these constraints and find the maximum or minimum values within the allowed range.

💡Mean and median

Mean and median are statistical measures of central tendency. The video humorously notes that Desmos can calculate these values directly from a given data set, simplifying what could otherwise be a time-consuming calculation by hand.

💡Transformations

Transformations in the context of the video refer to the shifting, stretching, or reflecting of a graph. Desmos can automatically adjust the graph of a function to reflect these transformations, helping students visualize and solve related problems.

💡Conceptual understanding

Conceptual understanding is the ability to grasp the fundamental ideas behind mathematical concepts, rather than just memorizing formulas or procedures. The video stresses the importance of understanding how to solve problems conceptually, as it is essential for success on the SAT.

💡Brilliant.org

Brilliant.org is an online platform mentioned in the video for its problem-solving focused courses, which align with the video's advocacy for understanding concepts deeply rather than relying on memorization. The platform is advertised as a way to improve SAT Math scores.

Highlights

Desmos calculator is a powerful tool for the SAT Math section.

Most people are not aware of the full capabilities of Desmos.

Desmos can simplify solving single variable equations by graphing.

Systems of equations can be easily solved using Desmos by finding points of intersection.

Desmos can handle quadratic equations and their transformations.

For equations with no real solutions, Desmos can help identify when the graph does not intersect the x-axis.

Systems of inequalities can be visualized on Desmos to find regions of overlap.

Desmos can be used to solve real-world problems involving constraints, like buying apples and bananas within a budget.

Desmos can quickly solve multiple problems, showcasing its efficiency for the SAT.

Brilliant.org is recommended for conceptual understanding and problem-solving practice.

Desmos can find x and y intercepts and vertices of quadratics with ease.

When a quadratic intersects a line at exactly one point, it is typically at the vertex.

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

Desmos can instantly calculate mean and median by inputting data.

Functions can be treated like single variable equations in Desmos for solving.

Desmos can assist in determining valid points on a circle given certain conditions.

Some tutors recommend Desmos for certain problems, while others advise against it; this video provides guidance.

Learning algebra and factoring is crucial for the SAT, even with Desmos available.

The video concludes with a summary of when to use Desmos and when to rely on traditional problem-solving methods.

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