Digital SAT Prep: Easy Desmos Hack for the Hardest Math Problems!

Strategic Test Prep
6 Sept 202311:34

TLDRIn this video, Laura Whitmore from STP addresses the increased difficulty of math problems on the digital SAT, particularly in module 2. She introduces a Desmos calculator hack to simplify solving complex problems, saving time and increasing the chance of correct answers. Laura demonstrates the strategy on four challenging problems from Blue Book test 4, showing how to use Desmos to find solutions graphically, which she claims is more efficient than algebraic methods. The video is aimed at helping students achieve a perfect score on the math section of the SAT.

Takeaways

  • 🔢 The difficulty of math problems on the digital SAT has increased, particularly in the last 10 problems of module 2.
  • ⏰ Using Desmos calculator can significantly reduce the time required to solve complex math problems, allowing for more time to review other answers.
  • 📈 Desmos is particularly useful for solving systems of equations, where the intersection point of two graphs is needed.
  • 🎯 For problems asking for a specific condition like 'one distinct real solution', adjusting the Desmos slider can help find the exact value needed.
  • 📉 When dealing with quadratic functions, adjusting the 'a' value in Desmos can help visualize the vertex touching a line, which is key for certain problems.
  • 🔍 For problems involving the product of solutions, using Desmos to graph and find the x-intercepts can simplify the process of finding the constant 'K'.
  • 📐 Desmos can also be used to find the radius of a circle by measuring the diameter from the graph.
  • 🤔 Logical reasoning combined with Desmos can help determine the correct answer for problems involving the properties of parabolas.
  • 👩‍🏫 The video offers a tutorial on how to use Desmos effectively for SAT prep, suggesting it as a superior method over complex algebraic solutions.
  • 📚 The presenter suggests using Desmos for a variety of SAT math problems, indicating it can simplify the process and potentially lead to a perfect score.

Q & A

  • What is the main challenge students face with the digital SAT math problems according to Laura Whitmore?

    -Students find the last 10 or so problems in module 2 of the digital SAT to be significantly difficult, taking them a long time to solve or not being able to solve them at all.

  • What is the proposed solution in the video to make solving digital SAT math problems easier?

    -The video suggests using the Desmos calculator to solve the problems graphically, which is claimed to be easier and faster than the traditional algebraic methods.

  • How does the Desmos calculator help with systems of equations on the SAT?

    -Desmos helps by allowing students to input equations and adjust variables using sliders to find the exact point where the graphs of the equations intersect, which is particularly useful for systems with one distinct real solution.

  • What is the strategy for solving problems with a quadratic and a line that intersect at exactly one point?

    -The strategy is to adjust the y-intercept 'a' of the quadratic equation using a slider in Desmos until the vertex of the parabola touches the line, indicating the exact point of intersection.

  • How does the video demonstrate solving a problem involving the product of the solutions to a given equation?

    -By using Desmos to graph the quadratic equation and adjusting the constants 'A' and 'B' with sliders, the video shows how to find the product of the x-intercepts, which corresponds to the product of the solutions.

  • What is the advantage of using Desmos over the complex algebraic methods suggested by the College Board for certain problems?

    -Desmos provides a visual and interactive approach that is easier to understand and less prone to errors, making it a more efficient way to solve certain types of math problems compared to the complex algebraic methods.

  • How does the video address the issue of finding the radius of a circle given its equation?

    -The video demonstrates using Desmos to graph the circle and then finding the endpoints of the diameter to calculate the radius by dividing the diameter's length by two.

  • What logical reasoning is used in the video to determine the correct answer for a problem involving a parabola with a given vertex?

    -The video uses logical reasoning to deduce that for the parabola to intersect the x-axis at two points, 'a' must be positive, 'B' must be negative, and 'C' is mostly positive, leading to the selection of the correct answer choice.

  • How does the video encourage viewers to engage with the content and the channel?

    -The video encourages viewers to engage by asking them to hit the Thumbs Up Button if they find the content helpful, subscribe to the channel for future content, and contact for one-on-one tutoring.

  • What is the humorous element mentioned in the video regarding the College Board's answer explanations?

    -The video humorously critiques the complexity of the College Board's answer explanations, suggesting they are overly complicated and not as straightforward as the Desmos method demonstrated.

Outlines

00:00

📚 Solving Complex SAT Math Problems with Desmos

Laura Whitmore introduces a strategy to simplify solving difficult math problems on the digital SAT, particularly the last 10 in module 2. She emphasizes the effectiveness of using the Desmos calculator to solve problems graphically, which is more efficient and easier to understand than the complex algebraic methods provided by the College Board. Laura demonstrates how to use Desmos to find the value of 'a' in a system of equations that has exactly one distinct real solution by adjusting the slider for 'a' until the quadratic's vertex touches a line. She also shows how to modify the range and step size of the slider for more precise adjustments. The video promises to cover four difficult problems from the Blue Book test 4, aiming to help students save time and potentially achieve a perfect score.

05:02

🔍 Using Desmos for Quadratic and Circle Equations

Laura continues her tutorial by addressing a problem involving the product of solutions to a quadratic equation, where the product is a constant multiple of the constants A and B. She uses Desmos to graph the equation and adjust sliders for A and B, ensuring they are positive as per the problem's conditions. By setting A and B to 1 for simplicity, she identifies the solutions and calculates the constant K by dividing the product of the solutions by the product of A and B. Laura then moves on to a problem involving a circle equation, where she advises against assuming the circle's center is at the origin. Instead, she uses Desmos to find the endpoints of the circle's diameter and calculates the radius by dividing the diameter's length by two. She concludes the section by promoting an app for additional math practice for the SAT.

10:05

🧠 Logical Reasoning and Desmos for Parabola Problems

In the final part of the video, Laura tackles a problem involving a parabola with a given vertex and x-axis intersections. She uses Desmos to graph the parabola in vertex form, introducing a slider for 'a' to determine the parabola's direction and width. By logical reasoning and adjusting the slider, she deduces that 'a' must be positive for the parabola to intersect the x-axis twice and identifies the correct values for 'a', 'b', and 'c' in the equation. Laura contrasts this approach with the lengthy and complex explanations provided by the College Board, advocating for the use of Desmos and logical reasoning as a more straightforward method. She ends the video by offering tutoring services for deeper math understanding and invites viewers to contact her for one-on-one sessions.

Mindmap

Keywords

💡Digital SAT

The Digital SAT refers to the computer-based version of the SAT exam, which is a standardized test widely used for college admissions in the United States. In the context of the video, the presenter discusses strategies for tackling the more challenging math problems that have been introduced in the digital format, particularly in the last module of the test.

💡Desmos Calculator

Desmos is an online graphing calculator that is used in the video to solve complex math problems visually. The presenter demonstrates how Desmos can be a more intuitive and efficient tool for solving problems that might otherwise require lengthy algebraic manipulations. It's highlighted as a way to simplify the process of finding solutions to equations, especially when dealing with systems of equations or quadratic functions.

💡Systems of Equations

A system of equations refers to a set of two or more equations that are solved simultaneously. In the video, the presenter uses Desmos to solve systems of equations graphically by plotting them on the same coordinate plane and adjusting parameters until the equations intersect at a single point, which is a method to find the exact solution.

💡Quadratic Functions

Quadratic functions are mathematical functions of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. The video discusses how to use Desmos to find the vertex of a parabola, which is crucial for determining the y-intercept and solving for specific parameters when the parabola intersects a line or the x-axis.

💡Slider

In the context of the Desmos calculator, a slider is a tool that allows users to adjust the value of a variable within a specified range. The presenter uses sliders to dynamically change the parameters of equations, such as 'a' in a quadratic function, to visually find the point where the graph meets specific conditions, like touching a line or intersecting the x-axis.

💡Vertex Form

The vertex form of a quadratic function is expressed as f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. The video explains how to use vertex form in Desmos to graph a parabola and adjust its shape and position to solve for conditions such as intersecting the x-axis at specific points.

💡Real Solutions

Real solutions refer to the values of the variable that satisfy an equation in the real number system. The video script mentions finding the conditions under which a system of equations has exactly one distinct real solution, which is crucial for certain types of math problems on the SAT.

💡Product of Solutions

In the context of quadratic equations, the product of the solutions can be found using the constant term and the coefficients of the equation. The video demonstrates how to use Desmos to find the product of the solutions to an equation by graphically representing the solutions and then calculating their product.

💡Circle Equation

A circle equation in the coordinate plane is typically given by the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. The video shows how to use Desmos to find the radius of a circle by graphing the equation and visually determining the diameter, then calculating the radius as half of the diameter.

💡Logical Reasoning

Logical reasoning is the process of using valid reasoning to arrive at conclusions. In the video, the presenter uses logical reasoning in conjunction with Desmos to solve problems that require understanding the implications of the graph's behavior, such as determining the sign of coefficients based on the graph's intersection with the x-axis.

Highlights

Digital SAT math problems have increased in difficulty, particularly in the last 10 problems of module 2.

Desmos calculator can simplify solving complex math problems on the digital SAT.

Using Desmos can save time and increase the chance of solving problems correctly.

Desmos is particularly useful for solving systems of equations with a single real solution.

Adjusting the 'a' value in Desmos can help find the exact point where a parabola touches a line.

Desmos allows for easy graphical solutions compared to complex algebraic methods.

For quadratic equations, Desmos can be used to find the product of the solutions by adjusting constants.

Setting constants A and B to positive values in Desmos is crucial for accurate problem-solving.

Desmos can visually represent the product of solutions by graphing a parabola and finding its x-intercepts.

Circle equations can be solved for radius using Desmos by finding the diameter and dividing by two.

Desmos is effective for finding the vertex form of a parabola and determining its direction based on intersections.

Logical reasoning combined with Desmos can simplify the process of selecting the correct answer from multiple choices.

Desmos can help determine the correct value of 'a' in a parabola equation by adjusting it until it intersects the x-axis at two points.

The video provides a step-by-step guide on how to use Desmos for various SAT math problems.

Desmos can be a game-changer for students struggling with the complexity of SAT math problems.

The video offers a humorous approach to a serious academic challenge, making learning more enjoyable.

STP offers tutoring services for deeper math review and one-on-one problem-solving assistance.

The video concludes with a call to action for students to subscribe for more SAT prep content.

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