Desmos and SAT Preparation Lecture

Introduction

• Focus on mastering 20 crucial Desmos questions for the SAT.
• Questions vary in difficulty from easy to challenging.
• Encourage active participation:
  • Use Desmos during the lecture.
  • Practice for the digital SAT on March 9.
  • Familiarize with Desmos to enhance speed and accuracy.

Tools and Tips

1. Using Desmos Effectively

   • Follow along with live demonstrations to build muscle memory.
   • Use Desmos for both graphing and basic calculations.
   • Physical calculators are secondary; Desmos is primary.

2. Equipment Recommendations

   • Use a mouse to pan and zoom quickly.
   • Desmos offers graphing, calculations, and basic features like finding intersections.

3. Understanding Desmos’ Power

   • Beyond graphing: solve equations, find intercepts, and perform calculations.
   • Utilize the reference sheet provided in SAT for geometry formulas.

Problem Solving with Desmos

Example Problems

1. Equation Solving

   • Example: Solve x = 70/(x+3) for a negative solution.
   • Approach: Input directly into Desmos, identify solutions by looking for intersections with the x-axis.

2. Graph Intercepts

   • Example: Find the y-intercept of f(x) = 27 * (2/3)^x.
   • Approach: Enter the function, locate where it hits the y-axis.

3. Area of Geometric Shapes

   • Example: Calculate x for a triangle with area 104 and base x-3.
   • Approach: Use the area formula and input the equation in Desmos to find solutions.

4. Exponential Growth

   • Example: Find y in a savings account problem using a table of values.
   • Approach: Desmos can fit exponential equations given data points.

5. Line Intersection

   • Example: Find intersection points for lines such as y = 7x and y = x + 18.
   • Approach: Enter both equations and determine intersection points graphically.

6. Function Minimum

   • Example: Find the minimum of f(x) = 12x² - 30x - 162.
   • Approach: Enter function and click on the vertex to find minimum.

7. Statistical Functions

   • Example: Find the median of a data set using Desmos.
   • Approach: Input data as a list and use Desmos functions like median() or mean().

8. Systems of Equations

   • Example: Solve 3(6x + 11) = d(9x + 4) for no solutions.
   • Approach: Visualize equations as lines and adjust to find parallelism.

9. Function Evaluations

   • Example: Evaluate g(x) = 6 + x³ for a specific x.
   • Approach: Enter function and evaluate directly for given values.

10. Solving Inequalities

    • Example: Determine if a point satisfies y < 2x + 6 and y < -1/3x + 8.
    • Approach: Graph inequalities and find overlapping solution regions.*

Conclusion

• Emphasize regular practice with Desmos.
• Understanding and utilizing Desmos can significantly simplify SAT math problems.
• Wishing students success in upcoming SAT exams.