Digital SAT Math Formula Bible

Overview

• Essential video for preparing for the digital SAT math section.
• Contains critical concepts and formulas.
• Includes reference to a recommended SAT crash course with a discount code.

Key Formulas and Concepts

Reference Sheet Formulas

• Accessible during both math modules
  • Area and circumference of a circle.
  • Conversions between radians and degrees.
  • Sum of angles in a triangle.
  • Volume formulas.
  • Special right triangles.

Slope and Linear Equations

1. Slope Formula

   • Slope ( m = \frac{y_2 - y_1}{x_2 - x_1} )
   • Example: Coordinates (7, 2) and (5, 1) gives slope ( \frac{1}{2} )

2. Slope-Intercept Form

   • Equation: ( y = mx + b )
   • Example: ( y = 2x + 7 ) with slope 2 and y-intercept 7

3. Point-Slope Form

   • Formula: ( y - y_1 = m(x - x_1) )
   • Example: ( y - 4 = 3(x - 3) )

Midpoint and Distance

4. Midpoint Formula

   • Formula: ( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) )
   • Example: Midpoint of (8, 4) and (6, 7) is (7, 5.5)

5. Distance Formula

   • Formula: ( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )
   • Example: Distance between (5, 3) and (1, 0) is 5

Circle Formulas

6. Length of an Arc

   • Formula: ( \frac{n}{360} \times 2\pi r )

7. Area of a Sector

   • Formula: ( \frac{n}{360} \times \pi r^2 )

8. Circle Equation

   • Formula: ( (x - h)^2 + (y - k)^2 = r^2 )
   • Example: Center (2, -5), radius 6

Quadratic and Exponential Functions

9. Quadratic Formula

   • Formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )

10. Exponential Growth & Decay

    • Formula: ( y = a(1 \pm r)^t )
    • Growth Example: Initial 200, growth rate 13%, 3 years

Trigonometry

11. SOHCAHTOA

    • Sine, Cosine, and Tangent definitions

12. Complementary Angles in Trigonometry

    • ( \sin(\theta) = \cos(90^\circ - \theta) )

Probability and Rational Functions

13. Probability

    • Formula: ( \frac{\text{favorable outcomes}}{\text{total outcomes}} )

14. Rational Functions

    • Graph characteristics: x-intercepts, vertical asymptotes, y-intercepts

Triangle Concepts

15. Pythagorean Theorem

    • Formula: ( a^2 + b^2 = c^2 )

16. Special Right Triangles

    • 45-45-90 and 30-60-90 triangles

17. Triangle Congruence and Similarity Theorems

    • Congruence: SSS, SAS, ASA, AAS, HL
    • Similarity: AA, SAS, SSS

Miscellaneous Formulas

18. Distance = Rate × Time

19. Sum and Product of Roots of Quadratics

    • Sum: ( -\frac{b}{a} )
    • Product: ( \frac{c}{a} )

20. Exponent Rules

    • Multiplication, division, zero exponent, etc.

21. Foiling and Binomials

    • FOIL method and squaring binomials

22. Inequalities

    • Flip inequality sign when dividing/multiplying by a negative number.

Conclusion

• Knowing these formulas and concepts is crucial for tackling the digital SAT math section.
• Recommended to practice using these concepts with practice tests and review sessions.