Florida's Geometry End-of-Course (EOC) exam can feel daunting, but with the right preparation and a solid grasp of key formulas, you can confidently conquer it. This comprehensive guide provides a curated list of essential formulas, categorized for easy reference, along with helpful tips and strategies to maximize your understanding and performance.
Disclaimer: This formula sheet is intended as a study aid and should not be considered a replacement for thorough textbook study and classroom instruction. Always consult your official course materials and teacher for the most accurate and up-to-date information.
I. Geometric Measurement & Calculation
A. Area Formulas
- Rectangle: Area = length × width
- Square: Area = side²
- Triangle: Area = (1/2) × base × height
- Parallelogram: Area = base × height
- Trapezoid: Area = (1/2) × (base₁ + base₂) × height
- Circle: Area = πr² (where 'r' is the radius)
B. Perimeter & Circumference
- Rectangle: Perimeter = 2(length + width)
- Square: Perimeter = 4 × side
- Triangle: Perimeter = side₁ + side₂ + side₃
- Circle: Circumference = 2πr or Circumference = πd (where 'd' is the diameter)
C. Volume Formulas
- Rectangular Prism: Volume = length × width × height
- Cube: Volume = side³
- Cylinder: Volume = πr²h (where 'h' is the height)
- Cone: Volume = (1/3)πr²h
- Sphere: Volume = (4/3)πr³
II. Geometric Relationships & Theorems
A. Pythagorean Theorem
- Right Triangles: a² + b² = c² (where 'a' and 'b' are legs, and 'c' is the hypotenuse)
B. Angle Relationships
- Complementary Angles: Two angles whose sum is 90°
- Supplementary Angles: Two angles whose sum is 180°
- Vertical Angles: Angles opposite each other when two lines intersect; they are congruent.
- Linear Pair: Two adjacent angles whose non-common sides form a straight line; they are supplementary.
C. Triangle Theorems
- Triangle Angle Sum Theorem: The sum of the angles in any triangle is 180°.
- Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
- Similar Triangles: Triangles with congruent angles and proportional sides.
D. Properties of Quadrilaterals
Remember the properties of parallelograms, rectangles, rhombuses, squares, and trapezoids, including their side lengths, angles, and diagonals.
III. Coordinate Geometry
- Distance Formula: √[(x₂ - x₁)² + (y₂ - y₁)²]
- Midpoint Formula: [(x₁ + x₂)/2, (y₁ + y₂)/2]
- Slope Formula: (y₂ - y₁)/(x₂ - x₁)
IV. Trigonometry (Basic)
- Right Triangle Trigonometry: SOH CAH TOA (sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent)
Exam Preparation Tips
- Practice, Practice, Practice: Work through numerous practice problems, focusing on different types of questions and problem-solving strategies.
- Review Key Concepts: Don't just memorize formulas; understand the underlying concepts and how they apply to different shapes and situations.
- Use Diagrams: Draw clear diagrams to help visualize problems and identify relevant information.
- Check Your Work: Always double-check your calculations and solutions to avoid careless mistakes.
- Manage Your Time: Practice pacing yourself during practice exams to build your time management skills for the actual EOC.
By mastering these formulas and utilizing effective study strategies, you'll significantly improve your chances of success on the Florida Geometry EOC. Good luck!
