Introduction
Mastering geometry is essential for success in the Geometry Regents Exam. This formula sheet provides a comprehensive overview of the key formulas and concepts you need to know to ace the exam.
Unit Circle
- Sin(a) = y-coordinate of point (x,y) on unit circle
- Cos(a) = x-coordinate of point (x,y) on unit circle
- Tan(a) = y-coordinate / x-coordinate of point (x,y) on unit circle
Area
- Triangle: A = (1/2) * b * h
- Square: A = s^2
- Rectangle: A = l * w
- Parallelogram: A = b * h
- Trapezoid: A = (1/2) * (b1 + b2) * h
- Circle: A = πr^2
Volume
- Cube: V = s^3
- Rectangular Prism: V = l * w * h
- Cylinder: V = πr^2h
- Cone: V = (1/3)πr^2h
- Sphere: V = (4/3)πr^3
Pythagorean Theorem
- a^2 + b^2 = c^2
Trig Ratios
- Sin(a) = Opposite / Hypotenuse
- Cos(a) = Adjacent / Hypotenuse
- Tan(a) = Opposite / Adjacent
Law of Sines
- (a / sin(A)) = (b / sin(B)) = (c / sin(C))
Law of Cosines
- a^2 = b^2 + c^2 – 2bc cos(A)
- b^2 = a^2 + c^2 – 2ac cos(B)
- c^2 = a^2 + b^2 – 2ab cos(C)
Coordinate Geometry
- Distance between two points (x1, y1) and (x2, y2): d = sqrt((x2 – x1)^2 + (y2 – y1)^2)
- Slope of a line passing through two points (x1, y1) and (x2, y2): m = (y2 – y1) / (x2 – x1)
- Equation of a line with slope m and y-intercept b: y = mx + b
Transformations
- Translation: T(x, y)
- Rotation: R(θ)
- Reflection: F(x-axis), G(y-axis), or H(line y = x)
Constructions
- Bisecting an angle
- Constructing a perpendicular bisector
- Constructing a tangent to a circle
Miscellaneous
- Circumference of a circle: C = 2πr
- Area of a sector of a circle: A = (1/2)r^2θ
- Volume of a pyramid: V = (1/3)Bh
- Volume of a frustum of a cone: V = (1/3)πh(r1^2 + r2^2 + r1r2)
Conclusion
This formula sheet provides a comprehensive overview of the key formulas and concepts you need to know for the Geometry Regents Exam. By understanding and applying these formulas, you can improve your problem-solving skills and increase your confidence on exam day.
Additional Resources
FAQs
Q: How much time should I spend studying for the Geometry Regents Exam?
A: It is recommended to spend at least 2-3 hours per week studying for the exam.
Q: What are some tips for success on the Geometry Regents Exam?
A: Practice regularly, understand the concepts, and review the formula sheet frequently.
Q: Is it possible to pass the Geometry Regents Exam without a tutor?
A: Yes, it is possible to pass the exam without a tutor. However, a tutor can provide valuable support and guidance.
Q: What if I am struggling with a particular concept?
A: There are many resources available to help you, such as online videos, textbooks, and tutors.
Q: How can I improve my problem-solving skills in geometry?
A: Practice regularly and try to identify patterns and relationships between different concepts.
Q: What are the most important formulas to know for the Geometry Regents Exam?
A: The Pythagorean Theorem, Trig Ratios, Law of Sines, and Law of Cosines are essential formulas to master.