List of Math Formulas for 9th-grade Students
Here are some important math formulas for 9th-grade students:
1. Pythagorean Theorem
In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
a2 + b2 = c2
2. Distance Formula
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula:
d = sqrt((x2 – x1)2 + (y2 – y1)2)
3. Slope Formula
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 – y1)/(x2 – x1)
4. Quadratic Formula
The roots of a quadratic equation ax2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± sqrt(b2 – 4ac))/2a
5. Law of Sines
In a triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant for all sides and angles.
a/sin A = b/sin B = c/sin C
6. Law of Cosines
In a triangle, the square of the length of a side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the angle between them.
a2 = b2 + c2 – 2bc cos A
7. Exponential Growth/Decay Formula
The amount A of a quantity that grows or decays exponentially with time t can be modeled using the formula:
A = A0 e(kt), where A0 is the initial amount, k is the growth/decay rate, and e is the base of natural logarithms.
These formulas cover a range of topics such as geometry, algebra, trigonometry, and exponential functions, and are essential for 9th-grade students to master as they continue to study more advanced math concepts.