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17 Important Math Formulas Students Should Know

17 Important Math Formulas Students Should Know

We all know that dealing with tough math problems is challenging enough without the added pressure of remembering the right formulas. That's why having the right tools at hand is crucial for students!
Just think about it: students are already wrestling with the step-by-step processes needed to solve tricky math problems. The last thing they need is to struggle with recalling intricate formulas on top of that.
Whether your child is getting ready to tackle homework assignments or needs to brush up on the essentials for a major test or quiz, these formulas are like secret weapons that can save the day.

Crucial Math Formulas

Mathematics has the potential to be both an exhilarating challenge and a potential source of frustration for students. However, the following formulas will prove indispensable regardless of where a student stands on the spectrum. We're here to ensure that every student has the support they need.

Foundational Knowledge for Elementary & Middle School

Area of Rectangle: area = length x width
Crucial for pre-algebra and later math courses, this formula calculates the area of a rectangle.

Perimeter of a Rectangle: 2(l + b)
This formula calculates the total distance around the outer edges of a rectangle by adding twice the length and twice the breadth of the rectangle.

Square Area: a²
All it takes is squaring the length of both sides to find the area of a square.

Square Perimeter: 4 x a
If you want the perimeter of a square, just multiply the side length by 4.

Circle Area Formula: A = π × r²
To find the area of a circle, you square the radius (multiply it by itself) and then multiply the squared radius by π. The result gives you the total area covered by the circle. This formula is essential in various fields like geometry, physics, engineering, and more.

Circle Circumference Formula: C = 2π × r
By multiplying the radius by 2π, you determine the total length of the circle's boundary.

Finding the Average: Sum of total numbers divided by the count of values.

This method is extensively used in statistics and various mathematical word problems to determine the average value of a set of numbers. The process involves two crucial steps:

  • Sum of Values: Add up all the individual values in the dataset.
  • Division by Count: Divide the sum obtained in the first step by the total count of values in the dataset.

Useful High School and SAT® Math Formulas

These high school math formulas are indispensable for geometry, algebra, calculus, and more. Additionally, they provide crucial assistance during the challenging math section of the SAT®.

The Quadratic Formula: x = −b ± √b²-4ac/2a
This formula is an indispensable tool for solving quadratic equations, particularly in advanced algebra courses such as Algebra II and beyond. The formula provides the values of x that satisfy the quadratic equation ax² + bx + c =0. where a, b, and c are constants and a is not equal to zero.

Probability: Number of favorable outcomes divided by the total number of favorable outcomes.

Whenever you're curious about the odds of something happening, this formula is your guide.

Distance formula: d=√(x₁ – x₂)² + (y₁ – y₂)²
Distance (d) equals the square root of the difference between the x-coordinates of the points squared, plus the difference between their y-coordinates squared.

It might sound a bit complex, but it's basically a fancy way of finding the length of the imaginary line that connects those two points. This is super useful in both geometry and algebra, because it helps us understand the space between points and solve problems that involve distances. Just plug in the coordinates of the two points, do some math magic, and you'll know how far apart they are.

Slope Formula: Slope = y₂ – y₁ / x₂ – x₁
This Formula allows you to calculate the steepness of the line connecting two points on a graph, providing insight into its incline or decline.

Slope Intercept Formula: y=mx+b
The Slope Intercept Formula is a fundamental equation in algebra used to describe and graph a straight line, where 'm' represents the slope of the line and 'b' represents the y-intercept, the point where the line crosses the y-axis.

Area of Triangle: Area = (1/2) (base) (height)
This formula is indispensable in geometry for calculating the total area of a triangle.

Sine (SOH): Sine = opposite / hypotenuse
By dividing the length of the side opposite to an angle by the length of the hypotenuse, this formula unveils the value of that angle, proving indispensable in trigonometry and geometry problem-solving.

Cosine (CAH): Cosine = adjacent / hypotenuse
Just like Sine, this formula reveals hidden angles in a triangle by dividing the length of the side adjacent to the angle by the hypotenuse's length.

Tangent (TOA): Tangent = opposite / adjacent
This equation aids in calculating unknown angles within a triangle.

Pythagorean Theorem: a²+b²=c²
This theorem is used to determine the hypotenuse's length in a right triangle. For any right triangle, the hypotenuse's square equals the sum of the squares of the other two sides.

When Math Problems Arise, We Bring Solutions!

At iD Tech, we offer more than just math tutoring. We offer a treasure trove of math resources to guide students and kids on their mathematical journey.
With these fantastic tips and tricks, you're all set to provide unwavering support to your student as they tackle math homework, assessments, quizzes, and the SAT® exam
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