What is the formula for the area of a rectangle?
A = l + w
A = l Ć w
A=lw
A = 2(l + w)
Math formulas are concise mathematical expressions that represent relationships between quantities, properties, or operations. They are used to describe and solve mathematical problems across various fields such as algebra, geometry, calculus, and statistics. Formulas often consist of variables, constants, and mathematical symbols, enabling calculations and predictions in a structured manner. These formulas serve as fundamental tools for understanding and solving mathematical problems efficiently.
Essential mathematical formulas cover arithmetic operation, algebra, geometry, and more. They include equations for basic operations like addition and multiplication, as well as formulas for calculating areas, volumes, and solving equations. These formulas form the foundation of mathematical understanding and problem-solving.
Algebraic Formulas | (š+š)²=šĀ²+2šš+šĀ² |
Geometric Formulas | š“=ššĀ² |
Trigonometric Formulas | sin┲š+cos┲š=1 |
Calculus Formulas | š/šš„(ā«š(š„)āšš„)=š(š„) |
Statistical Formulas | š„Ė=(āšāāšš„įµ¢)/šāā |
Probability Formulas | š(š“āŖšµ)=š(š“)+š(šµ)āš(š“ā©šµ) |
Number Theory Formulas | šĀ²+šĀ²=šĀ² |
Differential Equations | šš¦/šš„=šš¦ |
Matrix Formulas | š“ā šµā šµā š“ |
Geometry Formulas | š=4/3ššĀ³ |
Fundamental rules essential for solving algebraic problems efficiently and accurately. These formulas cover concepts like linear equations, quadratic equations, slopes, distances, and geometric shapes, forming the building blocks for more advanced algebraic manipulations.
Geometric formulas essential for calculating properties of shapes, areas, volumes, and angles. These formulas are crucial in geometry, helping solve problems related to triangles, circles, rectangles, and other geometric figures.
We study Geometry formulas under two headings that are,
Key formulas for 2D geometry, including those for calculating area, perimeter, and properties of shapes like triangles, squares, circles, and polygons
Shape | Formula |
---|---|
Square | Area: š“=š ² Perimeter: š=4š P=4s |
Rectangle | Area: š“=šĆš¤ Perimeter: š=2š+2w |
Triangle | Area: š“=1/2ĆšĆā Perimeter: š=š+š+š |
Circle | Area: š“=ššĀ² Circumference: š¶=2šš |
Parallelogram | Area: š“=šĆā Perimeter: š=2(š+š) |
Trapezoid | Area: š“=1/2(šā+šā)Ćā Perimeter: š=š+šā+š+šā |
Essential formulas for 3D geometry, covering calculations for volume, surface area, and characteristics of three-dimensional shapes such as spheres, cubes, cylinders, cones, and prisms.
Shape | Formula |
---|---|
Cube | Volume: V=s³ Surface Area: šš“=6š ² |
Rectangular Prism | Volume: š=šĆš¤Ćā Surface Area: šš“=2šš¤+2šā+2š¤ā |
Sphere | Volume: š=4/3ššĀ³ Surface Area: šš“=4ššĀ² |
Cylinder | Volume: š=ššĀ²ā Lateral Surface Area: šæšš“=2ššā Total Surface Area: ššš“=2šš(š+ā) |
Cone | Volume: š=1/3ššĀ²ā Lateral Surface Area: šæšš“=ššš Total Surface Area: ššš“=šš(š+š) |
Prism | Volume: š=šµā Lateral Surface Area: šæšš“=šā Total Surface Area: ššš“=šā+2šµ |
Pyramid | Volume: š=1/3šµā Lateral Surface Area: šæšš“=1/2šš Total Surface Area: ššš“=1/2šš+šµ |
Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1. There are three types of probability : theoretical probability , and subjective probability.
P(A) = n(A)/n(S)
Where,
P(A) is the Probability of an Event.
n(A) is the Number of Favourable Outcomes
n(S) is the Total Number of Events
Formula Type | Formula |
---|---|
Probability of an Event | š(šø)=Number of favorable outcomes / Total number of outcomesā |
Probability of the Complement of an Event | š(šøā²)=1āš(šø) |
Conditional Probability | š(š“ā£šµ)=š(š“ā©šµ)/š(šµ) |
Addition Rule | š(š“āŖšµ)=š(š“)+š(šµ)āš(š“ā©šµ) |
Multiplication Rule (Independent Events) | š(š“ā©šµ)=š(š“)Ćš(šµ) |
Multiplication Rule (Dependent Events) | š(š“ā©šµ)=š(š“)Ćš(šµā£š“) |
Bayesā Theorem | š(š“ā£šµ)={š(šµā£š“)Ćš(š“)}/š(šµ) |
Basic Trigonometric Formulas of Addition
Formula Type | Formula |
---|---|
Sine of Sum | sinā”(š+š)=sinā”š cosā”š+cosā”š sinā”š |
Cosine of Sum | cosā”(š+š)=cosā”š cosā”šāsinā”š sinā”š |
Tangent of Sum | tanā”(š+š)=(tanā”š+tanā”š)/1ātanā”štanā”šā |
Formula Type | Formula |
---|---|
Sine of Difference | sinā”(šāš)=sinā”š cosā”šācosā”š sinā”šsin |
Cosine of Difference | cosā”(šāš)=cosā”š cosā”š+sinā”š sinā”š |
Tangent of Difference | tanā”(šāš)=tanā”šātanā”š1+tanā”š tanā”šā |
Formula Type | Formula |
---|---|
Double Angle for Sine | sinā”2š=2sinā”šcosā”šsin2Īø=2sinĪøcosĪø |
Double Angle for Cosine | cosā”2š=cosā”2šāsinā”2šcos2Īø=cos2Īøāsin2Īø |
Double Angle for Tangent | tanā”2š=2tanā”š1ātanā”2štan2Īø=1ātan2Īø2tanĪøā |
Trigonometric Formulas for Division
Formula Type | Formula |
---|---|
Sine Division | sinā”š/sinā”šā |
Cosine Division | cosā”š/cosā”šā |
Tangent Division | tanā”š/tanā”š=(sinā”š/cosā”š)/(sinā”š/cosā”š)=(sinā”š cosā”š) / (cosā”š sinā”š) ā |
Cosecant Division | cscā”š/cscā”š=sinā”š/sinā”šā |
Secant Division | secā”š/secā”š=cosā”š/cosā”šā |
Cotangent Division | cotā”š/cotā”š=(sinā”š cosā”š) / (sinā”š cosā”š ā) |
Formula Type | Formula |
---|---|
Sine (sin) | sinā”š=opposite / hypotenuse |
Cosine (cos) | cosā”š=adjacent / hypotenusetā |
Tangent (tan) | tanā”š=opposite / adjacent |
Cosecant (csc) | cscā”š=1/sinā”š |
Secant (sec) | secā”š=1/cosā”š |
Cotangent (cot) | cotā”š=1/tanā”š |
Pythagorean Identity | sin┲š+²š=1 |
Sine of Sum | sinā”(š+š)=sinā”š cosā”š+cosā”š sinā”š |
Cosine of Sum | cosā”(š+š)=cosā”š cosā”šāsinā”š sinā”š |
Tangent of Sum | tanā”(š+š)=(tanā”š+tanā”š)/ (1ātanā”š tanā”š) |
Sine of Difference | sinā”(šāš)=sinā”š cosā”šācosā”š sinā”š |
Cosine of Difference | cosā”(šāš)=cosā”š cosā”š+sinā”š sinā”š |
Tangent of Difference | tanā”(šāš)= (tanā”šātanā”š) / (1+tanā”š tanā”š)ā |
Double Angle for Sine | sinā”2š=2sinā”š cosā”š |
Double Angle for Cosine | cosā”2š=cos┲šāsin┲šc |
Double Angle for Tangent | tanā”2š=2tanā”š1ātanā”2štā |
Half-Angle for Sine | sinā”š/2=±ā 1ācosā”š/2āā |
Half-Angle for Cosine | cosā”š/2=±ā 1+cosā”š/2āā |
Half-Angle for Tangent | tanā”š/2=±ā 1ācosā”š / 1+cosā”šāā |
A fraction represents a numerical value expressed as the quotient of two integers. The top number, called the numerator, indicates how many parts of the whole are being considered, while the bottom number, the denominator, denotes the total number of equal parts that make up the whole.
A percentage represents a ratio or a numerical value expressed as a part of 100. It is commonly denoted by the ā%ā symbol.
Percentage = (Given Value/Total Value) Ć 100
Using math formulas efficiently requires understanding and practice. Here are some tips to help you make the most of them:
The best formula to learn math is one thatās fundamental and widely applicable, such as the Pythagorean theorem, which relates to geometry and has real-world applications in areas like engineering and architecture.
A simple and intuitive formula for kids is the area formula for squares and rectangles (Area = length Ć width). Itās easy to understand and apply, making it a foundational concept in early math education.
The most famous formula in math is arguably Eulerās identity: ššš+1=0. It elegantly combines five fundamental mathematical constants (e, Ļ, i, 1, and 0) in a single equation, demonstrating the beauty and interconnectedness of mathematics.
One of the most used formulas in math is the quadratic formula: š„=āšĀ±šĀ²ā4ššĀ²š . Itās vital for solving quadratic equations and has applications in various fields, including physics, engineering, and economics.
The golden rule of algebra is to maintain equality by performing the same operation on both sides of an equation. This ensures that the equation remains balanced and valid, allowing for accurate mathematical manipulation and problem-solving.
Math formulas are concise mathematical expressions that represent relationships between quantities, properties, or operations. They are used to describe and solve mathematical problems across various fields such as algebra, geometry, calculus, and statistics. Formulas often consist of variables, constants, and mathematical symbols, enabling calculations and predictions in a structured manner. These formulas serve as fundamental tools for understanding and solving mathematical problems efficiently.
Essential mathematical formulas cover arithmetic operation, algebra, geometry, and more. They include equations for basic operations like addition and multiplication, as well as formulas for calculating areas, volumes, and solving equations. These formulas form the foundation of mathematical understanding and problem-solving.
Download This Math Formula PDF
Algebraic Formulas | (š+š)²=šĀ²+2šš+šĀ² |
Geometric Formulas | š“=ššĀ² |
Trigonometric Formulas | sin┲š+cos┲š=1 |
Calculus Formulas | š/šš„(ā«š(š„)āšš„)=š(š„) |
Statistical Formulas | š„Ė=(āšāāšš„įµ¢)/šāā |
Probability Formulas | š(š“āŖšµ)=š(š“)+š(šµ)āš(š“ā©šµ) |
Number Theory Formulas | šĀ²+šĀ²=šĀ² |
Differential Equations | šš¦/šš„=šš¦ |
Matrix Formulas | š“ā šµā šµā š“ |
Geometry Formulas | š=4/3ššĀ³ |
Fundamental rules essential for solving algebraic problems efficiently and accurately. These formulas cover concepts like linear equations, quadratic equations, slopes, distances, and geometric shapes, forming the building blocks for more advanced algebraic manipulations.
Download This Algebra Formulas PDF
a² ā b² = (a ā b)(a + b)
(a + b)² = a² + 2ab + b²
a²+ b² = (a + b)² ā 2ab
(a ā b)² = a² ā 2ab + b²
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
(a ā b ā c)² = a² + b² + c² ā 2ab + 2bc ā 2ca
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a ā b)³ = a³ ā 3a²b + 3ab² ā b³
a³ ā b³ = (a ā b)(a² + ab + b²)
a³ + b³ = (a + b)(a² ā ab + b²)
(a + b)ā“ = aā“ + 4a³b + 6a²b² + 4ab³ + bā“
(a ā b)ā“ = aā“ ā 4a³b + 6a²b² ā 4ab³ + bā“
aā“ā bā“ = (a ā b)(a + b)(a² + b²)
(aįµ)(aāæ) = aįµāŗāæ
(ab)įµ = aįµbįµ
(aįµ)āæ = aįµāæ
Geometric formulas essential for calculating properties of shapes, areas, volumes, and angles. These formulas are crucial in geometry, helping solve problems related to triangles, circles, rectangles, and other geometric figures.
We study Geometry formulas under two headings that are,
2-D Formulas
3-D Formulas
Key formulas for 2D geometry, including those for calculating area, perimeter, and properties of shapes like triangles, squares, circles, and polygons
Shape | Formula |
---|---|
Square | Area: š“=š ² |
Rectangle | Area: š“=šĆš¤ |
Triangle | Area: š“=1/2ĆšĆā |
Circle | Area: š“=ššĀ² |
Parallelogram | Area: š“=šĆā |
Trapezoid | Area: š“=1/2(šā+šā)Ćā |
Essential formulas for 3D geometry, covering calculations for volume, surface area, and characteristics of three-dimensional shapes such as spheres, cubes, cylinders, cones, and prisms.
Shape | Formula |
---|---|
Cube | Volume: V=s³ |
Rectangular Prism | Volume: š=šĆš¤Ćā |
Sphere | Volume: š=4/3ššĀ³ |
Cylinder | Volume: š=ššĀ²ā |
Cone | Volume: š=1/3ššĀ²ā |
Prism | Volume: š=šµā |
Pyramid | Volume: š=1/3šµā |
Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1. There are three types of probability : theoretical probability , and subjective probability.
P(A) = n(A)/n(S)
Where,
P(A) is the Probability of an Event.
n(A) is the Number of Favourable Outcomes
n(S) is the Total Number of Events
Formula Type | Formula |
---|---|
Probability of an Event | š(šø)=Number of favorable outcomes / Total number of outcomesā |
Probability of the Complement of an Event | š(šøā²)=1āš(šø) |
Conditional Probability | š(š“ā£šµ)=š(š“ā©šµ)/š(šµ) |
Addition Rule | š(š“āŖšµ)=š(š“)+š(šµ)āš(š“ā©šµ) |
Multiplication Rule (Independent Events) | š(š“ā©šµ)=š(š“)Ćš(šµ) |
Multiplication Rule (Dependent Events) | š(š“ā©šµ)=š(š“)Ćš(šµā£š“) |
Bayesā Theorem | š(š“ā£šµ)={š(šµā£š“)Ćš(š“)}/š(šµ) |
Basic Trigonometric Formulas of Addition
Formula Type | Formula |
---|---|
Sine of Sum | sinā”(š+š)=sinā”š cosā”š+cosā”š sinā”š |
Cosine of Sum | cosā”(š+š)=cosā”š cosā”šāsinā”š sinā”š |
Tangent of Sum | tanā”(š+š)=(tanā”š+tanā”š)/1ātanā”štanā”šā |
Basic Trigonometric Formulas of Subtraction
Formula Type | Formula |
---|---|
Sine of Difference | sinā”(šāš)=sinā”š cosā”šācosā”š sinā”šsin |
Cosine of Difference | cosā”(šāš)=cosā”š cosā”š+sinā”š sinā”š |
Tangent of Difference | tanā”(šāš)=tanā”šātanā”š1+tanā”š tanā”šā |
Basic Trigonometric Formulas of Multiplication
Formula Type | Formula |
---|---|
Double Angle for Sine | sinā”2š=2sinā”šcosā”šsin2Īø=2sinĪøcosĪø |
Double Angle for Cosine | cosā”2š=cosā”2šāsinā”2šcos2Īø=cos2Īøāsin2Īø |
Double Angle for Tangent | tanā”2š=2tanā”š1ātanā”2štan2Īø=1ātan2Īø2tanĪøā |
Trigonometric Formulas for Division
Formula Type | Formula |
---|---|
Sine Division | sinā”š/sinā”šā |
Cosine Division | cosā”š/cosā”šā |
Tangent Division | tanā”š/tanā”š=(sinā”š/cosā”š)/(sinā”š/cosā”š)=(sinā”š cosā”š) / (cosā”š sinā”š) ā |
Cosecant Division | cscā”š/cscā”š=sinā”š/sinā”šā |
Secant Division | secā”š/secā”š=cosā”š/cosā”šā |
Cotangent Division | cotā”š/cotā”š=(sinā”š cosā”š) / (sinā”š cosā”š ā) |
Formula Type | Formula |
---|---|
Sine (sin) | sinā”š=opposite / hypotenuse |
Cosine (cos) | cosā”š=adjacent / hypotenusetā |
Tangent (tan) | tanā”š=opposite / adjacent |
Cosecant (csc) | cscā”š=1/sinā”š |
Secant (sec) | secā”š=1/cosā”š |
Cotangent (cot) | cotā”š=1/tanā”š |
Pythagorean Identity | sin┲š+²š=1 |
Sine of Sum | sinā”(š+š)=sinā”š cosā”š+cosā”š sinā”š |
Cosine of Sum | cosā”(š+š)=cosā”š cosā”šāsinā”š sinā”š |
Tangent of Sum | tanā”(š+š)=(tanā”š+tanā”š)/ (1ātanā”š tanā”š) |
Sine of Difference | sinā”(šāš)=sinā”š cosā”šācosā”š sinā”š |
Cosine of Difference | cosā”(šāš)=cosā”š cosā”š+sinā”š sinā”š |
Tangent of Difference | tanā”(šāš)= (tanā”šātanā”š) / (1+tanā”š tanā”š)ā |
Double Angle for Sine | sinā”2š=2sinā”š cosā”š |
Double Angle for Cosine | cosā”2š=cos┲šāsin┲šc |
Double Angle for Tangent | tanā”2š=2tanā”š1ātanā”2štā |
Half-Angle for Sine | sinā”š/2=±ā 1ācosā”š/2āā |
Half-Angle for Cosine | cosā”š/2=±ā 1+cosā”š/2āā |
Half-Angle for Tangent | tanā”š/2=±ā 1ācosā”š / 1+cosā”šāā |
A fraction represents a numerical value expressed as the quotient of two integers. The top number, called the numerator, indicates how many parts of the whole are being considered, while the bottom number, the denominator, denotes the total number of equal parts that make up the whole.
(a + b/c) = [(a Ć c) + b]/c
(a/b + d/b) = (a + d)/b
(a/b + c/d) = (a Ć d + b Ć c)/(b Ć d)
a/b Ć c/d = ac/bd
(a/b)/(c/d) = a/b Ć d/c
A percentage represents a ratio or a numerical value expressed as a part of 100. It is commonly denoted by the ā%ā symbol.
Percentage = (Given Value/Total Value) Ć 100
Using math formulas efficiently requires understanding and practice. Here are some tips to help you make the most of them:
Understanding: Ensure you understand the concepts behind the formula. Knowing how and why a formula works will help you apply it correctly and recognize when itās applicable.
Practice: Practice applying the formula to different problems. This builds familiarity and confidence, making it easier to recall and use the formula when needed.
Memorization: Some formulas are fundamental and are worth committing to memory. Flashcards or repetitive practice can help with this.
Visualization: Visualize what the formula represents geometrically or conceptually. This can aid in understanding and recalling the formula.
Analogies: Relate new formulas to ones you already know. Drawing parallels can help you grasp new concepts faster.
Context: Understand the context in which the formula is used. This helps you identify when to apply it and when alternative approaches might be more appropriate.
Application: Look for opportunities to apply the formula in real-world scenarios or in solving problems. Practical application reinforces learning and understanding.
Derivation: If possible, try to understand how the formula is derived. This deepens your understanding and can help you generalize the formula to different situations.
Simplify: Break down complex formulas into smaller parts or terms. Understanding each component separately can make the overall formula more manageable.
Review: Regularly review formulas to keep them fresh in your memory. This prevents forgetting and ensures you can recall them when needed.
Resources: Use textbooks, online resources, or educational videos to supplement your learning. Different explanations or perspectives can sometimes clarify concepts.
Seek Help: Donāt hesitate to seek help if youāre struggling with a particular formula. Teachers, tutors, or online communities can provide guidance and support.
The best formula to learn math is one thatās fundamental and widely applicable, such as the Pythagorean theorem, which relates to geometry and has real-world applications in areas like engineering and architecture.
A simple and intuitive formula for kids is the area formula for squares and rectangles (Area = length Ć width). Itās easy to understand and apply, making it a foundational concept in early math education.
The most famous formula in math is arguably Eulerās identity: ššš+1=0. It elegantly combines five fundamental mathematical constants (e, Ļ, i, 1, and 0) in a single equation, demonstrating the beauty and interconnectedness of mathematics.
One of the most used formulas in math is the quadratic formula: š„=āšĀ±šĀ²ā4ššĀ²š . Itās vital for solving quadratic equations and has applications in various fields, including physics, engineering, and economics.
The golden rule of algebra is to maintain equality by performing the same operation on both sides of an equation. This ensures that the equation remains balanced and valid, allowing for accurate mathematical manipulation and problem-solving.
Text prompt
Add Tone
10 Examples of Public speaking
20 Examples of Gas lighting
What is the formula for the area of a rectangle?
A = l + w
A = l Ć w
A=lw
A = 2(l + w)
What is the formula for the circumference of a circle?
C=Ļr2
C=2Ļr
C=Ļd
C=2r
What is the quadratic formula?
x=āb±āb2ā4ac2a
x=āb±āb2+4ac2a
x=b±āb2ā4ac2a
x=b±āb2+4ac2a
What is the formula for the volume of a cylinder?
V = Ļr²h
V = Ļrh
V = 2Ļr²h
V = 2Ļrh
What is the formula for the slope of a line?
m=y2+y1x2āx1
m=y2āy1x2āx1
m=y2āy1x2+x1
m=y2+y1x2+x1
What is the formula for the area of a triangle?
A=12b+h
A=bĆh
A=12bĆh
A=12(b+h)
What is the formula for the Pythagorean theorem?
a² + b² = c
a² ā b² = c²
a² + b² = c²
a + b = c²
What is the formula for the area of a circle?
A = 2Ļr
A = Ļr
A = 2Ļr²
A = Ļr²
What is the formula for the distance between two points (xā,yā) and (xā,yā)?
d=ā(x2āx1)2+(y2āy1)2
d=ā(x2+x1)2+(y2+y1)2
d=(x2āx1)2+(y2āy1)2
d=(x2+x1)2+(y2+y1)2
What is the formula for the perimeter of a rectangle?
P = 2(l+w)
P = l Ć w
P = l + w
P = 2l Ć 2w
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