During the time of Class 10, you should have a knowledge about the different mathematical formulas. These are essential for the learning of algebra, trigonometry and statistics. It will also help you to prepare for exams and tests.
Basic formulas
Getting to know about basic maths formulas is a crucial part of Class 10 studies. These formulas are not only useful in solving math problems, but they also lay the foundation for other math related fields.
Formulas are a great way to speed up the process of solving mathematical problems. They are also used in practical situations, such as engineering, statistics, medicine, architecture and finance.
One of the most important maths formulas is the mean value formula, which is used to determine the mean value of a given set of numbers. Another important maths formula is the slope formula, which is used to determine the slope of a line connecting two points on a plane.
Maths formulas can be found in various forms, including the simplest of all. Using the aforementioned formulas, students can find the shortest route between two points and the distance between two points. The most important formulas are the ones which lay the foundation for future maths studies.
The basic formulas of maths cover several topics, including probability, probability vs. statistics, geometry, and quadratic equations. These formulas are important because they lay the foundation for high school and college exams.
The best way to learn maths formulas is by practicing. Students should write down formulas and practice solving problems using them. This will allow them to understand the formulas better and also helps them to memorize them. It is also important for students to know the names of important formulas, especially the shortest route.
A list of the most important maths formulas for Class 10 is a good way to start. This will help students understand how to tackle difficult questions in a better way. They will also be able to identify the important ones to focus on when preparing for the exam. This will also allow students to understand which formulas they need to memorize.
To make it easy for students to understand the complexities of maths formulas, Vedantu offers a variety of PDFs for Class 10 Math formulas. These formulas are all available for offline and online access. By taking advantage of this service, students can improve their problem solving skills and prepare for the Class 10 exam in no time.
Trigonometry
Getting acquainted with trigonometry formulas is an important part of class 10 maths. Trigonometry formulas are used for solving different problems and are very useful in various fields. Using these formulas, students can solve questions about height, angles and slopes. They can also determine the speed of celestial bodies. This knowledge is very important for competitive examinations.
Trigonometry is a branch of mathematics that is used to calculate the lengths and angles of a triangle. It also explains the relationship between lengths and angles. It is used in physics, engineering, and astronomy. The trigonometric formulas include ratios, functions, and identities. It is also used in chemistry.
In trigonometry, there are six fundamental trigonometric ratios. They are Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (cot), Secant (sec), and Cosecant (Csc). These formulas are used to calculate the angles and heights of a right-angled triangle. Trigonometric formulas are also used to calculate the lengths of other triangles.
The most important trigonometry formula is the right-angled triangle. The triangle is composed of three sides, a hypotenuse, an opposite side, and an adjacent side. The hypotenuse is the longest side. The opposite side is called the Perpendicular. The length of the hypotenuse is equal to the radius of the unit circle.
Trigonometry formulas are also used to determine the altitude of celestial bodies. They are also used to calculate the distance between a ship and the seashore. They are also used to calculate the sun’s height. They are also used for determining power output at different angles.
Trigonometry is a very challenging chapter. It is essential for students to memorize the formulas. They can use creative ways to memorize the formulas. If students practice the formulas, they will have a deep understanding of the important theorems and formulas. They can also use a calculator to solve the problems.
In trigonometry, there is a constant called periodicity. This constant varies for each of the trigonometric identities. For example, the periodicity constant for tan A = cos A + cos 2 A is tan A = tan 225 deg. It also holds true for cos 45 deg and cos 225 deg.
Algebra
During the maths course, students will come across a number of mathematical equations. Some of them will be complicated and will require a great deal of study to understand. However, there are certain formulas that can help students to solve those problems with ease. These formulas are usually called the Maths Formulas. Luckily, these formulas are easily available and can be downloaded.
The best part about maths formulas is that they can be used by students of all levels. They can help students to solve problems faster and they can also help students to learn more about the subject. For example, they can help students to figure out the formula for the binomial theorem.
Algebra formulas are important for students because they are used in a variety of math topics. They are also helpful in solving problems that involve exponents. These formulas are used to convert the numerator and denominator of an equation from the left to the right side of an expression.
The Binomial Theorem is a well-known mathematical formula that can be used to evaluate large exponents of an algebraic expression with two terms. The formula can also be used to simplify complex expansions.
The Golden Rule of Algebra states that the numerator and denominator can be multiplied by the same number without changing the fraction value. The formula is a good starting point, but rote learning is not enough. The real test is whether students are able to apply the formula to the problems they encounter.
During the class 11 maths course, the concept of permutations is important. Students can use permutations to find different arrangements of r things. This concept is also a good way to prove that the Binomial Theorem is true.
Algebra formulas can be a tricky topic for some students, but they can be made easier by using learning aids and obtaining proper guidance. However, it is still important to understand the concept behind the mathematical formulas. These formulas are a good way to boost your preparation for the exams.
They are also an important component of the theory of partial differential equations. They can be used to derive the logarithmic laws.
Statistics & probability
Using Statistics & Probability Formulas for class 10 can help you understand basic concepts and calculations related to probability. Besides using these formulas to calculate the probability of certain events, they can also be used in the insurance sector.
The basic formula of probability is P(A) = 1 – P(not A). The probability of an event is defined as the number of favourable outcomes divided by the number of total outcomes. Whenever an event is impossible, the probability of that event is zero. However, when it is possible, the probability is higher.
A probability is a mathematical description of the likelihood of an event. It is a number between 0 and 1. The probability of an event is always less than one, while it is greater than one. The probability of an event can extend to infinite sample spaces. It is used in various fields, such as sports, to predict the probability of various outcomes.
It also can be used to create probability-based forecasts. For instance, stockbrokers use probability to calculate the rate of return on client investments. Similarly, doctors use probability to determine the risk of vaccines.
It is also used by meteorologists to calculate weather data. It is also used by insurance companies to calculate the rate of return on client investments. A probability formula for class 9 is prepared by the senior faculty of Physics Wallah. The probability formula for class 10 is also compiled by Vedantu. It covers all the basic concepts and formulas related to probability.
Probability can be learned using Venn diagrams. This helps you learn the concept of probability easily. You can also take an online test to check your knowledge. You can also go over all the examples in the textbook to ensure that you understand the concepts.
You can use the worksheets to learn the concepts. Students can also download the useful educational material in PDF format. This includes concept maps, teacher notes, and flash cards. You can download them free of cost. These can also be used as wallpapers for your mobile. The formula sheets are also very helpful for quick revision.
Real Numbers Important Formulas
S No. | Type of Numbers | Description |
1 | Natural Numbers | N = {1,2,3,4,5 …………….} It is the counting numbers |
2 | Whole Numbers | W= {0,1,2,3,4,5……………} It is the counting numbers + zero |
3 | Integers | All whole numbers, including negative numbers + Positive numbers like -4,-3,-2,-1,0,1,2,3,4,5… so on.
Like whole numbers, integers don’t include fractions or decimals. |
4 | Positive Integers | Z+ = 1,2,3,4,5, …… |
5 | Negative Integers | Z– = -1,-2,-3,-4,-5, …… |
6 | Rational Numbers | A number is called rational if it can be expressed in the form of p/q where p and q are integers (q> 0). For example, P/q, ⅘. |
7 | Irrational Number | A number is called irrational if it cannot be expressed in the form of p/q where p and q are integers (q> 0). For example, √3. |
8 | Real Numbers | A real number is a number that can be found on the number line. Real Numbers are the numbers that we normally use and apply in real-world applications. Real numbers include Natural Numbers, Integers, Whole Numbers, Rational Numbers, Fractions, and Irrational Numbers. |
ALGEBRAIC FORMULAS
OTHER TRIGONOMETRIC FORMULAS
- sin(90° – θ) = cos θ
- cos(90° – θ) = sin θ
- tan(90° – θ) = cot θ
- cot(90° – θ) = tan θ
- sec(90° – θ) = cosecθ
- cosec(90° – θ) = secθ
- sin2θ + cos2 θ = 1
- sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
- Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Angle | 0° | 30° | 45° | 60° | 90° |
Sinθ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
Cosθ | 1 | √3/2 | 1/√2 | ½ | 0 |
Tanθ | 0 | 1/√3 | 1 | √3 | Undefined |
Cotθ | Undefined | √3 | 1 | 1/√3 | 0 |
Secθ | 1 | 2/√3 | √2 | 2 | Undefined |
Cosecθ | Undefined | 2 | √2 | 2/√3 | 1 |
CIRCLES FORMULAS
- Circumference of the circle = 2 π r
- Area of the circle = π r2
- Area of the sector of angle θ = (θ/360) × π r2
- Length of an arc of a sector of angle θ = (θ/360) × 2 π r
(r = radius of the circle)
SPHERE FORMULAS
Diameter of sphere | 2r |
Surface area of sphere | 4 π r2 |
Volume of Sphere | 4/3 π r3 |
CYLINDER FORMULAS
Curved surface area of Cylinder | 2 πrh |
Area of two circular bases | 2 πr2 |
Total surface area of Cylinder | Curved surface area of Cylinder + Area of Circular bases = 2 πrh + 2 πr2 |
Volume of Cylinder | π r2 h |
CONE FORMULAS
Slant height of cone | l = √(r2 + h2) |
Curved surface area of cone | πrl |
Total surface area of cone | πr (l + r) |
Volume of cone | ⅓ π r2 h |
- Cuboid Formulas
Perimeter of cuboid | 4(l + b +h) |
Length of the longest diagonal of a cuboid | √(l2 + b2 + h2) |
Total surface area of cuboid | 2(l×b + b×h + l×h) |
Volume of Cuboid | l × b × h |
Here, l = length, b = breadth and h = height. In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes.