Table of Contents
- Math formulas for class 10 | Ace your exams with these formulas
- Class 10 maths formulas for linear equations
- Class 10 Maths Formulas For Algebra & Quadratic Equations
- Class 10 maths formulas for circles
- Trigonometry formulas for class 10 maths
- Surface area and volume formulas for class 10
- Key takeaways
Math formulas for class 10 | Ace your exams with these formulas
Class 10 maths formulas for linear equations
|Linear equations in one, two, and three variables have the following forms:|
Linear Equation in one Variable ax + b=0 Where a ≠ 0 and a & b are real numbers
Linear Equation in Two Variables ax + by + c = 0 Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers
Linear Equation in Three Variables ax + by + cz + d = 0 Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers
The pair of linear equations in two variables are given as:
a1x+b1+c1=0 and a2x+b2+c2=0
Where a1, b1, c1, & a2, b2, c2 are real numbers & a12+b12 ≠ 0 & a22 + b22 ≠ 0
Quick Note: Linear equations can also be represented in graphical form.
Class 10 Maths Formulas For Algebra & Quadratic Equations
|To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.|
The Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by:
Now you know the basic quadratic equation.
Let us now go through the list of algebra formulas for Class 10–
(a+b ) = a+ b22 + 2ab
(a-b)2 = a2 + b2– 2ab
(a+b) (a-b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(a +b)3 = a3+ b3 + 3ab(a + b)
(a-b)3 = a3 – b3 – 3ab(a – b)
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(x + y +z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2– 2xy + 2yz – 2xz
x2 + y2 + z2 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
y2 + z2 =½ [(x +y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
(x3 + y3= (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
Quick Note: These formulas will be important in higher classes and various competitive examinations. So, memorize them and understand them well.
Class 10 maths formulas for circles
|Circle formulas act as a base for Mensuration. |
The Class 10 Maths Circle formulas for a circle of radius r are given below:
1. Circumference of the circle = 2 π r2. Area of the circle = π r23. Area of the sector of angle θ = (θ/360) × π r24. Length of an arc of a sector of angle θ = (θ/360) × 2 π r
Trigonometry formulas for class 10 maths
|The Trigonometry Formulas for Class 10 covers the basic trigonometric functions for a right-angled triangle i.e. Sine (sin), Cosine (cos), and Tangent (tan) which can be used to derive Cosecant (cos), Secant (sec), and Cotangent (cot).|
Let a right-angled triangle ABC is right-angled at point B and have is one of the other two angles.
|The Trigonometric Table comprising the values of these trigonometric functions for standard angles is as under:|
|Some other trigonometric formulas are given below–|
sin (90° – θ) = cos θcos (90° – θ) = sin θtan (90° – θ) = cot θcot (90° – θ) = tan θsec (90° – θ) = cosecθcosec (90° – θ) = secθsin2θ + cos2 θ = 1sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
Surface area and volume formulas for class 10
|Diameter of sphere||2r|
|Surface area of sphere||4 π r2|
|Volume of Sphere||4/3 π r3|
|Curved surface area of Cylinder||2 πrh|
|Area of two circular bases||2 π r2|
|Total surface area of Cylinder||Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 π r2|
|Volume of Cylinder||π r2 h|
|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|
|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|
- Due to the huge number of Math formulas, most students are terrified of mathematics.
- However, mathematics involves more than just memorizing facts from textbooks; it is also about solving and comprehending issues.
- Learning or understanding mathematics formulas is the most effective technique to make this topic enjoyable.
- As a result, mastering math formulae will help kids build confidence and improve their problem-solving abilities.
- It is critical to understand the method behind a certain formula since it aids in memorizing the formulas.
- We all know, practice makes perfect. As a result, constantly solving problems by repeating math formulas for repetition leads to memorization.
- Since our brain remembers what we write regularly, writing math formulas repeatedly might help you recall them for a longer period. So, make a habit of writing down difficult formulas.
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Q1. What is the world’s longest equation?
Answer – The Boolean Pythagorean Triples issue was initially introduced in the 1980s by California-based mathematician Ronald Graham is the longest arithmetic equation, according to Sciencealert, and includes roughly 200 gigabytes of text.
Q2. How many formulas are there in class 10 math?
Answer – Real numbers, polynomials, quadratic equations, triangles, circles, statistics, probability, and other topics are covered in class 10 math formulas.
Q3. How do you remember formulas?
Answer – You get flawless with practice. When you practice using the formulae, your brain understands and retains the application of the formula. You will notice results if you solve and practice problems by memorizing and applying the formulas.