Maths Formulas

Maths is a most difficult subject for some students because solving mathematical problems acquires lots of knowledge and formulas. Maths Formulas allow students for hands-on practice and assist them to score high both in class exam and board exam. You can check List of Important Maths Formulas for Class 6th-12th from here.

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Math Formula shows how things work out with assist of some equations like the equation for force or acceleration. When you understand the logic behind every problem and formulas, solving any kind of maths problem becomes easier. Competitive Exams are filled with Maths where you need Mathematical Formulas.

Maths Formulas

Maths Formulas for Class 6th to 10th:

Maths Formulas for Class 6th:

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Maths Formulas for Class 7th:

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Maths Formulas for Class 8th:

Maths Formulas for Class 9th:

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Maths Formulas for Class 10th:

Linear Equations:

 Pair of Linear Equations in two variables:

• Where a1, b1, c1, a2, b2, and c2 are all real numbers and a12+b12 ≠ 0 & a22 + b22 ≠ 0
• These linear equations can also be represented in graphical form.
• Algebra or algebraic equations

The standard form of Quadratic Equations:

 Algebraic formulae:

• (a+b)2 = a2 + b2 + 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
• (x – a)(x + b) = x2 + (b – a)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 + 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
• x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
• x2 + y2 =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]

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Basic formulas for powers

• pm x pn = pm+n
• {pm}⁄{pn} = pm-n
• (pm)n = pmn
• p-m = 1/pm
• p1 = p
• P0 = 1

Arithmetic Progression (AP)

• If a1, a2, a3, a4, a5, a6,… are the terms of AP and d is the common difference between each term, then we can write the sequence as;
• a, a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term.
• Now, nth term for Arithmetic progression is given as;

Sum of nth term in Arithmetic Progression;

Trigonometry Formulae

• Let a right-angled triangle ABC is right-angled at point B and have ∠θ.
• Sinθ= SideoppositetoangleθHypotenuse=PerpendicularHypotenuse = P/H
• Cosθ = AdjacentsidetoangleθHypotenuse = AdjacentsideHypotenuse = B/H
• Tanθ = SideoppositetoangleθAdjacentsidetoangleθ = P/B
• Sec θ = 1cosθ
• Cot θ = 1tanθ
• Cosec θ = 1sinθ
• Tan θ = SinθCosθ

Other Trigonometric formulas

• sin(900 – θ) = cos θ
• cos(900 – θ) = sin θ
• tan(900 – θ) = cot θ
• cot(900 – θ) = tan θ
• sec(900 – θ) = cosecθ
• cosec(900 – θ) = secθ
• sin2θ + cos2 θ = 1
• sec2 θ = 1 + tan2θ for 00 ≤ θ < 900
• Cosec2 θ = 1 + cot2 θ for 00 ≤ θ ≤ 900

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Circles

• Circumference of the circle = 2 π r
• Area of the circle = π r2
• Area of the sector of angle θ = θ360 X π r2
• Length of an arc of a sector of angle θ = θ360 X 2 π r (r = radius of the circle)
• Surface Area and Volumes

Sphere

• Diameter of sphere = 2r
• Circumference of Sphere = 2 π r
• Surface area of sphere = 4 π r2
• Volume of Cylinder = 4/3 π r2

Cylinder

• Circumference of Cylinder = 2 π r h
• Curved surface area of Cylinder = 2 π r2
• Total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 π r h + 2 π r2
• Volume of Cylinder = π r2 h

Cone

• Slant height of cone(s) = r2+h2−−−−−−√
• Curved surface area of cone = π r s
• Total surface area of cone = π r (s + r)
• Volume of cone = ⅓ π r² h

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Cuboid

• 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
• 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.

Statistics

• The mean of the grouped data can be found by 3 methods.
• Direct Method: x¯ = \(\frac{\sum_{i=1}^{n}fi xi}{\sum_{i=1}^{n}fi}\)

Where fi xi is the sum of observations from value i = 1 to n

And fi is the number of observations from value i = 1 to n

• Assumed mean method : x¯ = a + \(\frac{\sum_{i=1}^{n}fi di}{\sum_{i=1}^{n}fi}\)
• Step deviation method : x¯ = a + \(\frac{\sum_{i=1}^{n}fi ui}{\sum_{i=1}^{n}fi}\) X h

(II) The mode of grouped data;

Mode = l + \(\frac{f1 – f0}{2f1 – f0 – f2}\) X h

(III) The median for a grouped data;

Median = l + (n/2–cff) X h

Maths Formulas Details:

Well here on this page we have provided List of Maths Formulas of Class 6, 7, 8, 9, 10 and shortcuts for Learning Maths Formulas. Now most of the Bank, Government and Private Organizations conduct various competitive exams in order to recruit well talented and deserving aspirants for filing up the vacant positions.

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