**Maths Formulas **

There are numerous of students who face problems in learning the Mathematical Formulas and especially for the senior students it is very difficult for them to learn **Maths Formulas For Board Exam. **Students might learn the formulas but the problem arises when they are not able to apply Basic & Imp Maths Formula. So we are here to overcome this problem of students as we have given here all the essential formulas for Class 6 To 12. Students may also download the pdf of **Maths Formulas For Board Exam 2018** from the below section of this page.

By going through the given formulas you may get idea about all the formulas and you can easily learn the using techniques as well. We have also structured the details of **Maths Formulas For Board Exam 2018** for the sake of aspirants who will be appearing in borad examination so students are suggested to scroll down the page and gather all significant information which is well maintained by the expertise team unit of resultinbox.com

**Maths Formulas **

**List Of Important Math Formulas** **for 10th Students**

Here we have enlisted below all the Maths Formulas For Board Exam for the students of class 10th, it will be very helpful for the aspirants as by going through it they may get idea about the complete formulas which are used in their studies so students must go through it carefully:

Chapter |
Topics |
Marks |

Algebra | Quadratic Equations, Arithmetic Progressions |
26 |

Geometry | 12 | |

Circles Constructions | 22 | |

Trigonometry | 10 | |

Probability | 12 | |

Coordinate Geometry | 08 | |

Mensuration | 10 | |

Total | 100 |

__Algebra:__

- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (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 = 1212 [(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 = 1212 [(x-y)2 + (y-z)2 + (z-x)2]

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__Powers:__

- amxan = am+n
- aman=am−naman=am−n
- (am)n = amn
- (ambn)p = ampb np
- a-m = 1am1am
- amn=am−−−√namn=amn
- Rules of Zero:
- a1 = a
- a0 = 1
- a*0 = 0
- a is undefined

__Linear Equation:__

- Linear equation in one variable ax + b = 0, x = – −ba−ba
- Quadratic Equation: ax2 + bx + c = 0 x = −b±b2−4ac√2a−b±b2−4ac2a
- Discriminant D = b2 – 4ac

**Math Formulas:**

- When rate of discount is given Discount = MP∗Rate of Discount 100
- Simple Interest = PTR100PTR100 where P = Principal, T = Time in years R = Rate of interest per annum
- Principal = 100∗IR∗T100∗S.IR∗T
- Rate = 100∗IP∗T100∗S.IP∗T
- Time = 100∗IP∗R100∗S.IP∗R
- Principal = Amount – Simple Interest
- Discount = MP – SP

__Probability__

P(E) = Number of outcomes favorable to E

Total Number of Possible Outcomes

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__List Of Important Math Formulas____for 11th and 12th students__

Aspirants who will be appearing for Board examination must be searching for Maths Formulas For Board Exam, the students of class 11th and 12th may get here detailed chapter wise Math Formulas which is well furnished by the team unit of resultinbox.com

__Laws of Indices:__

aᵐ ∙ aⁿ = aᵐ + ⁿ

aᵐ/aⁿ = aᵐ – ⁿ

(iii) (aᵐ)ⁿ = aᵐⁿ

(iv) a = 1 (a ≠ 0).

(v) a-ⁿ = 1/aⁿ

(vi) ⁿ√aᵐ = aᵐ/ⁿ

(vii) (ab)ᵐ = aᵐ ∙ bⁿ.

(viii) (a/b)ᵐ = aᵐ/bⁿ

(ix) If aᵐ = bᵐ (m ≠ 0), then a = b.

(x) If aᵐ = aⁿ then m = n.

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__Surds:__

(i) The surd conjugate of √a + √b (or a + √b) is √a – √b (or a – √b) and conversely.

(ii) If a is rational, √b is a surd and a + √b (or, a – √b) = 0 then a = 0 and b = 0.

(iii) If a and x are rational, √b and √y are surds and a + √b = x + √y then a = x and b = y.

__Complex Numbers:__

(i) The symbol z = (x, y) = x + iy where x, y are real and i = √-1, is called a complex (or, imaginary) quantity;x is called the real part and y, the imaginary part of the complex number z = x + iy.

(ii) If z = x + iy then z = x – iy and conversely; here, z is the complex conjugate of z.

(iii) If z = x+ iy then

(a) mod. z (or, | z | or, | x + iy | ) = + √(x² + y²) and

(b) amp. z (or, arg. z) = Ф = tan−1−1 y/x (-π < Ф ≤ π).

(iv) The modulus – amplitude form of a complex quantity z is

z = r (cosф + i sinф); here, r = | z | and ф = arg. z (-π < Ф <= π).

(v) | z | = | -z | = z ∙ z = √ (x² + y²).

(vi) If x + iy= 0 then x = 0 and y = 0(x,y are real).

(vii) If x + iy = p + iq then x = p and y = q(x, y, p and q all are real).

(viii) i = √-1, i² = -1, i³ = -i, and i⁴ = 1.

(ix) | z₁ + z₂| ≤ | z₁ | + | z₂ |.

(x) | z₁ z₂ | = | z₁ | ∙ | z₂ |.

(xi) | z₁/z₂| = | z₁ |/| z₂ |.

(xii) (a) arg. (z₁ z₂) = arg. z₁ + arg. z₂ + m

(b) arg. (z₁/z₂) = arg. z₁ – arg. z₂ + m where m = 0 or, 2π or, (- 2π).

(xiii) If ω be the imaginary cube root of unity then ω = ½ (- 1 + √3i) or, ω = ½ (-1 – √3i)

(xiv) ω³ = 1 and 1 + ω + ω² = 0

__Variation:__

(i) If x varies directly as y, we write x ∝ y or, x = ky where k is a constant of variation.

(ii) If x varies inversely as y, we write x ∝ 1/y or, x = m ∙ (1/y) where m is a constant of variation.

(iii) If x ∝ y when z is constant and x ∝ z when y is constant then x ∝ yz when both y and z vary.

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__Arithmetical Progression (A.P.):__

(i) The general form of an A. P. is a, a + d, a + 2d, a + 3d,…..

where a is the first term and d, the common difference of the A.P.

(ii) The nth term of the above A.P. is t₀ = a + (n – 1)d.

(iii) The sum of first n terns of the above A.P. is s = n/2 (a + l) = (No. of terms/2)[1st term + last term] or, S = ⁿ/₂ [2a + (n – 1) d]

(iv) The arithmetic mean between two given numbers a and b is (a + b)/2.

(v) 1 + 2 + 3 + …… + n = [n(n + 1)]/2.

(vi) 1² + 2² + 3² +……………. + n² = [n(n+ 1)(2n+ 1)]/6.

(vii) 1³ + 2³ + 3³ + . . . . + n³ = [{n(n + 1)}/2 ]².

__Geometrical Progression (G.P.):__

(i) The general form of a G.P. is a, ar, ar², ar³, . . . . . where a is the first term and r, the common ratio of the G.P.

(ii) The n th term of the above G.P. is t₀ = a.rn−1n−1 .

(iii) The sum of first n terms of the above G.P. is S = a ∙ [(1 – rⁿ)/(1 – r)] when -1 < r < 1

or, S = a ∙ [(rⁿ – 1)/(r – 1) ]when r > 1 or r < -1.

(iv) The geometric mean of two positive numbers a and b is √(ab) or, -√(ab).

(v) a + ar + ar² + ……………. ∞ = a/(1 – r) where (-1 < r < 1).

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**Theory of Quadratic Equation:**

ax² + bx + c = 0 … (1)

(i) Roots of the equation (1) are x = {-b ± √(b² – 4ac)}/2a.

(ii) If α and β be the roots of the equation (1) then,

sum of its roots = α + β = – b/a = – (coefficient of x)/(coefficient of x² );

and product of its roots = αβ = c/a = (Constant term /(Coefficient of x²).

(iii) The quadratic equation whose roots are α and β is

x² – (α + β)x + αβ = 0

i.e. , x² – (sum of the roots) x + product of the roots = 0.

(iv) The expression (b² – 4ac) is called the discriminant of equation (1).

(v) If a, b, c are real and rational then the roots of equation (1) are

(a) real and distinct when b² – 4ac > 0;

(b) real and equal when b² – 4ac = 0;

(c) imaginary when b² – 4ac < 0;

(d) rational when b²- 4ac is a perfect square and

(e) irrational when b² – 4ac is not a perfect square.

(vi) If α + iβ be one root of equation (1) then its other root will be conjugate complex quantity α – iβ and conversely (a, b, c are real).

(vii) If α + √β be one root of equation (1) then its other root will be conjugate irrational quantity α – √β (a, b, c are rational).

__Permutation:__

(i) ⌊n (or, n!) = n (n – 1) (n – 2) ∙∙∙∙∙∙∙∙∙ 3∙2∙1.

(ii) 0! = 1.

(iii) Number of permutations of n different things taken r ( ≤ n) at a time ⁿP₀ = n!/(n – 1)! = n (n – 1)(n – 2) ∙∙∙∙∙∙∙∙ (n – r + 1).

(iv) Number of permutations of n different things taken all at a time = ⁿP₀ = n!.

(v) Number of permutations of n things taken all at a time in which p things are alike of a first kind, q things are alike of a second kind, r things are alike of a third kind and the rest are all different, is ⁿ<span style=’font-size: 50%’>!/₀

(vi) Number of permutations of n different things taken r at a time when each thing may be repeated upto r times in any permutation, is nʳ .

__Combination__:

(i) Number of combinations of n different things taken r at a time = ⁿCr = n!r!(n−r)!n!r!(n−r)!

(ii) ⁿP₀ = r!∙ ⁿC₀.

(iii) ⁿC₀ = ⁿCn = 1.

(iv) ⁿCr = ⁿCn – r.

(v) ⁿCr + ⁿCn – 1 = n+1n+1Crr

(vi) If p ≠ q and ⁿCp = ⁿCq then p + q = n.

(vii) ⁿCr/ⁿCr – 1 = (n – r + 1)/r.

(viii) The total number of combinations of n different things taken any number at a time = ⁿC₁ + ⁿC₂ + ⁿC₃ + …………. + ⁿC₀ = 2ⁿ – 1.

(ix) The total number of combinations of (p + q + r + . . . .) things of which p things are alike of a first kind, q things are alike of a second kind r things are alike of a third kind and so on, taken any number at a time is [(p + 1) (q + 1) (r + 1) . . . . ] – 1.

__Binomial Theorem:__

(i) Statement of Binomial Theorem : If n is a positive integer then

(a + x)n = an + nC1 an – 1 x + nC2 an – 2 x2 + …………….. + nCr an – r xr + ………….. + xn …….. (1)

(ii) If n is not a positive integer then

(1 + x)n = 1 + nx + [n(n – 1)/2!] x2 + [n(n – 1)(n – 2)/3!] x3 + ………… + [{n(n-1)(n-2)………..(n-r+1)}/r!] xr+ ……………. ∞ (-1 < x < 1) ………….(2)

(iii) The general term of the expansion (1) is (r+ 1)th term

= tr + 1 = nCr an – r xr

(iv) The general term of the expansion (2) is (r + 1) th term

= tr + 1 = [{n(n – 1)(n – 2)….(n – r + l)}/r!] ∙ xr.

(v) There is one middle term is the expansion ( 1 ) when n is even and it is (n/2 + 1)th term ; the expansion ( I ) will have two middle terms when n is odd and they are the {(n – 1)/2 + 1} th and {(n – 1)/2 + 1} th terms.

(vi) (1 – x)-1 = 1 + x + x2 + x3 + ………………….∞.

(vii) (1 + x)-1 = I – x + x2 – x3 + ……………∞.

(viii) (1 – x)-2 = 1 + 2x + 3×2 + 4×3 + . . . . ∞ .

(ix) (1 + x)-2 = 1 – 2x + 3×2 – 4×3 + . . . . ∞ .

__Logarithm:__

(i) If ax = M then loga M = x and conversely.

(ii) loga 1 = 0.

(iii) loga a = 1.

(iv) a logam = M.

(v) loga MN = loga M + loga N.

(vi) loga (M/N) = loga M – loga N.

(vii) loga Mn = n loga M.

(viii) loga M = logb M x loga b.

(ix) logb a x 1oga b = 1.

(x) logb a = 1/logb a.

(xi) logb M = logb M/loga b.

__Exponential Series:__

(i) For all x, ex = 1 + x/1! + x2/2! + x3/3! + …………… + xr/r! + ………….. ∞.

(ii) e = 1 + 1/1! + 1/2! + 1/3! + ………………….. ∞.

(iii) 2 < e < 3; e = 2.718282 (correct to six decimal places).

(iv) ax = 1 + (loge a) x + [(loge a)2/2!] ∙ x2 + [(loge a)3/3!] ∙ x3 + …………….. ∞.

__Logarithmic Series:__

(i) loge (1 + x) = x – x2/2 + x3/3 – ……………… ∞ (-1 < x ≤ 1).

(ii) loge (1 – x) = – x – x2/ 2 – x3/3 – ………….. ∞ (- 1 ≤ x < 1).

(iii) ½ loge [(1 + x)/(1 – x)] = x + x3/3 + x5/5 + ……………… ∞ (-1 < x < 1).

(iv) loge 2 = 1 – 1/2 + 1/3 – 1/4 + ………………… ∞.

(v) log10 m = µ loge m where µ = 1/loge 10 = 0.4342945 and m is a positive number.

**Basic formulas for Class 6th students**

These are the basic are formulas which are used in the studies of class 6th, students who are studying in class 6th me check the below given basic and useful formulas, we have also given details Maths Formulas For Board Exam for different classes for the ease of aspirants:

perimeter of a square | P = 4 × S |

area of a square | A = S² |

perimeter of a rectangle | P = 2×L⁺2×W |

area of a rectangle | A = L×W |

circumference of a circle (use when you know the radius | C = 2 ¶ R |

circumference of a circle (use when you know the diameter) | C = ¶ × D |

radius | D ÷ 2 |

diameter | 2 × R |

area of a circle | A = ¶ × R² |

area of a parallelogram | A = B ×H |

area of a triangle 1 | A = B × H ÷ 2 |

area of a triangle 2 | A = ½ × B × H |

volume of a rectangular prism | V = L × W × H |

** ****Mathematics Formula Chart for 7th and 8th Grade students**

Rule of Proportion Formula:
- Addition: ab+cd=ad+bcbdab+cd=ad+bcbd
- Subtraction: ab−cd=ad−bcbdab−cd=ad−bcbd
- Multiplication: ab=cdab=cd, then a*d = c*b
- Division: abcd=adbcabcd=adbc
When rate of discount is given Discount =MP∗Rate ofDiscount100MP∗Rate ofDiscount100 Simple Interest = PTR100PTR100 where P = Principal , T = Time in years R = Rate of interest per annum - Principal = 100∗S.IR∗T100∗S.IR∗T
- Rate = 100∗S.IP∗T100∗S.IP∗T
- Time = 100∗S.IP∗R100∗S.IP∗R
- Principal = Amount- Simple Interest
- Discount = MP-SP
1. AnB = BnA 2. AuB = BuA
1. (AnB)nC= An(BnC) 2. (AuB)uC= Au(Buc)
1.(x+a) (x+b) = x2+x(a+b)+(ab) 2.(a+b)2 = a2+2ab+b2 3.(a-b)2 = a2-2ab+b2 4.(a2-b2) = (a+b) (a-b)
- Commutative law: a*b = b*a
- Associative law: a*(b*c) = (b*c)*a = (c*a)*b
- Distributive law: a(b+c) = ab+ac
Diameter of a circle d = 2r , where r is radius Circumference of a circle C = 2pr , when radius is given Relation between circumference and diameter is C = pd
Area of a circle = pr2 , where r is the radius Area of rectangle = l*b ,where l is length and b is breadth Total surface area of cube = 6a2 sq.units Total surface area of cuboid = 2[lb+bh+hl] sq.units
Volume of cube = l3 Volume of Sphere =(4/3) × p × r3 p: 3.14,r: radius of sphere Volume of a cylinder: p × r2 × h p: 3.14, r: radius of the circle of the base, h: height of the cylinder
Perimeter of square : 4s , s is sides of square Perimeter of Rectangle : 2(l+w), l is length and w is width of rectangle
1 year : 52 Weeks 1 week : 7 Days 1 day : 24 Hours 1 Hour : 60 Minutes 1 Minute : 60 Seconds
1 liter = 1000 milliliters
1 gallon = 4 quarts 1 gallon = 128 fluid ounces 1 quart = 2pints 1 pint = 2 cups 1 cup = 8 fluid ounces |

** ****Algebraic Identities For Class 9**

Students of class 9th might get difficulty in learning the algebraic identities , so below we have provided all the useful Algebraic Identities for class 9 students, so students must check these thoroughly:

- (a+b)2=a2+2ab+b2
- (a−b)2=a2−2ab+b2
- (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=12[(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=12[(x−y)2+(y−z)2+(z−x)2]

__Important View__:

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