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Class 12 Maths Formulas & Calculators

Browse free Class 12 mathematics formulas, solved examples and working calculators. Indian school maths concepts.

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Population Variance

\sigma^2=\frac{\sum(x_i-\mu)^2}{N}

Population mean squared deviation.

Open calculator →Statistics

Population Standard Deviation

\sigma=\sqrt{\frac{\sum(x_i-\mu)^2}{N}}

Square root of population variance.

Open calculator →Algebra

Geometric Progression nth Term

a_n=ar^{n-1}

Find nth term of geometric sequence.

Open calculator →Algebra

Geometric Progression Sum

S_n=a\frac{r^n-1}{r-1}

Sum of n geometric terms when r ≠ 1; for r=1, S=na.

Open calculator →Algebra

Permutations

{}^nP_r=\frac{n!}{(n-r)!}

Ordered selections of r from n distinct objects.

Open calculator →Algebra

Combinations

{}^nC_r=\frac{n!}{r!(n-r)!}

Unordered selections of r from n distinct objects.

Open calculator →Algebra

Binomial General Term

T_{r+1}={}^{n}C_r a^{n-r}b^r

General term in expansion of (a+b)^n.

Learn formula →Trigonometry

Sine Rule

\frac a{\sin A}=\frac b{\sin B}=\frac c{\sin C}

Relates triangle sides to their opposite angles.

Learn formula →Trigonometry

Cosine Rule

c^2=a^2+b^2-2ab\cos C

Find third side using included angle.

Open calculator →Coordinate Geometry

Circle Equation

\((x-h)^2+(y-k)^2=r^2\)

Circle with centre (h,k) and radius r.

Learn formula →Coordinate Geometry

Straight Line Slope Intercept

\(y=mx+c\)

Line with slope m and y-intercept c.

Learn formula →Coordinate Geometry

Parabola Standard Equation

\(y^2=4ax\)

Right/left opening parabola based on sign of a.

Learn formula →Coordinate Geometry

Ellipse Standard Equation

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

Ellipse centered at origin for a,b>0.

Learn formula →Calculus

Power Rule for Derivatives

\frac{d}{dx}x^n=nx^{n-1}

Differentiate a power of x.

Learn formula →Calculus

Derivative of Sine

\frac{d}{dx}\sin x=\cos x

Angles in radians.

Learn formula →Calculus

Derivative of Cosine

\frac{d}{dx}\cos x=-\sin x

Angles in radians.

Learn formula →Calculus

Product Rule

(fg)\prime=f\prime g+fg\prime

Differentiate product of two differentiable functions.

Learn formula →Calculus

Quotient Rule

(f/g)\prime=\frac{gf\prime-fg\prime}{g^2}

Differentiate quotient when g ≠ 0.

Learn formula →Calculus

Chain Rule

\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}

Differentiate a composition of functions.

Learn formula →Calculus

Integral Power Rule

\int x^n dx=\frac{x^{n+1}}{n+1}+C

For n ≠ −1; indefinite integral.

Learn formula →Calculus

Logarithmic Integral

\int\frac1x dx=\ln|x|+C

Antiderivative of 1/x for x ≠ 0.

Learn formula →Calculus

Fundamental Theorem of Calculus

\int_a^b f(x)dx=F(b)-F(a)

F is an antiderivative of continuous f.

Learn formula →Vectors

Dot Product

\vec a\cdot\vec b=a_1b_1+a_2b_2+a_3b_3

Scalar product of vectors in 3D.

Open calculator →Vectors

Cross Product Magnitude

|\vec a\times\vec b|=|\vec a||\vec b|\sin\theta

Magnitude of vector product.

Learn formula →Vectors

Vector Magnitude

|\vec a|=\sqrt{a_1^2+a_2^2+a_3^2}

Length of 3D vector.

Open calculator →Matrices

2 by 2 Determinant

\det(A)=ad-bc

Determinant of matrix [[a,b],[c,d]].

Open calculator →Matrices

2 by 2 Matrix Inverse

A^{-1}=\frac1{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}

Inverse exists when determinant is not zero.

Learn formula →Probability

Complement Rule

\(P(A^c)=1-P(A)\)

Probability that A does not occur.

Open calculator →Probability

Addition Rule

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Probability of A or B.

Open calculator →Probability

Conditional Probability

P(A|B)=\frac{P(A\cap B)}{P(B)}

When P(B)>0.

Open calculator →Probability

Bayes Theorem

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

Bayes theorem requires P(B)>0.

Open calculator →Trigonometry

Degree to Radian

rad=deg\times\frac\pi{180}

Convert angle degrees to radians.

Open calculator →Trigonometry

Radian to Degree

deg=rad\times\frac{180}\pi

Convert radians to degrees.

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