Class 11 Maths Formulas &amp; Calculators

Quadratic Roots

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Find roots of ax²+bx+c=0, a ≠ 0.

Sum of Quadratic Roots

\alpha+\beta=-\frac ba

Sum of roots of ax²+bx+c=0.

Learn formula →Algebra

Product of Quadratic Roots

\alpha\beta=\frac ca

Product of roots of ax²+bx+c=0.

Learn formula →Algebra

Arithmetic Progression nth Term

\(a_n=a+(n-1)d\)

Find the nth term of an arithmetic progression.

Arithmetic Progression Sum

S_n=\frac n2[2a+(n-1)d]

Sum of first n terms of an arithmetic progression.

Distance Between Points

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Distance between two points in a plane.

Midpoint

M=(\frac{x_1+x_2}2,\frac{y_1+y_2}2)

Midpoint of a line segment.

Slope

m=\frac{y_2-y_1}{x_2-x_1}

Rate of change of y with x for nonvertical line.

Section Formula

P=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})

Point dividing segment internally in ratio m:n.

Sine Ratio

\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}

Right triangle definition for acute angle θ.

Cosine Ratio

\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}

Right triangle definition for acute angle θ.

Tangent Ratio

\tan\theta=\frac{\text{opposite}}{\text{adjacent}}

Right triangle definition when adjacent is nonzero.

Pythagorean Identity

\sin^2\theta+\cos^2\theta=1

Fundamental identity for all real angles.

Open calculator →Geometry

Tangent Identity

1+\tan^2\theta=\sec^2\theta

Where tangent and secant are defined.

Learn formula →Geometry

Sector Area

A=\frac{\theta}{360}\pi r^2

Area of circular sector for angle θ in degrees.

Arc Length

s=\frac{\theta}{360}2\pi r

Arc length for central angle θ in degrees.

Median (Odd n)

x_{(n+1)/2}

Central ordered observation for odd sample size.

Mode

\text{mode}=\text{most frequent value}

Most frequent value(s) in data set.

Classical Probability

P(E)=\frac{\text{favourable outcomes}}{\text{equally likely outcomes}}

Valid for equally likely outcomes.

Population Variance

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

Population mean squared deviation.

Population Standard Deviation

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

Square root of population variance.

Geometric Progression nth Term

a_n=ar^{n-1}

Find nth term of geometric sequence.

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.

Permutations

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

Ordered selections of r from n distinct objects.

Combinations

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

Unordered selections of r from n distinct objects.

Binomial General Term

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

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

Sine Rule

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

Relates triangle sides to their opposite angles.

Cosine Rule

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

Find third side using included angle.

Learn formula →Coordinate Geometry

Circle Equation

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

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

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.

Power Rule for Derivatives

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

Differentiate a power of x.

Derivative of Sine

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

Angles in radians.

Derivative of Cosine

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

Angles in radians.

Product Rule

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

Differentiate product of two differentiable functions.

Quotient Rule

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

Differentiate quotient when g ≠ 0.

Chain Rule

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

Differentiate a composition of functions.

Integral Power Rule

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

For n ≠ −1; indefinite integral.

Logarithmic Integral

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

Antiderivative of 1/x for x ≠ 0.

Open calculator →Matrices

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.

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.

Addition Rule

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

Probability of A or B.

Conditional Probability

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

When P(B)>0.

Bayes Theorem

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

Bayes theorem requires P(B)>0.

Degree to Radian

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

Convert angle degrees to radians.