Class 9 Maths Formulas &amp; Calculators

Square of a Sum

\((a+b)^2=a^2+2ab+b^2\)

Expand the square of a binomial.

Square of a Difference

\((a-b)^2=a^2-2ab+b^2\)

Expand the square of a difference.

Difference of Squares

\(a^2-b^2=(a-b)(a+b)\)

Factor a difference of two squares.

Product Identity

\((x+a)(x+b)=x^2+(a+b)x+ab\)

Expand two linear factors.

Linear Equation

ax+b=c\Rightarrow x=\frac{c-b}{a}

Solve an equation in one variable when a ≠ 0.

Exponent Product

a^m a^n=a^{m+n}

Same base: add exponents.

Exponent Quotient

\frac{a^m}{a^n}=a^{m-n}

Same nonzero base: subtract exponents.

Power of a Power

(a^m)^n=a^{mn}

Multiply exponents.

Learn formula →Geometry

Trapezium Area

A=\frac12(a+b)h

Average of parallel sides times perpendicular height.

Rhombus Area

A=\frac12d_1d_2

Half product of diagonals.

Cylinder Volume

V=\pi r^2h

Circular base area times height.

Cylinder Curved Surface Area

CSA=2\pi rh

Area of curved part of a right circular cylinder.

Cone Volume

V=\frac13\pi r^2h

One third of matching cylinder volume.

Sphere Volume

V=\frac43\pi r^3

Volume of a sphere.

Sphere Surface Area

S=4\pi r^2

Surface area of a sphere.

Pythagoras Theorem

\(a^2+b^2=c^2\)

Right triangle legs a,b and hypotenuse c.

Heron Formula

A=\sqrt{s(s-a)(s-b)(s-c)}

Triangle area from sides; s=(a+b+c)/2.

Quadratic Discriminant

\(D=b^2-4ac\)

Determines nature of quadratic roots.

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.

Product of Quadratic Roots

\alpha\beta=\frac ca

Product of roots of ax²+bx+c=0.

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.

Learn formula →Trigonometry

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.

Open calculator →Trigonometry

Cosine Ratio

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

Right triangle definition for acute angle θ.

Open calculator →Trigonometry

Tangent Ratio

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

Right triangle definition when adjacent is nonzero.

Open calculator →Trigonometry

Pythagorean Identity

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

Fundamental identity for all real angles.

Learn formula →Trigonometry

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.