Class 7 Maths Formulas &amp; Calculators

Square Area

\(A=a^2\)

Area enclosed by a square.

Fraction of a Quantity

\frac{a}{b}\times N

Find a fractional part of a whole number.

Fraction Addition

\frac ab+\frac cd=\frac{ad+bc}{bd}

Add two fractions using a common denominator.

Fraction Multiplication

\frac ab\times\frac cd=\frac{ac}{bd}

Multiply the numerators and denominators.

Average (Mean)

\bar x=\frac{\sum x_i}{n}

Add values and divide by number of values.

Percentage

p=\frac{\text{part}}{\text{whole}}\times100

Express part of a whole out of one hundred.

Percent of a Number

x\times\frac{p}{100}

Calculate a given percentage of a number.

Ratio Simplification

a:b=\frac{a}{g}:\frac{b}{g}

Divide both terms by their greatest common divisor.

HCF of Two Integers

\operatorname{HCF}(a,b)

Greatest positive integer dividing both integers.

LCM of Two Integers

\operatorname{LCM}(a,b)=\frac{|ab|}{\operatorname{HCF}(a,b)}

Smallest nonnegative common multiple; both nonzero for positive LCM.

Triangle Area

A=\frac12 bh

Half the product of base and perpendicular height.

Parallelogram Area

\(A=bh\)

Base times perpendicular height.

Circle Circumference

C=2\pi r

Distance around a circle of radius r.

Circle Area

A=\pi r^2

Area inside a circle of radius r.

Simple Interest

SI=\frac{PRT}{100}

Interest on principal P at annual rate R% for T years.

Profit

\text{Profit}=SP-CP

Selling price minus cost price.

Profit Percentage

\frac{SP-CP}{CP}\times100

Profit relative to cost price; CP must be positive.

Discount

D=\frac{MP\times d}{100}

Discount on marked price at rate d%.

Speed

v=\frac{d}{t}

Speed equals distance divided by elapsed time.

Distance

\(d=vt\)

Distance at constant speed.

Time

t=\frac{d}{v}

Travel time at constant nonzero speed.

Cube Volume

\(V=a^3\)

Volume of a cube with side a.

Cuboid Volume

\(V=lbh\)

Volume of a rectangular box.

Cube Total Surface Area

\(S=6a^2\)

Six equal square faces.

Cuboid Total Surface Area

\(S=2(lb+bh+hl)\)

Sum of areas of six rectangular faces.

Compound Amount

A=P(1+\frac{r}{100})^t

Amount with annual compounding.

Open calculator →Algebra

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.

Open calculator →Algebra

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.