Fundamental OF Mathematics formulas

Every formula JEE Advanced expects you to know for Fundamental OF Mathematics, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 243 practice questions

Formulas: 30
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Fundamental OF Mathematics, every formula

30 formulas, typeset and free. Print it, or keep it open beside your practice.

Number sets hierarchy
$N \subset W \subset Z \subset Q \subset R$
Closed interval
$[a, b] = {x : a \leq x \leq b}$
Open interval
$(a, b) = {x : a < x < b}$
Modulus definition
$∣ x ∣ = {x - x x \geq 0 x < 0$
|x|<a
$∣ x ∣ < a \Leftrightarrow - a < x < a (a > 0)$
|x|>a
$∣ x ∣ > a \Leftrightarrow x < - a or x > a$
Triangle inequality
$∣ x + y ∣ \leq ∣ x ∣ + ∣ y ∣$
Product/quotient of modulus
$∣ x y ∣ = ∣ x ∣∣ y ∣, \frac{x}{y} = \frac{∣ x ∣}{∣ y ∣}$
Laws of exponents
$a^{m} \cdot a^{n} = a^{m + n}, \frac{a ^{m}}{a ^{n}} = a^{m - n}$
Power of a power
$(a^{m})^{n} = a^{mn}$
Zero & negative exponent
$a^{0} = 1, a^{- n} = \frac{1}{a ^{n}}$
Fractional exponent
$a^{m / n} = n a^{m}$
Rationalizing a surd
$\frac{1}{a + b} = \frac{a - b}{a - b}$
(a±b)²
$(a \pm b)^{2} = a^{2} \pm 2 ab + b^{2}$
Difference of squares
$a^{2} - b^{2} = (a - b) (a + b)$
(a±b)³
$(a \pm b)^{3} = a^{3} \pm 3 a^{2} b + 3 a b^{2} \pm b^{3}$
Sum/difference of cubes
$a^{3} \pm b^{3} = (a \pm b) (a^{2} \mp ab + b^{2})$
a³+b³+c³−3abc
$a^{3} + b^{3} + c^{3} - 3 ab c = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a)$
Logarithm definition
$lo g_{a} x = y \Leftrightarrow a^{y} = x, a > 0, a \neq = 1$
Log product/quotient
$lo g (mn) = lo g m + lo g n, lo g \frac{m}{n} = lo g m - lo g n$
Log power & base change
$lo g_{a} m^{n} = n lo g_{a} m, lo g_{a} m = \frac{lo g _{b} m}{lo g _{b} a}$
Componendo–dividendo
$\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a + b}{a - b} = \frac{c + d}{c - d}$
Quadratic roots
$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
Discriminant
$D = b^{2} - 4 a c$
D>0 real distinct, =0 equal, <0 complex
Sign of a quadratic
$a > 0, D < 0 \Rightarrow a x^{2} + b x + c > 0 \forall x$
Wavy-curve (sign scheme)
$mark roots, alternate signs from the rightmost +$
AM ≥ GM
$\frac{a + b}{2} \geq ab$
a,b>0
Factorial
$n! = 1 \cdot 2 \dots n, 0! = 1$
Remainder theorem
$f (x) \div (x - a) leaves remainder f (a)$
Factor theorem
$(x - a) is a factor \Leftrightarrow f (a) = 0$

Know the Fundamental OF Mathematics formulas. Now use them.

Formulas only stick when you apply them under time. Adaptive practice picks the concept you keep dropping marks on.

Create a free account All formula sheets

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Fundamental OF Mathematics formulas

Fundamental OF Mathematics, every formula

Number sets hierarchy

Closed interval

Open interval

Modulus definition

|x|<a

|x|>a

Triangle inequality

Product/quotient of modulus

Laws of exponents

Power of a power

Zero & negative exponent

Fractional exponent

Rationalizing a surd

(a±b)²

Difference of squares

(a±b)³

Sum/difference of cubes

a³+b³+c³−3abc

Logarithm definition

Log product/quotient

Log power & base change

Componendo–dividendo

Quadratic roots

Discriminant

Sign of a quadratic

Wavy-curve (sign scheme)

AM ≥ GM

Factorial

Remainder theorem

Factor theorem

More JEE Advanced Mathematics formula sheets

Know the Fundamental OF Mathematics formulas. Now use them.

Join QuestPix, Today!