Top 50 Maths Formulas to Master for JEE Main 2027: Quick Revision Guide

50 Important Maths Formulas for JEE Main

The below-given list of JEE Main Maths formulas 2027 comprises all the main topics like algebra, trigonometry, coordinate geometry, calculus, vectors, 3D geometry, probability and statistics, etc. These Maths formulas for JEE Main 2027 will be handy during preparation.

1. Quadratic Formula:

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

2. Sum & Product of Roots:

$
\alpha+\beta=-\frac{b}{a}, \alpha \beta=\frac{c}{a}
$

3. Condition for Common Roots:

$
\left(a_1 b_2-a_2 b_1\right)\left(b_1 c_2-b_2 c_1\right)=\left(c_1 a_2-c_2 a_1\right)^2
$

4. AP $n$-th Term & Sum:

$
T_n=a+(n-1) d, S_n=\frac{n}{2}[2 a+(n-1) d]
$

5. GP $n$-th Term & Sum:

$
T_n=a r^{n-1}, S_n=\frac{a\left(1-r^n\right)}{1-r}
$

6. Infinite GP Sum:

$
S_{\infty}=\frac{a}{1-r}(|r|<1)
$

7. AM-GM-HM Inequality:

$\frac{a+b}{2} \ge \sqrt{ab} \ge \frac{2ab}{a+b}$

8. Binomial General Term:

$
T_{r+1}=\binom{n}{r} a^{n-r} b^r
$

9. Sum of Binomial Coefficients:

$
\sum_{r=0}^n\binom{n}{r}=2^n
$

10. Logarithmic Base Change:

$
\log _b a=\frac{\log _c a}{\log _c b} \mathrm{~d}
$

11. Euler's Form of Complex Number:

$
z=r(\cos \theta+i \sin \theta)=r e^{i \theta}
$

12. De Moivre's Theorem:

$
(\cos \theta+i \sin \theta)^n=\cos (n \theta)+i \sin (n \theta)
$

13. Matrix Inverse:

$
A^{-1}=\frac{\operatorname{adj}(A)}{|A|}
$

14. Cramer's Rule:

$x = \frac{D_x}{D}, \quad y = \frac{D_y}{D}, \quad z = \frac{D_z}{D} \quad (D \neq 0)$

15. Permutation & Combination:

$
\binom{n}{r}=\frac{P(n, r)}{r!}=\frac{n!}{r!(n-r)!}
$

16. Bayes' Theorem:

$
P\left(A_i \mid B\right)=\frac{P\left(A_i\right) P\left(B \mid A_i\right)}{\sum_{k=1}^n P\left(A_k\right) P\left(B \mid A_k\right)}
$

17. Sine Addition Formula:

$
\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B
$

18. Cosine Addition Formula:

$
\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B
$

19. Double Angle Sine:

$
\sin 2 \theta=2 \sin \theta \cos \theta=\frac{2 \tan \theta}{1+\tan ^2 \theta}
$

20. Double Angle Cosine:

$
\cos 2 \theta=\cos ^2 \theta-\sin ^2 \theta=2 \cos ^2 \theta-1=1-2 \sin ^2 \theta
$

21. Sine Rule:

$
\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2 R
$

22. Cosine Rule:

$
\cos A=\frac{b^2+c^2-a^2}{2 b c}
$

23. Inverse Tan Addition:

$
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right)(x y<1)
$

24. Inverse Identity:

$
\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}
$

25. Distance Formula:

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

26. Section Formula:

$
\left(\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}\right)
$

27. Perpendicular Distance to Line:

$
d=\frac{\left|a x_1+b y_1+c\right|}{\sqrt{a^2+b^2}}
$

28. Angle Between Lines:

$
\tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right|
$

29. Circle Equation:

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

30. Circle Tangent at

$\left(x_1, y_1\right): x x_1+y y_1+g\left(x+x_1\right)+f\left(y+y_1\right)+c=0$
31. Parabola Tangent Line

$\left(y^2=4 a x\right)$

$
y=m x+\frac{a}{m}
$

32. Ellipse Eccentricity:

$
e=\sqrt{1-\frac{b^2}{a^2}}(a>b)
$

33. Hyperbola Eccentricity:

$
e=\sqrt{1+\frac{b^2}{a^2}}
$

34. Standard Trig Limit:

$\lim_{x \to 0} \frac{\sin x}{x} = 1$

35. Standard Exponential Limit:

$\lim_{x \to 0} \frac{e^x - 1}{x} = 1$

36. Product Rule:

$
\frac{d}{d x}[u v]=u \frac{d v}{d x}+v \frac{d u}{d x}
$

37. Quotient Rule:

$
\frac{d}{d x}\left[\frac{u}{v}\right]=\frac{v \frac{d u}{d x}-u \frac{d v}{d x}}{v^2}
$

38. Integration by Parts:

$
\int u d v=u v-\int v d u
$

39. Standard Integral $\left(\frac{1}{x^2+a^2}\right)$ :

$
\int \frac{d x}{x^2+a^2}=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+C
$

40. Standard Integral

$
\left(\frac{1}{\sqrt{a^2-x^2}}\right): \int \frac{d x}{\sqrt{a^2-x^2}}=\sin ^{-1}\left(\frac{x}{a}\right)+C
$

41. King's Property:

$
\int_a^b f(x) d x=\int_a^b f(a+b-x) d x
$

42. Leibniz Rule:

$
\frac{d}{d x} \int_{\phi(x)}^{\psi(x)} f(t) d t=f(\psi(x)) \psi^{\prime}(x)-f(\phi(x)) \phi^{\prime}(x)
$

43. Linear Differential Equation:

$
y \cdot(I F)=\int Q \cdot(I F) d x+\text { CwhereIF }=e^{\int P d x}
$

44. Dot Product:

$
\vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta
$

45. Cross Product Magnitude:

$
|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta
$

46. Scalar Triple Product

$
[\overrightarrow{a b c}]=\vec{a} \cdot(\vec{b} \times \vec{c})
$

47. Vector Projection:

$
\operatorname{proj}_{\vec{b}} \vec{a}=\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}
$

48. Shortest Distance Between Skew Lines:

$
d=\left|\frac{\left(\vec{a}_2-\vec{a}_1\right) \cdot\left(\vec{b}_1 \times \vec{b}_2\right)}{\left|\vec{b}_1 \times \vec{b}_2\right|}\right|
$

49. Distance Between Parallel Planes:

$
d=\frac{\left|d_1-d_2\right|}{\sqrt{a^2+b^2+c^2}}
$

50. Distance from Point to Plane:

$
d=\frac{\left|a x_1+b y_1+c z_1+d\right|}{\sqrt{a^2+b^2+c^2}}
$

How to Utilise Maths Formulas for JEE Main Preparation

Instead of trying to memorise all the important JEE Main Maths formulas in one day, students must revise them chapter-wise and practise questions related to each formula.

1. Create a JEE Main Maths formula sheet: Note down all essential formulas at one place for revision.

2. Maths formulas for JEE Main 2027: Know the meaning of the formula.

3. Practice questions: Practice problems at the JEE Main level after studying each formula.

4. Revision: Dedicate a few minutes daily for revision of the formulas.

5. Previous year questions: Solving the JEE Main previous year questions will give an idea regarding the usage of formulas in JEE Main.

6. Mock tests: JEE Main mock tests help increase speed and knowledge of the formulas.

Also use JEE Mains 2027: Maths Set of 5 Sample Paper with Solution free PDF

Suggestion for Memorising JEE Main Mathematics Formulas

JEE Main Maths formulae will become easier for students to learn by regularly revising and practising them. Rather than memorising all the Maths formulas for the JEE Main exam 2027 in one go, there are some easy ways that will help you to learn them in a quick time.

1. Review formulas consistently rather than only before exams.

2. Categorise formulas according to chapters and subjects.

3. Practice writing down difficult formulas several times for better retention.

4. Learn to use formulas during practice sessions.

5. Use another paper containing formulas that you forget often.

6. Review important formulas before attempting test papers.

7. Learn to use the formula instead of remembering it only.

Also Check: JEE Main 2027 Daily Study Plan