{"id":297225,"date":"2026-02-26T13:20:47","date_gmt":"2026-02-26T07:50:47","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?p=297225"},"modified":"2026-03-02T11:38:28","modified_gmt":"2026-03-02T06:08:28","slug":"important-maths-formulas-class-12-with-memory-tricks","status":"publish","type":"post","link":"https:\/\/www.aakash.ac.in\/blog\/important-maths-formulas-class-12-with-memory-tricks\/","title":{"rendered":"Important Class 12 Maths Formulas: List with Memory Tricks"},"content":{"rendered":"

There is something different about math. You can\u2019t just read it and expect results. You can\u2019t even rely on practice only. What actually holds everything together are formulas.<\/span><\/p>\n

Every question in the CBSE Class 12 Math question paper comes down to applying a known rule or identity. If your important math formulas are clear, solving becomes smoother. If not, even simple questions feel unfamiliar.<\/p>\n

Since the Class 12 Maths syllabus 2025-26 is quite wide, revision needs to be smart. A well-organised math formula chart makes that easier and keeps you from missing key concepts.<\/p>\n

Class 12 Maths All Formulas Chapter Wise<\/span><\/h2>\n

1. Vector Algebra Formulas:\u00a0<\/span><\/h3>\n

With the right formulas at your fingertips, vector algebra formulas<\/a> becomes easy to handle, as most questions in the CBSE Class 12 Maths paper are straightforward and formula-based.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Concept<\/span><\/td>\nFormula<\/span><\/td>\n<\/tr>\n
Position vector<\/span><\/td>\nOP = \u221a(x\u00b2 + y\u00b2 + z\u00b2)<\/span><\/td>\n<\/tr>\n
Vector relation<\/span><\/td>\nPQ + QR = PR<\/span><\/td>\n<\/tr>\n
Commutative law<\/span><\/td>\nA + B = B + A<\/span><\/td>\n<\/tr>\n
Associative law<\/span><\/td>\nA + (B + C) = (A + B) + C<\/span><\/td>\n<\/tr>\n
Dot product<\/span><\/td>\nA \u00b7 B = |A| |B| cos\u03b8<\/span><\/td>\n<\/tr>\n
Cross product<\/span><\/td>\nA \u00d7 B = |A| |B| sin\u03b8<\/span><\/td>\n<\/tr>\n
Scalar multiplication<\/span><\/td>\nk(A + B) = kA + kB<\/span><\/td>\n<\/tr>\n
Additive identity<\/span><\/td>\nA + 0 = A<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

These are very common basic math formulas. Practice a few questions, and you will get comfortable.<\/span><\/p>\n

2. Trigonometry (Inverse) Formulas:<\/strong>
Though compact in number, inverse trigonometric formulas<\/a> play a crucial role in solving complex problems and are frequently applied in longer questions.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
Type<\/span><\/td>\nMaths Trigonometry Formula<\/span><\/td>\n<\/tr>\n
Negative identity<\/span><\/td>\nsin\u207b\u00b9(\u2212x) = \u2212sin\u207b\u00b9x<\/span><\/td>\n<\/tr>\n
Cos identity<\/span><\/td>\ncos\u207b\u00b9(\u2212x) = \u03c0 \u2212 cos\u207b\u00b9x<\/span><\/td>\n<\/tr>\n
Tan identity<\/span><\/td>\ntan\u207b\u00b9(\u2212x) = \u2212tan\u207b\u00b9x<\/span><\/td>\n<\/tr>\n
Cot identity<\/span><\/td>\ncot\u207b\u00b9(\u2212x) = \u03c0 \u2212 cot\u207b\u00b9x<\/span><\/td>\n<\/tr>\n
Sum identity<\/span><\/td>\nsin\u207b\u00b9x + cos\u207b\u00b9x = \u03c0\/2<\/span><\/td>\n<\/tr>\n
Sum identity<\/span><\/td>\ntan\u207b\u00b9x + cot\u207b\u00b9x = \u03c0\/2<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

These are useful in simplification. You will see them again and again.<\/span><\/p>\n

3. Calculus Formulas:<\/span><\/h3>\n

A strong grasp of calculus formulas is essential for tackling application-based and high-weightage questions, as they form the backbone of differentiation and integration problems.<\/p>\n

This is the most important part of the <\/span>CBSE Class 12 math question paper.<\/b> Most marks come from here.<\/span><\/p>\n

Basic Integration Formulas<\/span><\/p>\n\n\n\n\n\n\n\n\n
Type<\/span><\/td>\nImportant Math Formulas<\/span><\/td>\n<\/tr>\n
Power rule<\/span><\/td>\n\u222b x\u207f dx = x\u207f\u207a\u00b9 \/ (n+1) + C<\/span><\/td>\n<\/tr>\n
Exponential<\/span><\/td>\n\u222b e\u02e3 dx = e\u02e3 + C<\/span><\/td>\n<\/tr>\n
General exponential<\/span><\/td>\n\u222b a\u02e3 dx = a\u02e3 \/ ln(a) + C<\/span><\/td>\n<\/tr>\n
Log function<\/span><\/td>\n\u222b ln(x) dx = x ln(x) \u2212 x + C<\/span><\/td>\n<\/tr>\n
Reciprocal<\/span><\/td>\n\u222b (1\/x) dx = ln|x| + C<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Trigonometric Integration:<\/span><\/h3>\n

Mastering standard trigonometric integrals and identities<\/a> makes complex integration problems simpler, as these concepts are widely used in lengthy and application-based questions.<\/p>\n\n\n\n\n\n\n\n\n\n
Formula<\/span><\/td>\n<\/tr>\n
\u222b sin x dx = \u2212cos x + C<\/span><\/td>\n<\/tr>\n
\u222b cos x dx = sin x + C<\/span><\/td>\n<\/tr>\n
\u222b sec\u00b2x dx = tan x + C<\/span><\/td>\n<\/tr>\n
\u222b cosec\u00b2x dx = \u2212cot x + C<\/span><\/td>\n<\/tr>\n
\u222b sec x tan x dx = sec x + C<\/span><\/td>\n<\/tr>\n
\u222b cosec x cot x dx = \u2212cosec x + C<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Rules of Integration:<\/span><\/h3>\n

Understanding and applying the basic rules of integration<\/a> correctly helps simplify lengthy expressions and ensures accurate solutions to a wide range of calculus problems.<\/p>\n\n\n\n\n\n\n\n
Rule<\/span><\/td>\nFormula<\/span><\/td>\n<\/tr>\n
Sum rule<\/span><\/td>\n\u222b(f+g)dx = \u222bf dx + \u222bg dx<\/span><\/td>\n<\/tr>\n
Difference rule<\/span><\/td>\n\u222b(f\u2212g)dx = \u222bf dx \u2212 \u222bg dx<\/span><\/td>\n<\/tr>\n
Constant multiple<\/span><\/td>\n\u222bk f(x)dx = k\u222bf(x)dx<\/span><\/td>\n<\/tr>\n
Constant rule<\/span><\/td>\n\u222ba dx = ax + C<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Special Case<\/span><\/h3>\n\n\n\n\n
Concept<\/span><\/td>\nFormula<\/span><\/td>\n<\/tr>\n
Integration by parts<\/span><\/td>\n\u222bf(x)g(x) dx = f(x)\u222bg(x)dx \u2212 \u222b[f\u2019(x)\u222bg(x)dx]dx<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

If you practice these properly, calculus becomes manageable.<\/span><\/p>\n

4. Probability Formulas:<\/span><\/h3>\n

Clear knowledge of probability formulas<\/a> helps in solving numerical and case-based questions quickly, as most problems are based on direct application.<\/p>\n

This<\/span> Class 12 maths chapter<\/b> is short and scoring.<\/span><\/p>\n\n\n\n\n\n
Concept<\/span><\/td>\nFormula<\/span><\/td>\n<\/tr>\n
Conditional probability<\/span><\/td>\nP(A|B) = P(A \u2229 B) \/ P(B)<\/span><\/td>\n<\/tr>\n
Multiplication theorem<\/span><\/td>\nP(A \u2229 B) = P(A) P(B|A)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Most questions are direct, so do not skip this.<\/span><\/p>\n

5. Three-Dimensional Geometry Formulas:<\/span><\/h3>\n

Knowing the standard 3D geometry formulas<\/a> makes it easier to handle coordinate-based and application-oriented questions, as most problems rely on direct use of distance, angle, and plane equations.<\/p>\n

This part is also very direct. If formulas are clear, questions seem easy.<\/span><\/p>\n\n\n\n\n\n
Concept<\/span><\/td>\nFormula<\/span><\/td>\n<\/tr>\n
Plane equation<\/span><\/td>\nlx + my + nz = d<\/span><\/td>\n<\/tr>\n
Distance between two points<\/span><\/td>\n\u221a[(x\u2081\u2212x\u2082)\u00b2 + (y\u2081\u2212y\u2082)\u00b2 + (z\u2081\u2212z\u2082)\u00b2]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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