CBSE 12th Maths Important Formulas for Board Exam 2024, Download PDF

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Class 12 Maths Important Formulas PDF: In this article, students can find Class 12 Maths Important Formulas for board exam chapter wise. The list of important formulas for Class 12 Maths CBSE board exam will assist students in last-minute preparation for the exam

CBSE Class 12 Maths Important Formulas for Board Exam 2024:CBSE Class 12 annual board examinations are going on and it has scheduled its Class 12 Maths board exam for March 9, 2024. Since we are standing just two days away from the exam, students might be in dire need of all the important resources to boost their last-minute preparation. As we all know, this is the most important phase of the preparation process, the last-minute revision. Hence, students must wisely utilise this time by reading important and authentic study materials. To help you all in the preparation process, we have brought to you CBSE Class 12 Maths important formulas for board exam 2024 to boost your last-minute preparation. Here, students can find chapter-wise important formulas of Class 12 Maths that are extremely important from the exam’s point of view. Check the last-minute important formulas for Class 12 Maths here.

Important Formulas for CBSE Class 12 Maths Board Exam 2024

Find the chapter-wise list of important formulas for CBSE Class 12 Maths below. Only important and most widely used formulas in the board paper have been presented below. Though students must know all the formulas before they sit for their examination, memorizing the below-mentioned ones are extremely important. We would advise students to not miss out on the following formulas at any cost.

Inverse Trigonometric Class 12 Important Formulas

1. sin^-1x = – sin^-1x

2. cos^-1x = π – cos^-1x

3. tan^-1(-x) = -tan^-1x

4. cosec⁻¹(-x) = -cosec⁻¹x

5. sec^-1(-x) = π – sec^-1x

6. cot^-1(-x) = π – cot^-1x

7. sin^-1x + cos^-1x = π/2

8. tan^-1x + cot^-1x = π/2

9. sec^-1x + cosec^-1x = π/2

10. sin^-1(1/x) = cosec^-1x, if x ≥ 1 or x ≤ -1

11. cos^-1(1/x) = sec^-1x, if x ≥ 1 or x ≤ -1

12. tan^-1(1/x) = cot^-1x, x > 0

13. sin^-1x + cos^-1x = π/2, x ∈ [-1,1]

14. tan^-1x + cot^-1x = π/2, x ∈ R

15. sec^-1x + cosec^-1x = π/2, x ∈ R – [-1,1]

18. 2tan^-1x = sin^-1(2x/1+ x²)

= cos^-1(1-x²/1+x²)

= tan^-1(2x/1-x²)

19. 2sin^-1x = sin^-1(2x.√(1 – x²))

20. 2cos^-1x = cos^-1(2x² – 1)

Matrices Class 12 Important Formulas

1. Matrix Multiplication

AB ≠ BA

(AB)C = A(BC)

(B + C) = A.B + A.C

2. Addition/Subtraction of Matrices

A+B = B+A

(A+B) + C = A + (B+C)

k(A+B) = kA+kB

A + (-A) = 0

3. Scalar Multiplication

k(A+B) = kA+kB

kA = Ak

(k1+k2)A = k1A+k2A

Determinants Class 12 Important Formulas

1. Area of Triangle = (1/2) [x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)]

2. Determinant Expansion Formula–

Differentiation Class 12 Important Formulas

Standard Derivatives-
Standard Limits

Integration Class 12 Important Formulas

Standard Integrals–
Integration By Substitution

(i) ∫tanxdx = log|secx|+ C

(ii) ∫cotxdx = log|sinx|+ C

(iii) ∫secxdx= log|secx + tanx|+ C

(iv) ∫cosecxdx = log|cosecx – cotx|+ C

Three Dimensional Geometry Class 12 Important Formulas

Shortest Distance between Two lines

2. Acute Angle

3. If l, m, n are the direction cosines of a line, then l2+ m2 + n2 = 1

4. If l1, m1 , n1 and l2 , m2 , n2 are the direction cosines of two lines; and θ is the acute angle between the two lines; then cosθ = |l1 l2 + m1m2 + n1 n2 |

5. If a₁, b₁ , c₁ and a₂ , b₂ , c₂ are the direction ratios of two lines and θ is the acute angle between the two lines; then

6. If l, m, n are the direction cosines and a, b, c are the direction ratios of a line then

l = a/√a² + b² + c²;

m = b/√a² + b² + c²

n = c/√a² + b² + c²

Probability Class 12 Important Formulas

Conditional Probability: P(E|F) = P(E ∩ F)/P(F) where P(F) ≠ 0
P ((A U B) |F) =P (A|F)+P (B|F)-P ((A ∩ B)|F)
P(E’|F) = 1 -P(E|F)
Multiplication Theorem on Probability: If E and F are independent, then P (E ∩ F) = P (E) P (F)

For complete list of CBSE Class 12 Maths chapter-wise formulas, theorems, and definitions, check the link below