Certainly! Class 12 mathematics covers a wide range of topics. Here are some important formulas that you might encounter in Class 12:

1. **Quadratic Formula**:

The solutions of the quadratic equation ax^2 + bx + c = 0, where a ≠ 0, are given by:

x = (-b ± √(b^2 – 4ac)) / 2a

2. **Arithmetic Progression (AP)**:

The nth term of an AP is given by:

a_n = a + (n-1)d

The sum of the first n terms of an AP is given by:

S_n = (n/2) * (a + l), where ‘a’ is the first term, ‘l’ is the last term, and ‘n’ is the number of terms.

3. **Geometric Progression (GP)**:

The nth term of a GP is given by:

a_n = a * r^(n-1)

The sum of the first n terms of a GP (if |r| < 1) is given by:

S_n = a / (1 – r), where ‘a’ is the first term and ‘r’ is the common ratio.

4. **Trigonometric Ratios**:

In a right-angled triangle with sides ‘a’, ‘b’, and hypotenuse ‘c’, and an angle ‘θ’:

sin(θ) = a / c

cos(θ) = b / c

tan(θ) = a / b

5. **Trigonometric Identities**:

Pythagorean Identities:

sin^2(θ) + cos^2(θ) = 1

tan^2(θ) + 1 = sec^2(θ)

1 + cot^2(θ) = csc^2(θ)

6. **Limits**:

lim(x → a) f(x) = L

This represents the limit of a function ‘f(x)’ as ‘x’ approaches ‘a’, and it equals ‘L’.

7. **Derivatives**:

If f(x) is a function, the derivative of f(x) with respect to ‘x’ is denoted by f'(x) or dy/dx.

8. **Integrals**:

The integral of a function f(x) with respect to ‘x’ is denoted by ∫f(x) dx.

9. **Probability**:

Probability of an event A is given by:

P(A) = (Number of favorable outcomes) / (Total number of possible outcomes)

10. **Matrices**:

Matrix addition, subtraction, and multiplication formulas.

11. **Determinants**:

Formula to find the determinant of a 2×2 and 3×3 matrix.

12. **Vectors**:

Scalar multiplication, vector addition, subtraction, and dot product formulas.

These are just some of the important formulas in Class 12 mathematics. The specific topics covered may vary depending on the curriculum, so make sure to consult your textbook or syllabus for the complete set of formulas you need to study.

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