Certainly! Here are some important math formulas for Class 11 that cover various topics:
1. **Quadratic Formula**:
For the quadratic equation ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 – 4ac)) / 2a
2. **Arithmetic Progression (AP)**:
– nth term of an AP: a_n = a + (n – 1)d
– Sum of the first n terms of an AP: S_n = (n/2)[2a + (n – 1)d]
3. **Geometric Progression (GP)**:
– nth term of a GP: a_n = a * r^(n-1)
– Sum of the first n terms of a GP (when |r| < 1): S_n = a / (1 – r)
4. **Trigonometric Ratios**:
For a right-angled triangle with sides a, b, and hypotenuse c, and angles A, B, and C:
– sin A = a / c
– cos A = b / c
– tan A = a / b
5. **Trigonometric Identities**:
– Pythagorean Identity: sin^2θ + cos^2θ = 1
– Reciprocal Identities: cscθ = 1/sinθ, secθ = 1/cosθ, cotθ = 1/tanθ
– Quotient Identities: tanθ = sinθ / cosθ, cotθ = cosθ / sinθ
– Co-Function Identities: sin(90° – θ) = cosθ, cos(90° – θ) = sinθ, tan(90° – θ) = cotθ, cot(90° – θ) = tanθ
6. **Limits**:
– Limit of a function f(x) as x approaches ‘a’: lim(x→a) f(x)
7. **Derivatives**:
– Derivative of a function f(x) with respect to x: d/dx f(x) or f'(x)
– Basic rules: (d/dx)[c] = 0 (where c is a constant), (d/dx)[x^n] = nx^(n-1), (d/dx)[cf(x)] = c * f'(x)
8. **Integrals**:
– Integral of a function f(x) with respect to x: ∫ f(x) dx
– Basic rules: ∫ [c] dx = cx + C (where c is a constant), ∫ x^n dx = (x^(n+1))/(n+1) + C (for n ≠ -1)
9. **Probability**:
– Probability of an event A: P(A) = (Number of favorable outcomes) / (Total number of outcomes)
10. **Permutations and Combinations**:
– Permutations: nPr = n! / (n – r)!
– Combinations: nCr = n! / (r! * (n – r)!)
11. **Straight Lines**:
– Equation of a straight line: y = mx + c, where m is the slope and c is the y-intercept.
12. **Circles**:
– Equation of a circle with center (h, k) and radius r: (x – h)^2 + (y – k)^2 = r^2
These formulas should help you with your Class 11 math studies. Remember to understand their derivations and practice using them in various problems to strengthen your understanding.
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