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📘 CLASS 11 – MATHEMATICS (Maharashtra Board)

🔹 1. Angle & Trigonometry

  • Radian & degree

  • Trigonometric functions

  • Graphs

Formulas

sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1 1+tan⁡2θ=sec⁡2θ1+\tan^2\theta = \sec^2\theta

🔹 2. Trigonometry – II

  • Compound angles

  • Transformation formulas

Formulas

sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B\sin(A+B)=\sin A\cos B+\cos A\sin B

🔹 3. Determinants & Matrices

∣abcd∣=ad−bc\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad – bc

Matrix addition, multiplication, inverse.

🔹 4. Straight Lines

  • Slope

  • Equation of line

Formula

y=mx+cy = mx + c m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}

🔹 5. Circle

  • Equation of circle

(x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2

🔹 6. Conic Sections

  • Parabola

  • Ellipse

  • Hyperbola

🔹 7. Sequence & Series

  • AP, GP

Formulas

an=a+(n−1)da_n = a + (n-1)d Sn=n2(2a+(n−1)d)S_n = \frac{n}{2}(2a + (n-1)d) an=arn−1a_n = ar^{n-1}

🔹 8. Sets, Relations & Functions

  • Union, intersection

  • Types of functions

🔹 9. Complex Numbers

  • Form: a+bia + bi

i2=−1i^2 = -1

🔹 10. Limits & Differentiation

lim⁡x→0sin⁡xx=1\lim_{x\to 0}\frac{\sin x}{x}=1 ddx(xn)=nxn−1\frac{d}{dx}(x^n)=nx^{n-1}

📘 CLASS 12 – MATHEMATICS

🔹 1. Mathematical Logic

  • Statements

  • Truth tables

  • Logical connectives

🔹 2. Matrices & Determinants

  • Matrix inverse

  • Adjoint

  • Determinant properties

🔹 3. Trigonometric Functions

  • Compound angles

  • Inverse trigonometry

🔹 4. Pair of Straight Lines

ax2+2hxy+by2=0ax^2 + 2hxy + by^2 = 0

🔹 5. Vectors

∣a⃗∣=ax2+ay2+az2|\vec{a}| = \sqrt{a_x^2 + a_y^2 + a_z^2}

Dot & cross product.

🔹 6. Three-Dimensional Geometry

  • Plane, line

Formula

x−x1a=y−y1b=z−z1c\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}

🔹 7. Linear Programming

  • Objective function

  • Feasible region

🔹 8. Differentiation

ddx(sin⁡x)=cos⁡x\frac{d}{dx}(\sin x)=\cos x (uv)′=u′v+uv′(uv)’=u’v+uv’

🔹 9. Applications of Derivatives

  • Maxima-minima

  • Rate of change

🔹 10. Integration

∫xndx=xn+1n+1\int x^n dx = \frac{x^{n+1}}{n+1} ∫1xdx=ln⁡∣x∣\int \frac{1}{x} dx = \ln|x|

🔹 11. Definite Integrals

∫abf(x)dx\int_a^b f(x)dx

🔹 12. Differential Equations

dydx+Py=Q\frac{dy}{dx} + Py = Q

🔹 13. Probability

P(E)=Favourable outcomesTotal outcomesP(E) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}}