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12TH • RIGOROUS CURRICULUM.

Chapter-by-chapter theory notes, step-by-step textbook exercises, video lectures, and SLO-aligned board examination prep for Mathematics (12th).

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Syllabus

Curriculum Syllabus

Course chapter sequence roadmap and learning outcomes.

Mathematics (12th)

1. Graphical Representation of Functions

1.1 Graphical Representation of Functions
1.2 Algebraic and Transcendental Functions
1.3 Graph Transformations
1.4 Rational Functions and Asymptotes
1.5 Applications of Functions and Graph Modeling

2. Further Differentiation

2.1 Derivatives of Inverse Trigonometric Functions
2.2 Differentiation of Exponential and Logarithmic Functions
2.3 Implicit Differentiation
2.4 Parametric Differentiation
2.5 Higher Order Derivatives
2.6 Taylor and Maclaurin Series
2.7 Maxima, Minima, and Optimization

3. Integration

3.1 Indefinite Integrals
3.2 Integration by Substitution
3.3 Trigonometric Integrals and Substitutions
3.4 Integration by Parts
3.5 Integration by Partial Fractions
3.6 Definite Integrals and Fundamental Theorem of Calculus
3.7 Area Under and Between Curves

4. Differential Equations

4.1 Introduction to Differential Equations
4.2 Separable Differential Equations
4.3 Homogeneous Differential Equations and Applications

5. Analytical Geometry

5.1 Coordinate Systems and Distance Formula
5.2 Slope and Equations of Straight Lines
5.3 Angle Between Lines and Perpendicular Distance

6. Conic Section

6.1 The Circle
6.2 The Parabola
6.3 The Ellipse
6.4 The Hyperbola
6.5 Tangents and Normals to Conics
6.6 Applications and Reflective Properties of Conics

7. Kinematics

7.1 Rectilinear Motion, Velocity, and Acceleration

8. Numerical Method

8.1 Errors and The Bisection Method
8.2 Regula-Falsi Method (False Position Method)
8.3 Newton-Raphson Method
8.4 Numerical Integration

9. Inverse Trigonometric Functions and Their Graphs

9.1 Inverse Trigonometric Functions and Graphs
9.2 Addition and Subtraction Formulas for Inverse Trig

10. Solution of Trigonometric Equations

10.1 First and Second Degree Trigonometric Equations
10.2 General Solutions of Trigonometric Equations

11. Vector Valued Functions and Their Differentiations

11.1 Vector-Valued Functions and Space Curves
11.2 Differentiation and Integration of Vector Functions
11.3 Tangent Vectors, Velocity, Acceleration, and Curvature
INTERACTIVE LAB • CALCULUS & VECTORS

Explore Dynamic Tangent Secants & Riemann Sums

Visualize derivatives as tangent limits, integrate Riemann area under curves, and inspect vector geometry in 2D & 3D space.

scienceLaunch Mathematics Labs→Board MCQs & Past Papers