For IIT JEE mathematics preparation, it's crucial to focus on building a strong foundation in core mathematical concepts. Here are some key areas to cover:

1. **Algebra:** Master topics like equations (linear, quadratic, cubic), inequalities, sequences, series, and complex numbers. Understanding algebraic manipulations and problem-solving techniques is essential.

2. **Trigonometry:** Learn trigonometric functions, identities, equations, properties of triangles, and their applications in solving geometry and calculus problems.

3. **Calculus:** Delve into differential calculus (limits, derivatives, continuity) and integral calculus (integration techniques, definite and indefinite integrals). Understand applications of calculus in solving problems related to rates of change, area, and optimization.

4. **Coordinate Geometry:** Study the properties of lines, circles, conic sections (parabola, ellipse, hyperbola), and their equations in different coordinate systems. Learn methods for solving problems related to distances, slopes, and intersections.

5. **Vectors and 3D Geometry:** Understand vector operations, dot and cross products, and their applications in geometry and physics. Study the properties of lines, planes, and solids in three-dimensional space.

6. **Probability and Statistics:** Learn basic probability concepts, random variables, probability distributions, and statistical measures. Practice solving problems related to permutations, combinations, and probability distributions.

7. **Mathematical Reasoning:** Develop logical reasoning skills and problem-solving strategies. Practice solving different types of mathematical puzzles and problems to enhance critical thinking abilities.

8. **Previous Years' Papers:** Solve past years' IIT JEE mathematics papers to familiarize yourself with the exam pattern, types of questions, and time management. Analyze your mistakes and focus on improving weak areas.

9. **Mock Tests and Practice:** Regularly take mock tests and practice solving a variety of problems to improve speed and accuracy. Identify your strengths and weaknesses and adjust your study plan accordingly.

10. **Seek Guidance:** Don't hesitate to seek help from teachers, tutors, or online resources if you encounter difficulties in understanding any topic. Collaborate with peers and participate in study groups to exchange ideas and insights.

Consistent practice, conceptual clarity, and strategic preparation are key to success in IIT JEE mathematics. Remember to stay focused, motivated, and resilient throughout your preparation journey. Good luck!