ALLCBTs

GAOKAO Top Mathematics Questions.

Published on Jul 22, 2025 • Education

Welcome to Today’s Tutorial

Hi guys, welcome to today's tutorial.

In this session, we’ll be solving top GAOKAO mathematics questions that challenge your understanding of geometry, algebra, and analytical thinking.

You can watch the full class in the video below:

Question 1: Surface Area of a Sphere with a Tetrahedron Inscribed

Question:
A regular tetrahedron with edge length √2 is inscribed in a sphere. What is the surface area of the sphere?

Step 1: Understand the Parabola

Step 2: Apply the Line Condition

Since the line passes through the focus, plug the focus coordinates into the line equation:

Step 3: Find the Focus and Parabola

Now that p = 4p:

Final Answer:

Watch more educational videos and past questions: https://youtube.com/@allcbts

Conclusion

In this tutorial, we covered:

• How to compute the surface area of a sphere with an inscribed tetrahedron
• How to determine the focus of a parabola using a line condition

These questions are excellent examples of GAOKAO-level analytical mathematics. Mastering them boosts your ability to solve 3D geometry and conic section problems with confidence.

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