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I Used Google Gemini to Tutor My NCEA Exam

How Google AI Studio can coach you through calculus problems in real time for free

I’ve been experimenting with Google AI Studio, a powerful tool for building custom AI agents and chatbots. One of the coolest features is the ability to talk to the agent in real time while sharing your webcam or screen. I tested it by getting Gemini to tutor me through an NCEA Level 2 Calculus exam, and the results were impressive.

Setting Up Google AI Studio

NCEA Standards & Assessment page showing list of achievement standards by level and category
NCEA exam resource page with standards reference guide

All you need is a free Google account. Search for Google AI Studio, log in, and navigate to the “Stream Realtime” section. You have three options: talk directly, show your webcam, or share your screen. For this tutorial, I used screen sharing.

The model runs on Gemini 2.0 Flash Experimental with audio output enabled, and you can change the voice. There’s nothing to configure - it works right out of the box for free.

Testing with a Real NCEA Exam

I downloaded a 2024 Level 2 Mathematics and Statistics exam from the NZQA website and opened it on screen. The moment I shared my screen, Gemini immediately recognised the exam paper and was ready to help.

Question 1: Finding the Gradient

The first question asked to find the gradient of a function at a specific point. Rather than just giving me the answer, Gemini coached me through the process:

  • It confirmed I was applying the power rule correctly
  • When I made a mistake simplifying the derivative of -6x², it caught it immediately and guided me to the correct answer
  • It reminded me to multiply the coefficient by the power and reduce the power by one
  • Once I had the derivative, it confirmed I should substitute x = 2 to find the gradient

The response time was incredibly fast - almost no delay between asking a question and getting a response.

Excellence Question: Cylinder Optimisation

For the harder optimisation problem about minimising the surface area of a cylinder with a fixed volume of 500ml, Gemini walked me through every step:

  • Isolating height in terms of radius from the volume equation
  • Substituting into the surface area formula
  • Simplifying the expression
  • Taking the derivative and setting it equal to zero
  • Solving for the radius (approximately 4.30) and height (approximately 8.61)

What Makes This Special

Student handwritten solution showing calculus working with equation 12x squared minus 12x plus b
AI tutor providing guidance on student calculus workings

The key difference from simply asking ChatGPT for an answer is that Gemini actually coaches you through the problem. It doesn’t just give you the answer - it asks you to think, checks your working, catches your mistakes, and guides you to understand the concepts.

There is a 10-minute session limit, but you can reconnect and continue right where you left off. This is essentially a free 24/7 personal tutor that can see exactly what you’re working on and adapt to your learning pace.

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