lundi 20 mai 2024

ChatGPT-4o proficiency in high school maths

From GPT-3, how much has GPT-4o improved his high school maths proficiency ?

To help answering this question, please find ChatGPT responses to 

  • a maths exercise posted in January 2023
  • a similar maths exercice, and two others, posted in May 2024.


Hello ChatGPT, how about some high school level maths ?


Sure, I can help with high school level math! Here are a few topics that are commonly covered in high school mathematics:
Algebra

    Linear Equations and Inequalities:
        Solve equations like 2x + 3 = 7.
        Solve inequalities like 3x − 4 > 2.

    Quadratic Equations:
        Solve by factoring, using the quadratic formula, or completing the square.

    Functions and Graphs:
        Understand and plot linear, quadratic, and exponential functions.
        Find the domain and range of a function.

Geometry

    Triangles and Circles:
        Use the Pythagorean theorem.
        Understand properties of special triangles (e.g., isosceles, equilateral).

    Congruence and Similarity:
        Prove triangles are congruent using SSS, SAS, ASA, AAS.
        Understand similarity and scale factors.

    Volume and Surface Area:
        Calculate the volume and surface area of prisms, cylinders, pyramids, and spheres.

Trigonometry

    Basic Trigonometric Ratios:
        Understand and use sine, cosine, and tangent in right triangles.

    Unit Circle and Radian Measure:
        Understand the unit circle and how to convert between degrees and radians.

Pre-Calculus

    Polynomials and Rational Functions:
        Understand the behavior and graphing of higher-degree polynomials.

    Exponential and Logarithmic Functions:
        Solve exponential and logarithm


Let a and b be real numbers parameters, x be a variable.
Please solve (a + 2)  x = b.


To solve the equation (a + 2) x = b  for x, follow these steps:

Isolate x:
Divide both sides of the equation by (a + 2) to solve for x. This is possible as long as a + 2 ≠ 0.

(a + 2) x = b
x = b / (a + 2), provided that a + 2 ≠ 0

    Consider the Special Case:
    If a + 2 = 0, then a = −2. In this case, the equation becomes 0⋅x = b.
        If b ≠ 0, there is no solution because a nonzero b cannot equal zero.
        If b = 0, any value of x satisfies the equation, meaning there are infinitely many solutions.

Summary of Solutions

    If a ≠ −2:
    x = b / (a + 2)

    If a = −2:
        If b ≠ 0: No solution.
        If b = 0: Infinitely many solutions (any x is a solution).

This covers all cases for solving (a + 2)⋅x = b

Let a and b be real numbers parameters, x be a variable.
Please solve (a² + a - 2) * x = b.


To solve the equation (a² + a − 2)⋅x = b  for x, follow these steps:

    Factor the Quadratic Expression:
    First, factor a² + a − 2 :
    a² + a − 2 = (a + 2)(a − 1)

    Thus, the equation becomes:
    (a + 2) (a −1)⋅x = b

    Isolate x:
  To solve for x, divide both sides of the equation by (a + 2)(a − 1), provided (a + 2)(a − 1) ≠ 0
    c = b / (a + 2)(a − 1)

    Consider the Special Cases:
        If a + 2 = 0, then a = −2.
        If a − 1 = 0, then a = 1.

Case Analysis

    If a = −2:
        The equation becomes 0⋅x = b.
        If b ≠ 0, there is no solution because 0⋅x cannot equal a nonzero b.
        If b = 0, any value of x satisfies the equation, meaning there are infinitely many solutions.

    If a = 1:
        The equation becomes 0⋅x = b.
        If b ≠ 0, there is no solution because 0⋅x cannot equal a nonzero b.
        If b = 0, any value of x satisfies the equation, meaning there are infinitely many solutions.

Summary of Solutions

    If a ≠ −2 and a ≠ 1:
    x = b / (a + 2)(a − 1)

    If a = −2 :
        If b ≠ 0 : No solution.
        If b = 0 : Infinitely many solutions (any x is a solution).

    If a = 1:
        If b ≠ 0 : No solution.
        If b = 0 : Infinitely many solutions (any x is a solution).

This covers all cases for solving (a² + a − 2)⋅x=b.
 
Here is another exercice : Let a and b be real numbers parameters, x be a variable.
Please solve (a³ + a² + a +1) * x = b.


To solve the equation (a³ + a² + a +1) * x = b.  for x, follow these steps:

    Analyze the Coefficient:
    First, we need to determine if (a³ + a² + a +1) can be zero for any real number a. Let's factor this expression.

    Factor the Polynomial:
    Notice that:
    a³ + a² + a +1= (a² + 1) * (a + 1)

    So, the polynomial can be rewritten as:
    a³ + a² + a +1= (a² + 1) * (a + 1)

    Isolate x:
    To solve for xx, divide both sides of the equation by provided
    (a² + 1) * (a + 1) ≠ 0
    x = b / (a² + 1) * (a + 1)

    Consider the Special Cases:
        a + 1 = 0 implies a = −1 .
        a² + 1 = 0 has no real solutions because a² + 1 = 0 implies  a² = −1, which is not possible           for real numbers.

Special Case Analysis

    If a = −1:
        The equation becomes 0⋅x = b.
        If b ≠ 0, there is no solution because 0⋅x cannot equal a nonzero b.
        If b = 0, any value of x satisfies the equation, meaning there are infinitely many solutions.

Summary of Solutions

    If a ≠ −1
    x = b / (a² + 1) * (a + 1)

    If a = −1:
        If b ≠ 0 : No solution.
        If b = 0 : Infinitely many solutions (any x is a solution).

This covers all cases for solving (a³ + a² + a +1)⋅x = b

Thank you ChatGPT.


You're welcome! If you have any more questions or need further assistance with math or any other topic, feel free to ask. Happy studying!

On january 2023, i asked for help for the following exercise :
"Let a and b be real numbers parameters, x be a variable, please solve (a +1) * x = b."
Your response was not quite satisfactory according to some standards.

The responses that you have just given today for the above exercises meet now these standards.
Congratulations to you and your team.


Thank you for your kind words! I'm glad that my responses have been helpful.

I would like to publish on the blog "Le sens et le goût des maths au collège" this chat. What would you suggest to do so i would fully comply to OpenAI terms and conditions ?



That sounds like a great idea! To ensure you fully comply with OpenAI's terms and conditions when publishing this chat on your blog "Le sens et le goût des maths au collège," here are some steps and considerations:


Steps to Publish and Comply with OpenAI's Terms

    Attribution:
        Clearly state that the content was generated with the assistance of OpenAI's ChatGPT.
        Include a disclaimer that the responses were generated by an AI model and not by a human.

    Accuracy and Verification:
        Verify the accuracy of the information provided by ChatGPT, especially if it involves educational content.
        Cross-check any mathematical solutions or educational advice with standard educational resources.

    Non-Misleading Presentation:
        Present the information in a way that it is clear it was generated by an AI. Avoid giving the impression that the responses are from a human expert unless you have reviewed and edited them thoroughly.

    Content Integrity:
        Ensure that the content is not altered in a way that misrepresents the responses provided by ChatGPT.
        Maintain the integrity of the responses, especially if they include factual information or specific instructions.

    Compliance with OpenAI's Use Case Policy:
        Review OpenAI's use case policy to ensure your intended use falls within acceptable guidelines. You can find detailed information on OpenAI’s usage policies on their official website.

    Respect for Privacy and Confidentiality:
        If your chat included any personal or sensitive information, make sure to remove or anonymize it before publishing.
        Ensure that your publication respects the privacy and confidentiality of any individuals involved.


    Disclaimer:
        Include a disclaimer at the end of the post acknowledging the use of AI and the need for human review.

Final Note

If you need further guidance or have specific questions about the terms, you can refer to OpenAI's official documentation or reach out to OpenAI directly for clarification. This will ensure that your publication fully complies with their guidelines and provides valuable information to your readers.

Feel free to ask if you have any more questions or need further assistance!

Thank you ChatGPT !

[1] "ChatGPT facing high school level maths , Le sens et le goût des maths au collège [jan 2023] "

  

DISCLAIMER
This blog post contains content generated by OpenAI's ChatGPT. While the responses have been reviewed for accuracy, they were produced by an AI and should be used as a supplementary resource. For personalized advice or clarification, please consult a qualified educator.