Category: Graphs

The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300. Represent the situation algebraically

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1. Which of the following values of x make the equation x +7x- 18 = 0 true?

I. -9 II. 2 III. 9

A. I and III

B.II and III

C.I and II

D. I,II, and III

Compare $y=x^2$y=x2 and $y=x^2+3$y=x2+3.

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Work Request: Completion of IB Math IA (Tennis Racket Modelling)

I have an IB Mathematics AA Internal Assessment draft that is partially complete. The introduction, context, and most of the written sections are already written, but the final mathematical model and analysis need to be completed and polished.

Please complete the following tasks:

1. Complete the Desmos Graph (Tennis Racket)

Finish the full mathematical model of the tennis racket using Desmos.

Ensure the model includes:

A complete outer frame (racket head, throat, and handle)

Proper symmetry where appropriate

Clearly defined domain restrictions so curves do not overlap or extend beyond the frame

The final graph should look visually accurate and mathematically justified.

2. Finalize the String Bed

Complete both vertical and horizontal strings inside the racket head.

Use appropriate functions (e.g., steep parabolas or equivalent) so the strings appear realistic.

Apply domain restrictions so strings stay fully inside the frame.

Ensure even spacing and symmetry.

3. Write the Remaining Mathematical Analysis

Add clear written explanation covering:

Which types of functions were used (elliptic, quadratic, cubic, linear, square-root, etc.)

Why each function type was chosen for each part of the racket

How transformations (translations, stretches, reflections) were applied

How domain restrictions were determined and why they are necessary

How continuity between different curves was ensured

The analysis should be written at an IB Math AA level (clear, precise, not overly advanced).

4. Improve Mathematical Depth (IB Criteria)

Add at least one analytical extension, such as:

Area of the racket head using integrals, or

Arc length of part of the frame

Clearly explain the method, even if numerical evaluation is minimal.

This should strengthen Criterion E (Reflection) and overall mathematical sophistication.

5. Maintain Original Structure

Do not rewrite the entire IA.

Build on the existing draft and keep the same topic, structure, and style.

The final product should look like a natural continuatirston of the existing work.

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