School Problems — Step-by-Step Help

When to Use

Use when the user asks for help solving academic problems from school assignments:

• Physics problems (dilatação, calorimetria, cinemática, etc.)
• Math problems (equations, geometry, functions)
• Chemistry problems (stoichiometry, thermochemistry)
• Any problem with formulas and calculations

User Preferences (keila)

This user has specific preferences. If you notice similar patterns with other users, adapt accordingly:

• Language: Portuguese (Brazilian) with "você" — always
• Verbosity: Show ALL calculation steps. Never skip intermediate algebra. Every unit conversion must be visible.
• Algebra detail: When the user asks "pq" (why) about a step (e.g., sign change, equation isolation), break it down into separate sub-steps showing exactly what moves where. Never just say "because algebra" — show each sign flip.
• Confirmation: The user double-checks understanding with statements like "fica negativo né". Confirm when they're right and explain why clearly.
• Terminal trust: If the user has experienced forced-exit / crash errors from terminal commands, always present the execution plan in plain language first — list each step, wait for confirmation before running anything.
• Organization: Save solved problems to Obsidian vault (escola/<subject>/<problem-slug>.md) and commit with git.

Workflow

Step 1: Present the Plan First

If the user has had terminal issues before (forced exits, crashes), show the plan in plain language before running any commands:

O que vou fazer:
1. Extrair texto do PDF com PyMuPDF
2. Procurar a questão específica
3. Resolver passo-a-passo

Wait for user confirmation ("vai", "pode ir", "ok") before executing.

Otherwise, proceed directly to finding the problem.

If the problem is in a PDF, use ocr-and-documents skill to extract text:

import fitz
doc = fitz.open("T1 de Física - Dilatação_compressed.pdf")
for page in doc:
    print(page.get_text())

Pitfall — tables as images: Many school PDFs have coefficient tables, formula sheets, or graphs as embedded images, not text. PyMuPDF's get_text() won't capture them. Detect this:

# Check for images on the page
page = doc[0]
images = page.get_images()
print(f"Images found: {len(images)}")
for i, img in enumerate(images):
    xref = img[0]
    base = doc.extract_image(xref)
    with open(f"/tmp/table_{i}.{base['ext']}", "wb") as f:
        f.write(base["image"])

Then OCR the extracted image:

sudo apt-get install -y tesseract-ocr tesseract-ocr-por  # Portuguese language pack

import pytesseract
from PIL import Image
text = pytesseract.image_to_string(Image.open("/tmp/table_0.png"), lang="por")
# Interpret carefully — OCR may misread exponents (e.g., "105" = 10⁻⁵, "x108" = ×10⁻⁵)

Alternative: If the user provides the problem text directly (no PDF), skip to Step 2.

Step 2: Extract the Data

Identify and list all given values with their units:

Variable	Value	Unit	Notes
L₀	61.80	m	Initial length
T₀	17	°C	Initial temperature
ΔL	233	mm	→ convert to m (0.233 m)
α	2.4×10⁻⁵	°C⁻¹	From table (aluminum)

Critical — unit conversion: Always check if units are consistent. Common traps:

• mm → m (divide by 1000)
• cm → m (divide by 100)
• g → kg (divide by 1000)
• °C stays °C for ΔT calculations

Step 3: Identify the Formula

Match the problem type to the correct formula:

Topic	Formula	Variables
Dilatação linear	ΔL = L₀·α·ΔT	α = coefficient, ΔT = temp change
Dilatação superficial	ΔA = A₀·β·ΔT	β = 2α
Dilatação volumétrica	ΔV = V₀·γ·ΔT	γ = 3α
Calorimetria	Q = m·c·ΔT	c = specific heat
Calor latente	Q = m·L	L = latent heat

Relation between coefficients: For the same material:

• β = 2α (surface = 2 × linear)
• γ = 3α (volume = 3 × linear)

Step 4: Solve Step by Step

Present the solution as numbered steps, showing every substitution:

1️⃣ ΔL = L₀ · α · ΔT
   0.233 = 61.80 × 2.4×10⁻⁵ × ΔT

2️⃣ ΔT = 0.233 / (61.80 × 2.4×10⁻⁵)
   ΔT = 0.233 / 0.0014832
   ΔT = 157.09 °C

3️⃣ T_final = T₀ + ΔT
   T_final = 17 + 157.09
   T_final = 174.09 °C ✅

Key rules (from the user's assignment instructions):

• Show ALL calculations — incomplete answers are disqualified
• Include units in every step
• 30% of the exercise value is deducted for unit/scale errors
• Present the final answer clearly boxed/highlighted

Step 5: Handle Signs in Detail

Heating vs. Cooling:

• Heating (temp increases) → ΔT positive → ΔL/ΔA/ΔV positive (expansion)
• Cooling (temp decreases) → ΔT negative → ΔL/ΔA/ΔV negative (contraction)

When the problem says "resfriada" (cooled) or the final area is smaller than initial:

ΔA = A − A₀  →  if A < A₀, ΔA is NEGATIVE

Algebra sign trick — WALK THROUGH EVERY FLIP (common confusion):

Students often get stuck at this step. Show it like this:

−T_i = −637

# Both sides are negative. Multiply both sides by −1:
(−1) · (−T_i) = (−1) · (−637)

# Negative × negative = positive:
T_i = 637 °C ✅

Or equivalently: "O −T_i significa que T_i está com sinal trocado. Pra achar T_i, multiplica os dois lados por −1."

When showing sign flips, use this format:

12 − T_i = −625
     ↓ (12 passa pra direita subtraindo)
−T_i = −625 − 12
     ↓ (−625 − 12 = −637)
−T_i = −637
     ↓ (× −1 nos dois lados)
T_i = 637

Every arrow must explain the operation. Never skip a line.

Step 6: Save to Obsidian Vault

After solving, save the solution to the vault for future reference:

Path: escola/<subject>/<problem-slug>.md

With frontmatter:

---
tags: [subject, topic, assignment]
title: "Question N — Short Description"
---

Include in the note:

• Full problem statement (or reference to it)
• All given data
• Step-by-step solution
• Final answer highlighted

Always commit vault changes:

cd /mnt/c/Users/keila/Mateus/vault
git add "escola/<subject>/<file>.md"
git commit -m "update vault: resolucao questao N - <topic>"

Step 7: Offer to Save as Reference

After solving a non-trivial problem, ask if the user wants the solution saved to the vault. They appreciate having permanent notes they can review later.

Pitfalls

• OCR misreads: Tesseract OCR on physics tables frequently reads "×10⁻⁵" as "x105" or "x108". The comma separator also gets lost — "2,4" becomes "24". Always interpret OCR output critically and cross-reference with known values.

• Table image overwrites: When extracting multiple images from a PDF page with extract_image(), subsequent saves overwrite previous ones. Use unique filenames (table_0.jpeg, table_1.jpeg).

• Delta vs absolute: NEVER confuse Δ (variation/change) with the absolute value. ΔL = L_final − L_initial, not just L_final.

• β and γ from α: Students often plug α directly into surface/volume formulas. Always calculate β = 2α or γ = 3α first.

• Sign in cooling problems: When ΔA or ΔL is negative, the algebra with negative signs confuses students. Walk through each sign flip explicitly (see Step 5).

• No vision model: The current provider (DeepSeek/open-code-zen) does NOT support vision/image inputs. Never try vision_analyze on PDF table images or graphs.

• Extracting graph data without vision: When you need to read data from a small, low-quality graph image but vision is unavailable, use this approach:

  1. Extract the image from PDF with doc.extract_image(xref) → save as JPEG/PNG
  2. Install tesseract + Portuguese language pack: sudo apt-get install tesseract-ocr tesseract-ocr-por
  3. Enlarge the image (6x) with PIL and OCR with --psm 6 or --psm 4
  4. For axis labels and values, crop specific regions (y-axis area, x-axis area) and OCR each separately
  5. For the graph line itself, use binary pixel analysis:

     gray = np.mean(np.array(img), axis=2)
     # Find dark pixels (the line)
     dark_mask = gray < threshold
     # Group by y to find where the line crosses each row
     for y in range(y_min, y_max):
         row_dark = np.where(dark_mask[y])[0]
         if len(row_dark) in [5, 10]:  # line, not text block
             x_avg = row_dark.mean()
     

  6. Map pixel coordinates to data values:

     # Find axis boundaries from OCR and pixel analysis
     T_per_px = 60 / (x_60_label - x_origin)   # °C per pixel
     A_per_px = 100 / (y_origin - y_100_label)  # A-units per pixel
     T = (x_line - x_origin) * T_per_px
     A = (y_origin - y_line) * A_per_px
     

  7. Limitation: Pixel-level estimation has ~5-15% error. Best used when the answer key is available for cross-checking (work backwards from the answer to determine exact graph slope).

Reference Files

• references/coeficientes-dilatacao.md — Tabela de coeficientes de dilatação linear (α) dos materiais comuns + fórmulas de dilatação linear, superficial e volumétrica + conversões de unidades. Use esta tabela para resolver problemas de física do T1.