MegaCalc — PreCalc 12 Toolkit

A terminal-based step-by-step math calculator covering all major PreCalc 12 topics. Built in Python with optional graphing via Plotly.

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Getting Started

Requirements

• Python 3.8+
• Optional (for graphs): numpy and plotly

Install dependencies

pip install numpy plotly

Run

python main.py

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Project Structure

megacalc/
├── main.py                   ← Entry point / main menu
└── modules/
    ├── utils.py              ← Shared helpers (formatting, input, graph engine)
    ├── m01_transformations.py
    ├── m02_polynomials.py
    ├── m03_rational.py
    ├── m04_explog.py
    ├── m05_trig_functions.py
    ├── m06_trig_identities.py
    ├── m07_sequences.py
    ├── m08_combinatorics.py
    ├── m09_binomial.py
    └── m10_inverses.py

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Modules

1 · Function Transformations

Analyse y = a·f(b(x−h)) + k for any parent function.

• Describe all 4 transformation parameters step by step
• Map key points from parent to transformed graph
• Identify stretch/reflection/translation from two points
• Supported parents: linear, quadratic, cubic, sqrt, abs, rational, exponential, log, sin, cos, tan
• Graph: transformed vs parent curve

2 · Polynomial Functions

• End behaviour from degree and leading coefficient
• Evaluate at a point using Horner's method
• Rational Root Theorem — lists and tests all ±p/q candidates
• Synthetic division with full table
• Full factoring (iterative rational roots + quadratic formula)
• Root multiplicity with crossing/touching behaviour
• Graph: labelled roots and y-intercept

3 · Rational Functions

• Vertical asymptotes and holes (with hole coordinates)
• Horizontal and oblique asymptotes (polynomial long division shown)
• x- and y-intercepts
• Full analysis combining all of the above
• Solve rational equations (cross-multiply + check extraneous solutions)
• Graph: asymptotes as dashed lines, holes as open circles, all points labelled

4 · Exponential & Logarithmic Functions

• Laws of logarithms reference + evaluator
• Solve a·b^(mx+n) = c step by step
• Solve a·log_b(mx+n) = c step by step
• Change of base
• Growth & decay table + doubling time / half-life
• Compound interest (annual, semi, quarterly, monthly, daily, continuous)
• Graph: exponential or log with transformation parameters

5 · Trigonometric Functions

• Evaluate sin, cos, tan, sec, csc, cot at any angle
• Describe graph parameters: amplitude, period, phase shift, vertical shift
• Reciprocal trig reference + evaluator
• Unit circle table (all 16 standard angles, degrees + radians)
• Graph: any trig or reciprocal function with full a·f(bx−c)+d transformations

6 · Trig Identities & Equations

• Full identity reference sheet (Pythagorean, reciprocal, sum/difference, double-angle, half-angle, co-function)
• Numerically verify identities at multiple test angles
• Solve a·f(bx+c) = d in [0°, 360°] with CAST rule
• Solve using Pythagorean substitution
• Apply sum/difference identities step by step
• Apply double-angle identities (all three forms for cos)

7 · Sequences & Series

• Arithmetic sequence: nth term, partial sum, first terms
• Geometric sequence: nth term, partial sum, first terms
• Infinite geometric series with convergence check
• Sigma notation evaluator (any Python expression)
• Identify sequence type from terms (arithmetic, geometric, quadratic)

8 · Combinatorics & Counting

• Fundamental Counting Principle (multi-stage events)
• Permutations nPr
• Combinations nCr
• Permutations with repetition (n^r)
• Arrangements with repeated elements (n! / a!b!...)

9 · Binomial Theorem

• Expand (a+b)^n symbolically for any n up to 25
• Find a specific term T(k+1) = nCk · a^(n−k) · b^k
• Pascal's triangle (up to 20 rows)

10 · Inverses & Function Composition

• Inverse of linear: y = mx + b
• Inverse of power: y = axⁿ
• Inverse of exponential and logarithmic functions
• Numerically verify two functions are inverses (f(g(x)) = x)
• Compose functions symbolically with sample point table
• Evaluate f(g(a)) step by step

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Output Format

Every calculation follows the same pattern:

┌─ Step 1:  <what this step does>
│
   working lines (dimmed)
   key values highlighted

╔──────────────────╗
║  Answer:  value  ║
╚──────────────────╝

• Steps are colour-coded cyan headers — easy to skim
• Working is dimmed so it doesn't compete with results
• Final answers are in a green box — impossible to miss
• Fractions: decimal results show as 0.6667 (= 2/3) where possible

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Graphs

Graphs open in your browser as interactive Plotly charts.

• Hover over any point to see exact (x, y) coordinates
• Scroll to zoom, click-drag to pan
• Roots, intercepts, asymptotes, and holes are all labelled
• Trig graphs use π-based x-axis labels

Graphs are optional — if plotly or numpy aren't installed, the rest of the calculator works fine without them.

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Notes

• Fraction input supported everywhere: type 3/4 instead of 0.75
• All modules are independent — you can import any single module on its own
• Tested on Python 3.8+ on Linux, Windows, and macOS

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Originally started in Grade 12 as a set of Python CLI scripts to survive PreCalc 12.