Date: July 27, 2026
Course: Math Academy — Mathematical Foundations II
Timeline: September 2, 2025 – July 27, 2026 (~11 Months)
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After nearly 11 months of daily work starting back on September 2, 2025, I completed Math Academy’s Mathematical Foundations II (MF II) today.
I found the course extremely challenging. I still do not feel like I have a complete grasp on everything I am learning, but I am recognizing a
larger number of problems and patterns as I go.
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### Course Content Summary
Looking over the course contents, MF II covers a broad scope of material spanning advanced algebra through introductory calculus:
• Quadratics & Polynomials: Factoring methods, completing the square, Vieta’s formulas, synthetic/long division, and the Rational Roots and
Factor Theorems.
• Complex Numbers & Systems: Operations in the complex plane, complex roots, and computing magnitudes and arguments.
• Functions & Graph Transformations: Function composition, inverses, domain/range, and multi-step graph transformations.
• Exponentials & Logarithms: Logarithm laws, change of base, and solving exponential and logarithmic equations.
• Radicals & Rational Functions: Rational expressions, partial fractions, asymptotes, and radical equation solving.
• Sequences & Series: Recursive formulas, Fibonacci sequences, arithmetic and geometric sequences, and Sigma notation.
• Coordinate & Solid Geometry: 3D distance formulas, geometric transformations, polyhedra properties, and Euler’s formula.
• Trigonometry & Unit Circle: Radians, Law of Sines/Cosines, reciprocal trig functions, and graphing transformed trigonometric functions.
• Vectors: 2D vectors in component form, linear combinations, magnitudes, and vector operations.
• Limits & Introductory Calculus: Graphical/algebraic limits, continuity, derivative rules (Power, Product, Quotient, Chain Rule),
tangent/normal lines, and basic indefinite integrals.
• Statistics, Probability & Combinatorics: Z-scores, linear regression, compound probability, Venn diagrams, permutations, and combinations.
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### The MF III Diagnostic
At the end of MF II, the platform gave me a diagnostic for Mathematical Foundations III (MF III).
That diagnostic felt extremely painful and demoralizing at first—I wasn’t sure if I should have known more of the content. After completing it
and learning a bit more about how it works, I realized I wasn’t expected to understand most of it yet. It was designed to give a view into what
MF III will contain.
The diagnostic placed me at 10% of MF III with an estimated completion date of May 2027, which is about the same timeframe as MF II.
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### Pacing Goals and Next Steps
I am hoping to increase my output to around 50 XP per day. That rate would bring my estimated completion date to mid-December 2026, which would
be outstanding.
I am going to take a few days off and then start again on MF III, hoping the pieces start falling into place more than they have so far.
As of today not wanting to look or think about math or Math Academy so not sure how far I will make it towards my goal of learning math as an adult this year but it could just be a feeling I have today.