30 written chapters · 0 published teaching videos
Grade 12, one chapter at a time.
Explore the transition to university mathematics through calculus, probability, and careful reasoning. Connect rates, accumulation, and statistical models to their meaning rather than using formulas in isolation.
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Every chapter below opens a written lesson with worked examples and practice. Full lesson recordings are being prepared; the interactive animations are available now.
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Chapters and video availability
Each chapter follows an existing academy lesson. Numbers match the written study order; grade placement is a guide and school sequences may vary.
30 of 30 chapters · in study order
Chapter 1 · Algebra
Read distant graph behavior from the leading term
Compare a polynomial with its highest-degree term as input magnitude grows.
Written lesson available · video pending
Study this chapterChapter 2 · Algebra
Recognize a power law on logarithmic axes
Separate power-law fitting from exponential fitting.
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Study this chapterChapter 3 · Algebra
Find the line a rational graph approaches
Use a vanishing remainder to identify a slant asymptote.
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Study this chapterChapter 4 · Algebra
Undo a shifted exponential and state the recovered domain
Use logarithms to invert an exponential transformation.
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Study this chapterChapter 5 · Algebra
Control the tail of an infinite geometric sum
Check convergence and quantify how much a finite truncation misses.
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Study this chapterChapter 6 · Algebra
Solve a recurrence with two independent growth modes
Use a characteristic equation for a second-order linear recurrence.
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Study this chapterChapter 7 · Algebra
Find all complex roots using equally spaced angles
Apply polar powers while retaining every angular branch.
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Study this chapterChapter 8 · Geometry
Recognize a circle hidden in a polar equation
Translate a polar curve into a Cartesian equation.
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Study this chapterChapter 9 · Geometry
Eliminate a parameter without losing traversal information
Distinguish a curve's equation from how it is traced.
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Study this chapterChapter 10 · Trigonometry
Solve a polynomial equation in a trigonometric value
Separate algebraic roots from angle solutions and range checks.
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Study this chapterChapter 11 · Trigonometry
Derive a tangent difference from sine and cosine
Form a quotient identity and retain denominator restrictions.
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Study this chapterChapter 12 · Calculus
Diagnose a jump through unequal one-sided limits
Separate a function's assigned value from its nearby behavior.
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Study this chapterChapter 13 · Calculus
Control an oscillation by bounding its amplitude
Use two converging bounds when a factor oscillates without a limit.
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Study this chapterChapter 14 · Calculus
Derive a power derivative from the difference quotient
Cancel a nonzero increment before taking its limit.
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Study this chapterChapter 15 · Calculus
Differentiate a product with two changing factors
Include one contribution for the change in each factor.
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Study this chapterChapter 16 · Calculus
Differentiate a normalized ratio
Apply the quotient rule and inspect its retained domain.
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Study this chapterChapter 17 · Calculus
Differentiate a relation without solving it into one global function
Use the chain rule when both coordinates vary along a curve.
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Study this chapterChapter 18 · Calculus
Relate the sensitivity of a function to that of its inverse
Differentiate an inverse composition at matching input-output points.
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Study this chapterChapter 19 · Calculus
Differentiate when the base and exponent both vary
Use a logarithm to turn a variable power into a product.
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Study this chapterChapter 20 · Calculus
Connect volume change to a changing height
Use geometric similarity before differentiating a related-rates model.
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Study this chapterChapter 21 · Calculus
Guarantee a horizontal tangent between equal endpoint heights
Check Rolle's theorem and find its interior point.
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Study this chapterChapter 22 · Calculus
Recognize a horizontal tangent without a maximum or minimum
Use sign changes of derivatives to classify a stationary inflection.
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Study this chapterChapter 23 · Calculus
Minimize squared distance to avoid a square root
Find all closest points using symmetry and a nonnegative remainder.
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Study this chapterChapter 24 · Calculus
Distinguish net accumulation from total geometric area
Split at sign changes when integrating an absolute value.
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Study this chapterChapter 25 · Calculus
Change integral limits along with the variable
Use a substitution consistently in a definite integral.
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Study this chapterChapter 26 · Calculus
Reverse the product rule to integrate a product
Choose factors that simplify after differentiation.
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Study this chapterChapter 27 · Calculus
Turn an integral into an average height
Normalize accumulated area by interval length.
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Study this chapterChapter 28 · Calculus
Build a volume from nested circular slices
Subtract inner disk area from outer disk area before integrating.
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Study this chapterChapter 29 · Statistics
Analyze repeated measurements through within-pair changes
Preserve a matched design by summarizing paired differences.
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Study this chapterChapter 30 · Statistics
Compare observed categorical counts with a specified model
Compute a goodness-of-fit statistic from expected counts.
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