30 written chapters · 0 published teaching videos
Grade 11, one chapter at a time.
Use functions, trigonometry, sequences, and statistics to describe more complex relationships. Focus on interpreting a model as well as carrying out its calculations.
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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
Track a domain through two function machines
Find the allowed inputs of a composition before simplifying it.
Written lesson available · video pending
Study this chapterChapter 2 · Algebra
Choose a branch before inverting a quadratic
Restrict a domain to make a many-to-one function invertible.
Written lesson available · video pending
Study this chapterChapter 3 · Algebra
Read a horizontal scale from the inside expression
Factor an input transformation to identify its center and scale.
Written lesson available · video pending
Study this chapterChapter 4 · Algebra
Make two formula pieces meet continuously
Match one-sided values at a piecewise boundary.
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Study this chapterChapter 5 · Algebra
Use a known root to determine a coefficient
Apply the factor theorem to an unknown polynomial parameter.
Written lesson available · video pending
Study this chapterChapter 6 · Algebra
Solve a rational inequality by intervals
Track sign changes while excluding a denominator zero.
Written lesson available · video pending
Study this chapterChapter 7 · Algebra
Reject a root introduced by squaring
Check transformed equation candidates in the original radical equation.
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Study this chapterChapter 8 · Algebra
Solve an absolute-value equation with a quadratic inside
Separate the two possible signs and reject impossible squared values.
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Study this chapterChapter 9 · Algebra
Combine logarithms without admitting forbidden inputs
Preserve each logarithm's positivity requirement when solving.
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Study this chapterChapter 10 · Algebra
Recover an exponential model from two readings
Determine both the initial factor and multiplicative growth factor.
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Study this chapterChapter 11 · Algebra
Add repeated multiplicative contributions efficiently
Derive a finite geometric-sum formula by subtraction.
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Study this chapterChapter 12 · Algebra
Select one coefficient without expanding every term
Combine choice counts with power factors in the binomial theorem.
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Study this chapterChapter 13 · Algebra
Recognize quadratic sequences from their differences
Use a constant second difference to identify a quadratic rule.
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Study this chapterChapter 14 · Algebra
Predict whether a polynomial crosses or touches an axis
Use root multiplicity to interpret local sign changes.
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Study this chapterChapter 15 · Algebra
Expose a rational graph's shifted reciprocal structure
Rewrite a rational function to identify asymptotes and range restrictions.
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Study this chapterChapter 16 · Algebra
Divide complex numbers using a conjugate
Make a complex denominator real without changing the quotient.
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Study this chapterChapter 17 · Algebra
Describe a complex number by magnitude and angle
Choose an argument in the correct quadrant.
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Study this chapterChapter 18 · Trigonometry
Find an exact trigonometric value from familiar angles
Apply an angle-addition identity instead of rounding early.
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Study this chapterChapter 19 · Trigonometry
Keep quadrant information in a double-angle calculation
Find a doubled angle's sine and cosine without guessing its quadrant.
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Study this chapterChapter 20 · Trigonometry
State where a simplified identity is actually defined
Preserve domain restrictions while simplifying a trigonometric quotient.
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Study this chapterChapter 21 · Trigonometry
List every solution of a periodic equation
Combine reference-angle solutions with full-period shifts.
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Study this chapterChapter 22 · Trigonometry
Recognize an inverse trigonometric function's chosen output range
Reduce a composition to its principal angle rather than cancelling blindly.
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Study this chapterChapter 23 · Trigonometry
Separate horizontal shift from angular frequency
Read a factored sinusoidal model's amplitude, period, and phase shift.
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Study this chapterChapter 24 · Trigonometry
Find area without first finding an altitude
Derive triangle area from two sides and their included angle.
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Study this chapterChapter 25 · Algebra
Determine when a quadratic has a repeated real root
Use the discriminant as a condition on a parameter.
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Study this chapterChapter 26 · Algebra
Place a rational number between two different real numbers
Use a fine enough denominator to find a rational point in an interval.
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Study this chapterChapter 27 · Statistics
Separate an association from a controlled comparison
Recognize a confounder and use random allocation to address it.
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Study this chapterChapter 28 · Statistics
Predict how rescaling measurements changes their spread
Transform a mean and standard deviation without recalculating every observation.
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Study this chapterChapter 29 · Statistics
Read shared movement through centered products
Calculate covariance and distinguish its units from correlation.
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Study this chapterChapter 30 · Statistics
Find variables that are pairwise independent but not jointly independent
Test the difference between two-way and three-way independence.
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