Precalculus 9-12
A boathouse readied for Regatta Day: the complex plane, binomials, rational functions, inverses, trig identities and equations, the Laws of Sines and Cosines, conics, vectors, matrices and expected value.
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Precalculus
A free online high-school Precalculus course for Grades 9 to 12: the complex plane and polar form, the Fundamental Theorem of Algebra and the Binomial Theorem, rational functions, inverse functions, the tangent function and the addition formulas, inverse trigonometry, the Laws of Sines and Cosines, ellipses and hyperbolas, vectors, matrices, counting and expected value, built around the Boathouse the crew readies for a spring Regatta Day.
About the series
Precalculus is a free online high-school math course for Grades 9 to 12 that needs only graph paper, a tape measure, a protractor, a stopwatch, string and chalk, index cards and a cloth bag of numbered tokens. Comet and Wren, the older crew, take on the Boathouse, the old rowing shed on the lake behind the community center, and get it ready for a spring Regatta Day, and every week's math makes a piece of the regatta work: dock lights plotted on the complex plane, hull planks stacked in Pascal's rows, lap times that climb toward a wall, the winch rule run backwards, the mast's shadow, two oars at an angle, the depth gauge wave, a buoy sighted from two points on shore, a chalk oval on the lawn, rowing across the drift, the lane card grid and the boat outline stretched and flipped, and regatta heats drawn by lot. Students study a worked example, answer questions whose answers are computed and checked, and keep a Boathouse Log. The course maps week by week to the Common Core high-school (+) standards for complex numbers, vectors and matrices, functions, trigonometry, conic sections and expected value, states no fact about the world beyond the crew's own measurements, and ends with a Regatta Day table run for the family.
In every course
- Grades 9 to 12, about 20 minutes a day
- Twelve weeks, from the complex plane and binomials to vectors, matrices and expected value
- Every question answer computed and checked, never typed by hand
- Every number is the crew's own Boathouse measurement, never a fact about the world
- A hands-on Boathouse Lab every Wednesday with household materials
- The older crew, Comet and Wren, with Nova
- Maps to the Common Core high-school (+) standards for numbers, functions, trigonometry, geometry and probability
- A Saturday Dock Day for the family, with a note for the grown-up
- Free, start to finish. No card.
The course
The course is free, start to finish.
Questions families ask
What does it cost?
Nothing. Precalculus is free from start to finish, with no card. A free parent account saves each student's progress.
What do we need at home?
Graph paper, a tape measure, a protractor, a stopwatch or kitchen timer, string and chalk, two stakes or heavy cups, index cards, a cloth bag with numbered paper tokens, a few coins or a spinner, cardboard, scissors, tape and a notebook. Life vests on the water, and a grown-up is present on a dock or a ladder.
Is this a full Precalculus course?
It covers the Common Core high-school (+) standards usually taught in Precalculus: the complex plane and polar form, the Fundamental Theorem of Algebra, the Binomial Theorem, rational functions and their asymptotes, inverse functions and logarithms, the tangent function, symmetry and periodicity, the addition and subtraction formulas, inverse trigonometric functions and trigonometric equations, the Laws of Sines and Cosines, ellipses and hyperbolas, vectors, matrices and matrix transformations, permutations and combinations, and expected value. Limits and derivatives are not included. It is not a credit-bearing or accredited course.
What should a student know first?
Complex arithmetic, polynomial division, rational expressions, logarithms, the unit circle with sine and cosine, sinusoids and two-way-table probability (Algebra 2 Grades 9 to 12), plus right-triangle trigonometry and the equations of circles and parabolas (Geometry Grades 9 to 12). The course reviews each in a worked example as it goes.
Which standards does it cover?
The Common Core high-school standards N-CN, N-VM, A-APR, A-REI, F-IF, F-BF, F-TF, G-SRT, G-GPE, S-CP and S-MD, with the (+) codes, listed week by week in the course.
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