Precalculus Grades 9 to 12
Finish high-school math at the Boathouse: the complex plane, the binomial theorem, rational functions, inverses, trigonometric identities and equations, the laws of sines and cosines, conics, vectors, matrices and expected value, every answer checked.
Free, start to finish. No card. Every week opens without signing in.
- Grade
- Grades 9 to 12
- Length
- 12 weeks
- Pace
- 6 short lessons a week, about 20 minutes each
- Price
- Free, every week
About this course
Precalculus Grades 9 to 12 is a 12-week high-school math course. Students join Comet and Wren at the Boathouse, the old rowing shed on the lake that the crew gets ready for a spring Regatta Day, and every week's math makes part of the regatta work. The course covers the complex plane and polar form, the Fundamental Theorem of Algebra and the Binomial Theorem, rational functions and their asymptotes, inverse functions including 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 for fair decisions. Every week lists the Common Core (+) standards it practices. Short daily lessons with checked answers, a hands-on Boathouse Lab each week and a Saturday Dock Day for the family. No accounts, apps or software needed. 100% free, start to finish.
Kids will
- Work with complex numbers on the complex plane in rectangular and polar form, and factor polynomials over the complex numbers
- Expand binomials, graph rational functions with their asymptotes, and find and verify inverse functions
- Use the unit circle, the addition formulas and inverse trigonometric functions to find exact values and solve trigonometric equations
- Solve any triangle with the Laws of Sines and Cosines and write the equations of ellipses and hyperbolas from their foci
- Represent and combine vectors, and use matrices to transform the plane and solve systems of equations
- Count with permutations and combinations and use expected value to weigh and make fair decisions
The 12 weeks
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Week 1
The Complex Plane
Dock lights on a grid
CCSS N-CN.A.3, N-CN.B.4, N-CN.B.5, N-CN.B.6
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Week 2
Every Polynomial Factors
Planks in Pascal's rows
CCSS N-CN.C.8, N-CN.C.9, A-APR.C.5, A-APR.D.7
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Week 3
Rational Functions
Lap times that climb toward a wall
CCSS F-IF.C.7, F-IF.B.4, F-BF.A.1
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Week 4
Inverses Everywhere
The winch rule run backwards
CCSS F-BF.B.4, F-BF.B.5, F-BF.B.3
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Week 5
Tangent, Symmetry and the Turn
The mast's shadow
CCSS F-TF.A.3, F-TF.A.4
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Week 6
The Addition Formulas
Two oars at an angle
CCSS F-TF.C.9
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Week 7
Inverse Trig and the Water Wave
Reading the gauge backwards
CCSS F-TF.B.6, F-TF.B.7
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Week 8
Laws of Sines and Cosines
The buoy sighted from shore
CCSS G-SRT.D.9, G-SRT.D.10, G-SRT.D.11
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Week 9
Ellipses and Hyperbolas
The chalk oval on the lawn
CCSS G-GPE.A.3, G-GPE.A.1
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Week 10
Vectors
Rowing across the drift
CCSS N-VM.A.1, N-VM.A.2, N-VM.A.3, N-VM.B.4, N-VM.B.5
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Week 11
Matrices
The lane card grid
CCSS N-VM.C.6 to N-VM.C.12, A-REI.C.8, A-REI.C.9
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Week 12
Counting, Expected Value and Regatta Day
The heats drawn by lot
CCSS S-CP.B.8, S-CP.B.9, S-MD.A.1 to S-MD.A.4, S-MD.B.5 to S-MD.B.7
Try Week 1 today.
Open the course, pick Day 1 and go. Make a free parent account when you want progress saved for each kid.