Algebra II in 180 lessons, carried through trigonometry, polar coordinates, and a first working look at calculus.
About this course
Algebra II here covers considerably more than the name usually promises. The year begins with function notation, domain and range, piecewise and absolute value functions, transformations, composition, inverses, and end behavior, then works through polynomials with synthetic division, the remainder and factor theorems, the rational root theorem, Descartes' rule of signs, and complex zeros. Rational functions get a full unit including complex fractions, holes, and slant asymptotes. Exponential and logarithmic work covers the number e, continuous compounding, doubling time and half-life, the properties of logarithms and change of base, and applications to decibels, pH, and the Richter scale. After that come systems and linear programming, matrices and determinants through Cramer's rule and row reduction, the conic sections with parametric equations, sequences and series with sigma notation and the binomial theorem, and a probability and statistics unit covering permutations and combinations, conditional probability, expected value, binomial probability, and the normal distribution.
The last third of the year is where the course reaches past a standard Algebra II, and it is fair to say the title understates it. Two full units cover trigonometry: radians and the unit circle, all six functions and their graphs with amplitude, period, and phase shift, inverse trigonometric functions, the laws of sines and cosines, then identities proved rather than merely listed, sum and difference and double and half-angle formulas, and solving trigonometric equations. A further unit covers the complex plane, polar form, De Moivre's theorem and nth roots, and polar graphing. The fourteenth unit is a genuine first pass at calculus: limits and limit laws, continuity, average and instantaneous rate of change, the derivative and the power rule, tangent lines, Riemann sums, and area under a curve. The final unit is review and mixed application.
The course runs 180 lessons in 15 units of 12, about 55 minutes each, one lesson per school day. A typical lesson states the definition or formula plainly, works three to five examples in full, lists the key facts, and closes with a KJV connection; roughly half the lessons add a short practice set of about three problems, usually without printed answers, so those are yours to check. Every lesson ends with a ten-question quiz that grades itself. Listed materials are a pencil, graph paper, a graphing calculator, and a Bible. Your student should arrive with Algebra I genuinely finished, with factoring, quadratics, exponent rules, radicals, and function notation automatic rather than half-remembered, and geometry beforehand helps with the conics and trigonometry. Freedom Homeschool also offers a general eleventh-grade math course, a broad precalculus survey that covers much of the same ground in functions, matrices, conics, sequences, trigonometry, statistics, and limits while adding number theory, proof, and inferential statistics. The two overlap heavily, so most families should choose one or the other as the year's math rather than assign both; this is the one to pick if your student has not yet had a full Algebra II.
What the course covers
Function notation, transformations, composition, and inverses
Polynomial functions, synthetic division, and the rational root theorem
Rational functions, asymptotes, holes, and rational equations
Exponential and logarithmic functions, growth, decay, and compound interest
Systems of equations, linear programming, matrices, and determinants
Conic sections and parametric equations
Sequences, series, sigma notation, and the binomial theorem
Counting, probability, binomial distributions, and the normal curve
Trigonometric functions, identities, equations, and the laws of sines and cosines
Polar coordinates, complex numbers, limits, and an introduction to derivatives and integrals
What your student will be able to do
Evaluate, transform, compose, and invert functions and read their graphs
Factor and divide polynomials and find all real and complex zeros
Solve exponential and logarithmic equations and use them to model growth and decay
Solve systems by substitution, elimination, matrices, and Cramer's rule
Work from the unit circle to prove identities and solve trigonometric equations
Evaluate limits and compute basic derivatives, tangent lines, and Riemann sums
Scope and sequence
All 15 units of Algebra II for Grade 11, in the order they are taught.
11Algebra II: Bridge to Precalculus and Calculus10 q
12Cumulative Assessment Preparation and Final Reflection10 q
One whole lesson, exactly as it comes
This is a real lesson taken from the middle of the course — the teaching text, the practice, the homework, and the first three quiz questions with their answers. It is not a marketing excerpt.
x²-4y²-6x+8y-11=0. (x²-6x+9)-4(y²-2y+1)=-11+9-4=-6. (x-3)²-4(y-1)²=-6 → not standard. Divide by -6: (y-1)²/(3/2)-(x-3)²/6=1. Vertical hyperbola.
Christian Connection
2 Timothy 2:15: "Study to shew thyself approved unto God, a workman that needeth not to be ashamed." Identifying conics requires careful study — checking signs, completing the square, matching patterns. A diligent student is not ashamed when asked to classify a conic. God rewards diligence in spiritual study the same way: know His Word, handle it rightly, and never be ashamed.
Homework
Complete assigned practice problems. Show all work.
The first three of this lesson's 10 questions
4x²+9y²+Dx+Ey+F=0 is a(n):
hyperbola
parabola
circle
ellipse
Show the answer
Answer: ellipse
x²+y²+Dx+Ey+F=0 (A=C) is a:
ellipse
parabola
hyperbola
circle
Show the answer
Answer: circle
x²-4y²+Dx+Ey+F=0 (opposite signs) is a:
hyperbola
circle
ellipse
parabola
Show the answer
Answer: hyperbola
Another 7 questions follow in the lesson itself, each one graded the moment it is answered.
What comes with the download
180 full lessons
Across 15 units, each with objectives, a teaching passage written to be read aloud, guided practice, and homework.
1,800 quiz questions
Graded the instant they are answered, each with the explanation of why that answer is right.
A gradebook that works
Every score kept, a running average maintained, and a breakdown unit by unit — all in the file itself, nothing sent anywhere.
Progress and attendance
Tick lessons off as they are finished, watch the completion bar fill, and mark days present, absent, or excused.
Report card and certificate
Both printable, with your student's name, the grades, and the dates already filled in.
Backup you control
Export every record to a file you keep, and read it back later. A lost browser cache cannot take the year with it.
An answer key
Hidden from the student by default, there for the parent marking the work.
Nothing that phones home
No ads, no affiliate links, no analytics, no fonts fetched from elsewhere. Unplug the network cable and every one of these files still works.
What you will need
Drawn from the materials named across all 180 lessons of this course. Most families already own most of it.
Download Algebra II — Grade 11
Free, and free of everything else. 17 files, 17.7 MB in total. No account, no email address, no payment. What you download carries no advertising, no affiliate links and no tracking of any kind.
Use it on a screen
Open any of these straight from a folder or a USB stick. They run in the browser with the network cable unplugged, and nothing is ever sent anywhere.