Algebra II
Regents Algebra II — the Grade 11 course: functions and their transformations, polynomials, radicals and rational expressions, exponentials and logarithms, series, trigonometry, and inferential statistics.
Algebra II covers 21 units across 4 strands, with 336 practice questions, worked examples, and a printable page for every unit. Each unit has a lesson, practice with worked steps, challenge problems, and a chapter review; the course has chapter quizzes, a midterm and a final.
Every unit below is a page of its own: read the explanation, work the examples, then practise. Answers and worked steps are shown after each attempt, so a parent does not have to mark the routine questions.
Units in Algebra II
- Composing & Inverting Functions — Functions can be bolted together end to end, and any chain can be run backwards.
- Parent Functions & Transformations — A handful of basic shapes, moved and stretched, account for almost every graph you will meet.
- Polynomial Operations — Add and subtract by collecting like terms. Multiply by making sure every pair meets exactly once.
- Factoring — Factoring is multiplication run backwards. Always pull out the common factor first — it makes everything after it easier.
- Dividing Polynomials & the Factor Theorem — Dividing polynomials is the long division you already know, and a remainder of zero names a factor.
- Polynomial Functions & Their Graphs — The degree and the leading coefficient decide the shape before you plot a single point.
- Solving Quadratic Equations — Four methods, one goal. Factoring is fastest when it works; the quadratic formula always works.
- Radicals & Rational Exponents — A root is a fractional power. Once you accept that, every exponent rule you know still applies.
- Complex Numbers — One new number, i, and every polynomial equation finally has a solution.
- Radical Functions & Equations — Squaring both sides is legal, and it can still hand you an answer that is wrong.
- Rational Expressions & Equations — Fractions with letters in them obey the fraction rules you already know — plus one forbidden value.
- Exponential Functions & Growth — Linear growth adds the same amount each step. Exponential growth multiplies by the same amount — and always wins in the end.
- Logarithms — A logarithm is the exponent — nothing more, and nothing less.
- Exponential & Logarithmic Models — Growth and decay that depend on how much is already there, and the logs that solve them.
- Sequences, Explicit & Recursive — A sequence is a function whose inputs are the counting numbers. Describe it from the start, or from the term before.
- Series & Sigma Notation — Adding a long list of terms without adding them one at a time.
- Radians & the Unit Circle — Measure angles by the arc they cut, and trigonometry escapes the right triangle.
- Graphs of Sine & Cosine — Going round in circles, drawn flat, gives a wave — and four numbers describe any wave.
- Trigonometric Identities & Equations — One identity comes straight from Pythagoras, and it unlocks nearly every trig equation.
- The Normal Distribution — Some measurements cluster in a bell-shaped pattern that a normal distribution can approximate.
- Sampling, Simulation & Inference — A well-chosen thousand can speak for millions, provided you admit how far off you might be.