What should a Algebra 2 student know in math?
Polynomial and rational expressions, complex numbers, exponentials and logarithms, sequences and series, and probability with normal distributions.
Algebra 2 math practice — adaptive, verified, parent-run
8,119 verified practice questions across 82 Common Core concepts for Algebra 2
What should a Algebra 2 student know?
Algebra 2 extends Algebra 1 into richer functions: polynomial, rational, radical, exponential, and logarithmic. Complex numbers complete the number system your child has been building since first grade.
Sequences and series, systems of equations, and probability — including the normal distribution — round out the course. It's the final stepping stone to pre-calculus, statistics, and the math SAT/ACT sections.
The curriculum map
Every Common Core concept we cover for Algebra 2
Advanced Equations and Systems
- Calculate the sum of a finite geometric series
- Derive the geometric series sum formula
- Explain how extraneous solutions arise
- Explain why graph intersections give solutions to f(x)=g(x)
- Find approximate solutions to f(x)=g(x) using tables or technology
- Interpret linear-quadratic system solutions graphically
- Solve a linear-quadratic system by substitution
- Solve linear-quadratic systems
- Solve radical equations and check for extraneous solutions
- Solve rational and radical equations
- Solve rational equations and check for extraneous solutions
- Understand intersection points as solutions to f(x)=g(x)
Advanced Function Analysis
- Build new functions by adding, subtracting, multiplying, or dividing functions
- Combine functions using arithmetic operations
- Determine end behavior of polynomial functions
- Find inverse functions
- Graph a polynomial using zeros, multiplicity, and end behavior
- Graph polynomial functions
- Model real-world situations by combining standard functions
- Solve f(x)=c for a function with an inverse
- Write an expression for the inverse of a function
Conditional Probability and Normal Distributions
- Apply the Addition Rule for probability
- Calculate P(A|B) by restricting the sample space to B
- Compute conditional probability using P(A|B) = P(A and B)/P(B)
- Compute P(A or B) using the Addition Rule
- Construct two-way frequency tables from data
- Define sample spaces and describe events using set notation
- Describe events as subsets of a sample space
- Determine if two events are independent using P(A and B) = P(A)*P(B)
- Distinguish between independent and dependent events in context
- Estimate population percentages using the empirical rule and z-scores
- Explain conditional probability and independence in context
- Find conditional probability as fraction of outcomes
- Find unions, intersections, and complements of events
- Fit a normal distribution using mean and standard deviation
- Identify common misconceptions about probability and independence
- Interpret conditional probability as a fraction in context
- Interpret independence through conditional probability
- Interpret the Addition Rule in real-world contexts
- Recognize conditional probability in everyday situations
- Understand conditional probability
- Understand independence of two events
- Use normal distributions to estimate population percentages
- Use two-way tables to assess approximate independence
Exponential and Logarithmic Models
- Apply properties of logarithms to simplify expressions
- Convert between exponential and logarithmic forms
- Evaluate logarithmic solutions using technology
- Express exponential model solutions as logarithms
- Isolate the exponential term and express solution as a logarithm
- Model and solve real-world exponential growth/decay problems
- Solve exponential equations using logarithms
- Understand inverse relationship between exponents and logarithms
Polynomial and Rational Expressions
- Determine if a linear expression is a factor of a polynomial
- Evaluate a polynomial using the Remainder Theorem
- Find factors of a polynomial using synthetic division
- Identify zeros and sketch polynomial graphs
- Identify zeros of a polynomial from its factored form
- Know and apply the Remainder Theorem
- Perform polynomial long division
- Prove and use polynomial identities
- Rewrite a rational expression as quotient plus remainder fraction
- Rewrite rational expressions using long division
- Sketch a rough graph of a polynomial from its zeros
- Use polynomial identities to describe numerical relationships
- Verify polynomial identities algebraically
Sequences and Series
- Model real-world situations with sequences
- Translate between recursive and explicit sequence formulas
- Write arithmetic and geometric sequences
- Write explicit formulas for arithmetic and geometric sequences
- Write recursive formulas for arithmetic and geometric sequences
The Complex Number System
- Add and subtract complex numbers
- Determine if a sum or product is rational or irrational
- Explain properties of rational and irrational numbers
- Identify the real and imaginary parts of a complex number
- Interpret the discriminant to predict solution type
- Know the complex number system
- Multiply complex numbers using i^2 = -1
- Perform arithmetic with complex numbers
- Prove closure of rationals under addition and multiplication
- Represent complex numbers on the complex plane
- Solve quadratics with complex solutions
- Use the quadratic formula to find complex roots
Diagnosis, not just marking
Where Algebra 2 students actually go wrong
For these concepts we've written up the specific mistaken rules children apply — what each one sounds like at the kitchen table, and why it feels right to them. Free to read, no account needed.
Algebra 2 math — questions parents ask
How much math practice does a Algebra 2 student need each day?
Short and daily beats long and rare. Most families set a 10–30 minute time budget; Algo School sizes each Algebra 2 session to that budget and to your child's pace — a quick day never becomes a marathon.
How does Algo School help with Algebra 2 math at home?
Algo School generates short daily sessions from 8,119 verified Algebra 2 questions, checks every answer, and adapts the next session to what your child actually mastered. When they're stuck, an answer-guarded AI tutor coaches with questions and hints — and you get an email brief after every tutoring session. Homeschool families use the per-concept mastery record as their assessment evidence.
Math practice for every band — home and homeschool, Grade 1 through Algebra 2.
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