What should a Algebra 1 student know in math?
Solving equations, inequalities, and systems; linear, quadratic, and exponential functions; polynomials; and interpreting data.
Algebra 1 math practice — adaptive, verified, parent-run
13,290 verified practice questions across 136 Common Core concepts for Algebra 1
What should a Algebra 1 student know?
Algebra 1 is the gatekeeper course. Your child solves equations, inequalities, and systems, and learns to read functions — linear, quadratic, and exponential — as models of real situations.
Polynomial arithmetic and factoring build symbolic fluency; sequences and data interpretation connect algebra to statistics. Every later math and science course leans on this year's skills.
The curriculum map
Every Common Core concept we cover for Algebra 1
Advanced Function Analysis
- Describe stretches, compressions, and reflections of function graphs
- Describe vertical and horizontal shifts of function graphs
- Find the value of k given a transformed graph
- Graph exponential and logarithmic functions
- Graph logarithmic functions showing key features
Arithmetic with Polynomials
- Add and subtract polynomials by combining like terms
- Add, subtract, and multiply polynomials
- Multiply polynomials using the distributive property
- Understand that polynomials are closed under addition, subtraction, and multiplication
Building Functions
- Apply multiple transformations to graph a function
- Combine functions to model a relationship
- Describe horizontal translations: f(x + k)
- Describe vertical stretches and reflections: k·f(x)
- Describe vertical translations: f(x) + k
- Determine an explicit expression for a function from context
- Identify the effect of transformations on the graph of a function
- Write a function that describes a relationship
- Write a recursive definition for a sequence or function
Creating Equations
- Create equations and inequalities in one variable
- Create equations in two or more variables
- Graph equations on coordinate axes with appropriate labels and scales
- Interpret solutions of a system as viable or non-viable in context
- Model real-world constraints as a system of equations or inequalities
- Rearrange formulas involving squares and square roots
- Rearrange formulas to highlight a quantity of interest
- Represent constraints with equations, inequalities, and systems
- Solve a literal equation for a specified variable
- Write a linear equation in one variable from a word problem
- Write an equation in two variables to represent a relationship
- Write an inequality in one variable from a word problem
- Write a quadratic equation from a word problem
Interpreting Categorical and Quantitative Data
- Assess the fit of a model by analyzing residuals
- Calculate and compare IQR and standard deviation of data sets
- Calculate and compare mean and median of data sets
- Calculate and interpret relative frequencies from a two-way table
- Choose an appropriate plot type for a given data set
- Compare center and spread of data sets
- Compute and interpret the correlation coefficient
- Construct and read a two-way frequency table
- Create a scatter plot and describe the relationship between variables
- Distinguish between correlation and causation
- Evaluate claims of causation in real-world data
- Explain why correlation does not imply causation
- Fit a function to scatter plot data and use it to solve problems
- Fit a linear function to a scatter plot showing linear association
- Interpret differences in shape, center, and spread
- Interpret slope and intercept of a linear model in data context
- Interpret slope of a linear regression model in context
- Interpret the correlation coefficient in context
- Interpret y-intercept of a linear regression model in context
- Represent data with plots
- Summarize categorical data in two-way frequency tables
Interpreting Functions
- Analyze quadratic functions using different forms
- Calculate and interpret average rate of change
- Calculate average rate of change over an interval
- Compare properties of two functions in different representations
- Convert a quadratic function to factored form to find zeros
- Convert a quadratic function to vertex form to find extrema
- Describe the end behavior of exponential functions
- Determine the appropriate domain for a function in context
- Determine whether a relation is a function
- Evaluate a function for given inputs
- Graph absolute value functions and identify their vertex
- Graph a linear function and identify its intercepts
- Graph a piecewise-defined function from its rule
- Graph a quadratic function and identify vertex, intercepts, and axis of symmetry
- Graph exponential functions showing key features
- Graph linear and quadratic functions showing key features
- Graph piecewise, step, and absolute value functions
- Identify and interpret intercepts of a function
- Identify arithmetic and geometric sequences as functions
- Identify growth or decay rate from an exponential function
- Identify intervals of increase, decrease, and sign of a function
- Interpret average rate of change in real-world context
- Interpret exponential functions using exponent properties
- Interpret function notation statements in context
- Interpret key features of graphs and tables
- Recognize sequences as functions
- Relate domain of a function to its graph
- Rewrite exponential functions to reveal different time-scale rates
- Understand functions and function notation
- Use and interpret function notation
- Use function notation and evaluate functions
Linear, Quadratic, and Exponential Models
- Compare exponential and polynomial growth using tables and graphs
- Construct a linear function from two points or a description
- Construct an exponential function from data or a description
- Construct linear and exponential functions from data
- Distinguish between linear and exponential growth
- Interpret initial value and growth/decay factor of an exponential model in context
- Interpret parameters in linear and exponential functions
- Interpret slope and y-intercept of a linear model in context
- Prove that exponential functions grow by equal factors over equal intervals
- Prove that linear functions grow by equal differences over equal intervals
- Recognize situations with constant percent rate of change as exponential
- Recognize situations with constant rate of change as linear
Reasoning with Equations and Inequalities
- Construct a valid argument for an equation-solving process
- Derive the quadratic formula by completing the square
- Explain reasoning in solving equations
- Graph a linear inequality in two variables as a half-plane
- Graph solutions to linear inequalities and systems of inequalities
- Graph the solution set of a system of linear inequalities
- Identify feasible solutions within a system of inequalities
- Justify each step when solving a linear equation
- Prove that elimination preserves system solutions
- Recognize when quadratic equations yield complex solutions
- Solve a system of linear equations approximately by graphing
- Solve a system of linear equations by elimination
- Solve a system of linear equations by substitution
- Solve equations with letter coefficients for a specified variable
- Solve linear equations and inequalities in one variable
- Solve linear inequalities and represent solutions on a number line
- Solve multi-step linear equations in one variable
- Solve quadratic equations by completing the square
- Solve quadratic equations by factoring
- Solve quadratic equations by taking square roots
- Solve quadratic equations in one variable
- Solve quadratic equations using the quadratic formula
- Solve systems of linear equations
- Understand that a graph represents the solution set of an equation
- Verify that a point lies on the graph of an equation
Seeing Structure in Expressions
- Choose equivalent forms to reveal properties
- Complete the square to reveal maximum or minimum value
- Factor a quadratic expression to reveal its zeros
- Interpret complicated expressions by viewing parts as single entities
- Interpret expressions in context
- Interpret parts of an expression: terms, factors, and coefficients
- Recognize and apply algebraic structure to rewrite expressions
- Rewrite expressions using factoring patterns
- Use exponent properties to transform exponential expressions
- Use structure to rewrite expressions
The Real Number System
- Convert between radical and rational exponent form
- Evaluate expressions with rational exponents
- Explain rational exponents as extensions of integer exponent properties
- Extend properties of exponents to rational exponents
- Rewrite expressions involving radicals and rational exponents
- Simplify expressions with radicals and rational exponents
Diagnosis, not just marking
Where Algebra 1 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 1 math — questions parents ask
How much math practice does a Algebra 1 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 1 session to that budget and to your child's pace — a quick day never becomes a marathon.
How does Algo School help with Algebra 1 math at home?
Algo School generates short daily sessions from 13,290 verified Algebra 1 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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