Algebra curriculum

A full algebra path from linear models through quadratics, exponentials, radicals, rational expressions, and function fluency.

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High school / Algebra 1-2 / AP readiness

Algebra curriculum

A full algebra path from linear models through quadratics, exponentials, radicals, rational expressions, and function fluency.

Pacing

8 units, 24-32 weeks self-paced

Units

8 unit sequence

Practice

32 checked answers

Support

Self-paced or tutor-guided

Outcomes

Translate between verbal, numeric, algebraic, and graphical representations.
Solve equations and inequalities with clear reasoning and checks.
Use functions as models for linear, exponential, quadratic, and rational relationships.

Khan Academy companion path

Use these linked courses for video instruction and mastery practice, then return here for PeerTutor original checks and tutor help on the exact unit that got stuck.

Algebra

External video content is linked, not copied. PeerTutor practice is original and cites each source path separately.

Unit sequence

Built for independent progress first, then tutor support where the student gets stuck.

01
Foundations, expressions, and equations
- Evaluate and simplify expressions.
- Solve one-variable equations and literal formulas.
Practice: Build an equation from a real situation, solve it, and verify the answer in context.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Expression fluency
Simplify: 3(2x - 5) + 4x.
Equation solving
Solve 5y - 7 = 18.
y = 3y = 5y = 11/5y = 25
Unit readiness
Which target best matches the Algebra unit "Foundations, expressions, and equations"?
Evaluate and simplify expressions.Solve one-variable equations and literal formulas.Write linear models from graphs, tables, and points.Use slope, intercepts, and rate of change.
Practice artifact
Which practice artifact should you produce for "Foundations, expressions, and equations" before asking a tutor for help?
Build an equation from a real situation, solve it, and verify the answer in context.Skip the unit and start a new subject.Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.
02
Linear relationships
- Use slope, intercepts, and rate of change.
- Write linear models from graphs, tables, and points.
Practice: Create a table, graph, and equation for the same linear relationship.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Slope
A line goes through (2, 5) and (6, 13). What is its slope?
Linear model
Which equation has slope -3 and y-intercept 4?
y = 4x - 3y = -3x + 4y = 3x - 4y = -4x + 3
Unit readiness
Which target best matches the Algebra unit "Linear relationships"?
Write linear models from graphs, tables, and points.Evaluate and simplify expressions.Solve one-variable equations and literal formulas.Use slope, intercepts, and rate of change.
Practice artifact
Which practice artifact should you produce for "Linear relationships" before asking a tutor for help?
Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.Create a table, graph, and equation for the same linear relationship.Skip the unit and start a new subject.
03
Systems and inequalities
- Solve systems by graphing, substitution, and elimination.
- Represent constraints with inequalities.
Practice: Model a budget or scheduling constraint as a system and explain the feasible region.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Systems
Solve the system: x + y = 9 and x - y = 1. Give the ordered pair.
Inequalities
For x + y <= 10 with x,y >= 0, which point is feasible?
(8, 4)(6, 4)(-1, 3)(11, 0)
Unit readiness
Which target best matches the Algebra unit "Systems and inequalities"?
Evaluate and simplify expressions.Solve one-variable equations and literal formulas.Solve systems by graphing, substitution, and elimination.Use slope, intercepts, and rate of change.
Practice artifact
Which practice artifact should you produce for "Systems and inequalities" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Model a budget or scheduling constraint as a system and explain the feasible region.Skip the unit and start a new subject.
04
Functions and transformations
- Use function notation and domain/range.
- Describe transformations from parent functions.
Practice: Compare two functions given in different forms and defend which grows faster.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Function notation
If f(x) = 2x^2 - 3, what is f(4)?
Transformations
g(x) = (x - 2)^2 + 5 moves y = x^2 how?
left 2, up 5right 2, up 5right 5, up 2left 5, down 2
Unit readiness
Which target best matches the Algebra unit "Functions and transformations"?
Evaluate and simplify expressions.Solve one-variable equations and literal formulas.Describe transformations from parent functions.Use slope, intercepts, and rate of change.
Practice artifact
Which practice artifact should you produce for "Functions and transformations" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Compare two functions given in different forms and defend which grows faster.Skip the unit and start a new subject.
05
Exponents and exponential models
- Apply exponent rules and scientific notation.
- Model growth and decay.
Practice: Fit an exponential model to a short data table and interpret the parameters.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Exponent rules
Simplify: (2x^3)^2.
Exponential models
A quantity starts at 80 and halves every year. Which model fits?
80(2)^t80(0.5)^t0.5(80)^t80 - 0.5t
Unit readiness
Which target best matches the Algebra unit "Exponents and exponential models"?
Solve one-variable equations and literal formulas.Evaluate and simplify expressions.Apply exponent rules and scientific notation.Use slope, intercepts, and rate of change.
Practice artifact
Which practice artifact should you produce for "Exponents and exponential models" before asking a tutor for help?
Memorize vocabulary without checking any examples.Skip the unit and start a new subject.Fit an exponential model to a short data table and interpret the parameters.Watch videos without writing or solving anything.
06
Polynomials and factoring
- Add, multiply, and factor polynomials.
- Use factoring to reveal zeros.
Practice: Factor multiple forms of quadratics and check by expansion.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Factoring
Factor x^2 + 7x + 12.
Zeros
If a quadratic factors as (x - 2)(x + 5), what are its zeros?
2 and 5-2 and 52 and -5-2 and -5
Unit readiness
Which target best matches the Algebra unit "Polynomials and factoring"?
Use slope, intercepts, and rate of change.Use factoring to reveal zeros.Solve one-variable equations and literal formulas.Evaluate and simplify expressions.
Practice artifact
Which practice artifact should you produce for "Polynomials and factoring" before asking a tutor for help?
Skip the unit and start a new subject.Factor multiple forms of quadratics and check by expansion.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
07
Quadratic functions
- Use standard, vertex, and factored forms.
- Solve quadratics by factoring, completing the square, and the quadratic formula.
Practice: Analyze a projectile model using vertex and intercepts.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quadratics
For y = (x - 3)^2 - 4, what is the vertex?
Projectile interpretation
For h(t) = -16t^2 + 64t + 5, which t gives the maximum height?
1245
Unit readiness
Which target best matches the Algebra unit "Quadratic functions"?
Use slope, intercepts, and rate of change.Solve one-variable equations and literal formulas.Evaluate and simplify expressions.Use standard, vertex, and factored forms.
Practice artifact
Which practice artifact should you produce for "Quadratic functions" before asking a tutor for help?
Skip the unit and start a new subject.Analyze a projectile model using vertex and intercepts.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
08
Radicals, rationals, and algebra review
- Simplify radical and rational expressions.
- Identify extraneous solutions.
Practice: Solve mixed radical and rational equations with written domain checks.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Radicals
Solve sqrt(x) = 7.
Rational domain
Which value is excluded from (x + 2)/(x - 5)?
-2057
Unit readiness
Which target best matches the Algebra unit "Radicals, rationals, and algebra review"?
Identify extraneous solutions.Use slope, intercepts, and rate of change.Solve one-variable equations and literal formulas.Evaluate and simplify expressions.
Practice artifact
Which practice artifact should you produce for "Radicals, rationals, and algebra review" before asking a tutor for help?
Solve mixed radical and rational equations with written domain checks.Watch videos without writing or solving anything.Skip the unit and start a new subject.Memorize vocabulary without checking any examples.