Algebra Curriculum

Mathematics

A structured, level-by-level path through Algebra. Start with Foundations of Variables & expressions and Core methods in Linear equations at the Intermediate level, then build toward advanced practice and expert-level mastery — with hands-on projects and quizzes at every stage.

3 levels 9 modules 27 topics 6 weeks · about 24 hours · 8 weeks · about 32 hours · 10 weeks · about 40 hours
Intermediate

Intermediate Algebra

6 weeks · about 24 hours

3 modules

Advanced

Advanced Algebra

8 weeks · about 32 hours

3 modules

Expert

Expert Algebra

10 weeks · about 40 hours

3 modules

Algebra Course Curriculum

9 modules across 3 levels.

Intermediate

Intermediate Algebra

Start with Variables & expressions, Linear equations and Inequalities. Each module explains the idea, shows a worked example and ends with a short project, so Algebra becomes something you can do rather than something you have only read about.

6 weeks · about 24 hours 3 modules

Topics

Project

Write a one-page explanation of Variables & expressions in your own words, with an example you chose yourself, and test it against the module checklist.

Learning Path

1

Foundations of Variables & expressions

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

2

Core methods in Linear equations

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Foundations of Variables & expressions

3

Applying Inequalities

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Core methods in Linear equations

Practice Problems

EasyExplain Variables & expressions to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines variables & expressions precisely, gives one concrete example, and names the limitation it runs into.
MediumExplain Linear equations to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines linear equations precisely, gives one concrete example, and names the limitation it runs into.
HardExplain Inequalities to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines inequalities precisely, gives one concrete example, and names the limitation it runs into.

Glossary

Variables & expressions

A central idea in the intermediate Algebra path, covered in the module of the same name.

Example: apply Variables & expressions to a small, familiar case step by step, then check your reasoning against the walkthrough.

Linear equations

A central idea in the intermediate Algebra path, covered in the module of the same name.

Example: apply Linear equations to a small, familiar case step by step, then check your reasoning against the walkthrough.

Inequalities

A central idea in the intermediate Algebra path, covered in the module of the same name.

Example: apply Inequalities to a small, familiar case step by step, then check your reasoning against the walkthrough.

About the Algebra curriculum

The Algebra curriculum is a complete, self-paced course in mathematics, organised into 3 progressive levels and 9 modules. It opens with Foundations of Variables & expressions and Core methods in Linear equations, moves through Applying Inequalities and finishes with expert-level work on Leading practice in Functions & transformations and Mastering Modelling word problems.

Across the whole path you work through 27 individual topics — from Variables & expressions and Hands-on: variables & expressions at the start to Putting modelling word problems to work and Checking your understanding of modelling word problems by the end. The levels are estimated at 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Each level assumes the one before it, so you can work straight through from Intermediate to Expert, or start at the level that matches what you already know.

It suits analysts, researchers and students who need to reason with numbers and defend a conclusion, not just run a tool. The emphasis is on interpretation: every technique is introduced with the question it answers, the assumption it needs and the way it fails, so you can apply it to unfamiliar data.

Every module pairs a written summary with a worked example, a short quiz to check the idea landed, and a project brief drawn from real practice. You are never asked to take a concept on trust: the reasoning, the common mistakes and the situations where the approach stops working are all laid out, so you finish a module able to explain the idea rather than only recognise it.

What you’ll be able to do

By the end of the Algebra path you should be able to work confidently with:

Variables & expressions

Hands-on: variables & expressions

Common pitfalls in variables & expressions

Linear equations

Putting linear equations to work

Common pitfalls in linear equations

Inequalities

Hands-on: inequalities

How the Algebra curriculum is structured

Intermediate 6 weeks · about 24 hours 3 modules 9 topics

Intermediate Algebra

Start with Variables & expressions, Linear equations and Inequalities. Each module explains the idea, shows a worked example and ends with a short project, so Algebra becomes something you can do rather than something you have only read about.

Modules: Foundations of Variables & expressions · Core methods in Linear equations · Applying Inequalities

  • Variables & expressions: Variables & expressions is introduced from first principles, with the few terms you actually need and an example that shows how the idea behaves in practice.
  • Hands-on: variables & expressions: Variables & expressions is where many Algebra learners first get stuck, so the module slows down, isolates the difficult step and rebuilds it with you.
  • Common pitfalls in variables & expressions: Variables & expressions is introduced from first principles, with the few terms you actually need and an example that shows how the idea behaves in practice.

Project: Write a one-page explanation of Variables & expressions in your own words, with an example you chose yourself, and test it against the module checklist.

Advanced 8 weeks · about 32 hours 3 modules 9 topics

Advanced Algebra

Build on the intermediate level through Systems of equations, Polynomials & factoring and Quadratic functions. The emphasis shifts from knowing the ideas to choosing between them — trade-offs, failure modes and the reasoning behind each decision.

Modules: In depth Systems of equations · Patterns and trade-offs in Polynomials & factoring · Scaling Quadratic functions

  • Systems of equations: Here Systems of equations becomes a design decision. You compare alternatives, justify a choice and test it against a harder problem.
  • Hands-on: systems of equations: Systems of equations is pushed past the textbook case: competing approaches, their trade-offs and the situations where each one breaks down.
  • Checking your understanding of systems of equations: Here Systems of equations becomes a design decision. You compare alternatives, justify a choice and test it against a harder problem.

Project: Produce a short case analysis in which Systems of equations drives the recommendation, including the alternatives you rejected and why.

Expert 10 weeks · about 40 hours 3 modules 9 topics

Expert Algebra

Work at the edge of Algebra through Exponents & radicals, Functions & transformations and Modelling word problems. The modules assume fluency and ask for judgement: designing, critiquing and defending work at a professional standard.

Modules: Frontiers of Exponents & radicals · Leading practice in Functions & transformations · Mastering Modelling word problems

  • Exponents & radicals: Exponents & radicals is examined at the frontier, with an emphasis on open problems, rigorous argument and decisions you can defend.
  • Putting exponents & radicals to work: This module asks you to critique and extend Exponents & radicals rather than simply apply it, producing work another expert could review.
  • Checking your understanding of exponents & radicals: Exponents & radicals is examined at the frontier, with an emphasis on open problems, rigorous argument and decisions you can defend.

Project: Write a professional-standard brief on Exponents & radicals — argument, evidence, limitations — plus a plan for taking the work further.

How to study Algebra, phase by phase

  1. 1

    Phase 1 — Intermediate

    Set aside around 6 weeks · about 24 hours. Work through 3 modules, starting with Foundations of Variables & expressions and Core methods in Linear equations. Finish the phase by completing the project brief: Write a one-page explanation of Variables & expressions in your own words, with an example you chose yourself, and test it against the module checklist.

  2. 2

    Phase 2 — Advanced

    Set aside around 8 weeks · about 32 hours. Work through 3 modules, starting with In depth Systems of equations and Patterns and trade-offs in Polynomials & factoring. Finish the phase by completing the project brief: Produce a short case analysis in which Systems of equations drives the recommendation, including the alternatives you rejected and why.

  3. 3

    Phase 3 — Expert

    Set aside around 10 weeks · about 40 hours. Work through 3 modules, starting with Frontiers of Exponents & radicals and Leading practice in Functions & transformations. Finish the phase by completing the project brief: Write a professional-standard brief on Exponents & radicals — argument, evidence, limitations — plus a plan for taking the work further.

  4. 4

    Phase 4 — Consolidate

    Return to the sections that felt weakest, redo their quizzes from memory, and rebuild the Write a one-page explanation of Variables & expressions in your own words, with an example you chose yourself, and test it against the module checklist. without following along. Explaining Algebra to someone else in plain language is the clearest signal that the Expert level has landed.

Once you have finished, the Algebra path is a reasonable foundation for analytics, data science, research and quantitative roles. Because the curriculum is generated and kept as a structured outline rather than fixed videos, you can revisit any module, regenerate the outline at a different depth, or save it to your library and work through it over weeks rather than in one sitting.

Algebra — Frequently Asked Questions

Common questions about studying Algebra on LearnAnyCourse.

What does the Algebra curriculum cover?

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The Algebra curriculum is organised into 3 levels (Intermediate, Advanced and Expert) and 9 modules, including Foundations of Variables & expressions, Core methods in Linear equations, Applying Inequalities, In depth Systems of equations, Patterns and trade-offs in Polynomials & factoring and Scaling Quadratic functions.

How long does it take to learn Algebra?

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Each level is designed to take about 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Most learners work through one level at a time at their own pace.

Is the Algebra curriculum free?

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Yes. Every Algebra curriculum on LearnAnyCourse is free to read and study — create an account only if you want to save curricula to your personal library.

Do I need prior experience to study Algebra?

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The curriculum starts at the intermediate level and builds upward, so you can begin with the fundamentals and progress to expert-level Algebra topics without jumping ahead.

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