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← High school

Learn Algebra I unit by unit

Master equations, inequalities, functions, systems, and quadratics.

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7Core units
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Units at a glance

Every unit in this course, what you will be able to do once you finish it, and roughly when it lands in a 14-week schedule.

Algebra I course map: 7 units
#UnitWhat you can do after itWeeks
01Linear equationsYou can solve an equation for one unknown even when it has parentheses or letters on both sides.Weeks 1-2
02InequalitiesYou can solve an inequality and show the answer on a number line or in interval form.Weeks 3-4
03Functions and graphsYou can decide whether a rule is a function, read values off its graph, and use notation like f(3).Weeks 5-6
04Systems of equationsYou can find the point where two lines cross by graphing, substitution or elimination.Weeks 7-8
05ExponentsYou can multiply, divide and stack powers without ever writing them out long, including zero and negative exponents.Weeks 9-10
06PolynomialsYou can add, subtract and multiply polynomials and pull them back apart into factors.Weeks 11-12
07Quadratic functionsYou can solve a quadratic by factoring, square roots or the quadratic formula, and sketch the parabola it makes.Weeks 13-14

Algebra I course units

Work in order for a complete course, or jump directly to the unit you need for an upcoming assessment.

01

Linear equations

Weeks 1-2

You can solve an equation for one unknown even when it has parentheses or letters on both sides. You can also put your answer back in to prove it works.

  • Solve 3(x - 4) = 2x + 5 by clearing the parentheses first.
  • Clear fractions out of x/3 + 2 = 7 by multiplying every term by 3.
  • Rearrange a formula such as P = 2L + 2W to get W by itself.

Worked example

Solve 3(x - 4) = 2x + 5

  1. 3x - 12 = 2x + 5
  2. 3x - 2x = 5 + 12

Answerx = 17 (check: 3(13) = 39 and 2(17) + 5 = 39)

Most common mistakeDistributing to only the first term: 3(x - 4) becomes 3x - 4 instead of 3x - 12, which gives x = 9.

Explain linear equationsPractice linear equations
02

Inequalities

Weeks 3-4

You can solve an inequality and show the answer on a number line or in interval form. You know the one move that flips the inequality sign around.

  • Solve -2x + 1 > 9 and flip the sign when you divide by a negative.
  • Graph x >= -3 with a filled dot and an arrow to the right.
  • Turn 'at most 40 hours' into h <= 40 and solve a pay problem with it.

Worked example

Solve -2x + 1 > 9

  1. -2x > 8
  2. Divide by -2 and flip the sign

Answerx < -4 (check x = -5: -2(-5) + 1 = 11, and 11 > 9)

Most common mistakeKeeping the sign the same after dividing by a negative: answering x > -4, which wrongly accepts x = 0 even though -2(0) + 1 = 1 is not greater than 9.

Explain inequalitiesPractice inequalities
03

Functions and graphs

Weeks 5-6

You can decide whether a rule is a function, read values off its graph, and use notation like f(3). You can also state the domain and range in plain words.

  • Run the vertical line test on a graph to decide if it is a function.
  • Evaluate f(x) = x squared - 2x at x = 5.
  • State that the domain of f(x) = 1/(x - 3) is every number except 3.

Worked example

If f(x) = x squared - 2x, find f(5)

  1. Replace every x with 5: f(5) = 5 squared - 2(5)
  2. = 25 - 10

Answerf(5) = 15

Most common mistakeReading f(5) as f times 5: multiplying the whole rule by 5 to get 5x squared - 10x instead of replacing the x's and getting the single number 15.

Explain functions and graphsPractice functions and graphs
04

Systems of equations

Weeks 7-8

You can find the point where two lines cross by graphing, substitution or elimination. You can also spot when two lines never cross or are secretly the same line.

  • Solve by substitution when one equation already has y by itself.
  • Add two equations to cancel a variable, as with 2x + y = 7 and 3x - y = 8.
  • Read a final line of 0 = 5 as a sign that there is no solution at all.

Worked example

Solve 2x + y = 7 and 3x - y = 8

  1. Add the two equations so y cancels: 5x = 15
  2. x = 3

AnswerPut x = 3 back in: 6 + y = 7, so the answer is (3, 1)

Most common mistakeAdding the left sides but forgetting the right sides: writing 5x = 7 and reporting x = 1.4 instead of x = 3.

Explain systems of equationsPractice systems of equations
05

Exponents

Weeks 9-10

You can multiply, divide and stack powers without ever writing them out long, including zero and negative exponents. You can also write very large and very small numbers in scientific notation.

  • Simplify x cubed times x to the fifth as x to the eighth by adding exponents.
  • Rewrite 2 to the power -3 as 1/8.
  • Write 0.00042 as 4.2 x 10 to the power -4.

Worked example

Simplify (2x cubed) to the fourth power

  1. Raise both parts: 2 to the fourth times x cubed to the fourth
  2. 16 times x to the twelfth

Answer16x to the twelfth power

Most common mistakeRaising only the variable: writing 2x to the twelfth instead of 16x to the twelfth, because the 2 out front was never raised to the fourth power.

Explain exponentsPractice exponents
06

Polynomials

Weeks 11-12

You can add, subtract and multiply polynomials and pull them back apart into factors. You can also read the zeros straight off a factored form.

  • Multiply (x + 3)(x - 5) and collect the middle terms.
  • Pull the greatest common factor out of 6x cubed + 9x squared.
  • Factor x squared - 9 as a difference of two squares.

Worked example

Multiply (x + 3)(x - 5)

  1. Every term times every term: x squared - 5x + 3x - 15
  2. Collect -5x + 3x = -2x

Answerx squared - 2x - 15

Most common mistakeMultiplying only the first pair and the last pair: writing x squared - 15 and losing the middle term -2x entirely.

Explain polynomialsPractice polynomials
07

Quadratic functions

Weeks 13-14

You can solve a quadratic by factoring, square roots or the quadratic formula, and sketch the parabola it makes. You can also find the vertex and say whether it is the high point or the low point.

  • Solve x squared - 2x - 15 = 0 by factoring into (x - 5)(x + 3).
  • Use the quadratic formula on 2x squared + 3x - 2 = 0.
  • Find the vertex of y = x squared - 6x + 5 with x = -b/(2a).

Worked example

Find the vertex of y = x squared - 6x + 5

  1. x = -b/(2a) = 6/2 = 3
  2. y = 9 - 18 + 5 = -4

AnswerThe vertex is (3, -4), and it is the lowest point

Most common mistakeDropping the minus in -b/(2a): using x = -6/2 = -3, which lands on the point (-3, 32), far up the other arm of the parabola.

Explain quadratic functionsPractice quadratic functions

Prepare for Algebra I practice

Start with the earliest uncertain prerequisite

Before timing yourself, check whether you can explain Linear equations from a blank page. Then connect it to Inequalities. If either explanation depends on copying a formula, review the unit first and complete two untimed examples.

Use tools to verify, not to choose the method for you

The Algebra calculator can test calculations and representations used in Algebra I. Make the setup yourself, predict the sign or scale, and compare the tool result with that prediction. Use the formula library to check conditions as well as notation.

Know when to move to the full test

Move from Algebra I practice to the complete course test after you can correct a missed problem without reopening the worked answer. Record the earliest wrong decision—not only the final score—so the next study session has a precise target.

Before and after the syllabus

Learn the ideas, then practise them

The unit list tells you what is covered. These two pages are where the method is explained and where you find out whether it stuck.

GuidesAlgebra explainedConcepts, worked methods and checks behind this course.
PracticeMixed Algebra I questionsAnswer review after every attempt.
ReferenceFormulas for this courseConditions and a worked example for each one.
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Assess

Take the complete Algebra I test

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Reference

Review essential formulas

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Calculate

Use the Algebra calculator

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Plan

Prepare around your exam date

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Questions about the Algebra I course

Where should I start?

Start with Linear equations if you are following the full sequence. If that unit feels automatic, open the Algebra I practice page, choose mixed review, and let the first errors identify the earliest prerequisite to revisit.

How do I know I am ready for the course test?

You are ready when you can choose a method without a hint, show the governing steps, and explain why the result is reasonable. Use the complete Algebra I test only after you can correct practice errors from a blank page.

Which calculator supports this course?

The Algebra calculator supports the calculations and representations used in this course. Use it to test or visualize a result after making your own setup.