Free Algebra 1 Worksheets With Answers
Algebra 1 rewards fluency more than cleverness: the students who do well are the ones who can solve, factor and graph without stopping to think about the mechanics. These free questions build that fluency, with every step shown.
10 free questions · Answer keys included · No sign-up to practice
Skills covered in Algebra 1
Covers the standard Algebra 1 sequence: linear equations and inequalities, systems, exponents and polynomials, factoring, quadratic functions, and function notation.
- Solving multi-step linear equations and inequalities
- Slope-intercept and point-slope form
- Systems of equations by substitution and elimination
- Laws of exponents and polynomial arithmetic
- Factoring trinomials and differences of squares
- Solving quadratics by factoring and the quadratic formula
- Function notation, domain and range
- Interpreting linear and quadratic graphs
Free Algebra 1 practice questions with answers
Filter by topic or difficulty, or work straight through. Every answer opens to show the steps, so the page works as a worksheet and an answer key at the same time.
- Question 1easyLinear equations
Solve: 3x − 9 = 0
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Answer: x = 3
Add 9: 3x = 9. Divide by 3: x = 3.
- Question 2easyExponents
Simplify: (x³)⁴
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Answer: x¹²
Power raised to a power means multiply the exponents: 3 × 4 = 12.
- Question 3easyFunctions
If f(x) = x² − 3, find f(−2).
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Answer: 1
Substitute: (−2)² − 3 = 4 − 3 = 1. Note the brackets keep the square positive.
- Question 4easyFactoring
Factor: x² − 16
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Answer: (x + 4)(x − 4)
This is a difference of squares, since 16 = 4², so it factors as (x + 4)(x − 4).
- Question 5easyLinear equations
Write the equation of a line with slope 2 through (0, −5).
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Answer: y = 2x − 5
The point is the y-intercept, so b = −5 and the equation is y = 2x − 5.
- Question 6mediumFactoring
Factor: x² + 7x + 12
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Answer: (x + 3)(x + 4)
Find two numbers multiplying to 12 and adding to 7: 3 and 4.
- Question 7mediumSystems
Solve the system: y = 2x and x + y = 9
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Answer: x = 3, y = 6
Substitute y = 2x into the second equation: x + 2x = 9, so 3x = 9 and x = 3, giving y = 6.
- Question 8mediumQuadratics
Solve: x² − 5x + 6 = 0
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Answer: x = 2 or x = 3
Factor to (x − 2)(x − 3) = 0, so either factor can be zero.
- Question 9hardQuadratics
Solve 2x² + 3x − 2 = 0 using the quadratic formula.
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Answer: x = 0.5 or x = −2
With a=2, b=3, c=−2 the discriminant is 9 + 16 = 25, so x = (−3 ± 5) ÷ 4, giving 0.5 and −2.
- Question 10hardSystems
Solve: 3x + 2y = 16 and x − 2y = 0
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Answer: x = 4, y = 2
Add the equations to eliminate y: 4x = 16, so x = 4. Then 4 − 2y = 0 gives y = 2.
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What Algebra 1 students are expected to master
Algebra 1 is less conceptually demanding than its reputation suggests and far more demanding on fluency. Almost every question in the course reduces to solving, factoring or graphing, and a student who has to think hard about each of those will run out of time and working memory on the multi-part problems that carry the marks. The goal is for the mechanics to become automatic so attention is free for the structure.
Factoring is the highest-leverage skill in the course. It appears in solving quadratics, simplifying rational expressions, and finding the zeros of a function, so a student who is shaky at factoring will find three separate units harder than they should be. It is worth over-practising relative to everything else.
The Algebra 1 mistakes that cost the most marks
Sign errors during substitution dominate. Evaluating f(x) = x² − 3 at x = −2 requires writing (−2)², and a student who writes −2² will get −4 − 3 = −7 instead of 1. The bracket is not a formality; it is the whole difference. Requiring brackets on every negative substitution eliminates a large share of lost marks.
The second is dropping a solution from a quadratic. A student who factors (x − 2)(x − 3) = 0 and reports only x = 2 has done all the hard work and given half an answer. Writing both factors as separate equations before solving makes the second solution structurally impossible to forget.