Algebra 1 practice test: 12 free questions with worked answers

Each daily paper is a short timed practice test of 8 original questions. The Pre-Algebra and Algebra 1 paper covers expressions and equations, straight-line graphs, sequences, ratio, percents, probability and data. Quadratics, systems of equations, inequalities and exponents come up in the Geometry, Algebra 2 and SAT Math paper. Both also include some geometry, such as angles and area, which belongs to a geometry course rather than Algebra 1.

What's on an Algebra 1 test

Algebra 1 courses differ a little from state to state, but almost all of them build to the same skills:

• Expressions and equations: simplifying, solving linear equations and rearranging formulas.
• Inequalities: solving them and showing the answer on a number line.
• Linear functions: slope, intercepts and writing the equation of a line.
• Systems of equations: solving two equations at once by substitution, elimination or graphing.
• Exponents and polynomials: the laws of exponents, adding, multiplying and factoring.
• Quadratics: factoring, the quadratic formula and graphs of parabolas.
• Exponential functions and sequences: growth and decay, arithmetic and geometric sequences.
• Data: scatter plots, lines of best fit and what the slope means in context.

Free Algebra 1 practice test: 12 questions

We wrote these questions for this page. Give yourself 40 minutes, write your working on paper, and use a calculator only for questions 8 and 10. The answers are in the next section.

1. Solve 5(x − 2) = 3x + 8.
2. Solve −3x + 7 > 19.
3. Find the equation of the line through (−2, 5) and (4, −7) in slope-intercept form.
4. If f(x) = 2x² − 3x, find f(−2).
5. Solve the system 2x + y = 11 and x − y = 1.
6. Simplify (3x²y)³ ÷ (9x⁴y).
7. Factor x² − 2x − 35, then solve x² − 2x − 35 = 0.
8. Solve 2x² + 3x − 4 = 0. Give your answers to 2 decimal places.
9. Find the vertex and the x-intercepts of y = x² − 6x + 5.
10. A town has 1,200 people, and its population grows by 5% each year. Write a function for the population after t years and use it to find the population after 3 years.
11. An arithmetic sequence starts 7, 11, 15. Write a formula for the nth term and find the 25th term.
12. A line of best fit for test scores y against hours studied x is y = 4.5x + 52. What does the slope mean, and what score does the line predict for 6 hours?

Algebra 1 practice test answers

Equations and inequalities (questions 1 and 2)

1. Distribute, then collect x on one side: 5x − 10 = 3x + 8, so 2x = 18 and x = 9. Check: 5(7) = 35 and 3(9) + 8 = 35.

2. Subtract 7: −3x > 12. Dividing by a negative number flips the inequality sign, so x < −4. On a number line, that is an open circle at −4 with the arrow pointing left. Forgetting to flip the sign is the most common mistake on this kind of question. Check others with the Inequality Solver.

Lines and functions (questions 3 and 4)

3. The slope is −2. Put the point (−2, 5) into y = mx + b: 5 = −2(−2) + b, so b = 1 and the line is y = −2x + 1. Check with the other point: −2(4) + 1 = −7. See it drawn in the Linear Graph tool.

4. Replace every x with −2, in brackets: f(−2) = 2(−2)² − 3(−2) = 8 + 6 = 14. Without brackets, −2² looks like −4, which gives the wrong answer.

Systems of equations (question 5)

5. Add the two equations to eliminate y: 3x = 12, so x = 4. Then 4 − y = 1, so y = 3. The solution is (4, 3), the point where the two lines cross. Check in the first equation: 2(4) + 3 = 11. The Simultaneous Equations Solver shows each step.

Exponents and factoring (questions 6 and 7)

6. Cube every factor inside the bracket first: (3x²y)³ = 27x⁶y³. Then divide the numbers and subtract the exponents: 27 ÷ 9 = 3, x⁶ ÷ x⁴ = x², and y³ ÷ y = y². The answer is 3x²y².

7. Look for a pair of numbers with a product of −35 and a sum of −2: −7 and 5 work. So x² − 2x − 35 = (x − 7)(x + 5). If the product is zero, one bracket must be zero, so x = 7 or x = −5. The Factoring Calculator checks your work.

Try one yourself. This factoring question comes from our Algebra course. Answer it here and press Mark.

Quadratics (questions 8 and 9)

8. This doesn't factor neatly, so use the quadratic formula with a = 2, b = 3 and c = −4.

So x = 0.85 or x = −2.35 to 2 decimal places. Watch the sign of c: −4ac = −4(2)(−4) = +32.

9. The vertex is at x = −b ÷ 2a = 6 ÷ 2 = 3, and y = 9 − 18 + 5 = −4, so the vertex is (3, −4). The quadratic factors as (x − 1)(x − 5), so the x-intercepts are x = 1 and x = 5. The vertex sits halfway between them, which is a quick check.

Here x is the input and y is the value of x² − 6x + 5. The parabola opens upward because the x² term is positive, so the vertex is its lowest point.

Exponential growth, sequences and data (questions 10 to 12)

10. Growing by 5% means multiplying by 1.05 each year, so P(t) = 1,200(1.05)^t. After 3 years, P(3) = 1,200 × 1.05³ = 1,389.15, so about 1,389 people. Adding 5% of 1,200 three times gives 1,380, which is linear growth, not exponential.

11. The first term is 7 and the common difference is 4, so the nth term is 7 + 4(n − 1), which simplifies to 4n + 3. The 25th term is 4(25) + 3 = 103. The Sequences and Series Calculator works these out.

12. The slope, 4.5, means each extra hour of study goes with a score about 4.5 points higher. For 6 hours the line predicts 4.5(6) + 52 = 79. The 52 is the predicted score for no study at all. A line of best fit shows a trend, not proof that studying caused the higher scores.

What to practice next

The links: Algebra course, Graphing Functions course, Exponent Calculator, Quadratic Graph and Linear Regression Calculator.

Algebra 1 end-of-course exams and official practice tests

Many states give an Algebra 1 end-of-course (EOC) exam, and its name, format and weight differ from state to state. Ask your teacher which test you will take, then use your state education department's own practice tests, because they match the real format.

New York publishes the most. Its past Regents Examinations in Algebra I come with scoring keys, rating guides, model responses and conversion charts, so you can sit a real paper and score it. The June 2026 exam had 35 questions in four parts and ran for 3 hours, from 9:15 a.m. to 12:15 p.m., and its conversion chart turned a top raw score of 82 into a scale score of 100. NYSED's June 2027 Regents exams run from June 15 to June 24, so check your school's timetable for the Algebra I day.

Use the daily paper as a short timed practice test

1. Open today's Pre-Algebra and Algebra 1 paper and set the suggested time, 30 to 35 minutes.
2. Show every step, as you would on a constructed-response question.
3. Mark it with the mark scheme and write the topic next to each lost mark.
4. When the Algebra 1 paper feels easy, move on to the Geometry, Algebra 2 and SAT Math paper for quadratics and systems.

Common Algebra 1 mistakes

• Not flipping the inequality sign when you multiply or divide by a negative number.
• Squaring a negative without brackets: (−2)² = 4, but −2² = −4.
• Distributing to only the first term: 5(x − 2) is 5x − 10, not 5x − 2.
• Adding exponents when you should multiply: (x²)³ = x⁶, not x⁵.
• Treating percent growth as linear: 5% growth each year multiplies by 1.05 each time.
• Stopping at the factored form when the question asks you to solve the equation.

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