• 70 questions

Basic Algebra Test

Unofficial practice on the first weeks of algebra: expressions, like terms and one-variable equations, each answer worked out.

A ribbon c centimeters long is cut into 5 equal pieces. Which expression gives the length of one piece?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with any school, district or testing agency. Bank checked October 9, 2026.

Next step Review the number work: pre-algebra testNext step: algebra test in five levels

All 70 questions

Writing expressions from words 10

  • A plumber charges $40 to come to the house plus $55 for each hour of work. Which expression gives the charge, in dollars, for h hours? Common Core State Standards for Mathematics, 6.EE.B.6: use variables to represent numbers and write expressions when solving a problem
  • A ribbon c centimeters long is cut into 5 equal pieces. Which expression gives the length of one piece? Common Core State Standards for Mathematics, 6.EE.B.6: use variables to represent numbers and write expressions when solving a problem
  • Movie tickets cost $12 each. Which expression gives the cost, in dollars, of t tickets? Common Core State Standards for Mathematics, 6.EE.B.6: use variables to represent numbers and write expressions when solving a problem
  • Which expression means "5 more than three times a number t"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "8 less than a number m"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
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Writing expressions from words, continued

  • Which expression means "17 decreased by a number p"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "a number n increased by 14"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "the product of 9 and a number k"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "the quotient of a number w and 6"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "twice the sum of a number y and 7"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers

Evaluating expressions 10

  • Evaluate 2(k + 9) when k = 6. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 3a + 2b when a = 5 and b = 9. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 3x² when x = 4. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 4x + 7 when x = 6. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 30 − 3n when n = 8. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 50 − p² when p = 6. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate a² + 5 when a = 7. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate w/4 + 11 when w = 36. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • The perimeter of a rectangle is P = 2L + 2W. What is P when L = 13 and W = 8? Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Renting a kayak for h hours costs 9h + 15 dollars. What is the cost of renting it for 4 hours? Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations

Like terms and the distributive property 16

  • Simplify 2(x + 5) + 3x. Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify 2x + 3y + 5x + y. Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Simplify 4(k + 2) + 3(k + 1). Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify 4a + 7 + 3a. Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Simplify 5k + k. Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Simplify 6x + 9x. Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Simplify 8n + 3 − 2n + 6. Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify 9w − 4 − 6w − 1. Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
  • Simplify 12y − 5y. Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Use the distributive property to rewrite 3(x + 8). Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Use the distributive property to rewrite 5(2y − 3). Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Use the distributive property to rewrite 6(3a + 2). Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Use the distributive property to rewrite 7(4 + n). Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Which expression is equivalent to 8x + 20? Common Core State Standards for Mathematics, 6.EE.A.4: identify when two expressions are equivalent
  • Which expression is equivalent to p + p + p + p + p? Common Core State Standards for Mathematics, 6.EE.A.4: identify when two expressions are equivalent
  • Which pair are like terms? Common Core State Standards for Mathematics, 6.EE.A.2.b: identify parts of an expression: sum, term, product, factor, quotient, coefficient

One-step equations 10

  • Solve 6w = 45. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve 8y = 96. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve 34 = a + 19. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve k/7 = 9. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve m/4 = 2.5. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve n − 26 = 15. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve p − 3.5 = 10. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve x + 17 = 42. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Which equation has the solution x = 6? Common Core State Standards for Mathematics, 6.EE.B.5: use substitution to determine whether a number makes an equation or inequality true
  • Which value of x makes 5x = 35 true? Common Core State Standards for Mathematics, 6.EE.B.5: use substitution to determine whether a number makes an equation or inequality true

Two-step equations 12

  • Solve 2x + 3 = 10. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 2y + 15 = 9. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 3x + 4 = 25. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 4(a + 3) = 36. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 5n − 8 = 32. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 6(x − 4) = 18. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 7w − 5 = −26. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 9 + 4t = 33. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve 10 − 2p = 4. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve k/3 + 6 = 11. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Solve m/5 − 2 = 4. Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • Subtracting 7 from both sides of 3x + 7 = 22 leaves which equation? Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r

Inequalities and word problems 12

  • A club has $80 and earns $15 for each car it washes. It needs more than $200. What is the fewest cars it must wash? Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • A rectangle has a perimeter of 54 cm and a length of 16 cm. What is its width? Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • A taxi ride costs $4 plus $3 for each mile. A ride cost $31. How many miles was it? Common Core State Standards for Mathematics, 7.EE.B.4.a: solve equations of the form px + q = r and p(x + q) = r
  • After spending $37, Mia has $85 left. The equation x − 37 = 85 gives the amount she started with. How much was it? Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Riders on a carnival swing must be at least 36 inches tall. Which inequality describes a rider's height h, in inches? Common Core State Standards for Mathematics, 6.EE.B.8: write an inequality of the form x > c or x < c for a constraint or condition
  • Six equal bags of soil weigh 150 pounds in all. How much does one bag weigh? Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve 2y − 3 < 11. Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • Solve 3n ≤ 27. Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • Solve x + 5 > 12. Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • Solve −2x < 10. Common Core State Standards for Mathematics, 7.EE.B.4.b: solve inequalities of the form px + q > r or px + q < r
  • The sum of a number and 19 is 46. What is the number? Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Which value is a solution of x > 6? Common Core State Standards for Mathematics, 6.EE.B.5: use substitution to determine whether a number makes an equation or inequality true

How this list was compiled: Our own questions. The six topics follow the Expressions and Equations standards for grades 6 and 7 of the Common Core State Standards for Mathematics (https://www.thecorestandards.org/Math/, read 2026-10-09). Each question names the standard it practices and links to that standard's page. Every answer is arithmetic or algebra on what the question prints, worked out a second time on 2026-10-09. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a state test, a placement test, a released form, a textbook or another practice test.

How it works

This free basic algebra test has 70 questions of our own, to answer on screen or print with a key. No graphs, second unknowns or quadratics. It is not any school's test.

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A test of 20

Exam mode draws 20 questions across the topics and scores each topic, so the result names the skill to go back to. The 20 is our number, not any exam's.

Where the topics come from

The topics follow the Expressions and Equations standards for grades 6 and 7 in the Common Core State Standards for Mathematics, read October 9, 2026. Each question names its standard. The split into six topics is ours.

  • Whatever you do to one side of an equation, do to the other side too.
  • In a two-step equation, undo the adding or subtracting first, then the multiplying or dividing.

Questions and answers

What is on a basic algebra test?

Each school writes its own. This one covers how a first algebra unit begins: turning words into expressions, evaluating them, combining like terms, the distributive property, equations solved in one or two steps, and simple inequalities.

Are these basic algebra questions with answers?

Yes. Each of the 70 questions shows its answer once you choose, with the steps that reach it. The steps name what is undone at each stage, so a wrong answer shows where the method slipped.

Can I use this as a basic algebra quiz on one skill?

Yes. For basic algebra practice on a single skill, pick its topic and every question stays on that skill. To hand out a quiz on paper or as a PDF, Print the question sheet lists 20 questions, with the answer key if you tick it.

Are there more basic algebra practice tests after this one?

Yes. Exam mode draws a different 20 each time, so every run is a new test. When these feel easy, the algebra test in five levels goes on to lines, systems and quadratics.

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