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6th Math: Expressions & Equations practice questions and exam guide

150 multiple-choice questions and 85 flashcards, organised into 6 chapters, written to the Common Core State Standards blueprint. Every question carries a full rationale.

Last reviewed 2026-10-26 · CoStudy · how we write and review questions

  • 235 total items
  • 150 multiple choice
  • 85 flashcards
  • 6 chapters

Study 6th Math: Expressions & Equations in CoStudy →

About the 6th Math: Expressions & Equations exam

Common Core State Standards (CCSS) — Mathematics, Grade 6: Expressions & Equations (6.EE.A.1-4, 6.EE.B.5-8, 6.EE.C.9). Public standards from corestandards.org.

CoStudy's 6th Math: Expressions & Equations bank holds 235 items organised into 6 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.

What the 6th Math: Expressions & Equations bank covers

Each chapter follows a domain of the published exam outline. Practise one on its own (chapter URLs are in the app and on this page for navigation; they are not sitemap targets):

Free 6th Math: Expressions & Equations practice questions

A sample of 12 multiple-choice questions from the bank, with the full rationale shown.

Word: Maria has $50. She buys n notebooks at $4 each and now has $26. Equation?

  1. 50 + 4n = 26
  2. 50 − 4n = 26
  3. 26 + 4n = 50
  4. Both B and C

Answer: D — Both B and C

D) Both B and C are equivalent setups: 50 − 4n = 26 is the spending model; 26 + 4n = 50 is the inverse. A) Adds 4n instead of subtracting.

Solve 1/3 x = 6.

  1. x = 2
  2. x = 6
  3. x = 18
  4. x = 1/2

Answer: C — x = 18

Multiply both sides by 3: x = 18. (A), (B), (D) miscalculate.

Lara had some marbles. She got 8 more, and now has 23. How many did she start with?

  1. 31
  2. 15
  3. 8
  4. 23

Answer: B — 15

x + 8 = 23, so x = 15. (A) adds; (C), (D) misread.

Solve: x + 7 = 12

  1. x = 5
  2. x = 7
  3. x = 12
  4. x = 19

Answer: A — x = 5

A) Subtract 7. B/C/D) Each is incorrect.

In d = 60t (distance = 60 mph · time), which is the independent variable?

  1. d
  2. 60
  3. t
  4. Both vary independently

Answer: C — t

C) Time is the input we choose; distance depends on it. A) d is the dependent variable. B) 60 is a constant rate. D) Only one is independent here.

Word: 6 friends share x marbles equally; each gets 9. How many marbles total?

  1. 15
  2. 3
  3. 54
  4. 1.5

Answer: C — 54

C) x/6 = 9, so x = 54. A) Added: 6 + 9. B) Subtracted. D) Inverted division.

Which graph represents x ≥ 2 on a number line?

  1. Open circle at 2, arrow right
  2. Closed circle at 2, arrow left
  3. Closed (filled) circle at 2, arrow right
  4. Open circle at 2, arrow left

Answer: C — Closed (filled) circle at 2, arrow right

C) ≥ includes 2 (closed circle) and 'greater' goes right. A) Open circle would mean strictly >. B) Wrong direction. D) Wrong direction AND wrong circle.

Factor: 10x + 15.

  1. 5(2x + 3)
  2. 5(2x + 15)
  3. 10(x + 5)
  4. 15(x + 1)

Answer: A — 5(2x + 3)

A) GCF(10, 15) = 5. Divide each: 5(2x + 3). B) Forgot to divide the constant by 5. C) Used GCF 10 incorrectly — 10 doesn't divide 15. D) Used 15, doesn't divide 10.

x > 5 graphed on number line:

  1. Open circle at 5, shade right
  2. Closed circle at 5, shade right
  3. Open circle, shade left
  4. Closed left

Answer: A — Open circle at 5, shade right

A) Open = not included; right = greater. B) ≥. C/D) Each is incorrect.

Inequality x − 3 ≥ 7. Solution:

  1. x ≥ 10
  2. x ≤ 10
  3. x = 4
  4. x > 10

Answer: A — x ≥ 10

A) Add 3 to both sides. B/C/D) Each is incorrect.

Word: Jen's age (y) is 4 less than twice Jake's age (x). Which equation?

  1. y = 4 − 2x
  2. y = 2x − 4
  3. y = 2(x − 4)
  4. y = 4x − 2

Answer: B — y = 2x − 4

B) Twice Jake's age = 2x; "4 less than" = subtract 4. A) Reversed: 4 − 2x. C) Subtracted before doubling. D) Swapped 4 and 2.

Translate "twice a number plus 5":

  1. 2x + 5
  2. 2 + 5x
  3. x² + 5
  4. 5 + 2x²

Answer: A — 2x + 5

A) Twice a number = 2x. B/C/D) Each is incorrect.

6th Math: Expressions & Equations flashcards

6 sample cards from the 85 in the bank.

Worked example: Distribute 4(x + 7) and simplify.

Step 1 — Multiply 4 by each term in parentheses: 4 · x = 4x; 4 · 7 = 28. Step 2 — Combine: 4x + 28. Answer: 4x + 28.

What is an 'equation'?

A math statement saying two expressions are EQUAL. Has an equals sign. Like x + 5 = 12.

Combine like terms: 3x + 7x.

10x.

Evaluate 100 − 3n when n = 25.

25. (100 − 75 = 25.)

What is a 'constant'?

A number with no variable. In 3x + 7, the 7 is a constant.

Combine like terms: 2y + 5x − y + x.

y + 6x. (Or 6x + y.)

Practise the full 6th Math: Expressions & Equations bank

These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.

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6th Math: Expressions & Equations — frequently asked

What is the 6th Math: Expressions & Equations exam?

Common Core State Standards (CCSS) — Mathematics, Grade 6: Expressions & Equations (6.EE.A.1-4, 6.EE.B.5-8, 6.EE.C.9). Public standards from corestandards.org.

How is CoStudy’s 6th Math: Expressions & Equations bank organised?

It holds 235 items across 6 chapters: Numerical Expressions and Whole-Number Exponents; Writing and Evaluating Algebraic Expressions; Equivalent Expressions and Properties of Operations; Solving One-Variable Equations; Inequalities and Their Solutions; Dependent and Independent Variables. Free samples on this page include the full rationale, with no account. Chapter counts in the bank are our mix; they are not a promise that the live exam uses the same item counts.

Does CoStudy replace the certifying body?

No. the certifying body owns the outline, the badge, and the sitting rules. This is independent practice with written rationales. We do not sell live items and we do not guarantee a pass.

Where do 6th Math: Expressions & Equations fees, cut scores, and pass rates live?

On the certifying body’s site. CoStudy will not invent a sitting fee or a pass rate. If a table on this page lacks a citation, treat it as unverified.

Are these real 6th Math: Expressions & Equations exam questions?

No. CoStudy does not have live items. The samples below are original practice written to the published outline, with rationales. Anyone selling “real exam dumps” is describing something you should not buy.

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