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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.
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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.
Each chapter follows a domain of the published exam outline. Practise one on its own:
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?
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.
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?
Answer: B — 15
x + 8 = 23, so x = 15. (A) adds; (C), (D) misread.
Solve: x + 7 = 12
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?
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?
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?
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.
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:
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:
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?
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":
Answer: A — 2x + 5
A) Twice a number = 2x. B/C/D) Each is incorrect.
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.)
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.
Open 6th Math: Expressions & Equations →
The 6th Math: Expressions & Equations bank holds 235 items: 150 multiple-choice questions, 85 flashcards. 18 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
It is organised into 6 chapters that follow the published exam blueprint: 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. The number of questions in each chapter is proportional to that domain's published weight, so working through the bank exposes you to roughly the mix the real exam uses.
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.
The samples on this page are free to read in full, rationales included, with no account. The complete 235-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.