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150 multiple-choice questions and 85 flashcards, organised into 5 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 7: Expressions and Equations (7.EE.A.1-2, 7.EE.B.3-4). Public standards from corestandards.org.
CoStudy's 7th Math: Expressions & Equations bank holds 235 items organised into 5 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.
Solve: 5 − 3x = −7
Answer: D — x = 4
D) Subtract 5: −3x = −12; divide by −3: x = 4. A) Sign error. C) Forgot to divide. B) Sign error after dividing.
Simplify: (1/2)(4x − 6)
Answer: B — 2x − 3
(1/2)(4x) = 2x; (1/2)(−6) = −3 → 2x − 3. (A) only halved x; (C) only halved the constant; (D) sign error on constant.
A car travels at 60 mph for t hours. The distance d is:
Answer: C — d = 60t
C) Distance = rate × time. A/B) Added/subtracted units. D) Inverted the relationship.
Solve: 4x − 9 = −1
Answer: A — x = 2
4x = −1 + 9 = 8; x = 2. (B) used 9 − 1 = 8 then divided by −4; (C) same with wrong sign; (D) sign error.
Solve: 3(x + 4) = 21
Answer: A — x = 3
A) Distribute: 3x + 12 = 21 → 3x = 9 → x = 3. Alternatively, divide both sides by 3 first. B) Forgot to subtract 12. C) Forgot to divide. D) Random.
Simplify: 4x + 7 − 2x + 3
Answer: A — 2x + 10
A) 4x − 2x = 2x; 7 + 3 = 10. B) Summed x terms incorrectly. C) Lost a constant. D) Both errors.
A pizza is $12 plus $1.50 per topping. With $19.50, how many toppings?
Answer: D — 5
D) 1.5t + 12 = 19.5 → 1.5t = 7.5 → t = 5. A) Off by one. C) Used 9/1.5. B) Divided 19.5 by 1.5.
Solve: (x − 4)/3 = 2
Answer: C — x = 10
C) Multiply by 3: x − 4 = 6; add 4: x = 10. A) Subtracted instead of adding. B) Stopped after multiplying. D) Added 4 then multiplied.
Solve: 3x ≤ 15
Answer: A — x ≤ 5
Divide by 3 (positive — no flip): x ≤ 5. (B) multiplied by 3; (C) flipped inequality unnecessarily; (D) changed ≤ to <.
Solve: x/3 + 1 ≥ 4
Answer: A — x ≥ 9
x/3 ≥ 3; x ≥ 9. (B) forgot to multiply by 3; (C) multiplied 5 × 3; (D) added 3 and 4.
Inequality 2x + 5 > 13. x =
Answer: D — x > 4
D) Subtract 5, divide by 2. A/B/C) Each is incorrect.
Solve: (3x − 6)/2 = 9
Answer: C — x = 8
C) Multiply by 2: 3x − 6 = 18; add 6: 3x = 24; x = 8. A) Used 24/(−6). B) Stopped at 18/3. D) Skipped a step.
6 sample cards from the 85 in the bank.
Worked Example: Solve inequality −3x + 4 > 13 (flip the sign).
Step 1: Subtract 4 from both sides: −3x + 4 − 4 > 13 − 4, giving −3x > 9. Step 2: Divide both sides by −3 — NEGATIVE divisor, so FLIP the inequality: −3x/(−3) < 9/(−3), giving x < −3. Step 3: Check with x = −4 (satisfies x < −3): −3(−4) + 4 = 12 + 4 = 16 > 13 ✓. Step 4: Graph — open circle at −3, arrow left. Answer: x < −3.
Combine: 5x + 7x.
12x.
Solve: 3(x − 1) + 4 = 16.
x = 5. (3x − 3 + 4 = 16; 3x + 1 = 16; 3x = 15; x = 5.)
Combine: 0.5x − 0.3 + 2.5x + 1.
3x + 0.7.
Distribute: −3(2x − 4).
−6x + 12.
Solve: −2x > 6.
x < −3. (Flip sign when dividing by −2.)
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 7th Math: Expressions & Equations →
The 7th 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 5 chapters that follow the published exam blueprint: Equivalent Linear Expressions; Rewriting Expressions in Different Forms; Multi-Step Real-World Problems; Solving Equations of the Form px + q = r and p(x + q) = r; Solving Multi-Step Inequalities. 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 7: Expressions and Equations (7.EE.A.1-2, 7.EE.B.3-4). 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.