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150 multiple-choice questions, 50 flashcards and 10 scenario simulations, 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 5: Operations & Algebraic Thinking (5.OA.A.1, 5.OA.A.2, 5.OA.B.3). Public standards from corestandards.org.
CoStudy's 5th Math: Operations & Algebraic Thinking bank holds 210 items. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong, and the bank includes 10 scenario-based simulations.
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
On a coordinate plane, the point (3, 5) means:
Answer: D — 3 right, 5 up
(x, y): x = right, y = up. (B) swaps; (C) swaps; (A) misreads.
Which expression represents 'three times the sum of 5 and 2'?
Answer: B — 3 × (5 + 2)
'Sum of 5 and 2' is (5+2), then multiplied by 3 = 3 × (5+2). (A),(C),(D) miss the parentheses.
On coordinate plane, y-axis is:
Answer: C — Vertical
C) Correct. B) x-axis. C/D) wrong.
Perimeter of a rectangle L × W:
Answer: D — 2L + 2W
D) Correct. B) half. C) area. A) wrong.
Sum of a and b, divided by 2:
Answer: C — (a + b) ÷ 2
C) Correct. B/C/D) wrong.
Which is TRUE? (2+3)×4 ___ 2+(3×4)
Answer: C — >
C) Correct — 20 > 14. B/C/D) wrong.
The origin is at:
Answer: A — (0, 0)
A) Correct. B/C/D) wrong.
Evaluate: (2 + 4)³ ÷ 8
Answer: C — 27
C) Correct — 6³=216, ÷8. B/C/D) wrong.
Which quadrant contains (5, 3)?
Answer: D — I
D) Correct — both positive. B) −x,+y. C) both neg. A) +x,−y.
Which coordinate plane quadrant has both coordinates positive?
Answer: B — I
B) Correct. A) −x,+y. C) both neg. D) +x,−y.
'5 less than the quotient of n and 3':
Answer: D — n/3 − 5
D) Correct. B/C/A) wrong.
Write: 'the product of 4 and (n + 6)'
Answer: A — 4(n + 6)
A) Correct. B) missed parens. C/D) wrong.
6 sample cards from the 50 in the bank.
Evaluate: 3 + 4 × 2.
11. (Multiply first: 4 × 2 = 8; then 3 + 8 = 11.)
Two patterns: A = 0, 3, 6, 9... B = 0, 6, 12, 18... What's the relationship?
B is always 2× A.
What does the y-coordinate tell you?
How far to move vertically (up or down).
What is the order of operations? (PEMDAS)
Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right).
If you're plotting weight gained per week, what should be on the y-axis?
Weight (the dependent variable).
Evaluate: 4 × (5 + 3) ÷ 2.
16. (5+3=8; 4×8=32; 32÷2=16.)
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 5th Math: Operations & Algebraic Thinking →
The 5th Math: Operations & Algebraic Thinking bank holds 210 items: 150 multiple-choice questions, 50 flashcards and 10 scenario-based simulations. 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.
Common Core State Standards (CCSS) — Mathematics, Grade 5: Operations & Algebraic Thinking (5.OA.A.1, 5.OA.A.2, 5.OA.B.3). Public standards from corestandards.org.
The samples on this page are free to read in full, rationales included, with no account. The complete 210-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.