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150 multiple-choice questions and 83 flashcards, organised into 2 chapters, written to the CCSS Mathematics blueprint. Every question carries a full rationale.
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CCSS Mathematics, Grade 8: Number System (8.NS.A.1-2) and integer exponents (8.EE.A.1). Public standards from corestandards.org.
CoStudy's 8th Math: The Number System bank holds 233 items organised into 2 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.
Which is RATIONAL?
Answer: A — 1/4
A) Fractions of integers are rational. B/C) Non-repeating, non-terminating decimals — irrational. D) Imaginary.
Locate √50 on the number line. It is closest to:
Answer: D — 7.1
D) √50 ≈ 7.07, closest to 7.1. B) Halfway between 7 and 8 — too large. C) That's √64. A) Took half of 50.
Which is NOT a perfect square?
Answer: C — 50
√50 is not an integer (≈7.07), so 50 is not a perfect square. (A) 7² = 49; (B) 9² = 81; (D) 12² = 144.
Convert 2/9 to decimal:
Answer: C — 0.222... (repeating)
C) Repeating. A/B/D) Each is incorrect.
Square root of 0:
Answer: A — 0
A) Standard. B/C/D) Each is incorrect.
Negative exponent: 2⁻³ =
Answer: B — 1/8
B) Reciprocal. A/C/D) Each is incorrect.
Which is the LARGEST?
Answer: C — π + 1
C) π + 1 ≈ 4.14, largest. A) √15 ≈ 3.87. B) 3.9. D) √14 ≈ 3.74. Common error: pick √15 since the root looks 'big'.
Is π rational?
Answer: B — No — π is irrational (non-terminating, non-repeating decimal)
B) Standard. A/C/D) Each is incorrect.
On a number line marked in tenths, √13 would be placed near:
Answer: A — 3.6
A) 3.6² = 12.96 ≈ 13. B) That's √10. C) That's √16 — off-by-one trap. D) Half of 13 — wrong operation.
Locate √11 on a number line. It falls between:
Answer: B — 3 and 4
B) 3² = 9 and 4² = 16; since 9 < 11 < 16, √11 ≈ 3.32. A) That's √4 to √9. C) That's √16 to √25 (off-by-one). D) Too large.
Order from greatest to least: √50, 7, 7.5, √40.
Answer: A — 7.5, √50, 7, √40
A) √50 ≈ 7.07; √40 ≈ 6.32. So 7.5 > √50 ≈ 7.07 > 7 > √40 ≈ 6.32. B) Puts √50 above 7.5 — wrong. C) Reverse order. D) Wrong placement.
Which is closest to √70 on a number line?
Answer: B — 8.4
8² = 64 and 9² = 81. √70 ≈ 8.37. (A) 8.1² ≈ 65.6; (B) 8.4² ≈ 70.6 ✓; (C) 8.6² = 73.96; (D) 7.8² = 60.8.
6 sample cards from the 83 in the bank.
Is 0.121212... rational?
Yes — every repeating decimal is rational (here it equals 12/99 = 4/33).
Convert 1/8 to a decimal.
0.125.
Worked example: Convert 0.444... to a fraction.
Step 1: Let x = 0.444... . Step 2: Multiply both sides by 10 → 10x = 4.444... . Step 3: Subtract the original: 10x − x = 4.444... − 0.444... = 4. Step 4: This gives 9x = 4. Step 5: Divide both sides by 9 → x = 4/9. Answer: 0.444... = 4/9.
Is √2 rational or irrational?
Irrational. Its decimal goes on forever without repeating.
Is √7 rational?
No — √7 is irrational (7 isn't a perfect square).
Is π rational or irrational?
Irrational. 3.14159265... never terminates or repeats.
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 8th Math: The Number System →
The 8th Math: The Number System bank holds 233 items: 150 multiple-choice questions, 83 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 2 chapters that follow the published exam blueprint: Rational and Irrational Numbers; Approximating Irrational Numbers on the Number Line. 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.
CCSS Mathematics, Grade 8: Number System (8.NS.A.1-2) and integer exponents (8.EE.A.1). Public standards from corestandards.org.
The samples on this page are free to read in full, rationales included, with no account. The complete 233-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.