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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 7: Geometry (7.G.A.1-3, 7.G.B.4-6). Public standards from corestandards.org.
CoStudy's 7th Math: Geometry 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.
The circumference of a circle with radius 7 is approximately (π ≈ 3.14):
Answer: C — 43.96
C) C = 2πr ≈ 2(3.14)(7) ≈ 43.96. A) Used πr only. B) r². D) Area, not circumference.
A composite figure consists of a 6×4 rectangle with a semicircle (diameter 4) attached. Area (π ≈ 3.14):
Answer: C — 30.28
C) Rect = 24; semicircle = ½·π·2² = 6.28; total ≈ 30.28. A) Forgot semicircle. B) Used full circle (12.56). D) Doubled.
Supplementary angles sum to:
Answer: B — 180°
B) Standard. A/C/D) Different.
What cross-section is formed when a cylinder is cut perpendicular to its height?
Answer: C — Circle
A horizontal cut perpendicular to the axis gives a circle. (A/B) not round; (D) an angled cut gives an ellipse, not perpendicular.
Area of circle with radius 5 (π ≈ 3.14):
Answer: C — 78.5
C) A = πr² = 3.14·25. A/B/D) Each is incorrect.
Triangle sum:
Answer: A — 180°
A) Standard. B/C/D) Each is incorrect.
Which figure has exactly one pair of parallel sides?
Answer: C — Trapezoid
A trapezoid has exactly one pair of parallel sides. Parallelogram, rectangle, and rhombus all have two pairs of parallel sides.
Area of a triangle with base 9 and height 6:
Answer: B — 27
B) ½·9·6 = 27. A) Forgot ½. C) Added 9+6. D) Used 6·6.
A cylinder has radius 4 and height 10. Volume (π ≈ 3.14):
Answer: A — 502.4
A) V = πr²h = 3.14·16·10 = 502.4. B) Used r not r². C) Used (1/2)πr²h. D) Doubled.
A scale model car is 6 inches long; the real car is 12 feet long. Scale ratio (model:real)?
Answer: D — 1:24
Convert: 12 feet = 144 inches; ratio = 6:144 = 1:24. (A) ignored units; (C) used feet directly; (B) only divided by 6.
Two angles are complementary. One is 24°. The other is:
Answer: C — 66°
C) 90 − 24 = 66°. A) Used supplement. B) Arithmetic. D) Subtracted from 360°.
Two angles form a linear pair. One is 3x + 10 and the other is x + 50. Find x.
Answer: B — 30
Linear pair sums to 180°: (3x + 10) + (x + 50) = 180 → 4x + 60 = 180 → 4x = 120 → x = 30. (A) solved 4x = 80; (C/D) arithmetic errors.
6 sample cards from the 85 in the bank.
Can you make a triangle with sides 5, 7, and 9?
Yes. 5+7 = 12 > 9; 5+9 > 7; 7+9 > 5.
What are 'complementary angles'?
Two angles that add up to 90°.
Two angles are supplementary, one is 3x and the other is 60. Find x.
x = 40. (3x + 60 = 180; 3x = 120; x = 40.)
What are 'adjacent angles'?
Two angles that share a vertex and a side but no overlap.
WORKED EXAMPLE — Two lines intersect; one angle is 105°. Find the vertical angle.
STEP 1 — Vertical angles are formed by two intersecting lines opposite each other. STEP 2 — Vertical Angles Theorem: vertical angles are congruent (equal). STEP 3 — The angle opposite the 105° angle is therefore also 105°. STEP 4 — Sanity check: the two linear-pair angles would each be 75° (since 180 − 105 = 75) and they too match each other. ANSWER: 105°.
WORKED EXAMPLE — Two angles are complementary and form a right angle. One is 38°. Find the other.
STEP 1 — Complementary angles sum to 90°. STEP 2 — Write: 38 + x = 90. STEP 3 — Subtract: x = 90 − 38. STEP 4 — Compute: x = 52°. STEP 5 — Check: 38 + 52 = 90 ✓. ANSWER: 52°.
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.
The 7th Math: Geometry 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: Scale Drawings and Geometric Figures; Constructing Geometric Figures (Triangles, Unique vs Multiple); Cross-Sections of Three-Dimensional Figures; Circumference and Area of Circles; Angle Relationships (Supplementary, Complementary, Vertical, Adjacent); Area, Surface Area, and Volume in Real-World Problems. 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: Geometry (7.G.A.1-3, 7.G.B.4-6). 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.