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27 multiple-choice questions and 36 flashcards on Recognizing Proportional Relationships, about 18% of the 7th Math: Ratios & Proportional Relationships bank. Every one carries a written rationale.
Recognizing Proportional Relationships is one of 4 chapters in CoStudy's 7th Math: Ratios & Proportional Relationships bank, and it holds 27 of the bank's 150 multiple-choice questions — roughly 18% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
A proportional relationship between two quantities has a graph that is:
Answer: C — A straight line passing through the origin
C) y = kx graphs as a line through (0, 0). A) Horizontal means y is constant. B) Non-linear. D) Random.
In a proportional relationship, the graph passes through:
Answer: B — Same as A — proportional relationships always pass through (0, 0); k = slope
y = kx → at x = 0, y = 0. (A), (B) same; (C), (D) misread.
A proportional relationship between x and y satisfies:
Answer: C — y = kx (for a constant k, the 'constant of proportionality')
Proportional = y/x is constant = k. (A) is linear with offset; (B) is quadratic; (D) is linear inverse.
On a map with scale 1 inch = 25 miles, a distance of 3.5 inches represents how many real miles?
Answer: C — 87.5 miles
C) 3.5 × 25 = 87.5 miles. A) Added instead of multiplying. B) Used 3 inches. D) Rounded up incorrectly.
A blueprint scale is 1/4 inch = 1 foot. A wall measuring 3 inches on the blueprint is how many feet long in reality?
Answer: C — 12 ft
C) 3 ÷ (1/4) = 3 × 4 = 12 feet. A) Multiplied 3 × 1/4. B) Used scale numerator. D) Doubled.
A scale model uses 1 cm : 4 m. The actual length of a model that is 7.5 cm is:
Answer: D — 30 m
D) 7.5 × 4 = 30 m. A) Reversed (divided). B) Added scale. C) Used 4.4.
A graph of y = 5x is a straight line through:
Answer: D — (0, 0) with slope 5
y = kx passes through origin. (A), (C), (B) misread.
x = 1, 2, 3; y = 5, 8, 11. Is this proportional?
Answer: C — No — y/x is 5, 4, 11/3 — not a constant — this is a non-proportional linear relationship (y = 3x + 2)
Not constant y/x. (A), (B), (D) misread.
A scale model uses ratio 1:50. A real building is 200 ft tall. The model's height is:
Answer: A — 4 ft
200/50 = 4 ft. (B), (C), (D) miscalculate.
Identify the equation NOT representing a proportional relationship:
Answer: D — y = 5x + 2
D) Has a non-zero y-intercept (+2), so it does not pass through origin. A, B, C) All of the form y = kx and pass through (0, 0).
4 cards from the 36 in this chapter.
What's 20% of 350?
70.
On a graph through (3, 12), what's the constant of proportionality?
4. (k = y/x = 12/3 = 4.)
Is this proportional: (1, 5), (2, 10), (3, 14)?
No. 5/1 = 5, but 14/3 ≠ 5.
If 3 buses carry 90 students, how many for 240 students?
8 buses. (90/3 = 30/bus; 240/30 = 8.)
These are a sample. The full Recognizing Proportional Relationships chapter runs 63 items with per-chapter progress tracking, on the web and in the iOS app.
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