Home › Certifications › 7th Math: Ratios & Proportional Relationships › Constant of Proportionality (Equations and Graphs)
26 multiple-choice questions and 6 flashcards on Constant of Proportionality (Equations and Graphs), about 17% of the 7th Math: Ratios & Proportional Relationships bank. Every one carries a written rationale.
Constant of Proportionality (Equations and Graphs) is one of 4 chapters in CoStudy's 7th Math: Ratios & Proportional Relationships bank, and it holds 26 of the bank's 150 multiple-choice questions — roughly 17% 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.
The constant of proportionality k in a relationship where y = 8 when x = 2 is:
Answer: D — 4
D) k = y/x = 8/2 = 4. A) Reversed: used x/y. C) Subtracted instead of dividing. B) Multiplied instead of dividing.
A graph passes through (3, 21) and represents a proportional relationship. The equation is:
Answer: D — y = 7x
D) k = y/x = 21/3 = 7, so y = 7x. A) Used x value. C) Reversed ratio (x/y instead of y/x). B) Used y value as k.
What is the percent change from 50 to 75?
Answer: B — 50% — (75 − 50)/50 = 25/50 = 0.50
Percent change = (new − old)/old × 100. (A) is absolute change; (C), (D) miscalculate.
In a proportional relationship, doubling x:
Answer: B — Doubles y
B) In y = kx, replacing x with 2x gives y = k(2x) = 2(kx). A) Wrong; y depends on x. C) Inverse relationship, not proportional. D) Quadratic relationship, not proportional.
Simple interest formula is:
Answer: B — I = P × r × t — Principal × annual rate × time in years
Standard simple interest. (A) misses time; (C), (D) misread.
A population of 200 grows by 25%. New population:
Answer: C — 250
Increase = 0.25 × 200 = 50. New = 250. (A) is +25; (B) is the increase; (D) subtracts.
An item costing $50 has 8% sales tax. Final price:
Answer: A — $54
Tax = 0.08 × 50 = $4. Total = $54. (B), (C), (D) miscalculate.
In y = kx, if the point (5, 35) is on the graph, then k =
Answer: D — 7
D) k = y/x = 35/5 = 7. A) Reversed: x/y. B) Used x. C) Used y.
A $80 jacket is 25% off. The sale price is:
Answer: B — $60
Discount = 0.25 × 80 = $20. Sale price = 80 − 20 = $60. (A) is discount; (C), (D) miscalculate.
A graph showing y vs. x is a straight line through (0, 0) and (4, 10). The constant of proportionality is:
Answer: B — 2.5
B) k = y/x = 10/4 = 2.5. A) Reversed (x/y). C) Used x-coordinate. D) Used y-coordinate.
4 cards from the 6 in this chapter.
$120 per week is how much per day?
$120/7 ≈ $17.14/day.
A person earns $42,000/year. Hourly rate (assume 40 hr/week, 52 weeks)?
$20.19/hr. (42000 / (40 × 52) = 42000 / 2080 ≈ 20.19.)
A pool fills at 4 gallons/min. In hours, what's the rate?
240 gal/hr.
How much would $1000 earn at 6% simple interest in 5 years?
$300. (1000 × 0.06 × 5 = 300.)
These are a sample. The full Constant of Proportionality (Equations and Graphs) chapter runs 32 items with per-chapter progress tracking, on the web and in the iOS app.
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