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23 multiple-choice questions and 4 flashcards on Dependent and Independent Variables, about 15% of the 6th Math: Expressions & Equations bank. Every one carries a written rationale.
Dependent and Independent Variables is one of 6 chapters in CoStudy's 6th Math: Expressions & Equations bank, and it holds 23 of the bank's 150 multiple-choice questions — roughly 15% 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.
Maya has $40 and saves an additional $5 per week (w). The total savings t is:
Answer: B — t = 40 + 5w
Starting balance + per-week × weeks. (A), (C) swap the roles; (D) misadds.
In the equation y = 3x + 2, which is the INDEPENDENT variable?
Answer: A — x
A) x is the input (independent); y depends on x. B) y is dependent. C/D) Constants, not variables.
A function table: x = 1 → y = 5; x = 2 → y = 7; x = 3 → y = 9. What is y when x = 5?
Answer: D — 13
D) Pattern: y = 2x + 3. y(5) = 13. A) Off-by-one error. C) Used y = 3x. B) Used y = 5x.
A plumber charges a $40 service fee plus $25/hour. The cost c for h hours is:
Answer: A — c = 40 + 25h
Service fee + hourly rate × hours. (B) swaps; (C), (D) ignore one part.
A function table shows: input 1 → output 4, input 2 → output 7, input 3 → output 10. The rule is:
Answer: C — y = 3x + 1
C) Each output increases by 3 — slope is 3; check: 3(1)+1 = 4, 3(2)+1 = 7, 3(3)+1 = 10. A/B/D) Each matches only one or two rows.
Which inequality represents 'at least 50'?
Answer: C — x ≥ 50
'At least' = ≥. (A), (B), (D) misread.
Word: A book costs $8. How many books can you buy with $50? Equation and answer.
Answer: A — 8b = 50; b = 6 (with $2 left)
A) Cost-per-book × books = total. With 8b ≤ 50, the largest whole number is 6. B) Inverted division. C) Swapped roles. D) Treated cost as additive.
Word: Jen's age (y) is 4 less than twice Jake's age (x). Which equation?
Answer: B — y = 2x − 4
B) Twice Jake's age = 2x; "4 less than" = subtract 4. A) Reversed: 4 − 2x. C) Subtracted before doubling. D) Swapped 4 and 2.
If y = 3x and x is the independent variable, what is the relationship?
Answer: D — Same as A — y is a function of x; each x gives one y; y triples per unit increase in x
Function of one variable; (D) is the correct precise statement. (A) is approximately right but understates the triple-per-unit rate; (C), (B) misread.
In d = 60t (distance = 60 mph · time), which is the independent variable?
Answer: C — t
C) Time is the input we choose; distance depends on it. A) d is the dependent variable. B) 60 is a constant rate. D) Only one is independent here.
1 cards from the 4 in this chapter.
What is the 'independent variable'?
The variable that doesn't depend on others. Often x. The 'input'.
These are a sample. The full Dependent and Independent Variables chapter runs 27 items with per-chapter progress tracking, on the web and in the iOS app.
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