Skip to main content
Student Acer
Race to 1,000:first to win· Win $50 →
← All practice sets

AP Precalculus

AP Precalc 2.1–2.3: Conceptual MCQ (Set A)

Shared by Ashton · Oct 25, 2026 · 3 plays

15 hard questions on why things are true in 2.1–2.3: proportional vs. constant change, sequences vs. functions, what a and b force, and exponential limits. No calculator. Every choice has an explanation.

Report this set

15 questions across 15 sections. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Sections (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

x: 0, 1, 3, 4, 6 | f(x): 5, 10, 40, 80, 320 — Selected values of f are shown in the table. Which of the following is true?
  1. A. f cannot be exponential, because the ratios of consecutive output values (2, 4, 2, 4) are not constant.
  2. B. f could be exponential, because over input-value intervals of equal length, the output values are multiplied by the same factor. ✓
  3. C. f could be linear, because the output values increase as the input values increase.
  4. D. f could be quadratic, because the differences of consecutive output values increase.

Correct answer: B. Every 1-unit step multiplies by 2, and every 2-unit step multiplies by 4 = 2². That's exactly what an exponential with b = 2 does: f(x) = 5 · 2ˣ fits every point.

x: 0, 1, 2, 3, 4 | h(x): 7, 10, 16, 28, 52 — Which of the following statements about h is true?
  1. A. The output values of h are proportional over equal-length input-value intervals, so h is of the form abˣ.
  2. B. h is quadratic, because its second differences are constant.
  3. C. The output values of h are not proportional over equal-length input-value intervals, but the output values of h(x) − 4 are. ✓
  4. D. The output values of h(x) − 4 are not proportional over equal-length input-value intervals, but the output values of h are.

Correct answer: C. The differences 3, 6, 12, 24 double, which is the fingerprint of a shifted exponential: h(x) = 3 · 2ˣ + 4. Subtracting 4 gives 3, 6, 12, 24, 48, which is proportional (×2 each step).

An arithmetic sequence aₙ and a geometric sequence gₙ both have only positive terms, and neither sequence is constant. They share their first term and their fifth term. Which of the following must be true about the third terms?
  1. A. a₃ > g₃ ✓
  2. B. a₃ < g₃
  3. C. a₃ = g₃
  4. D. It depends on whether the sequences are increasing or decreasing.

Correct answer: A. The arithmetic middle term is the average, (a₁ + a₅)/2. The geometric middle term is the geometric mean, √(g₁g₅). For two different positive numbers, the average is always bigger. Example: 2 and 32 give a₃ = 17 but g₃ = 8.

Graph of f(x) = a · bˣ: every point is below the x-axis. It passes through (0, −2) and (1, −1). As x increases, the graph rises toward the x-axis (y = 0). As x decreases, it drops steeply downward. — Which of the following is true?
  1. A. a < 0 and b > 1, so lim(x→∞) f(x) = −∞.
  2. B. a < 0 and 0 < b < 1, so lim(x→−∞) f(x) = −∞ and lim(x→∞) f(x) = 0. ✓
  3. C. a > 0 and 0 < b < 1, because the outputs approach 0 as x → ∞, which is exponential decay.
  4. D. a < 0 and 0 < b < 1, so f is decreasing because it has a decay factor.

Correct answer: B. The outputs are negative, so a < 0 (a = f(0) = −2). From x = 0 to 1 the output is multiplied by ½, so b = ½. The graph rises toward 0 as x → ∞ and falls to −∞ as x → −∞.

For an exponential function f, the average rate of change on [0, 2] is 6 and the average rate of change on [2, 4] is 24. What is the average rate of change of f on [4, 6]?
  1. A. 42
  2. B. 48
  3. C. 96 ✓
  4. D. 144

Correct answer: C. For an exponential, the changes over equal-length intervals are proportional too: f(4) − f(2) = b²[f(2) − f(0)]. The rate grew from 6 to 24, a factor of 4, so the next one is 24 × 4 = 96.