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AP Precalculus

AP Precalc Unit 2A (2.1–2.6): Conceptual MCQ

Shared by ashtont · Nov 2, 2026 · 0 plays

16 conceptual questions for the Unit 2A AP Readiness test (2.1–2.6): equal-length intervals, translation vs dilation, changing time units, vertical shifts in data, residuals and choosing a model. Every question has a stimulus.

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16 questions across 16 sections. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

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Sections (none selected means all)

Sample questions

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

Which of the following is true?
  1. A. g could be linear, because the outputs increase as the inputs increase.
  2. B. g cannot be exponential, because the ratios of consecutive outputs (9, 3, 9, 3) are not constant.
  3. C. g could be exponential, because over input intervals of equal length the outputs are multiplied by the same factor. ✓
  4. D. g could be quadratic, because the differences between outputs increase.

Correct answer: C. Every 2-unit interval multiplies by 9, and every 1-unit interval multiplies by 3. Since 9 = 3², g(x) = 4(3)ˣ fits every point.

Which of the following must be true on the interval 0 ≤ x ≤ 10?
  1. A. The average rate of change of g over [0, 2] equals its average rate of change over [8, 10].
  2. B. g(10) > f(10)
  3. C. The average rate of change of f over [0, 2] equals its average rate of change over [8, 10]. ✓
  4. D. The graphs of f and g intersect exactly once.

Correct answer: C. F is linear, so its rate of change is the same on every interval.

Which of the following describes f?
  1. A. f is increasing, concave up, and lim (x→−∞) f(x) = 0.
  2. B. f is decreasing, concave up, and lim (x→∞) f(x) = 0.
  3. C. f is decreasing, concave down, and lim (x→−∞) f(x) = 0. ✓
  4. D. f is decreasing, concave down, and lim (x→−∞) f(x) = −∞.

Correct answer: C. B > 1 makes |f| grow, and a < 0 flips the graph below the x-axis, so f falls faster and faster. On the left, bˣ → 0, so f → 0.

Which statement best explains what this rewrite shows?
  1. A. Translating 7(3)ˣ right 2 units gives the same graph as vertically dilating it by a factor of 1/9. ✓
  2. B. Translating 7(3)ˣ left 2 units gives the same graph as vertically dilating it by a factor of 1/9.
  3. C. The rewrite moves the horizontal asymptote down 2 units.
  4. D. Translating 7(3)ˣ right 2 units gives the same graph as vertically dilating it by a factor of 9.

Correct answer: A. 3^(x−2) = 3ˣ·3^(−2) = 3ˣ/9. For exponentials, every horizontal translation is also a vertical dilation.

Which of the following statements about k is true?
  1. A. k(x) = 25ˣ, so each 1-unit increase in x multiplies the output by 25. ✓
  2. B. k is a horizontal dilation of 5ˣ by a factor of 2.
  3. C. The output of k doubles each time x increases by 1.
  4. D. k(x) = 10ˣ, so each 1-unit increase in x multiplies the output by 10.

Correct answer: A. By the power property, 5^(2x) = (5²)ˣ = 25ˣ.