AP Precalculus
AP Precalc Unit 2A (2.1–2.6): Hard Solving MCQ
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16 hard solving questions for the Unit 2A AP Readiness test (2.1–2.6): sequences, exponent properties, two-point and translated exponential models, regression and residuals, unit conversions. Every question has a stimulus.
16 questions across 13 sections. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
What is the value of f(6)?
- A. 3.25
- B. 3
- C. 0.125
- D. 3.125 ✓
Correct answer: D. The differences −4, −2, −1 halve, so b = 1/2. Subtracting 3 gives 8, 4, 2, 1, so f(x) = 8(1/2)ˣ + 3 and f(6) = 8/64 + 3 = 3.125.
What is the value of g₇?
- A. 136.6875
- B. 60.75
- C. 91.125
- D. −91.125 ✓
Correct answer: D. R³ = −40.5/12 = −3.375, so r = −1.5. Then g₇ = g₅·r² = −40.5 × 2.25 = −91.125.
What is the smallest n for which gₙ − aₙ > 1000?
- A. 6
- B. 7 ✓
- C. 8
- D. 5
Correct answer: B. D = (36 − 4)/2 = 16 and r = √9 = 3. n = 6: 972 − 84 = 888. n = 7: 2916 − 100 = 2816 > 1000.
Which of the following is true about h?
- A. h(x) = 27·9ˣ
- B. h(x) = 3^(4x + 3)
- C. h is a decreasing exponential function.
- D. h(x) = 243 for all x. ✓
Correct answer: D. 9^(−x+2) = 3^(−2x+4). Adding exponents: (2x + 1) + (−2x + 4) = 5, and 3⁵ = 243.
Which of the following is equivalent to g(x)?
- A. 3(2)ˣ ✓
- B. 12(2)ˣ
- C. 48(2)ˣ − 4
- D. 96(2)ˣ
Correct answer: A. 2^(x−4) = 2ˣ/16, and 48/16 = 3.