AP Precalculus
AP Precalc 2.1–2.3: Problem-Solving MCQ (Set B)
Shared by Ashton · Oct 25, 2026 · 3 plays
16 computation questions for 2.1–2.3: writing formulas from two terms, counting terms, finding a and b, average rate of change, and growth and decay in context. Calculator only on the car questions. Each wrong choice explains the mistake behind it.
16 questions across 14 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.
The terms of an arithmetic sequence aₙ are graphed as points. Two of them are labeled: (5, 17) and (12, −11). — What is a₃₀?
- A. −79
- B. −83 ✓
- C. −87
- D. −103
Correct answer: B. D = (−11 − 17)/(12 − 5) = −28/7 = −4, so aₙ = 17 − 4(n − 5) and a₃₀ = 17 − 4(25) = −83. Check from the other point: −11 − 4(18) = −83.
A geometric sequence has g₂ = −6 and g₅ = 162. What is g₈?
- A. 4374
- B. 1458
- C. −1458
- D. −4374 ✓
Correct answer: D. 162 = −6 · r³, so r³ = −27 and r = −3 (an odd gap has only one real root). Then g₈ = 162 · (−3)³ = −4374.
How many terms are in the arithmetic sequence 7, 11, 15, …, 203?
- A. 49
- B. 50 ✓
- C. 51
- D. 196
Correct answer: B. 203 = 7 + 4(n − 1), so 196 = 4(n − 1), n − 1 = 49 and n = 50.
A geometric sequence has first term g₁ = ¾ and common ratio 2. Which term equals 384?
- A. the 9th
- B. the 512th
- C. the 11th
- D. the 10th ✓
Correct answer: D. 384 = ¾ · 2^(n − 1), so 2^(n − 1) = 512 = 2⁹, n − 1 = 9 and n = 10.
The graph of an exponential function f(x) = abˣ passes through the labeled points (0, 3) and (2, 12). — What is f(−1)?
- A. −1.5
- B. 0.75
- C. 1.5 ✓
- D. 0
Correct answer: C. A = f(0) = 3. 12 = 3b², so b² = 4 and b = 2. Then f(−1) = 3 · 2⁻¹ = 1.5.