AP Precalculus
AP Precalc Unit 2A (2.1–2.6): Hard Solving FRQ
Shared by Ashton · Nov 2, 2026 · 0 plays
Hard multi-part FRQs for the Unit 2A AP Readiness test (2.1–2.6): drug decay with unit change, competing sequences, exponential regression and residuals, a three-point translated exponential. Rubric and sample answer for every part.
14 questions across 4 sections. Write your answer, then check it against the rubric and score yourself.
Sample questions
Open an item to see its answer.
(a) Find a and b. Show your work.
Sample answer: Divide: b³ = 81.92/160 = 0.512, so b = 0.8. Then a = 160/0.64 = 250. D(t) = 250(0.8)ᵗ.
(b) Rewrite D so the input q is the number of 15-minute intervals. What percent of the drug is lost every 15 minutes?
Sample answer: t = q/4, so D = 250(0.8)^(q/4) = 250(0.8^(1/4))^q ≈ 250(0.94574)^q. It keeps about 94.57%, so it loses about 5.43% every 15 minutes.
(c) When does the amount first drop below 30 mg? Give the answer to the nearest hundredth of an hour.
Sample answer: Graph y = 250(0.8)ˣ and y = 30. They intersect at t ≈ 9.50 hours, so the drug drops below 30 mg just after 9.50 hours.
(d) Find the average rate of change of D from t = 2 to t = 5 and interpret it.
Sample answer: (81.92 − 160)/(5 − 2) = −78.08/3 ≈ −26.03 mg per hour. Between hours 2 and 5 the amount fell about 26.03 mg per hour on average.
(a) Find explicit expressions for aₙ and gₙ.
Sample answer: d = (50 − 30)/4 = 5 and a₁ = 25, so aₙ = 25 + 5(n − 1) = 20 + 5n. r³ = 48/6 = 8, so r = 2 and g₁ = 3: gₙ = 3(2)^(n−1).