AP Precalculus
AP Precalc 2.1–2.3: FRQ Practice 2
Shared by ashtont · Oct 26, 2026 · 0 plays
4 new multi-part FRQs on 2.1–2.3 (16 parts): two savings plans (arithmetic vs. geometric), medicine decay with a calculator part, complete-the-table for an exponential and a linear function, and find-the-error on a geometric sequence. Each part has a point-by-point rubric and a sample answer.
16 questions across 4 sections. Write your answer, then check it against the rubric and score yourself.
Sample questions
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Maya and Jake each save money every week. Maya deposits $50 in week 1 and adds $15 more each week than the week before. Jake deposits $5 in week 1 and doubles his deposit each week. Let Mₙ and Jₙ be the amounts they deposit in week n. No calculator. — (a) Write an explicit expression for Mₙ and for Jₙ. Then find M₈ and J₈.
Sample answer: Maya's deposits are arithmetic with d = 15, so Mₙ = 50 + 15(n − 1). Jake's are geometric with r = 2, so Jₙ = 5(2)^(n − 1). M₈ = 50 + 15(7) = 155 and J₈ = 5(2)⁷ = 5 · 128 = 640.
Maya and Jake each save money every week. Maya deposits $50 in week 1 and adds $15 more each week than the week before. Jake deposits $5 in week 1 and doubles his deposit each week. Let Mₙ and Jₙ be the amounts they deposit in week n. No calculator. — (b) Find the first week in which Jake deposits more than Maya. Show the values you compared.
Sample answer: Week 5: M₅ = 110 and J₅ = 80, so Maya's is bigger. Week 6: M₆ = 125 and J₆ = 160, so Jake's is bigger. The first week is week 6.
Maya and Jake each save money every week. Maya deposits $50 in week 1 and adds $15 more each week than the week before. Jake deposits $5 in week 1 and doubles his deposit each week. Let Mₙ and Jₙ be the amounts they deposit in week n. No calculator. — (c) Maya says: "If I added $100 more each week instead of $15, Jake's deposit would never pass mine." Is she correct? Find the first week Jake's deposit would pass hers, and explain why this always happens.
Sample answer: No. Her new deposits would be 50 + 100(n − 1). Week 8: 750 for Maya and 640 for Jake. Week 9: 850 for Maya and 1280 for Jake, so Jake passes her in week 9. Maya's deposits go up by the same amount each week, but Jake's are multiplied by 2, so the amount his deposit goes up by doubles every week. Eventually his weekly increase is bigger than any fixed $100, and he passes her.
Maya and Jake each save money every week. Maya deposits $50 in week 1 and adds $15 more each week than the week before. Jake deposits $5 in week 1 and doubles his deposit each week. Let Mₙ and Jₙ be the amounts they deposit in week n. No calculator. — (d) Rewrite Jₙ in the form gₙ = gₖ · r^(n − k) using week 4. Then explain why the graph of Jₙ is a set of separate points and not a curve.
Sample answer: J₄ = 5(2)³ = 40, so Jₙ = 40(2)^(n − 4). The input n counts weeks, so it's only 1, 2, 3, … There's no week 2.5, so the graph is separate points (they lie on the curve y = 40(2)^(x − 4) but aren't connected).
A patient takes a 400 mg dose of a medicine. The amount left in the bloodstream t hours later is modeled by D(t) = 400(0.75)ᵗ. Calculator allowed. — (a) Identify the initial amount and the percent of the medicine lost each hour. Is this exponential growth or decay? Justify using the values of a and b.
Sample answer: The initial amount is a = 400 mg. Each hour 75% stays, so 25% is lost. Since a > 0 and 0 < b < 1, D shows exponential decay.