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♾️AP Calculus AB/BC
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♾️AP Calculus AB/BC

FRQs – Graphing calculator required
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Unit 1: Limits and Continuity
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FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 81/8

1. The following functions are defined for this question: w(t)=t2+3tt+1w(t) = \dfrac{t^2+3t}{t+1}w(t)=t+1t2+3t​

h(t)={t2+3tt+1,t≠34.5,t=3h(t) = \begin{cases} \dfrac{t^2+3t}{t+1}, & t ≠ 3 \\ 4.5, & t=3 \end{cases}h(t)=⎩⎨⎧​t+1t2+3t​,4.5,​t=3t=3​

k(t)=4.5k(t) = 4.5k(t)=4.5

Water flows into a holding tank. For 0≤t≤80 ≤ t ≤ 80≤t≤8, the amount of water in the tank, in gallons, is modeled by the function WWW defined by W(t)=t2+3tt+1W(t)=\dfrac{t^2+3t}{t+1}W(t)=t+1t2+3t​, where ttt is measured in minutes. The graph of WWW for 0≤t≤80 ≤ t ≤ 80≤t≤8 is shown in Figure 1.

  • w(t)=t2+3tt+1w(t) = \dfrac{t^2+3t}{t+1}w(t)=t+1t2+3t​

  • h(t)={t2+3tt+1,t≠34.5,t=3h(t) = \begin{cases} \dfrac{t^2+3t}{t+1}, & t ≠ 3 \\ 4.5, & t=3 \end{cases}h(t)=⎩⎨⎧​t+1t2+3t​,4.5,​t=3t=3​

  • k(t)=4.5k(t) = 4.5k(t)=4.5

Figure 1. Graph of W(t) = (t^2 + 3t)/(t + 1) for 0 ≤ t ≤ 8, with t in minutes and W(t) in gallons; the reference line t = 2 is shown.

Figure 1
A.

Find the average rate of change of WWW over the interval 1.9≤t≤2.11.9 ≤ t ≤ 2.11.9≤t≤2.1. Show the setup for your calculations.

B.

Use average rates of change over intervals containing t=2t=2t=2 to estimate W′(2)W'(2)W′(2). Show the setup for your calculations.

C.

Write a limit expression, using correct notation, for W′(2)W'(2)W′(2). Then evaluate the limit.

D.

A new function HHH is defined by

H(t)={t2+3tt+1,t≠3k,t=3H(t)=\begin{cases}\dfrac{t^2+3t}{t+1}, & t ≠ 3\\ k, & t=3\end{cases}H(t)=⎩⎨⎧​t+1t2+3t​,k,​t=3t=3​

where kkk is a constant. Find the value of kkk such that HHH is continuous at t=3t=3t=3. Justify your answer using the definition of continuity at a point.

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FRQ Directions
Free Response Question Practice

This practice environment simulates the AP AP Calculus AB/BC Free Response Questions section. Here are some guidelines:

  • Read each question carefullybefore responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.