AP Calculus AB/BC - Scoring Guidelines - Part A and Part B

Q: What is the goal of Part A in Question 1?

Part A guides how to score solutions using graphing calculator–required work, including approximating derivatives from table values, midpoint sums for integrals, average rates from definite integrals, and local linear approximations.

Q: How is R'(5) approximated in Question 1?

Using tabulated values around t = 5, the guideline approximates R'(5) and requires correct computations and units, interpreting the result as the rate of change of the vehicle-crossing rate.

Q: What types of reasoning are assessed in Part B of Question 2?

Part B assesses interpretation of a derivative graph on [0,4] for where f is decreasing and concave down, justification of absolute minimum values, evaluation of a definite integral, and finding g'(2) for g(x)=x^3f(x).

Sep 22, 2026

Uploaded by River Wang

Scoring guidelines for AP Calculus AB/BC Question 1 and Question 2 outline how to award points for student work in modeling and calculus interpretation tasks. Part A requires a graphing calculator and emphasizes approximations from tabular data (including R'(5)), midpoint sums for definite integrals, average rates from definite integrals, and linear local approximations for solving a specified rate. Part B forbids calculators and evaluates derivative-graph analysis (increasing/decreasing and concavity), absolute extrema, integral evaluation, and derivative computations for a defined auxiliary function.

LanguageEnglish

CategoryExam

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Question 1

Part A (AB or BC): Graphing Calculator Required

Scoring Guidelines for Question 1

Question 2

Part B (AB or BC): Calculator not Permitted

Scoring Guidelines for Question 2

AP CALCULUS AB/BC Scoring Guidelines Part A (AB or BC): Graphing Calculator Required | t (hours) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | | --- | --- | --- | --- | --- | --- | --- | --- | | R(t) (vehicles per hour) | 2935 | 3653 | 3442 | 3010 | 3604 | 1986 | 2201 | 1. On a certain weekday, the rate at which vehicles cross a bridge is modeled by the differentiable function R for 0 ≤ t ≤ 12, where R(t) is measured in vehicles per hour and t is the number of hours since 7:00 a.m. (t = 0). Values of R(t) for selected values oft are given in the table above. (a) Use the data in the table to approximate Rʹ(5). Show the computations that lead to your answer. Using correct units, explain the meaning of Rʹ(5) in the context of the problem. (b) Use a midpoint sum with three subintervals of equal length indicated by the data in the table to approximate the value of ∫ 120R(t )dt. Indicate units of measure. (c) On a certain weekend day, the rate at which vehicles cross the bridge is modeled by the function H defined by H(t) = -t3-3t2 + 288t + 1300 for 0 ≤ t ≤ 17, where H(t) is measured in vehicles per hour and t is the number of hours since 7:00 a.m. (t = 0). According to this model, what is the average number of vehicles crossing the bridge per hour on the weekend day for 0 ≤ t ≤ 12? (d) For 12 < t < 17, L(t), the local linear approximation to the function H given in part (c) at t = 12, is a better model for the rate at which vehicles cross the bridge on the weekend day. Use L(t) to find the time t, for 12 < t < 17, at which the rate of vehicles crossing the bridge is 2000 vehicles per hour. Show the work that leads to your answer. AP Calculus AB/BC Course and Exam Description | SG 1 |
Part A (AB or BC): Graphing calculator required
Scoring Guidelines for Question 1 9 points | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Learning Objectives: | CHA-2.D | | CHA-3.A | | CHA-3.C | | CHA-3.F | | CHA-4.B | | LIM-5.A | | | | | | | | | | | | | | | | | | | | | (a) Use the data in the table to approximate R ʹ (5) . Show the computations that lead to your answer. Using correct units, explain the meaning of R ʹ (5) in the context of the problem. | | | | | | | | | | | | | | | | Model Solution | | | | | | | | | | | | | Scoring | | | Approximation using values
R′(5) ≈ R(66)~~ ~~−~~ ~~R4(4) = 3010~~ ~~−23442 = −216 from table
At time t = 5 hours (12 p. m.), the rate at which vehicles cross the bridge Interpretation with units | | | | | | | | | | | | | | 1 point
2.B | | | | | | | | | | | | | | | | 1 point | | is decreasing at a rate of approximately 216 vehicles per hour per hour. | | | | | | | | | | | | | | 3.F 4.B | | Total for part (a) | | | | | | | | | | | | | | 2 points | | (b) Use a midpoint sum with three subintervals of equal length indicated by the data in the table to approximate the value of ∫120R(t) dt. Indicate units of measure. | | | | | | | | | | | | | | | | ∫120R(t) dt ≈ 4 (R(2) + R(6) + R(10))
= 4 (3653 + 3010 + 1986)
Midpoint sum setup
Approximation using values | | | | | | | | | | | | | | 1 point
1.E | | | | | | | | | | | | | | | | 1 point | | = 34,596 vehicles from the table with units | | | | | | | | | | | | | | 2.B 4.B | | Total for part (b) | | | | | | | | | | | | | | 2 points | | (c) What is the average number of vehicles crossing the bridge per hour on the weekend day for 0 ≤ t ≤ 12? | | | | | | | | | | | | | | | | 1
12 − 0
∫120H(t) dt
= 2452
Definite
integral
Answer
Definite integral
Answer with supporting work | | | | | | | | | | | | | | 1 point
1.D 4.C | | | | | | | | | | | | | | | | 1 point
1.E | | Total for part (c) | | | | | | | | | |

FAQs

What is the goal of Part A in Question 1?

Part A guides how to score solutions using graphing calculator–required work, including approximating derivatives from table values, midpoint sums for integrals, average rates from definite integrals, and local linear approximations.

How is R'(5) approximated in Question 1?

Using tabulated values around t = 5, the guideline approximates R'(5) and requires correct computations and units, interpreting the result as the rate of change of the vehicle-crossing rate.

What types of reasoning are assessed in Part B of Question 2?

Part B assesses interpretation of a derivative graph on [0,4] for where f is decreasing and concave down, justification of absolute minimum values, evaluation of a definite integral, and finding g'(2) for g(x)=x^3f(x).

Sep 22, 2026

Uploaded by River Wang

AP Calculus AB/BC - Scoring Guidelines - Part A and Part B_Page 1

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