The AP Calculus AB 2018 International Practice Exam Scoring Guidelines provide detailed scoring criteria for free-response questions. These guidelines are essential for educators and students preparing for the AP Calculus AB exam, offering insights into the evaluation of student responses. Each question is broken down with specific scoring rubrics, helping users understand how to achieve maximum points. The document also includes explanations for correct answers, making it a valuable resource for exam preparation and review. Ideal for AP Calculus students and teachers aiming to enhance their understanding of the exam format and scoring.

Key Points

  • Includes scoring guidelines for all free-response questions from the 2018 AP Calculus AB exam.
  • Provides detailed rubrics for evaluating student responses, ensuring clarity in grading.
  • Offers explanations for correct answers to assist in understanding key concepts.
  • Serves as a resource for teachers and students preparing for the AP Calculus AB exam.
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AP® Calculus AB
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AP® Calculus AB
356
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© 2018 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
(a)
( )
( ) ( )
51
20.5 15.1
3 1.35
51 4
gg
g
−
−
≈
′
= =
−
At time
3t
=
minutes, the rate at which grain is being added to the silo is
increasing at a rate of 1.35 cubic feet per minute per minute.
1 : approximation
2 :
1 : interpretation with units
(b)
The total amount of grain added to the silo from time
t 0=
to time
8t =
is
( )
8
0
g t dt
∫
cubic feet.
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
8
0
110 5 51 6 65 8 86
15.1 1 20.5 4 18.3 1 22.7 2 160.8
g t dt g g g g≈ ⋅− + ⋅−+ ⋅ − + ⋅−
= ⋅+ ⋅ + ⋅+ ⋅ =
∫
1 : integral expression
3 :
1 : right Riemann sum
1 : approximation
(c)
( )
8
0
99.051497w t dt =
∫
The approximate
amount of unspoiled grain remaining in the silo at
time
8t =
is
( )
8
0
160.8 61.749w t dt−=
∫
(or 61.748) cubic feet.
1 : integral
2 :
1 : answer
(d)
( ) ( )
6 6 18.3 16.063173 2.236827 0gw−=− = >
Because
( ) ( )
6 6 0gw− ,
the amount of unspoiled grain is increasing at
>
time
6t = .
( ) ( )
1 : considers 6 6
2 :
1 : answer
gw−
AP
®
CALCULUS AB
2018 SCORING GUIDELINES
Question 1
AP
®
CALCULUS AB
2018 SCORING GUIDELINES
© 2018 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
Question 2
(a)
( )
5 0.538462v
′
=
The accelerati
on of the snail at time
t = 5
minutes is 0.538 inches per
minute per minute.
1 : answer
(b)
( )
15
0
76.043074v t dt =
∫
The d
isplacement of the snail over the
interval
0 15t≤≤
minutes is
76.043 inches.
{
1 : integral
2 :
1 : answer
(c)
( )
15
0
1
5.069538
15
v t dt =
∫
( )
2
1.4ln 1 5.069538 6.031tt+ = ⇒=
minutes
{
1 : average value expression
2 :
1 : answer
(d)
The velocity of the ant at time t,
12 15t≤≤ ,
is
2dt t c= +
∫
2
inches
per minute for some constant c.
For
12 15t≤≤ ,
the displacement of the ant is
( )
( )
15
15
2
12
12
2 81 3
t
t
t c dt t ct c
=
=
+=+ =+
∫
inches.
Thus,
81 3 76.043074 1.652309c+ = ⇒=−c.
The velocity
of the ant at time
12t =
is
B =2⋅−12 1.652309 82 =24.3
(or 22.347) inches per minute.
— OR —
The velocity of the ant at time t,
12 15t≤≤ ,
is
( )
2 12t− B+
inches per
minute.
For
12 15t≤≤ ,
the displacement of the ant is
( )
( )
( )
( )
2
15
2
12
15
1
2 2 91
t
t
t B dt Bt Bt
=
=
− −+ =+=
∫
1 2 3+
inches.
9 3 76.043074 22.348BB+ = ⇒=
(or 22.347) inches per minute
1 : ant’s velocity
1 : ant’s displacement
4 :
1 : equation
1 : answer
© 2018 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
AP
®
CALCULUS AB
2018 SCORING GUIDELINES
Question 3
(a)
( ) ( )
7
0
9
7 3 7 21 3 24
2
f g t dt
π
=+= =⋅ −+ −
∫
9
2
π
( ) ( )
73 733fg
′
=+ =+=6
( )
( )
1 : 7
2 :
1 : 7
f
f
′
(b)
On the interval
4 3,x−≤ ≤
( ) ( )
3f x gx
′
= + .
Because
( )
0fx
′
≥
for
4 3x−≤ ≤,
f is nondecreasing over
the entire interval, and the maximum must occur when
3x = .
2 : answer with justification
(c)
( )
0
1
lim
2
x
gx
−
→
′
= −
( )
0
lim
x
gx
+
→
′
does not exist.
{
1 : left-hand limit
2 :
1 : right-hand limit
(d)
( )
( )
( )
2
0
2
lim 7 6 7 0
x
f x g t dt
−
→−
+ =−+ + =
∫
( )
36
2
lim 1 0
x
x
e
+
→−
−=
Using L’Hospital’s Rule,
( ) ( ) ( )
36 36
22
7 32
31
lim lim
3 3
13
xx
xx
fx f x g
ee
++
→− →−
′
+ +−
+
= = = =
4
3
−
.
1 : limits equal 0
3 :
1 : applies L’Hospital’s Rule
1 : answer
Note: max
13
[1-0-0] if no limit notation
attached to a ratio of derivatives
/ 7
End of Document
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FAQs

What are the scoring criteria for the AP Calculus AB free-response questions?
The scoring criteria for the AP Calculus AB free-response questions are outlined in detail within the guidelines. Each question is assigned a specific point value based on the accuracy and completeness of the response. The guidelines break down the scoring into categories, such as correct reasoning, appropriate use of calculus concepts, and clarity of explanation. This structured approach helps educators fairly assess student performance and provides students with a clear understanding of what is expected in their answers.

How can students use the scoring guidelines to improve their AP Calculus skills?
Students can utilize the scoring guidelines to identify areas where they need improvement in their calculus skills. By reviewing the scoring rubrics, students can see what constitutes a high-scoring response and learn to apply similar strategies in their own work. Additionally, the explanations for correct answers provide insights into the reasoning behind solutions, allowing students to deepen their understanding of calculus concepts. This targeted practice can enhance their performance on the actual exam.

What topics are covered in the 2018 AP Calculus AB exam free-response questions?
The 2018 AP Calculus AB exam free-response questions cover a range of topics, including limits, derivatives, integrals, and the Fundamental Theorem of Calculus. Each question is designed to assess students' understanding of these core concepts and their ability to apply calculus to real-world problems. The guidelines provide a comprehensive overview of how each topic is evaluated, ensuring that students are well-prepared for similar questions on the exam.

Who can benefit from the AP Calculus AB scoring guidelines?
The AP Calculus AB scoring guidelines are beneficial for both students and educators. For students, these guidelines offer a clear framework for understanding how their responses will be evaluated, helping them to focus their study efforts effectively. Educators can use the guidelines to grade student work consistently and fairly, ensuring that all students are assessed according to the same standards. This resource is essential for anyone involved in AP Calculus education.