Reasoning from Tabular Data

AP Calculus:
®
Reasoning from Tabular Data
2008
Curriculum Module
y t
t (yrs)
0
4
10
13
20
2500
2724
3108
3697
4283
y t (people)
y 12
y 12
y 12
y 12
y 13
y 10
13 10
3697 3108
196.333
3
y t
1 20
y t dt
20 0
1 1
4 2500 2724
20 2
1
6 2724 3108
2
1
3 3108 3697
2
1
7 3697 4283
2
1
20
20
0
y t dt
1
yrs
people yrs
people.
1
b
b a
a
f x dx
R t
12
0
12
0
R t dt
4 R 2
R 6
12
0
R 10
R t dt
R t dt
4 13.4 14.3 14.8
1
12
R t
gal
hr
hr
gal.
1
750 24t t 2
60
P t
P t
1
12
12
0
12
0
P t dt
1
169.2
12
P t dt
1
b
b a
a
f x dx
f (b) f (a)
b a
1
12
12
0
P t dt
1
hr
gal
hr
hr
gal
hr
14.1 gal/hr.
vA t
vA t
vA t
vA t
0 t 10
2 6.8
3 7.4
2 15.6
3 24.9
141.7
10
0
cm
sec
sec
v A t dt
cm
aB t
vB t
vB t
13 1 7 C
2t
C
7 dt
19
t2
7t
vB t
C
t2
7t 19
2t 7
vB 5
9 7.4
vA 5
y t
y t
y 18
y 18
25
10
25
10
y t dt
y t dt
W t
72 380e
W t
W 18
0.036t
y t
y 7
y 7
0 t 10
P t
2t 50
P t
P 7
1
10
10
0
P t dt
2
T x
T x
12
0
T x dx
T x
1
12
12
0
T x dx
R t
0 t
R t
20
R t
20
0
W t
R t dt.
25e 0.03t
W t
vA t
vA
0 t 10
vA t
0 t 10
aB t
2t
2
v t
v t
8 t 10
12
0
v t dt
257 292
20 15
y 18
25
y t dt
10
W 18
y 25
7 F / min.
y 10
112 F
7.156
W t
300
y 7
4330 3815
8 6
1
10
10
0
y t dt
257.5
1
2 2500 2912 3360 3815 4330
10
P 7
1
10
12
0
10
0
P t dt
T x dx
T 12
T 0
13 F.
T 7
T 4
7 4
99 101
3
2
F / min.
3
3383.4
1
12
12
0
T x dx
1 1
4 108 101
12 2
20
0
R t dt
4 28
1
3 101 99
2
5 33
1
5 99 95
2
8 42
3 46
751 gallons
0 t
20
0
1
20
20
0
20
0
100.25 F.
20,
R t dt.
W t dt
W t dt
aA t
aA 8
10
0
v A t dt
v A 10 v A 7
10 7
1
2 0 9
2
115 61
ft / sec
ft
18
= 18 2
3
sec
sec
1
3 9 36
2
1
2 36 61
2
1
3 61 115
2
437.5 ft
vB t
vB t
11 9 6 C
vB 7
59 61 v A 7
2t
2 dt
C
t2
2t
4
C
vB t
t2
2t
4
v 0
37
20 17
v 2
v 10
17
20 38
v 12
t1
v t1
20
v 2
v t1
v t2
v t2
t2
v 10
17
a t
v t
20 and t1
17 17
10 2
0
t2 for the t1 and t2
t1, t2
a t
v t
v 10 v 8
10 8
12
0
v t dt
4 v 2
12
0
v t dt
v 6
v 10
20 20
t2 t1
17 6
2
0
5.5
4 17 1 17
cm / sec
sec
140 cm
5.5
cm
sec2
20