calculus bc -- practice exam #3 – day 1 -- no...
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CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR
Name Row Period 1 If 7 , then xy dyxy e
dx= − = A) yx e− B) xy e− C)
xy
xy
ye yx xe
+−
D) yx− E)
xy
xy
ye yx xe
++
2 The volume of the solid that results when the area between the curve xy e= and the line 0y = , from 1 to 2,x x= = is revolved around the axis is:x −
A) ( )4 22 e eπ − B) ( )4 2
2e eπ − C) ( )2
2e eπ − D) ( )22 e eπ − E) 22 eπ
3 ( )( )
183 4x dx
x x− =
+ −∫ A) ( )( )
53 4dx
x x+ −∫ B) ( )( )3 4
dxx x+ −∫ C) 2
3 4dx dxx x
++ −∫ ∫
D) 15 143 4dx dx
x x−
+ −∫ ∫ E) 3 23 4dx dxx x
−+ −∫ ∫
4 2If 5 4 and ln then dyy x x x tdt
= + = =
A) 10 4t+ B) 10 ln 4t t t+ C) 10 ln 4t
t+ D) 2
5 4t t+ E) 410 ln t
t+
5 25
0
sin cosx xdxπ
=∫ A) 16
B) 16− C) 0 D) ‒6 E) 6
6 ( )3The tangent line to the curve 4 8 at the point 2,8 has an intercept at:y x x x= − + −
A) ( )1,0− B) ( )1,0 C) ( )0, 8− D) ( )0,8 E) ( )8,0 7 ( ) ( )The graph in the plane represented by 3sin and 2cos is:xy x t y t− = =
A) a circle B) an ellipse C) a hyperbola D) a parabola E) a line 8
24 9dxx
=−∫ A) 11 3sin C
6 2x− ⎛ ⎞+⎜ ⎟⎝ ⎠
B) 11 3sin C2 2
x− ⎛ ⎞+⎜ ⎟⎝ ⎠ C) 1 36sin C
2x− ⎛ ⎞+⎜ ⎟⎝ ⎠
D) 1 33sin C2x− ⎛ ⎞+⎜ ⎟⎝ ⎠
E) 11 3sin C3 2
x− ⎛ ⎞+⎜ ⎟⎝ ⎠
9 1lim 4 sin is:x
xx→∞
⎛ ⎞⎜ ⎟⎝ ⎠
A) 0 B) 2 C) 4 D) 4π E) nonexistant
10
The position of a particle moving along the x − axis at time t is given by x t( )= ecos 2t( ), 0 ≤ t ≤ π .
For which of the following values of t will x ' t( )= 0?
I. t = 0 II. t = π2
III. t = π
A) I only B) II only C) I and III only D) I and II only E) I, II, and III 11 ( ) ( )
0
sec seclim h
hh
π π→
+ −= A) −1 B) 0 C) 1
2 D) 1 E) 2
12 Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm3). A) ‒19.2 B) ‒15.36 C) ‒1.92 D) ‒0.01 E) ‒0.0001
CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR
13 A particle which is at position ( )1,3 with velocity ( )0, 1− when 0t = , moves with acceleration
( )211,
1 t
⎛ ⎞⎜ ⎟⎜ ⎟+⎝ ⎠
. Where is the object when 2t = .
A) ( )3,3 ln3− B) ( )2, ln3 C) ( )2,3 ln3− D) ( )3, ln3− E) ( )3,3 ln3+ 14
( )1
1
0
sin x dx− =∫ A) 0 B) 22
π + C) 22
π − D) 2π E)
2π−
15 The equation of the line normal to
2
2
55xyx
−=+
at x = 2 is
A)81 60 142x y− = B) 81 60 182x y+ = C) 20 27 49x y+ = D) 20 27 31x y+ = E) 81 60 182x y− = 16 If c satisfies the conclusion of the Mean Value Theorem for derivatives for ( ) 2sinf x x= on the interval
[0, ]π , then c could be A)0 B) 4π C)
2π D) π E) There is no value of c on[0, ]π
17 The average value of ( ) lnf x x x= on the interval [1, ]e is
A) 2 14
e + B) 2 1
4( 1)ee++
C) 14e + D)
2 14( 1)ee+−
E) 23 1
4( 1)ee+−
18 A 17−foot ladder is sliding down a wall at a rate of 5 feet/second. When the top of the ladder is 8 feet from the ground, how fast is the foot of the ladder sliding away from the wall ( )in feet/second .
A) 758
B) 83
C) 38
D) −16 E) 753
−
19 If 3 cosdy y xdx
= , and y = 8 when x = 0 , then y = ?
A) 3sin8 xe B) 3cos8 xe C) 3sin8 3xe + D) 2
3 cos 82y x+ E)
2
3 sin 82y x+
20
The length of the curve determined by 23 and 2 from 0 to 9 is:x t y t t t= = = =
A) 9
2 4
0
9 4t t dt+∫ B) 162
2
0
9 16t dt−∫ C) 162
2
0
9 16t dt+∫ D) 3
2
0
9 16t dt−∫ E) 9
2
0
9 16t dt+∫
21 If a particle moves in the xy‒plane so that at time t > 0, its position vector is ( )2 3
, ,t te e− then its velocity
vector at time 3t = is: A) ( )( )ln 6, ln 27− B) ( )( )ln 9, ln 27− C) ( )9 27,e e−
D) ( )9 276 , 27e e−− E) ( )9 279 , 27e e−− 22 The graph of ( ) 211f x x= + has a point of inflection at:
A) ( )0, 11 B) ( )11,0− C) ( )0, 11− D) 11 33,2 2
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
E) There is no point of inflection
******* PROBLEMS 23 – 28 ARE ON THE NEXT PAGE *****
CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR
23 What is the volume of the solid generated by rotating about the y −axis the region enclosed by
siny x= and the x −axis, from 0x = to x π= ? A) 2π B) 22π C) 24π D) 2 E) 4 24 ( )
2 2
sin 1/ tdt
tπ
∞=∫ A) 1 B) 0 C) 1− D) 2 E) Undefinded
25
A rectangle is to be inscribed between the parabola 24y x= − and the x −axis. A value of x that
maximizes the area of the rectangle is A) 0 B) 23
C) 23
D) 43
E) 32
26 29
dxx
=−∫ A) 1sin 3x C− + B) 2ln 9x x C+ − + C) 11 sin
3x C− +
D) 1sin3x C− + E) 21 ln 9
3x x C+ − +
27 Find
1
lim xxx
→∞ A) 0 B) 1 C) ∞ D) 1− E) −∞
28 What is the sum of the Maclaurin series ( ) ( )
3 5 7 2 1
... 1 ...?3! 5! 7! 2 1 !
nn
nπ π π ππ
+
− + − + + − ++
A) 1 B) 0 C) ‒1 D) e E) There is no sum. JJJJJ END OF PART A JJJJJ
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