1. No category

Math 31
Multiple Choice Test
Sample
1. Sketch each of the functions on the qxes below. Which are not differentiable at x
y=l, x -
#1
2[
y=~
#2
..
...
+
OJ
<.
.
'"
y=(x ­ 2)
o1 ~ ~
2 1
5 "
1
#3
•
2
'~-iT-IT--
.
2 1
1
•
2 1 0 1 12 ~ 4 5 ~
L.
a) 1 only
b) 1 and 2
2
2 x- 3
b) 1/2
c) -1
d) 1
2
3. Evaluate
3n -2n+5
lim
n~oo
a) 0
1-3n-2n
b) 2/3
2
c)-3/2
d)
2
4. Evaluate
x~
a) 0
sin (2 x)
lim
b) 1
0
8x
2
c) 1/2
d) 1/4
1
",
d) 1,2 and 4
c) 1,2 and 3
x-I
-
o1
P ~ ~. 5
-
I'"
1
a) 0
LU
x-2
<.
lim
2
x ~ -1 x
1
1
y=-­
#4
,'"
2. Evaluate
..~-
•
2 1 0 1 P ~ ~
=2?
.. _ ~ ..L . -
.. ~
El
Math 31
Sample
1
5. Evaluate
x-­
x
lim
x~ 1 x- 1
a) 0
c) 1/2
b) 2
d) 1
3
X
2
6. A point of contact of a tangent to a curve y=- - 2 x + 5 x + 2 that has a slope of 2 is:
3
b) (-1,-6)
a) (0,-1)
c) (1,-20/3)
d)(3,8)
4
7. Find the equation of the tangent to the graph of f(x)=x - 3 x + 1 at (1,-1)
a) y
=x - 2
b) Y =-1
8. If y=3'cos(x
2
)
c) y
=7x - 8
d) y
=-x + 1
,then dy is
dx
2
9. If y=ln(x + 1) ,then dy is
dx
1
a)-­
2
x +1
-1
2x
b)-­
2x+1
2
dy
10. If Y =2 'x'y - 3 ,then at x
dx
a) -1
c)-­
2
x + 1
2x
d)-­
c) -1 and 3
d) 0
X
=2 is
b)-2
11. If g(x) = x 2'cos(x) ,then g '(11)
- equals
\2
2
b)~
4
11
2
d)
c)­
4
2
-7t
2
+1
Sample
Math 31
12. At which point on the graph of y
=g(x) below is
g' (x) < 0 and g" (x) > 0 ?
B
a) A
c) C
b) B
d) D
13. Which statement below is true about the curve y=
/-4
?
2+7x-4/
a) The line x =-1/4 is a vertical asymptote.
b) The line x =1 is a vertical asymptote.
c) The line x = 1/4 is a horizontal asymptote.
d) the line x =2 is a horizontal asymptote.
2
3
dy
14. If y=(4 x + 1) '(1- x) • then is
dx
2
a) 5'(1 - x)2'(16 x + 1)
2
b) -5'(1 - x)2'(16 x - 1)
2
c) 12'(1- x)2'(16 x + 1)
d) -24:(1- x)2'(16 /
3
15. The graph of y=x - x
- 1)
2
is
2
2
a) decreasing when 0< x< - and increasing when x < 0 and x>­
3
3
b) decreasing when 0< x< 1 and increasing when x < 0 and x> 1
2
2
c) decreasing when x< 0 and x> - and increasing when 0< x< ­
3
3
-2
-2
d) decreasing when -< x< 0 and increasing when x< and x > 0
3
3
3
Sample
Math 31
16. A value of x for which y=x
-
17. The second derivative of y=4
a) 9 - ­
2
9 x + 4 has a local maximum value is
-
d)-3
i -~
x
4
b) 8 - ­
2
X
3 x
c) -1
b) 9
a) 3
3
3
X
is
2
c)4 +­
3
x
4
d) 8 +­
3
X
4
18. A point of inflection for the curve y=x - 8 x
a) (6,-432)
b) (4,-256)
3
3
is
c) (2,-112)
d) (8,0)
2
m
d s
2
19. The acceleration of a body is --=3 t + 20
after a time of t seconds. Its initial
2
2
dt
S
m
velocity. is 5 - . Hence, at the end of 2 seconds the body will have travelled a distance of
s
a) 48 m
d) 36 m
c) 54 m
b)60 m
20. If the distance "s" of a particle from a fixed point is determined as a value of a function of
time "t" by the equation s=32 - 2
i
+t
3
in metres, then the acceleration (in m) at the time
2
s
when t
= 1 second is
a) -1
c) 2
b) 1
d)-2
21. A particle moves along a straight line and its position from a fixed point "A" at time "t" is given
by s= 2 + 3·sin ( t) + cos ( t) . The value of "t" when the parti c1e fi rst comes to rest is
a) 0.4
22. EV<lluate'
b) 1.2
I
c) 3.0
x
e
--dx
1 + eX
X
X
d) 71.6
a) x + e + C
b) In ( e +
\
1) + C
c) x'ln(e + 1) + C
4
X
\
d) x ·In ( e + 1) + C
Math 31
Sample
J;
x
23.
J4 ­ x
dx
2
0
a)-2
b) -1
d) 1
c) 2
1
2
b) -'cos (2 x) + C
2
25. Evaluate
a) 21/10
l
0
J
4 (5
-1
c) -
(
'sin 4 x
2) + C
8
)5
x' ,x + 1 dx
b) 13/6
c) 63/6
d) 63/5
ANSWERS
1. d
2.
b
3. c
4.
6. d
7. a
8. a
9. d
10. c
11. b
12. d
13. a
14. b
15. a
16. d
17. b
18. b
19. c
20. c
21. b
22. b
23. d
24. a
25. a
5
c
5. b