Download PRACTICE FINAL EXAM B 2017 MC (No Func Comb Plus Limit and

PRE CALCULUS 12
PRACTICE FINAL B
January 2017
Millar
1.
If f(x)
= 2x
and g(x)
a) -6
2.
3.
= x- 4,
what is the value of g(f(3))?
c) 0
b) -2
e) 6
d) 2
Find the quotient and remainder of (x3 + 8x2 + 19x + 13)---;- (x- 3).
a) (x2 + 11x +52) R13
b) ( x2 + 5x + 4) R -1
d) (x2 + 5x + 4) R 1
e) (x2 +11x+52) R-1
Write the division statement for (x 5
- 3x 3
c) (x2 + 11x +52) R 169
+ 2x- 8)---;- (x- 4).
a) (x4 + 4x 3 + 13x 2 + 52x + 210)(x- 4) + 832
b) (x 4 + 4x 3 + 13x 2 + 54)(x- 4) + 208
c) ( x4 + x 2 + 6) ( x + 4) - 16
d) (x4 + x2 + 6)(x- 4) + 32
e) (x4 + x2 + 6)(x- 4) + 16
4.
When x 2 + 3x + b is divided by x +a, the quotient is x + 6 and the remainder is 14. Find
a and b.
= -4, b = -3
a) a= -5, b = 3
b) a
d) a= 3, b = 4
e) a= 5, b = -3
c) a = -3, b = -4
Page 2
5.
Use the Rational Root Theorem to find the number of possible rational roots of
8x3 - 5x2 + 2x - 3 = 0.
a) 8
6.
b) 10
Find m so that 2x- 3 is a factor of 8x 4
b) -27
a) -31
7.
d) 16
- 2x 3
e) 24
+ 3x2 + mx + 6.
c) 23
d) 27
e) 31
Which of the following polynomial function written in factored form best represents the
graph and table given in the figure?
a) P(x) = (x- 3)(x- 1)2
b) P(x) = (x + 3)(x- 1?
c) P(x) = - (x +
d) P(x) =
e) P(x)
8.
c) 12
3)(x- 1) 2
•2
(x- 1)3
v\
= - (x- 1) 3
Determine an equation in general form whose roots are ±3v'2 and -4.
a) x3
- 4x 2 - 22x
c) x 3
+ 4x2
- 9x
e) x 3
+ 4x2
- 18x
+ 72 = 0
- 36
=0
- 72 = 0
y
X
b) 3v'2x 3
-
3v'2x2
d) 3v'2x3
-
4x 2
-
- 4x =
18x
0
+ 72 = 0
I)
•1
I)
1
2
3
k=·3
-- .
·1.
I)
·2.
•12
Page 3
9.
If the graph of y = f(x) is shown, what is the solution for the inequality f(x)
the solution on a numberline.
a)
-4
-3
-2
d)
1
0
+2
y
3
4
)
b)
c)
+
-1
< 0? Show
X
+
(
-4
-3
-2
+
-1
-4
-3
-2
-1
(
e)
f
-2
-1
f
0
I
+
0
1
0
1
2
f
2
3
4
3
4
f
1
2
10. Write log5 x =a in exponential form.
b) 5a
11.
Solve: logx 243 =
a) 6
12.
=a
d) 5x
=X
b) 9
c) 3
e) 27
d) 10
loga x, a > 1, determine the
1
y-coordinate of the point on the graph whose x-coordinate is -.
Given that (m, n) is a point on the graph of f(x)
=
m
a)
1
n
b) -n
c) n
d)
1
n
Page 4
13. Which one of the following logarithmic expressions does not have the value 3?
a) log 10 1000
14. What is the equation of the asymptote of y
a)
y
=0
b) y
=4
=
3x-4 ?
c) x = -4
d)
X=
0
e) x = 4
15. Which of the following is equal to log(tanB)?
a) log(sinB) +log(cos B)
b) log(tan 2B)
d) log(sin B cos B)
e) log(sin B) - log(cos B)
c) log(cos2 B- 1)
.
.
. log 12
16. Wnte 1
as a smgle loganthm.
og2
b) log 10
a) log 6
100
17. Which of the following expressions is equivalent to log 10m -log-?
n
a) 3 + logm + logn
b) 1 + logm -logn
d) 1 + logm + logn
e) 3 + logm -logn
18. Find x if x
a) 1
=
c) -1 + logm + logn
(log5 17)(1og17 125).
b) 2
c) 3
d) 4
e)
!
Page 5
19.
Solve the following system for (x, y):
logy = log(5x
log5 y = 2x
20.
+ 2)
In which quadrant does the terminal ray of a standard position angle of
c) III
b) II
a) I
l 1r
radians lie?
d) IV
e) there is no terminal ray
21.
Convert the angular measure of
b) 88°
22.
radians to degrees. (Round to the nearest degree.)
c) 140°
e) 440°
What is the value(s) of() if sin()= 0.548 where () is measured in radians and 0
(Answer to 2 decimal places.)
a) 0.58, 2.56
23.
7(;
b) 0.58, 3.72
c) 2.56, 3.72
d) 2.56, 5.24
< () < 27r?
e) 3.72, 5.24
The graph shows an equilateral triangle whose vertices lie on a unit circle. Point P lies
on the terminal arm of an angle of 60° in standard position. What are the coordinates of
points Q and R ?
a) Q(1, 0)
y
R(0.5, -0.866)
1
b) Q(-1,0)
R(0.866, -0.5)
c) Q(-1,0)
R(0.5, -0.866)
d) Q(0,-1)
R(0.5, -0.866)
e) Q(-1,0)
R( -0.866, -0.5)
Q
1
X
Page 6
24.
The angle
angle e.
e is in
the fourth quadrant and tan
e = -¥.
Point P is on the terminal arm of
Which is a possible coordinate for P?
25.
The smallest positive zero of the function y =cos k
value of k if k > 0.
a)
26.
!
c)
b)
d) (7, -6)
(x + ) occurs
J
d)
e) (21, -9)
at
x
= - Find the
e)
371"
8
Which of the following relations has a graph which is the same as the graph of
y = sin(x
+ 1r)?
a) y
3 .
= 2 smx
d) y = sin ( x - 1r)
27.
c) ( -9, 21)
b) (9,-21)
a) ( -21, 9)
b) y
e)
Given the graph of y =a sin b(x
a)
J
b) ;
c) 21r
= COS X
y = 3cosx
+c)+ d, determine the period.
d) 47r
e)
8
y
Page 7
28.
Given the graph y =a cos b(x +c)+ d, determine the value of d.
b)
a)
c) 3
1r
e) 21r
d) 6
-1T
29.
For which angle x given below is tan x not defined?
a) x
30.
=0
Simplify:
a) sin2 x
32.
b)
X=
Simplify the expression:
a) - cscA
31.
1T
C)
- 7r
X-
3
d)
X= 1r
e) x =
3;
cscA
cscA- sin A
b) cscA
c) sec2 A
d) secA
e) - cot 2 A
v'sec 2 x- 1
v'csc 2 x- 1
b) tan 2 x
c) cot 2 x
e) cot4 x
Simplify: cos(a - {3) cos {3 - sin( a - {3) sin {3
a) cos 2a
b) cos a
c) cos {3
d) sma
e) sin {3
Page 8
33.
If esc A=
a)
-i
with LA is in quadrant III. What is the value of cos(2A)?
c)
b)
275
24
e
d)
25
34.
How many solutions does the trigonometric function cos2
interval 0 < < 27r?
e
a) 1
e) infinitely many
b) 2
c) 0
e- sin2 e = 0.4
d) 4
25
49
)
have in the
Page 9
35.
This figure shows the graph of f. Use this figure to answer the following question(s).
y
5
--------..,4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
At which of the following x-values does f have a removeable discontinuity? Choose the
BEST answer.
I.
-6
II.
0
III. 3
IV. 5
v.
7
VI. 10
a) I, II, and IV
b) IV and VI
d) II, III, and V
e) V only
1
36.
x3-
c) I, IV, and VI
3
lim--x---+64 X - 27
1
a) 3
1
b) 12
1
c) 27
1
d) 9
e) 27
Page 10
37 .
.
lIffi
X+
5 .
--IS
x--+2+ X-
2
a) 1
38.
lim
b) 2
e) oo
1
c) 10
1
d) 3
e) undefined
c)
d) 0
e) 27
c)
d) smx
e) undefined
49
a) 0
1
7
b)
. sin3 3x
lIffi
3
x--+0 sin 4x
a)
40.
d) 0
Vx -7 =
x--+9 X-
39.
c) -oo
27
b)
64
. 1- cos2 x
lIffi
x--+0
-4x2
a) -
00
64
IS
b) 0
Page 11
41.
lx -71 =
lim
x---+7+ X -
42.
7
a) 1
b) does not exist
d)
e) ±1
00
Which of the following functions has a horizontal asymptote at y
X
b) v2x + 1
43.
c) -1
Consider
j (X)
c)
2x 2
- 6x
+1
=-
?
x-1
d) 2x 2
+1
f as defined below:
=
{
x 2 - 36
X_ 6
25
for X =/:- 6,
for x = 6
Which of the following are true about f?
I.
lim f(x) exists
x---+6
II.
f(6) exists
III.
f (x) is continuous at x = 6
a) None
b) I only
d) III only
e) I and II only
c) II only
2x- 5
e) 1- 4x2
Page 12
44. The functions f and
g have the values shown in the table and are differentiable.
=
If A= () then A'(2)
a) 23
45. f and
b)
23
64
23
c) 64
9
8
4
d) 9
e) -23
X
f'
f
1
0 5
2 8 3
4 14 9
6 26 27
g
g'
-7 41
1
-5
-3 4
-1 16
g are differentiable functions and have the values shown in the table.
If A= y/g(X) then A'( -2)
a) -
1
d) 3
=
3
c) -
b) impossible
2
e) 6
X
f'
f
g
g'
-8 4 3 -2 6
-6 10 12
0 9
-2 16 9 36 18
2 30 15 52 24
. d t he den.vat1.ve, d
46. Fm
-d,yo f f( x ) = x22 - 2 .
X
a) 1
X
8x
b) (x2 + 2)2
+2
4x 2
c) (x2 + 2)
8x
d) - (x2 + 2)2
e)
-8x2 - 8x
(x2 + 2)2
Page 13
47.
If f(x) =
x3
+ 4x2
X
a) 3
48.
49.
50.
-3
, then !'(1) =
c) 5
b) 6
Find an equation of the tangent line to the graph of f(x)
2
(x + 1)2 (x- 1)
a)
y =
d)
y = 2(x- 1)
Differentiate f(x) = -4(2- x?
b)
X-
2y
e)
y =
-x + 1
=
1
=
j when
x
c) y- 1 =
4
= 1.
x
+ 5(2- x) + 9.
a) -(2-x)
b) -8(2- x)
d) 8(2- x)- 5
e) 13(2-x)
At what points on the ellipse
e)
d) 9
2
+
i:
=
+5
c) -8x+5
1 is the slope of the tangent line equal to 2?
Page 14
51.
Factor x3
52.
Solve for x: 7x+2
53.
Solve cos 2()
54.
When a spaceship is fired into orbit (from a site not on the equator) it goes into an orbit
that takes it alternately north and south of the equator. Its distance from the equator is
approximately a cosine function of time.
- 19x
- 30.
= 5 · 23x?
= sin()- 2
for 0
< () < 37T. Answer to 2 decimal places.
Suppose a space ship is fired into orbit. 10 minutes after it leaves the launch site it
reaches its farthest distance north of the equator, 3000 km. 50 minutes later it reaches its
farthest distance south of the equator, also 3000 km. The spaceship completes an orbit
once every 100 minutes.
Let y equal the number of kilometres the spaceship is north of the equator (south will be
negative).
Let t equal the number of minutes elapsed since lift-off.
What is the equation expressing y in terms of t ?
55.
Prove: sin
3()
= 3 sin()- 4 sin 3 ()
56.
(4, 9)
(0, -2)
(6, -5)
The graph off' is shown. Graph f(x)
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PRE CALCULUS 12
PRACTICE FINAL B
Millar
January 2017
1.
Answer:
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Page 2