Download PracticeFinal1

Mathematics 142 final exam
Friday, June 19, 2009
please show your work to get full credit
Evaluate each of the following:
North Seattle Community College
✓ ◆
⇡
(a) sec
5
Winter Quarter 2012
(c) 60e .02x when x = 40
PRECALCULUS
Practice Final 1
The terminal side ofpa central
angle
A
in
standard
position
intercepts the unit circle at
p
STUDENT
NAME:
__________________________
e point (x, y) = ( 1/ 5 , 2/ 5). Find the exact values (some involving square roots) of
e six trigonometric functions name:
of A.
Mathematics 142 final exam
QUIZ SCORE: ______________________________
Friday, June 19, 2009
4. your
Solve
fortox:get full credit
please
show
work
Solve for t:
✓
◆
x
.05x
10
log
= 43
80e
= 20
10 5
1. Evaluate each of the following:
1. Evaluate each of the following:
If a sequence is defined by ak✓=⇡ ◆
6(1.02)k for k 1
(a) sec
(b) log3 19
(c) 60e .02x when x = 40
5
) Write down the first four terms of
(b) What kind of sequence is this?
e sequence.
2. The terminal side of a central angle A in standard position intercepts the unit
2. The terminal side ofpa central
angle A in standard position intercepts the unit circle at
circle
at the point (x, p
y) = (-1/ 5, 2/ 5 ). Find the values of all six trig functions.
40
the point (x,X
y) = ( 1/ 5 , 2/ 5). Find the exact values (some involving square roots) of
) Find the
of
ak
thevalue
six trigonometric
functions of A.
3. k=1
(a) Solve for t: 80e-0.5t = 20
(b) Solve for x: 10log (𝑥
) = 43
10!!
4. Solve for x:
Solveoffor
t: indicated angle, side length, or arclength:
Find the3.value
each
✓
◆
st
4. If a sequence
is defined by ak = 6 (1.02)k for k≥1,
then xwrite=the
.05x
10
log
431 six terms of
80e
=
20
insert
diagrams
here
5
the sequence.
10
(b) log3 19
k
5. Findisalldefined
the solutions
θ between
radians for each of the following
If a sequence
by2⇡akradians
=of
6(1.02)
for k0ofand
1the2πfollowing
Find all5. solutions
between 0 and
for each
trigonometric
trigonometric
equations:
uations: (a) Write(a)
2 θfirst
down
the
6 cos
= 3 four terms of
(b) (b)
3 sinWhat
θ + 4kind
cos θof=sequence
0
is this?
the
sequence.
page by
two
) 3 cos2 ✓ = 6
(b) 4 cos ✓ + 3 sin ✓ = 0 ( hint: divide both sides of equation
cos ✓ )
6. Expand and simplify:
(a)
(b)
40
X
!
(c) Find the value ✓
of
ak◆
e2x y 3
2⇡
Expand and simplify: 6 cos ✓ k=1 9. Expand and simplify: ln xpw
3
continues
on angle,
next page
6. Find the value of each
indicated
side length, or arclength:
!
1 3 period and horizontal shift.
7. For y = 60sin 10.
(40xFor
+ !the
) find
the
insert
diagrams
angle
✓ amplitude,
= coshere
7
8. A sum of $600 is deposited into a bank with 3% rate per annum.
Find
thetriangle to find the exac
(b) Use
your
(a)
Draw
a
right
triangle
illustrating
7. Find amount
all solutions
0 and after
2⇡ radians
forcompounding
each of the following
trigonometric
in thebetween
bank account
10 years
value
of
✓
◆
the angle ✓. (Two (b)
side lengths of the trianequations:(a) monthly,
1 3
continuously.
tan
cos
gle should be whole numbers)
7
(a) 3 cos2 9.
✓ =Show
6 that ln(sec θ(b)
4
cos
✓
+
3
sin
✓
=
0
( hint: divide both sides of
equation
by
cos
✓
)
(your answer will involve a square root)
+ tan θ) + ln(sec θ – tan θ) = 0
✓
◆
✓
◆
2⇡
⇡
8. Expand and simplify: 611.
cos For
✓ the sinusoidal function y = 60 sin 40x +
3
6
continues
on next page
(a) Compute
the amplitude,
period, and horizontal shift.
(b) Use your calculations to draw a graph of the sinusoidal function, showing the
location of quarter-cycle points.
10. Describe for which values of x or θ each equation is valid
(a) cos(cos-1 x) = x
(b) cos-1 (cos θ) = θ
33) The roof of a building is in the shape of the hyperbola y2 - x2 = 50, where x and y are in meters. Refer to the
figure
and determine
height h of
theyoutside
11. Solve
for y, andthe
simplify:
log
= 3x –walls.
log N
12. Write down equations for any asymptotes each graph has. It is not necessary
to actually sketch the graph.
(a) f(x) = log(9-7x)
a13.
= bFind
= 6 mthe
A) 9.3 m
(b) g(x) = tan(x/100)
equation for the following in their standard forms:
C) -14 m
B) 86 m
D) 44 m
(a) Ellipse: length of the minor axis is 16 and the foci are located at
34) The
of a 4).
building is in the shape of the hyperbola y2 - x2 = 18, where x and y are in meters.
(1±roof
105,
Determine the
distance, w, the outside walls are apart, if the height of each wall is 11 m.
(b) Hyperbola: centered at (0, 0) with vertices at (0, ±3) and a focus at (0,
34).
(c) Parabola: Opening to the left with the vertex at (−6, 3) and passing
through (−14,−9).
!!
!!
14.A)A20.3
comet
follows the hyperbolic
path described
by − !"= 1, where
x
m
B) 103 m
C) 10.15 m!"
D) 11.8 m
and y are in millions of kilometers. If the sun is the focus of the path, how
x2 y2
close
the sun
is the vertex
of the path?
35) A
cometto
follows
the hyperbolic
path described
by
= 1, where x and y are in millions. If the sun is the
24
13
focus of the path, how close to the sun is the vertex of the path?
A) 1.2 million
B) 6.1 million
C) 4.9 million
D) 37 million
15. For the arithmetic sequence 100,80,60,40,..., find an expression for an,
calculate a80 , and calculate S80 .
16. Find patterns and identify the nth term for each of these patterns:
(a) 3, 15, 27, 39, 51, ...
(b) 4, -16, 64, -256, 1024, ...
17. Find the sum of the sequences:
!
𝑎
6
!!!
!
𝑏
𝑘
!!!
!
𝑐
4𝑘 − 5
!!!
!
𝑑
𝑘(𝑘 + 10)
!!!
18. A new piece of equipment cost a company $53,000. Each year, for tax
purposes, the company depreciates the value by 25%.What value should
the company give the equipment after 6 years?
19. A pendulum bob swings through an arc 70 inches long on its first swing.
Each swing thereafter, it swings only 85% as far as on the previous swing.
What is the length of the arc after 12 swings? Round your answer to two
decimal places, if necessary.
20. Determine whether the infinite geometric series converges or diverges.
If it converges, find its sum.
!
!
(a) 5 + ! + !" + ⋯
!
(b)
!!!
3
4
2
!!!