Adv Alg/Precalculus Problem Sets
4th Term
READ THE DIRECTIONS CAREFULLY!
 Problem sets are designed to review concepts taught in previous courses as well as
those taught in this class. Problem sets must be taken seriously and emphasis should
be on the process to answer each question and not necessarily the answer itself.
 Problem sets are due according to the schedule below.
 You may seek help any time before the due date. STUDENTS ARE NOT
ALLOWED TO ASK FOR HELP ON THE DAY IT IS DUE!!! Students must also
have work to show the teacher before asking questions.
 ALL Work must be shown to receive credit. Work done on a separate sheet of
paper must be attached to the actual problem set. Calculations performed on a
calculator must be shown/written on the paper.
 Problem sets WILL NOT be accepted late if you are at school on the due date. If
you are absent on the due date, it is YOUR responsibility to turn in the assignment
on the first day back to school. Absences for school related activities (sports, field
trips, club activities, etc.) DO NOT excuse you from submitting problem sets on the
due date.
 No retakes on Problem Set Quizzes – quizzes are timed!
 All Problem Sets are due at the beginning of class.
 Should we have a snow day on the day these are due, they are due ON the day we
return to school.
Packet
Due at the BEGINNING
of class on:
1
4/24, 4/25
2
5/4, 5/5
3
5/14, 5/15
4
5/29, 6/1
Adv Alg/Precalculus 4th Term
Problem Set Quiz Date:
5/4, 5/5 (combined 1 & 2)
5/29, 6/1 (combined 3 & 4)
Adv Alg/Precalculus 4th Term
Adv Alg/Precalculus (4th term)
Name ___________________
Problem Set #4
Period ______
Directions: This problem set is a study guide for the final exam and should be approached as such.
It should be worked without a calculator unless the directed otherwise. Show all work for full
credit. Place answers in the appropriate blanks.
1) Evaluate:
(a)
(b)
(c)
(d)
(e)
3ln 5
7 ln 6 - 2 ln 7
1) _______
–3.8222
–2.6559
0.5582
–11.6058
None of these
2) Find the domain of the function: f ( x) = 3log(5 x - 2) .
2) _______
(a) (- ¥ , ¥ )
æ 1 ö
(b) çç- , ¥ ÷
÷
÷
çè 3 ø
æ2
ö
(c) çç , ¥ ÷
÷
÷
çè 5
ø
(d) (0.064, ¥ )
(e) None of these
3) Evaluate: ln e1- x
(a)
(b)
(c)
(d)
(e)
e1-
x
e
1- x
ln(1 - x )
None of these
4) Simplify: ln 5e3
(a)
(b)
(c)
(d)
(e)
3) _______
3 + ln 5
3ln 5
3 + 3ln5
5e3
None of these
Adv Alg/Precalculus 4th Term
4) _______
5) Use the change of base formula to identify the expression
that is equivalent to log3 10 .
(a)
(b)
(c)
(d)
(e)
5) _______
ln 3
ln10
10 log 3
10
ln
3
1
log 3
None of these
æx3 y 2 ÷
ö
÷
6) Write as a sum, difference, or multiple of logarithms: log b çç
.
÷
çè w ÷
ø
6) _______
(a) x3 + y 2 - w
1
1
(b) log b x + log b y - 2 log b w
3
2
1
(c) 3log b x + 2 log b y - log b w
2
3log x + 2 log y
(d)
1
log w
2
(e) None of these
7) Solve for x: log x 8 = - 3
7) _______
(a) 2
(b) 512
1
(c)
2
(d) –2
(e) None of these
8) Simplify: e 2 ln( x+ 1)
(a)
(b)
(c)
(d)
(e)
( x + 1)2
2( x + 1)
e2 ln( x + 1)
x- 1
None of these
Adv Alg/Precalculus 4th Term
8) _______
9) Solve for x: 21- x = 3x
9) _______
ln 2
ln 6
1
(b) ln
3
2
(c) ln
3
(d) ln 3 + ln 2
(e) None of these
(a)
10) Solve for x: log(7 - x) - log(3 x + 2) = 1
(a)
(b)
(c)
(d)
(e)
19
31
13
31
27
29
9
4
None of these
11) Find the number of years required for a $2000 investment
to triple at a 9.5% interest rate compounded continuously.
(a)
(b)
(c)
(d)
(e)
11) _______
12.6
13.7
11.6
15.1
None of these
12) Solve for t: e- 0.0097 t = 12 .
(a)
(b)
(c)
(d)
(e)
10) _______
–256.1759
–1237.1134
16,778,844.47
–2.5886
None of these
Adv Alg/Precalculus 4th Term
12) _______
13) Determine the principal, P, that must be invested at a
rate of 7.5% interest compounded quarterly so that the
balance, B, in 20 years will be $35,000.
(a)
(b)
(c)
(d)
(e)
$2333.33
$14,000.00
$9635.17
$7918.78
None of these
14) An initial deposit of $2800 is made in a savings account
for which the interest is compounded continuously. The
balance will triple in eight years. What is the annual rate of
interest for this account?
(a)
(b)
(c)
(d)
(e)
13) _______
14) _______
6.9%
13.7%
11.6%
9.9%
None of these
15) Solve for x: 16 = 27 x- 5
(a) 0.1143
(b) –0.3010
13
(c)
7
9
(d)
7
(e) None of these
Adv Alg/Precalculus 4th Term
15) _______
Adv Alg/Precalculus (4th term)
Name ___________________
Problem Set #3
Period ______
Directions: This problem set is a study guide for the final exam and should be approached as such.
It should be worked without a calculator unless the directed otherwise. Show all work for full
credit. Place answers in the appropriate blanks.
1) Given a triangle with a = 112, b = 130, and A = 56° , find c.
(a) 103.2
(b) 98.1
(c) 42.2
(d) 42.2 and 103.2
(e) No solution
1) _______
2) A television antenna sits on the roof. Two 72-foot support wires are
positioned on opposite sides of the antenna. The angle of elevation
each makes with the ground is 26° . How far apart are the ends of the two guy wires?
(a) 24.9 feet
(b) 21.5 feet
(c) 112.1 feet
(d) 129.4 feet
(e) None of these
2 _______
3) Given a triangle with a = 17, b = 39, and c = 50, find A .
(a) 16.88°
(b) 73.12°
(c) 163.12°
(d) 106.88°
(e) None of these
3) _______
4) Given a triangle with a = 2178, B = 23°, and c = 1719, find b .
(a) 2184.9
(b) 805,937.8
(c) 2062.1
(d) 897.7
(e) None of these
4) _______
5) Use Heron’s formula to find the area of the triangle with
a = 41.6, b = 54.2, and c = 47.1 .
(a) 946.5
(b) 1276.4
(c) 1006.5
(d) 1127.1
(e) None of these
5) _______
Adv Alg/Precalculus 4th Term
6) A trigonometry class wants to determine the length of a pond near
the school (shown below). From point A, they measure the distance
to each end of the pond and the angle between these sides. What is the
approximate length of the pond?
(a) 352 feet
(b) 289 feet
(c) 407 feet
(d) 331 feet
(e) None of these
300 ft
6) _______
215 ft
78°
A
7) The domain of f ( x) = 3 - e x is:
(a) (3, ¥ )
(b) [0,¥
7) _______
)
(c) (- ¥ , ¥ )
(d) (- ¥ ,3)
(e) None of these
8) The range of f ( x) = 1 + e- x is:
(a) (- ¥ , ¥ )
(b) (0, ¥ )
(c) (- 1, ¥ )
(d) (1, ¥ )
(e) None of these
8) _______
9) $3500 is invested at a rate of 4.5% compounded continuously.
What is the balance at the end of 10 years?
(a) $315,059.96
(b) $5472.45
(c) $5221.39
(d) $5489.09
(e) None of these
9) _______
10) Determine the amount of money that should be invested at
a rate of 6.5% compounded monthly to produce a final
balance of $15,000 in 20 years.
(a) $4102.34
(b) $5216.07
(c) $2458.83
(d) $14,056.14
(e) None of these
10) _______
Adv Alg/Precalculus 4th Term
Adv Alg/Precalculus (4th term)
Problem Set #2
Name ___________________
Period ______
Directions: This problem set is a study guide for the final exam and should be approached as such.
It should be worked without a calculator unless the directed otherwise. Show all work for full
credit. Place answers in the appropriate blanks.
- 33
4
1) Given sin x = and cos x =
, find cot x .
1) ________
7
7
(a)
- 4 33
33
(b)
- 7 33
33
(c)
7
4
(d)
-
33
4
2) Factor and simplify: cos 2 x - sin 2 x cos 2 x
(a) cos 4 x
3) Simplify:
(b) - cos 4 x
(c) 1 - sin 2 x
4) Add and simplify:
3) ________
(b) sec x - tan x
(c) sec x - cot x
1 + cos  + sin 
sin  + sin  cos 
 11
,
6 6
(d) cos x + tan x
1 + cos 
sin 
+
sin 
1 + cos 
4) ________
(b) 1 + 2 cos  + cos 2 
5) Find all solutions in the interval [0, 2): 2cos x (a)
(d) 2cos x
cos x
1 + sin x
(a) cos x + cot x
(a)
2) ________
(b)
Adv Alg/Precalculus 4th Term
5 7 
,
6 6
(c)
 5
,
3 3
(c)
2
sin 
(d) cos 2 
3= 0
5) ________
(d)
2 4
,
3 6
6) Find all solutions in the interval [0, 2): 6sin 2 x - sin x - 2 = 0
(calculator permitted)
7  11
(a) 0.6667, 0.5
(b) 0.7297, 2.4119,
,
6 6
(c)
 11
,
6 6
6) _______
(d) 0.7297, 3.871
7) Find all solutions in the interval [0, 2): 3tan x - 3 = 0
(a) 0, 
8) Evaluate: sin
2- 1
2
(a)
(b)
3
(c)
 5
,
4 4
(d)
3 7 
,
4 4
  

  
 Use the fact that
12 4 6 


12
(b)
9) Evaluate: tan 240°
(a) -
 3
,
2 2
7) _______
(b)
6- 2
2
6- 2
4
(c)
8) _______
2- 6
4
(d)
(Use the fact that 240° = 180° + 60°)
3
1-
3
(c) 0
9) _______
3
(d)
10) Find all solutions in the interval [0, 2): 2sin 2 x - 5sin x = - 3
(a)
3
2
(b)
Adv Alg/Precalculus 4th Term
 3
,
2 2
(c)
3
,1
2
(d)
10) _______

2
Adv Alg/Precalculus (4th term)
Name ___________________
Problem Set #1
Period ______
Directions: This problem set is a study guide for the final exam and should be approached as such.
It should be worked without a calculator unless the directed otherwise. Show all work for full
credit. Place answers in the appropriate blanks.
Questions 1 – 6: Evaluate:


1) sin    
2

3 

2) cos   

4 

3

3) sin  cos 1 
5

12 

4) tan  2sin 1 
13 

2
1
5) cos  tan 1 
3
2
æ
1
2ö
6) sin ççcos- 1 - sin - 1 ÷
÷
çè
ø
3
5÷
Adv Alg/Precalculus 4th Term
Questions 7 – 10: Given: sin  
3
4
and sec   0 , find the indicated value
7) cot 
8) sin(2 )
 
9) tan  
2


10) cos    
2

Adv Alg/Precalculus 4th Term