Adv Alg/Precalculus Problem Sets
4th Quarter
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.
 All Problem Sets are due at the beginning of class.
 Students must turn in all problem sets and must earn at least a 50% on each in order
to be eligible for grade replacement from the Quarter 4 Assessment.
Packet
Due at the BEGINNING
of class on:
1
4/26, 4/27
2
5/10, 5/11
3
5/24, 5/25
Adv Alg/Precalculus 4th Quarter
Adv Alg/Precalculus 4th Quarter
Adv Alg/Precalculus (4th Quarter)
Name ___________________
Problem Set #3
Period ______
Directions: This problem set is a study guide for the 4th quarter test 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:
3ln 5
7 ln 6 - 2 ln 7 (calculator active)
(a) –3.8222
(b) –2.6559
1) _______
(d) –11.6058
(c) 0.5582
(e) None of these
2) Find the domain of the function: f ( x) = 3log(5 x - 2) .
ж 1
(b) зз- , Ґ
зи 3
(a) (- Ґ , Ґ )
ц
ч
ч
ч
ш
ж2
(c) зз , Ґ
зи5
ц
ч
ч
ч
ш
2) _______
(d) (0.064, Ґ )
(e) None of these
3) Simplify: ln 5e3
(a) 3 + ln5
3) _______
(b) 3ln 5
(d) 5e3
(c) 3 + 3ln5
(e) None of these
4) Solve for x: log x 8 = - 3
(a) 2
4) _______
(b) 512
(c)
1
2
(d) –2
(e) None of these
жx3 y 2 ц
ч
ч
5) Write as a sum, difference, or multiple of logarithms: logb зз
.
ч
зи w ш
ч
(a) x3 + y 2 -
(c) 3log b x + 2 log b y (e) None of these
Adv Alg/Precalculus 4th Quarter
1
1
log b x + log b y - 2 log b w
3
2
3log x + 2 log y
(d)
1
log w
2
(b)
w
1
log b w
2
5) _______
6) Solve for x: log(7 - x) - log(3 x + 2) = 1
(a)
19
31
(b) -
13
31
6) _______
(c) -
27
29
(d)
9
4
(e) None of these
7) Find the number of years required for a $2000 investment
to triple at a 9.5% interest rate compounded continuously. (calculator active)
(a) 12.6
(b) 13.7
(c) 11.6
(d) 15.1
7) _______
(e) None of these
8) 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? (calculator active)
(a) 6.9%
(b) 13.7%
8) _______
(c) 11.6%
(d) 9.9%
(e) None of these
9) Simplify: e 2 ln( x+ 1)
9) _______
(a) ( x + 1) 2
(b) 2( x + 1)
(c) e2 ln( x + 1)
(d) x - 1
10) Solve for x: 21- x = 3x
(a)
ln 2
ln 6
(b) ln
Adv Alg/Precalculus 4th Quarter
(e) None of these
10) _______
1
3
(c) ln
2
3
(d) ln 3 + ln 2
(e) None of these
Adv Alg/Precalculus (4th term)
Name ___________________
Problem Set #2
Period ______
Directions: This problem set is a study guide for the 4th quarter test 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. (calculator active)
(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
2 _______
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? (calculator
active)
(a) 24.9 feet
(b) 21.5 feet
(c) 112.1 feet
(d) 129.4 feet
(e) None of these
3) Given a triangle with a = 17, b = 39, and c = 50, find A . (calculator active)
(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 . (calculator active)
(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 (calculator active)
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 Quarter
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? (calculator active)
(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, Ґ )
(b) [0,Ґ
7) _______
)
(c) (- Ґ , Ґ )
(d) (- Ґ ,3)
(e) None of these
8) The range of f ( x) = 1 + e- x is:
(a) (- Ґ , Ґ )
(b) (0, Ґ )
(c) (- 1, Ґ )
(d) (1, Ґ )
(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? (calculator active)
(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. (calculator active)
(a) $4102.34
(b) $5216.07
(c) $2458.83
(d) $14,056.14
(e) None of these
10) _______
Adv Alg/Precalculus 4th Quarter
Adv Alg/Precalculus (4th term)
Problem Set #1
Name ___________________
Period ______
Directions: This problem set should be worked without a calculator unless the directed otherwise.
Show all work for full credit. Place answers in the appropriate blanks. Took out the part about
final review since trig won’t be on Q4 Test.
- 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)
5 7 
,
6 6
Adv Alg/Precalculus 4th Quarter
(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)
3
(c)
 5
,
4 4
(d)
3 7 
,
4 4
  

  
 Use the fact that
12 4 6 


12
6- 2
2
(b)
9) Evaluate: tan 240°
(a) -
 3
,
2 2
(b)
7) _______
6- 2
4
(c)
8) _______
(d)
2- 6
4
(Use the fact that 240° = 180° + 60°)
(b)
3
1-
3
(c) 0
9) _______
(d)
3
3

10) Evaluate sin  cos 1 
5

(a)
4
5
(b)
10) _______
- 4
5
Adv Alg/Precalculus 4th Quarter
(c)
3
5
(d)
- 3
5