Precalculus First Semester Final Exam Ver B Rev 12/22
Calculator Allowed Sequences and Series
The front row of a theater has 25 seats. Each of the rows
behind it has two more seats than the row before it.
Represent the situation in Sigma Notation. How many
total seats are there in the first 20 rows?
(show formula use or you will not get full credit)
∞
4
� 10( )𝑛𝑛−1
5
𝑛𝑛=1
Write an explicit function an to find the nth term of the
sequence
0.5, 1, 2, 4, 8, 16, 32….
An=
A sequence is generated recursively using the rule
a1=4 , an=2an-1-1
List the first five terms of the sequence
Calculator Allowed- Exponents and Logs
Find log31,000 to the nearest hundredth
Solve 22x-1=1,000 to the nearest hundredth
If I deposit $2,000 in an account that pays 6.5% interest
compounded quarterly, how much will be in the account
after 20 years? (nearest cent)
Solve log5(20x+25)=4 to the nearest hundredth
The population of a bacteria colony is growing at a rate of
10% per hour. How many hours will it take until the
population is 10 times its original size? (nearest
hundredth)
How long would it take to grow $2000 into $5000 in an
account offering 6% annual interest compounded
continuously. (nearest hundredth of a year)
Precalculus First Semester Final Exam Ver B Rev 12/22
Calculators Allowed Exponents and Logs
Solve
log4(x+2) – log4(x-1) = 1
Expand completely using logarithmic properties
𝑥𝑥 3 √𝑦𝑦
𝑧𝑧
log
Calculator Allowed Trig Basics
3𝜋𝜋
4
Convert 225ᶛ to radians (exact answer)
Convert
Name an angle 0° ≤ 𝜃𝜃 ≤ 360° that is coterminal to an
angle of 1,200ᶛ
Find the arc length to the nearest hundredth of a meter
to degrees
If a wheel with a radius of 10 inches is rotating at a rate of 4 rotations per second. What is the linear velocity in miles
per hour? [nearest hundredth, 1 mi=5280 ft][show all work/conversions]
Functions/Calculator Allowed
Write a polynomial of degree three in standard form
when two of the zeroes are 3 and 2i
Given f(x)=3x+4
g(x)= 2x2-1
Find (f+g)(5)
Find g(f(-3))
Find f-1(x)
Find the equation of the line passing through
(-4,-1) and (8,8) in slope-intercept form.
Divide using synthetic division
(x4-6x2+4x-7)÷(x-2)
Precalculus First Semester Final Exam Ver B Rev 12/22
Functions and graphs (no calculator)
Find the x-intercepts of f(x)=x2-11x+18
What is the domain and range of (interval notation
preferred)
Write a verbal description of the graph of
f(x) = -2|x-3|+1 using the vocabulary of function
transformation
List the zeroes of f(x)=6x3-4x2+15x-10
f(x) = −√𝑥𝑥 + 3 + 2
Domain:
Range:
1
Sketch the graph of f(x)=(x-4)2-2
Sketch the graph of f(x) = 𝑥𝑥 2 +2𝑥𝑥−8
Solve: x2+6x-16 < 0
Write your solution set(s) in interval notation.
Solve: 𝑥𝑥 2 −4 ≥ 0
Write your solution set(s) in interval notation.
𝑥𝑥−3
Precalculus First Semester Final Exam Ver B Rev 12/22
No Calculator Functions
Use the rational root theorem to list all possible rational
zeroes of
f(x) =6x3 -31x2+25x+12
What is the equation of the slant asymptote for
f(x)=
𝑥𝑥 3 +𝑥𝑥 2 −4
𝑥𝑥 2 +1
3
Given that 2 is a zero of f(x) =6x3 -31x2+25x+12, find the
remaining zeroes
Use Descarte’s Rule of Signs to determine the number of
positive real zeroes and negative real zeroes of
f(x)=2x3-3x2-18x-8
# Positive Real Zeroes:_______________________
#Negative Real Zeroes: ______________________
Sketch the graph of f(x)=3x and g(x)=log3x on the same
axis. Label each graph
Sketch the graph of f(x) = x(x+1)(x-3)2
I am interested in the intercepts, behavior at the
intercepts and end-behavior of the graph.
Simplify log(0.0001)
Sketch the graph of a periodic function with a midline of
4, an amplitude of 3 and a period of 4 seconds from
0≤t≤12. Label carefully
Convert to an exponential equation
log216=4
Solve without a calculator
92x-1=27