22) Calculator

Precalculus First Semester Final Exam A (revised 12/22) Calculator Allowed Sequences and Series The front row of a theater has 20 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 25 rows? (show formula use or you will not get full credit)

Write an explicit function an to find the nth term of the sequence 0.25, 1, 4, 16, 64, 256, 1024…. An=

∞

4 � 20( )𝑛𝑛−1 5

𝑛𝑛=1

A sequence is generated recursively using the rule a1=3 , an=2an-1+1 List the first five terms of the sequence

Calculator Allowed- Exponents and Logs Find log33,000 to the nearest hundredth

Solve 22x-1=10,000 to the nearest hundredth

If I deposit $2,000 in an account that pays 5% interest compounded monthly, how much will be in the account after 20 years? (nearest cent)

Solve log3(20x+1)=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 4 times its original size? (nearest hundredth)

How long would it take to grow $2000 into $5000 in an account offering 5% annual interest compounded continuously. (nearest hundredth of a year)

Precalculus First Semester Final Exam A (revised 12/22) Calculators Allowed Exponents and Logs Solve log4(x+2) – log4(x-1) = 1

Expand completely using logarithmic properties 𝑥𝑥 4 √𝑦𝑦 𝑧𝑧

log

Calculator Allowed Trig Basics 4𝜋𝜋 3

Convert 315ᶛ to radians (exact answer)

Convert

Name an angle 0° ≤ 𝜃𝜃 ≤ 360° that is coterminal to an angle of 1,300ᶛ

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 3 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 4 and 2i

Given f(x)=2x+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 (-8,-12 ) and (4,-3) in slope-intercept form.

Divide using synthetic division (x4-6x2+4x-7)÷(x-3)

Precalculus First Semester Final Exam A (revised 12/22) Functions and graphs (no calculator) Find the x-intercepts of f(x)=x2-9x+14

What is the domain and range of (interval notation preferred)

Write a verbal description of the graph of f(x) = -2|x+3|+4 using the vocabulary of function transformation

List the zeroes of f(x)=6x3-4x2+15x-10

f(x) = −√𝑥𝑥 + 2 + 3 Domain: Range:

1

Sketch the graph of f(x)=(x-5)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 −9 ≥ 0 Write your solution set(s) in interval notation.

𝑥𝑥−1

Precalculus First Semester Final Exam A (revised 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)=2x and g(x)=log2x 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(0.000001)

Sketch the graph of a periodic function with a midline of 6, an amplitude of 4 and a period of 3 seconds from 0≤t≤12. Label carefully

Convert to an exponential equation log381=4 Solve without a calculator 42x-1=128