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Name _______________________________ Date __________ KJ Paulk Algebra II – Chap.8 TEST Show all work. 1. The speed of an object falling from rest in a vacuum is directly proportional to the time it has fallen. After an object has fallen for 1.5 s, its speed is 14.7 m/s. What is its speed after it has fallen 5 s? Let “” be the constant of variation and define all other variables. Also, find the value of . 2. Suppose varies jointly as and ! and inversely as . Also, = 120 when = 5, = 3, and = 2. Find when = 80, = 1, and = 6. (Recall: When two values vary jointly, they both vary directly.) 3. Divide: !"! ! ! ! ! ! !!! – ! !! ! – !! ! ! Use LONG division.
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Name _______________________________ Date __________ KJ Paulk Algebra II – Chap.8 TEST -‐ Show all work. 1.
The speed of an object falling from rest in a vacuum is directly proportional to the time it has fallen. After an object has fallen for 1.5 s, its speed is 14.7 m/s. What is its speed after it has fallen 5 s? Let “𝑘” be the constant of variation and define all other variables. Also, find the value of 𝑘.
2.
Suppose 𝑦 varies jointly as 𝑟 and 𝑠!and inversely as 𝑡. Also, 𝑦 = 120 when 𝑟 = 5, 𝑠 = 3, and 𝑡 = 2. Find 𝑟 when 𝑦 = 80, 𝑠 = 1, and 𝑡 = 6. (Recall: When two values vary jointly, they both vary directly.)
3.
Divide: !"!! ! !! ! !!! – ! !!! – !! ! !
Use LONG division.
Algebra II – Chapter 8 – TEST Page 2 4.
Divide: !!!! !!!! !! ! !
! ! ! Use SYNTHETIC division.
5.
Find a polynomial equation with integral coefficients that has roots: !!,−2 , 3
6.
A 3rd degree polynomial equation has the roots at 𝑥 = 5 and 2 − 𝑖 . What other root(s) must it have? Write the equation in factored form. (Do NOT expand.)
Algebra II – Chapter 8 – TEST Page 3 7.
Given: 𝑥 − 3 𝑥 − !!
𝑥 + 4 𝑥 + 3 𝑥 − 3 𝑥 + 6𝑖 𝑥 − 6𝑖 = 0 For the given equation, find:
A. Degree of the equation: _____________________
B. Total Number of roots: _______________________
C. List the Rational root(s): ________________________________
D. List the Irrational root(s): _______________________________
E. List the Complex root(s): ________________________________
F. List the roots that could grow into a plant: __________________
8.
Given: 2𝑥! + 𝑥! − 3𝑥! − 𝑥! − 3𝑥! − 2𝑥 + 2 = 0 David tried to find the zeros by using his TI-‐89 calculator. He used two different Algebra functions and got different solutions as shown: v zeros 2𝑥! + 𝑥! − 3𝑥! − 𝑥! − 3𝑥! − 2𝑥 + 2 , 𝑥
and the calculator found the following four zeros: −1, !!, ± 2
v czeros 2𝑥! + 𝑥! − 3𝑥! − 𝑥! − 3𝑥! − 2𝑥 + 2 , 𝑥
and the calculator found the following six zeros: −1, !!, ± 2 , ±𝑖
Answer the following questions:
A. Degree of the equation: __________________________
B. Total Number of roots: ____________________________
C. List all of the Possible Rational root(s): _____________________________________
D. Why did the above two functions provide different solutions?
Algebra II – Chapter 8 – TEST Page 4 9.
Determine 𝑘 so the first polynomial is a factor of the second.
𝑥 − 2 ; 𝑥! − 4𝑥! + 𝑘𝑥 + 6
