MT 101 GIKIEST Number Roots Factorization Odd Powers & Parabolas Worksheet

Hello, I have an final exam for Mathematics about algebra essentials

Question 1 [3+4+3 points]
Find all solutions to the equations:
(a) 𝑥 2 − 8𝑥 = −15
(b) 𝑥 4 − 81 = 0
3
(c)
√5𝑦 + 1
2
= −2
Question 2 [4+3+3 points]
Given the parabola 𝑓(𝑥) = 2𝑥 2 − 12𝑥 + 14
(a) Find the vertex and axis of symmetry.
(b) Find the Maximum or Minimum value.
(c) Solve the equation: 𝑓(𝑥) = 14
Question 3 [4+3+3 points]
Let 𝑓(𝑥) = 𝑥 3 − 2𝑥 2 + 1
(a) Find the remainder when 𝑓(𝑥) is divided by 𝑥 − 2
(b) Show that 𝑓(𝑥) has a zero in the interval [-1, 0].
(c) Show that (𝑥 − 1) is a factor of 𝑓(𝑥)
Question 4 [4+3+3 points]
Let 𝑓(𝑥) = √5 − 𝑥 2
(a) Find the domain and range of 𝑓(𝑥)
(b) Determine the x- and y-intercepts of the graph of 𝑓(𝑥)
(c) Show that 𝑓(𝑥) is not one to one.
Question 5 [3+3+4 points]
The population of Kuwait was 3 million in 2010 and grew to 4.25 million by
2020.
(a) Write a model of the form 𝑃(𝑡) = 𝑝0 𝑒 𝑘𝑡 where 𝑝0 is the initial
Population and t is the number of years since 2010.
(b) Use your model in part (a) to predict the population of Kuwait in the
Year 2025.
(c) Use your model in part (a) to predict when the population will
Double.
Important Instructions Regarding FTHE:
• The cutoff date to submit your FTHE file on Wednesday, April 28, 2021 (12:05 AM).
• We advise you to submit the FTHE file before the cutoff date to avoid any technical problems.
• FTHE questions file will be available on Tuesday, April 27,2021 at 12:05 AM.
• Use the MS Word file “StdID_StdName_MT101_FTHE_Answer Booklet” to write your answers (or use a new word file).
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