MAT 101 Final Exam | Questions and Answers | 2026 Revised
Update | 100% Correct - Straighterline. - 44 Questions and
Answers Already Graded A+ Premium Exam Tested And
Verified
Subject Area MAT 101 Final Exam | Questions and Answers | 2026 Revised Update | 100%
Correct - Straighterline.
Description Comprehensive examination on MAT 101 Final Exam | Questions and Answers |
2026 Revised Update | 100% Correct - Straighterline..
Expected Grade A+
Total Questions 44
Duration 3 hours
Learning Outcomes 1. Demonstrate mastery of core concepts
Accreditation Aligned with US university standards.
Page 1
,Question 1 of 44
Solve for x: 2^(x+1) = 3^(2x). Express answer in terms of natural logarithms.
A. x = (ln 2 - ln 3) / (ln 2 - 2 ln 3)
B. x = (ln 2) / (2 ln 3 - ln 2)
C. x = (ln 3 - ln 2) / (2 ln 3 - ln 2)
D. x = (ln 2) / (ln 2 - 2 ln 3)
The correct answer is:
Correct Action: x = (ln 2) / (2 ln 3 - ln 2)
Rationales
• x = (ln 2) / (2 ln 3 - ln 2) (Correct):
This is the correct action. Take ln both sides: (x+1) ln 2 = 2x ln 3 -> x ln 2 + ln 2 = 2x ln 3 -> ln 2 = 2x ln 3 - x ln 2 = x (2
ln 3 - ln 2) -> x = ln 2 / (2 ln 3 - ln 2).
• x = (ln 2 - ln 3) / (ln 2 - 2 ln 3) (Incorrect):
This option is not appropriate. It does not match the expected clinical reasoning required.
• x = (ln 3 - ln 2) / (2 ln 3 - ln 2) (Incorrect):
This option is not appropriate. It does not match the expected clinical reasoning required.
• x = (ln 2) / (ln 2 - 2 ln 3) (Incorrect):
This option is not appropriate. It does not match the expected clinical reasoning required.
Page 2
,Question 2 of 44
Which of the following is equivalent to log_5(3) * log_3(5) without using logarithms?
A. 0
B. 1
C. log_5(3)
D. log_3(5)
The correct answer is:
Correct Action: 1
Rationales
• 1 (Correct):
This is the correct action. By change of base: log_5(3) = ln3/ln5, log_3(5)=ln5/ln3, product =1. Alternatively, using
property log_a(b)*log_b(a)=1.
• 0 (Incorrect):
This option is not appropriate. Alternatively, using property log_a(b)*log_b(a)=1.
• log_5(3) (Incorrect):
This option is not appropriate. Alternatively, using property log_a(b)*log_b(a)=1.
• log_3(5) (Incorrect):
This option is not appropriate. Alternatively, using property log_a(b)*log_b(a)=1.
Page 3
, Question 3 of 44
Determine the number of real zeros of the polynomial P(x) = 2x^5 - 3x^4 + x^3 + 2x^2 - x - 1.
A. 1
B. 2
C. 3
D. 4
The correct answer is:
Correct Action: 3
Rationales
• 3 (Correct):
This is the correct action. Descartes' rule: sign changes in P(x): +2 to -3 (1), -3 to +1 (2), +1 to +2 (none), +2 to -1 (3), -1 to
-1 (none) -> 3 or 1 positive; P(-x) = -2x^5-3x^4-x^3+2x^2+x-1: 2 sign changes -> 2 or 0 negative. Possible real zeros:
3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3 real zeros.
• 1 (Incorrect):
This option is not appropriate. Possible real zeros: 3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3
real zeros
• 2 (Incorrect):
This option is not appropriate. Possible real zeros: 3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3
real zeros
• 4 (Incorrect):
This option is not appropriate. Possible real zeros: 3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3
real zeros
Page 4
Update | 100% Correct - Straighterline. - 44 Questions and
Answers Already Graded A+ Premium Exam Tested And
Verified
Subject Area MAT 101 Final Exam | Questions and Answers | 2026 Revised Update | 100%
Correct - Straighterline.
Description Comprehensive examination on MAT 101 Final Exam | Questions and Answers |
2026 Revised Update | 100% Correct - Straighterline..
Expected Grade A+
Total Questions 44
Duration 3 hours
Learning Outcomes 1. Demonstrate mastery of core concepts
Accreditation Aligned with US university standards.
Page 1
,Question 1 of 44
Solve for x: 2^(x+1) = 3^(2x). Express answer in terms of natural logarithms.
A. x = (ln 2 - ln 3) / (ln 2 - 2 ln 3)
B. x = (ln 2) / (2 ln 3 - ln 2)
C. x = (ln 3 - ln 2) / (2 ln 3 - ln 2)
D. x = (ln 2) / (ln 2 - 2 ln 3)
The correct answer is:
Correct Action: x = (ln 2) / (2 ln 3 - ln 2)
Rationales
• x = (ln 2) / (2 ln 3 - ln 2) (Correct):
This is the correct action. Take ln both sides: (x+1) ln 2 = 2x ln 3 -> x ln 2 + ln 2 = 2x ln 3 -> ln 2 = 2x ln 3 - x ln 2 = x (2
ln 3 - ln 2) -> x = ln 2 / (2 ln 3 - ln 2).
• x = (ln 2 - ln 3) / (ln 2 - 2 ln 3) (Incorrect):
This option is not appropriate. It does not match the expected clinical reasoning required.
• x = (ln 3 - ln 2) / (2 ln 3 - ln 2) (Incorrect):
This option is not appropriate. It does not match the expected clinical reasoning required.
• x = (ln 2) / (ln 2 - 2 ln 3) (Incorrect):
This option is not appropriate. It does not match the expected clinical reasoning required.
Page 2
,Question 2 of 44
Which of the following is equivalent to log_5(3) * log_3(5) without using logarithms?
A. 0
B. 1
C. log_5(3)
D. log_3(5)
The correct answer is:
Correct Action: 1
Rationales
• 1 (Correct):
This is the correct action. By change of base: log_5(3) = ln3/ln5, log_3(5)=ln5/ln3, product =1. Alternatively, using
property log_a(b)*log_b(a)=1.
• 0 (Incorrect):
This option is not appropriate. Alternatively, using property log_a(b)*log_b(a)=1.
• log_5(3) (Incorrect):
This option is not appropriate. Alternatively, using property log_a(b)*log_b(a)=1.
• log_3(5) (Incorrect):
This option is not appropriate. Alternatively, using property log_a(b)*log_b(a)=1.
Page 3
, Question 3 of 44
Determine the number of real zeros of the polynomial P(x) = 2x^5 - 3x^4 + x^3 + 2x^2 - x - 1.
A. 1
B. 2
C. 3
D. 4
The correct answer is:
Correct Action: 3
Rationales
• 3 (Correct):
This is the correct action. Descartes' rule: sign changes in P(x): +2 to -3 (1), -3 to +1 (2), +1 to +2 (none), +2 to -1 (3), -1 to
-1 (none) -> 3 or 1 positive; P(-x) = -2x^5-3x^4-x^3+2x^2+x-1: 2 sign changes -> 2 or 0 negative. Possible real zeros:
3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3 real zeros.
• 1 (Incorrect):
This option is not appropriate. Possible real zeros: 3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3
real zeros
• 2 (Incorrect):
This option is not appropriate. Possible real zeros: 3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3
real zeros
• 4 (Incorrect):
This option is not appropriate. Possible real zeros: 3+0=3 or 1+2=3 or 1+0=1. By rational root test and graphing, there are 3
real zeros
Page 4
