MATH 142 PRACTICE EXAM – QUESTIONS AND ANSWERS | VERIFIED AND WELL
DETAILED ANSWERS | PLUS RATIONALES | DOWNLOAD AND PASS | LATEST
EXAM UPDATE
*CORE DOMAINS*
*1. Differential Calculus*
*2. Integral Calculus*
*3. Sequences and Series*
*4. Transcendental Functions*
*5. Mathematical Modeling*
*6. Professional Ethics in Mathematics*
*7. Applied Numerical Analysis*
*INTRODUCTION*
*The purpose of this MATH 142 practice exam is to provide students with a comprehensive e
SECTION ONE: QUESTIONS 1–100
,What is the derivative of f(x) = e^(3x)?
A. e^(3x)
B. 3e^(3x)
C. (1/3)e^(3x)
D. e^(x)
🟢 B. 3e^(3x)
🔴 Explanation: By the chain rule, the derivative of e^u is e^u * u'. Here, u = 3x, and
the derivative of 3x is 3.
A mathematical model for population growth is represented by P(t) = P_0 * e^(kt).
What represents the rate of change of the population?
A. P(t)
B. k * P(t)
C. (1/k) * P(t)
D. P_0 * k
🟢 B. k * P(t)
🔴 Explanation: The derivative of P(t) with respect to t is P'(t) = P_0 * k * e^(kt),
which is equivalent to k * P(t).
Which series test is used to evaluate the convergence of a series with all positive
terms by comparing it to a known convergent or divergent series?
A. Alternating Series Test
B. Ratio Test
C. Direct Comparison Test
,D. Integral Test
🟢 C. Direct Comparison Test
🔴 Explanation: The Direct Comparison Test requires comparing the terms of a
series to another series whose convergence behavior is already known.
If a function is continuous on a closed interval [a, b], what does the Extreme Value
Theorem guarantee?
A. The function has a derivative at every point
B. The function is integrable
C. The function attains both an absolute maximum and minimum
D. The function is monotonic
🟢 C. The function attains both an absolute maximum and minimum
🔴 Explanation: The Extreme Value Theorem explicitly states that a continuous
function on a closed interval must reach its maximum and minimum values.
An engineer notices a peer falsifying data in a load-bearing capacity model. What is
the ethical course of action?
A. Confront the peer and ask them to fix it
B. Report the issue to the compliance department
C. Ignore it as long as the safety factor is high
D. Modify other parts of the project to compensate
🟢 B. Report the issue to the compliance department
🔴 Explanation: Ethical guidelines mandate the reporting of professional
misconduct, especially when safety and data integrity are compromised.
, Find the indefinite integral of 4x^3 dx.
A. x^4 + C
B. 12x^2 + C
C. x^ + C
D. x^ + C
🟢 A. x^4 + C
🔴 Explanation: Using the power rule for integration, the integral of x^n is x^(n+1) /
(n+1). Thus, 4 * (x^) = x^4.
Which of the following describes the convergence of the geometric series sum of
r^n?
A. Converges for all r
B. Converges for |r| < 1
C. Converges for |r| > 1
D. Converges only if r = 0
🟢 B. Converges for |r| < 1
🔴 Explanation: A geometric series converges if and only if the absolute value of the
common ratio r is strictly less than 1.
What is the definition of the derivative of f(x) at point x?
A. lim (h->0) [f(x+h) - f(x)] / h
B. lim (h->0) [f(x+h) + f(x)] / h
C. lim (h->0) [f(x) - f(x+h)] / h
D. lim (h->0) [f(x+h) - f(x)] / x
DETAILED ANSWERS | PLUS RATIONALES | DOWNLOAD AND PASS | LATEST
EXAM UPDATE
*CORE DOMAINS*
*1. Differential Calculus*
*2. Integral Calculus*
*3. Sequences and Series*
*4. Transcendental Functions*
*5. Mathematical Modeling*
*6. Professional Ethics in Mathematics*
*7. Applied Numerical Analysis*
*INTRODUCTION*
*The purpose of this MATH 142 practice exam is to provide students with a comprehensive e
SECTION ONE: QUESTIONS 1–100
,What is the derivative of f(x) = e^(3x)?
A. e^(3x)
B. 3e^(3x)
C. (1/3)e^(3x)
D. e^(x)
🟢 B. 3e^(3x)
🔴 Explanation: By the chain rule, the derivative of e^u is e^u * u'. Here, u = 3x, and
the derivative of 3x is 3.
A mathematical model for population growth is represented by P(t) = P_0 * e^(kt).
What represents the rate of change of the population?
A. P(t)
B. k * P(t)
C. (1/k) * P(t)
D. P_0 * k
🟢 B. k * P(t)
🔴 Explanation: The derivative of P(t) with respect to t is P'(t) = P_0 * k * e^(kt),
which is equivalent to k * P(t).
Which series test is used to evaluate the convergence of a series with all positive
terms by comparing it to a known convergent or divergent series?
A. Alternating Series Test
B. Ratio Test
C. Direct Comparison Test
,D. Integral Test
🟢 C. Direct Comparison Test
🔴 Explanation: The Direct Comparison Test requires comparing the terms of a
series to another series whose convergence behavior is already known.
If a function is continuous on a closed interval [a, b], what does the Extreme Value
Theorem guarantee?
A. The function has a derivative at every point
B. The function is integrable
C. The function attains both an absolute maximum and minimum
D. The function is monotonic
🟢 C. The function attains both an absolute maximum and minimum
🔴 Explanation: The Extreme Value Theorem explicitly states that a continuous
function on a closed interval must reach its maximum and minimum values.
An engineer notices a peer falsifying data in a load-bearing capacity model. What is
the ethical course of action?
A. Confront the peer and ask them to fix it
B. Report the issue to the compliance department
C. Ignore it as long as the safety factor is high
D. Modify other parts of the project to compensate
🟢 B. Report the issue to the compliance department
🔴 Explanation: Ethical guidelines mandate the reporting of professional
misconduct, especially when safety and data integrity are compromised.
, Find the indefinite integral of 4x^3 dx.
A. x^4 + C
B. 12x^2 + C
C. x^ + C
D. x^ + C
🟢 A. x^4 + C
🔴 Explanation: Using the power rule for integration, the integral of x^n is x^(n+1) /
(n+1). Thus, 4 * (x^) = x^4.
Which of the following describes the convergence of the geometric series sum of
r^n?
A. Converges for all r
B. Converges for |r| < 1
C. Converges for |r| > 1
D. Converges only if r = 0
🟢 B. Converges for |r| < 1
🔴 Explanation: A geometric series converges if and only if the absolute value of the
common ratio r is strictly less than 1.
What is the definition of the derivative of f(x) at point x?
A. lim (h->0) [f(x+h) - f(x)] / h
B. lim (h->0) [f(x+h) + f(x)] / h
C. lim (h->0) [f(x) - f(x+h)] / h
D. lim (h->0) [f(x+h) - f(x)] / x
