Wgu C958 — Calculus I-Comprehensive Exam Full Package Questions Answers

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WGU C958 — CALCULUS I-COMPREHENSIVE EXAM FULL PACKAGE
QUESTIONS ANSWERS AND RATIONALES 2026-27 LATEST UPDATED
VERSION INSTANT DOWNLOAD PDF..!!




INTRODUCTION
The WGU C958 Calculus I Comprehensive Exam is the Objective Assessment (OA) required
for Western Governors University students to demonstrate competency in differential and
integral calculus. This course is designed for students in computer science, mathematics
education, and related STEM programs who must apply theoretical calculus concepts to real-
world situations. The exam covers limits, derivatives, integrals, and differential equations,
with a focus on application and problem-solving rather than rote memorization . The
assessment consists of approximately 59 questions distributed across four competency
areas: Limits (19%), Derivatives (44%), Integrals (30%), and Differential Equations (7%) . This
question bank delivers advanced, scenario-based questions modeled on the official WGU
curriculum, featuring detailed rationales that explain why the correct answer is right and
every distractor is wrong. Each question is designed to replicate the application-level
thinking and computational rigor required to pass the OA on your first attempt.

CORE DOMAINS TESTED

• Limits (19%): Evaluating limits numerically, algebraically, and graphically; infinite
limits; L'Hôpital's Rule; continuity conditions; asymptotic behavior

• Derivatives (44%): Power rule, product/quotient/chain rules, implicit differentiation,
related rates, higher-order derivatives, applications including optimization, Mean
Value Theorem, curve sketching

• Integrals (30%): Antiderivatives, definite and indefinite integrals, Riemann sums,
substitution, Fundamental Theorem of Calculus, area between curves, applications of
integration

• Differential Equations (7%): Basic differential equations, solving separable equations,
initial value problems, modeling with differential equations

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QUESTIONS 1-200
Q1: A particle moves along a straight line with position function s(t) =
t³ − 6t² + 9t + 2 for t ≥ 0. At what time t does the particle first come to
rest?
A) t = 1
B) t = 1
C) t = 3
D) t = 0
Rationale: The correct answer is B. The particle comes to rest when
velocity v(t) = s'(t) = 0. s'(t) = 3t² − 12t + 9 = 3(t² − 4t + 3) = 3(t−1)(t−3).
Setting equal to zero gives t = 1 and t = 3. The first time it comes to
rest is t = 1. Option A duplicates the correct answer. Option C is the
second time the particle comes to rest. Option D is incorrect because
at t = 0 the particle is moving with v(0) = 9.
Q2: Find the derivative of f(x) = ln(x² + 3x + 2).
A) (2x + 3)/(x² + 3x + 2)
B) 1/(x² + 3x + 2)
C) (2x + 3)
D) ln(2x + 3)
Rationale: The correct answer is A. Using the chain rule, d/dx[ln(u)] =
(1/u)(du/dx) = (1/(x² + 3x + 2))(2x + 3) = (2x + 3)/(x² + 3x + 2). Option
B is incorrect because it omits the chain rule factor (2x + 3). Option C
is incorrect because it omits the denominator. Option D is incorrect
because it incorrectly applies the derivative to the logarithm
argument.

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Q3: A circular oil slick is expanding with radius increasing at 2 meters
per hour. How fast is the area increasing when the radius is 10
meters?
A) 20π m²/hr
B) 40π m²/hr
C) 100π m²/hr
D) 200π m²/hr
Rationale: The correct answer is B. Area A = πr². dA/dt = 2πr · dr/dt =
2π(10)(2) = 40π m²/hr. Option A is incorrect because it omits one
factor of r or dr/dt. Option C is incorrect because it squares the
radius. Option D is incorrect because it multiplies by an extra factor of
2.
Q4: Evaluate lim(x→∞) (4x² + 3x)/(2x² − 5).
A) ∞
B) 0
C) 2
D) 4
Rationale: The correct answer is C. Divide numerator and
denominator by x²: (4 + 3/x)/(2 − 5/x²). As x→∞, terms with x in the
denominator approach 0, leaving 4/2 = 2. Option A is incorrect
because the numerator and denominator have the same degree.
Option B is incorrect because the limit is not zero. Option D is
incorrect because the leading coefficients ratio is 4/2 = 2, not 4.
Q5: Use implicit differentiation to find dy/dx for x² + y² = 25.
A) −x/y
B) −x/y
C) x/y
D) −y/x
Rationale: The correct answer is B. Differentiate both sides: 2x +

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2y(dy/dx) = 0. Solving for dy/dx gives dy/dx = −x/y. Option A
duplicates the correct answer. Option C is incorrect because it omits
the negative sign. Option D is incorrect because it inverts the ratio.
Q6: A cylindrical tank with radius 4 meters is being filled with water
at a rate of 2 m³/min. How fast is the water level rising when the
water is 3 meters deep?
A) 1/(8π) m/min
B) 1/(8π) m/min
C) 1/(2π) m/min
D) 1/π m/min
Rationale: The correct answer is B. Volume V = πr²h = π(16)h = 16πh.
dV/dt = 16π(dh/dt). 2 = 16π(dh/dt). dh/dt = 2/(16π) = 1/(8π) m/min.
Option A duplicates the correct answer. Option C is incorrect because
it uses the wrong denominator. Option D is incorrect because it omits
the factor of 8.
Q7: Evaluate lim(x→3) (x² − 9)/(x − 3).
A) 0
B) 3
C) 6
D) Undefined
Rationale: The correct answer is C. Factor the numerator: (x² − 9) = (x
− 3)(x + 3). The expression becomes (x − 3)(x + 3)/(x − 3). Cancel (x −
3), leaving (x + 3). As x approaches 3, the limit is 3 + 3 = 6. Option A is
incorrect because substituting directly gives 0/0. Option B is incorrect
because it is one of the factors. Option D is incorrect because the limit
exists despite the removable discontinuity.
Q8: Evaluate lim(x→0) sin(5x)/x.