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1. A 5.0 kg block slides down a 30° incline with μk = 0.20. Draw a free body diagram and find the acceleration.
Along incline:
mg sin θ − μkmg cos θ = ma
a = g(sin30 − 0.2 cos30)
= 9.8(0.5 − 0.173)
a = 3.2 m/s²
2. A 0.50 kg ball is thrown upward at 15 m/s. Find the maximum height using energy conservation. Then sketch a velocity-time graph for the complete motion.
KE → PE:
½mv² = mgh
h = v²/2g = (15)²/(2 × 9.8)
= 225/19.6
h = 11.5 m
v decreases as ball rises, passes through
zero at max height, then increases
downward (negative) on the way back.
3. Two masses m1 = 3.0 kg and m2 = 5.0 kg are connected by a string over a frictionless pulley. Find the acceleration and tension.
m₁: T − m₁g = m₁a
m₂: m₂g − T = m₂a
Add: a = (m₂−m₁)g/(m₁+m₂)
= (2)(9.8)/8
a = 2.45 m/s²
T = m₁(g+a) = 3(12.25)
T = 36.75 N
Student Exam
EDITABLEFeedback:
Question 1 — Inclined Plane (30 pts): 30/30
Free body diagram is complete with all three forces correctly identified and labeled. The decomposition into components was handled cleanly. Excellent work.
Question 2 — Energy & Kinematics (35 pts): 28/35
Energy conservation is correct and h = 11.5 m is right. However, the v-t graph is drawn as a curve when it should be a straight line. Under constant gravitational acceleration, v(t) = v₀ − gt is linear. Review Section 3.4 on uniformly accelerated motion to see why constant acceleration always produces a linear v-t graph (−7 pts).
Question 3 — Atwood Machine (35 pts): 35/35
Clear diagram. Newton's 2nd law applied correctly to each mass, then combined to eliminate T. Both a and T correct.
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MKT 350 – Midterm Exam: Market Analysis and Strategy

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EDITABLEFeedback:
Question 1 — Integration by Substitution (25 pts): 25/25
You correctly applied u-substitution with u = x² + 1 and showed clear work throughout. Your final answer was simplified properly.
Question 2 — Integration by Parts (25 pts): 18/25
You correctly identified u and dv, but there was a sign error during the evaluation step. The integral of e^x was handled well, but the negative sign was dropped when…
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Class-level analytics surface which concepts need revisiting and which students need support. Faculty teach more effectively; students benefit from courses that adapt to actual learning gaps and get more targeted practice.
Grade Distribution
Performance
84
Average /100
85
Median /100
23
Students
Class Performance Summary
The class performed well overall on the Calculus II midterm, with a mean score of 84/100 and a median of 85/100. Students demonstrated strong competence in integration by substitution (Q1) and partial fraction decomposition (Q3). The primary area of difficulty was integration by parts (Q2), where 12 of 23 students made sign errors during evaluation — suggesting a procedural gap rather than a conceptual one. Graph labeling (Q4) was another common weakness, with 8 students omitting axis labels entirely.
Students
Outstanding work, nearly flawless execution
Exceptional performance, minor formatting issue
Near-perfect work, minor notation inconsistency
Excellent work throughout, minor notation issues
Excellent across all sections, minor graph labeling issue
Excellent method selection, minor sign error
Strong across the board, minor graph scale issue
Strong partial fractions, minor sign slip
Good overall, small algebraic slip in partial fractions
Solid understanding, small arithmetic error in Q2
Good partial fractions, minor sign tracking issue
Solid partial fractions work, needs axis labels
Good setup on all problems, arithmetic errors
Solid fundamentals, arithmetic errors in evaluation
Solid fundamentals, forgot constant of integration
Correct methods chosen, lost points on graph labels
Strong substitution, sign error in integration by parts
Correct approach on Q1/Q3, lost points on Q2/Q4
Correct substitution, missing axis labels and +C
Good substitution, struggles with partial fractions
Substitution correct, struggles with parts/graphing
Struggles with integration by parts, needs graphing practice
Needs review of integration by parts and partial fractions
Common Errors
Students correctly identify the method but frequently drop the negative sign during evaluation.
Correct general shape drawn but axis labels and scale markings consistently omitted.
Decomposition setup correct, but errors when solving the system for coefficients.
Correct antiderivatives reached but +C constant omitted.
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UC Berkeley
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