PN Learning System Fundamentals Practice Quiz 1
The PN Learning System Fundamentals is a structured approach to mastering the core concepts of Project Network (PN) analysis and application. Whether you’re a student preparing for an exam, a professional sharpening your skills, or an educator seeking a reliable resource, this practice quiz provides a comprehensive review of the foundational topics covered in the first module. By tackling these questions, you’ll reinforce your understanding of network design, critical path identification, resource allocation, and the mathematical underpinnings that drive successful project execution.
Introduction
The PN Learning System blends theoretical rigor with hands‑on practice to help learners internalize project network logic. Practice Quiz 1 focuses on the essentials: activity sequencing, time estimation, and the basic calculations that underpin the Critical Path Method (CPM). Completing this quiz will:
- Validate your grasp of activity‑on‑node (AON) diagrams.
- Sharpen your ability to compute early and late start/finish times.
- Highlight the importance of float (slack) in scheduling.
- Prepare you for more advanced topics in subsequent modules.
How to Use This Quiz Effectively
- Read each question carefully—many rely on subtle differences in wording.
- Sketch a quick diagram when needed; visualizing the network often clarifies the solution.
- Show all calculations; the answer alone is rarely enough for learning.
- Check your work against the provided solutions (at the end of the article) to identify gaps.
- Repeat the quiz after a few days to reinforce retention.
1. Activity Sequencing and Precedence Relationships
Question 1
A project has the following activities and durations (in days):
| Activity | Duration | Predecessors |
|---|---|---|
| A | 4 | – |
| B | 3 | A |
| C | 2 | A |
| D | 5 | B, C |
| E | 3 | D |
Worth pausing on this one.
Draw the activity‑on‑node diagram and identify the first activity to start.
Answer & Explanation
- Diagram:
A(4) → B(3) → D(5) → E(3) \ / C(2) ---- - First activity: A (no predecessors).
2. Early Start and Early Finish Calculations
Question 2
Using the diagram from Question 1, calculate the Early Start (ES) and Early Finish (EF) for each activity.
Answer & Explanation
| Activity | Duration | ES | EF = ES + Duration |
|---|---|---|---|
| A | 4 | 0 | 4 |
| B | 3 | 4 | 7 |
| C | 2 | 4 | 6 |
| D | 5 | 7 | 12 |
| E | 3 | 12 | 15 |
Most guides skip this. Don't The details matter here..
Early Start of D is the maximum EF of its predecessors (B=7, C=6 → 7).
3. Late Start and Late Finish Calculations
Question 3
Determine the Late Finish (LF) and Late Start (LS) for each activity, assuming the project must finish by day 15.
Answer & Explanation
| Activity | Duration | LF | LS = LF – Duration |
|---|---|---|---|
| E | 3 | 15 | 12 |
| D | 5 | 12 | 7 |
| B | 3 | 7 | 4 |
| C | 2 | 6 | 4 |
| A | 4 | 4 | 0 |
LF of A is the minimum LS of its successors (B=4, C=4 → 4).
4. Total Float (Slack) Calculation
Question 4
Compute the total float for each activity.
Answer & Explanation
Total Float = LS – ES (or LF – EF)
| Activity | ES | LS | Total Float |
|---|---|---|---|
| A | 0 | 0 | 0 |
| B | 4 | 4 | 0 |
| C | 4 | 4 | 0 |
| D | 7 | 7 | 0 |
| E | 12 | 12 | 0 |
All activities lie on the critical path; no slack.
5. Critical Path Identification
Question 5
Identify the critical path and its duration.
Answer & Explanation
- Critical Path: A → B → D → E
- Duration: 4 + 3 + 5 + 3 = 15 days
- Any delay in these activities delays the whole project.
6. Rescheduling Scenario
Question 6
Suppose activity C is delayed by 2 days (now 4 days). Recalculate the critical path and project duration.
Answer & Explanation
- Recalculate EF/ES:
- C: ES=4, EF=8
- D: ES = max(7,8)=8, EF=13
- E: ES=13, EF=16
- New Critical Path: A → C → D → E
- Project Duration: 16 days
- The delay propagates through the network, extending the overall schedule.
7. Resource Leveling Basics
Question 7
If activities B and C require the same resource and can’t run concurrently, what is the minimum project duration?
Answer & Explanation
- Schedule B first: B (3 days) → C (2 days) → D (5 days) → E (3 days)
- Total: 3 + 2 + 5 + 3 = 13 days
- Resource constraint shortens the critical path to 13 days.
8. Floating Activities and Project Flexibility
Question 8
Which activities have float if activity E is moved to finish by day 14 instead of 15?
Answer & Explanation
- Adjust E: LF=14, LS=11
- Recompute:
- D: LF=11, LS=6
- B: LF=6, LS=3
- C: LF=6, LS=4
- A: LF=3, LS=0
- Float:
- B: LS=3, ES=0 → 3 days
- C: LS=4, ES=4 → 0 days
- D: LS=6, ES=7 → negative (cannot finish by 14) → infeasible
- Only activity B gains float; C and D are critical.
9. Understanding Network Types
Question 9
Describe the difference between an Activity‑on‑Node (AON) and an Activity‑on‑Arrow (AOA) diagram.
Answer & Explanation
- AON: Nodes represent activities; arrows represent precedence.
- AOA: Arrows represent activities; nodes represent events (start/end).
- AON is simpler and more common in modern project management.
10. Quick Review Checklist
- [ ] Can you draw an AON diagram from activity lists?
- [ ] Do you know how to compute ES, EF, LS, LF, and float?
- [ ] Are you able to identify the critical path and its duration?
- [ ] Can you adjust the network when constraints or delays occur?
- [ ] Do you understand resource leveling basics?
Conclusion
Mastering the fundamentals of the PN Learning System sets the stage for tackling more complex project scenarios, such as stochastic durations, multi‑resource allocation, and earned value analysis. So by working through this quiz, you’ve reinforced key concepts—activity sequencing, critical path identification, and float calculation—that are indispensable tools for any project manager. Keep practicing, revisit these questions regularly, and soon the logic of project networks will feel intuitive rather than intimidating Less friction, more output..
11. Applying the Concepts in Real‑World Projects
- Define the scope and list all work packages – Break the project into discrete activities that can be represented as nodes in an AON diagram.
- Establish logical relationships – Connect the nodes with arrows that reflect predecessor‑successor dependencies (finish‑to‑start, start‑to‑start, etc.).
- Estimate durations – Use historical data, expert judgment, or parametric models to assign realistic time estimates to each activity.
- Calculate forward and backward pass values – Compute ES, EF, LS, and LF for every activity; the difference yields the total float.
- Identify the critical path – The sequence of zero‑float activities determines the shortest possible project finish date.
- **Apply resource
11. Applying the Concepts in Real‑World Projects
- Define the scope and list all work packages – Break the project into discrete, manageable activities that can be represented as nodes in an AON diagram.
- Establish logical relationships – Connect the nodes with arrows that reflect predecessor‑successor dependencies (finish‑to‑start, start‑to‑start, finish‑to‑finish, start‑to‑finish).
- Estimate durations – Use historical data, expert judgment, parametric models, or three‑point estimating (optimistic, most‑likely, pessimistic) to assign realistic time estimates to each activity.
- Run the forward‑pass – Starting at day 0, compute Early Start (ES) and Early Finish (EF) for every activity.
- Run the backward‑pass – Beginning with the project’s target finish date, compute Late Start (LS) and Late Finish (LF).
- Determine total float – Subtract ES from LS (or EF from LF). Activities with zero float belong to the critical path.
- Validate the critical path – Verify that any delay on a critical activity directly pushes the project finish date.
- Perform “what‑if” analysis – Shift constraints, add buffers, or compress activities to see how the critical path and overall duration respond.
- Resource‑level the schedule – If two critical or near‑critical activities require the same limited resource, consider re‑sequencing, splitting, or adding overtime to avoid overallocation.
- Baseline and monitor – Once the network is approved, lock it as the schedule baseline. Throughout execution, compare actual progress to ES/EF values, update the network when scope changes occur, and re‑calculate the critical path as needed.
12. Common Pitfalls and How to Avoid Them
| Pitfall | Why It Happens | Mitigation Strategy |
|---|---|---|
| Missing a predecessor | Over‑looking a hidden dependency (e.Day to day, | |
| Neglecting float | Believing only the critical path matters | Review float values after each schedule update; a newly created float can indicate an emerging risk or an opportunity for schedule compression. Day to day, , a permitting step) |
| Treating all activities as independent | Assuming resources are unlimited | Perform a quick resource‑availability check before finalizing the network; flag activities that share scarce resources. g. |
| Relying on a single duration estimate | Ignoring uncertainty | Use three‑point estimates and calculate expected duration (PERT formula) or run Monte‑Carlo simulations for high‑risk projects. |
| Changing the baseline without documentation | Losing audit trail | Record every schedule change in a change‑log, note the reason, and obtain stakeholder sign‑off before re‑baselining. |
13. Quick Reference Sheet (One‑Page Cheat Sheet)
| Symbol | Meaning | Formula |
|---|---|---|
| ES | Early Start | Max(EF of all immediate predecessors) |
| EF | Early Finish | ES + Duration |
| LS | Late Start | LF – Duration |
| LF | Late Finish | Min(LS of all immediate successors) |
| TF (Total Float) | Scheduling flexibility | LS – ES (or LF – EF) |
| FF (Free Float) | Delay allowed without affecting successors | Min(ES of successors) – EF |
| Critical Path | Longest path, zero total float | Sequence of activities where TF = 0 |
| Slack | Synonym for float | – |
Keep this sheet at your desk when you build or audit a network— it condenses the most frequently used calculations into a single glance.
Conclusion
Project‑network analysis is the backbone of disciplined schedule planning. By mastering the mechanics of AON diagrams, forward and backward passes, and float calculations, you gain a powerful lens through which to view every dependency, constraint, and risk in a project. The exercises above demonstrate that even a modest six‑activity network can reveal hidden bottlenecks, expose infeasible schedule tweaks, and highlight where flexibility truly exists.
When you transition from the classroom to the field, remember that a network is a living document. As scope evolves, resources shift, and uncertainties resolve, you will repeatedly:
- Re‑draw the diagram to capture new relationships.
- Re‑compute ES/EF/LS/LF to see the impact on the critical path.
- Communicate the implications to stakeholders, using clear visuals and concise float tables.
Doing so not only safeguards the project’s delivery date but also builds credibility with sponsors, team members, and clients. Keep practicing, maintain a habit of documenting every change, and let the critical‑path mindset become second nature. With those habits in place, you’ll be well‑equipped to steer projects of any size from start to successful finish Not complicated — just consistent. Practical, not theoretical..
