AP24 — PERT, Critical Path, EVM, and Project Management
WBS, forward and backward passes for critical path and float, PERT three-point estimates, EVM SPI, CPI and EAC, and baseline change control for AP Subject A, with five original questions.
AP Subject A · Installment 24 · An independent study resource for the 2026 exam and Syllabus Ver.7.2. It is not affiliated with IPA and does not guarantee a pass. Open the series hub
- Revised / source checked: 2026-10-21
- Exam basis: 2026 IPA Applied Information Technology Engineer Examination Syllabus Ver.7.2. Proposals or review materials for 2027 or later are not used as this article’s exam scope.
Learning index
PDF pages and printed footer pages use different numbering systems.
- PDF 83 / printed 79: projects and project management; process and subject groups
- PDF 84 / printed 80: integration, overall plan, change requests, approved changes, baselines, CCB
- PDF 85 / printed 81: scope, WBS, activity definition, work packages, scope control
- PDF 86 / printed 82: sequencing and duration estimates, network analysis, PERT/CPM/PDM, milestones, compression, variance/trend analysis, EVM
- PDF 87 / printed 83: cost estimating, budgeting and control, actual/forecast cost, EVM, cost baseline, reserves
Shared terminology table
| English | 한국어 | 日本語 |
|---|---|---|
| work breakdown structure (WBS) | 작업 분류 체계(WBS) | WBS（作業分解構成図） |
| work package | 작업 패키지 | ワークパッケージ |
| schedule network | 일정 네트워크 | スケジュールネットワーク |
| predecessor | 선행 활동 | 先行アクティビティ |
| earliest start / earliest finish (ES/EF) | 최조 시작 시각/최조 종료 시각(ES/EF) | 最早開始/最早終了（ES/EF） |
| latest start / latest finish (LS/LF) | 최지 시작 시각/최지 종료 시각(LS/LF) | 最遅開始/最遅終了（LS/LF） |
| total float | 총여유시간 | トータルフロート |
| critical path | 임계경로(주공정) | クリティカルパス |
| PERT | PERT | PERT |
| planned value (PV) | 계획가치(PV) | 計画価値（PV） |
| earned value (EV) | 획득가치(EV) | 出来高（EV） |
| actual cost (AC) | 실제원가(AC) | 実コスト（AC） |
| baseline | 기준선 | ベースライン |
| change control board (CCB) | 변경통제위원회(CCB) | 変更管理委員会（CCB） |
1. WBS and the schedule network
A project is a temporary undertaking that creates a unique result under defined objectives and constraints. Project management connects initiating, planning, executing, monitoring and controlling, and closing while coordinating scope, schedule, cost, and other subjects.
A WBS hierarchically decomposes deliverables and work scope; its manageable lowest-level elements may be work packages. A schedule network represents activities and their logical dependencies. A WBS is therefore not itself an activity sequence diagram.
2. CPM forward and backward passes
Assume an activity-on-node, finish-to-start network; project start at t=0; integer-day durations; and no lag, calendars, or resource constraints.
| Activity | Duration | Predecessor(s) | ES | EF | LS | LF | Total float |
|---|---|---|---|---|---|---|---|
| A | 3 | none | 0 | 3 | 0 | 3 | 0 |
| B | 4 | none | 0 | 4 | 4 | 8 | 4 |
| C | 5 | A | 3 | 8 | 3 | 8 | 0 |
| D | 2 | A | 3 | 5 | 7 | 9 | 4 |
| E | 4 | B, C | 8 | 12 | 8 | 12 | 0 |
| F | 3 | D | 5 | 8 | 9 | 12 | 4 |
| G | 2 | E, F | 12 | 14 | 12 | 14 | 0 |
In the forward pass, EF=ES+duration; at a merge, ES is the maximum predecessor EF. The backward pass starts at finish 14 and uses LS=LF-duration; at a backward split, LF is the minimum successor LS. Total float is LS-ES (or LF-EF). The project duration is 14 days and the critical path is A-C-E-G. Its activities have zero total float, though other networks can have multiple critical paths.
3. PERT three-point estimate
For optimistic O=4, most likely M=7, and pessimistic P=16, expected duration is (O+4M+P)/6=(4+28+16)/6=8 days. Variance is ((P-O)/6)^2=((16-4)/6)^2=4; standard deviation is 2 days. The expected duration summarizes uncertainty; it is not a promised completion date.
4. EVM checkpoint
Let BAC=1000, PV=600, EV=480, AC=540. PV, EV, and AC must use the same monetary/budget-value unit.
SV=EV-PV=-120;CV=EV-AC=-60.SPI=EV/PV=0.80: behind the baseline schedule.CPI=EV/AC=0.888...≈0.89: cost-inefficient/over budget for earned work.- Under the explicit assumption that current cost efficiency continues,
EAC=BAC/CPI=1125,ETC=EAC-AC=585, andVAC=BAC-EAC=-125.
This EAC depends on that forecast assumption. EVM exposes variance but does not explain it, so it does not replace root-cause analysis.
5. Baselines and controlled change
Approved scope, schedule, and cost baselines are performance references. For a scope-expanding request, analyze impacts and alternatives, obtain approval through the defined change process or CCB, and then update the approved baselines and related documents. Do not treat every request as automatic approval or retroactively rewrite the baseline after doing the work.
AP25 covers service-management SLA, incident, problem, and change management. AP26 covers audit, internal control, and security management.
6. Original four-choice questions
Q1
What are the project duration and critical path for the network above?
- ア 12 days and B-E-G
- イ 14 days and A-C-E-G
- ウ 14 days and A-D-F-G
- エ 16 days and A-C-F-G
Answer: イ (2). ア misses that E waits for C to finish at 8. イ matches the forward pass and zero-float path. ウ uses the D-F branch, whose activities each have four days of float. エ invents a C-F link and has the wrong duration.
Q2
What is activity D’s total float?
- ア 0 days
- イ 2 days
- ウ 3 days
- エ 4 days
Answer: エ (4). ア incorrectly places D on the critical path. イ mistakes D’s duration for float. ウ confuses float with F’s duration. エ is correct: LS-ES=7-3=4.
Q3
For PERT values O=4, M=7, and P=16, what is the expected duration?
- ア 7 days
- イ 7.5 days
- ウ 8 days
- エ 9 days
Answer: ウ (3). ア uses only the most likely value. イ is neither the simple mean nor the PERT weighted mean. ウ correctly gives (4+4×7+16)/6=8. エ is the simple mean (4+7+16)/3.
Q4
Which interpretation of PV=600, EV=480, and AC=540 is correct?
- ア SPI=0.80 and CPI≈0.89: behind the baseline schedule and cost-inefficient for earned work.
- イ SPI=1.25 and CPI=0.80: ahead of schedule.
- ウ SPI=0.90 and CPI=1.13: cost-efficient.
- エ Both SPI and CPI equal 1, so performance is on plan.
Answer: ア (1). ア gives both correct ratios and interpretations. イ reverses SPI and also miscalculates CPI. ウ uses incorrect numerators. エ ignores that EV differs from both PV and AC.
Q5
What is the best response to a scope-expanding change request?
- ア Start immediately and retain the existing baseline.
- イ Analyze impact, use the defined approval/CCB process, then update approved baselines.
- ウ Change the baseline on request and omit analysis.
- エ Reject every scope change unconditionally.
Answer: イ (2). ア risks unauthorized work and distorted measurement. イ has the correct analysis–approval–update order. ウ confuses a request with approval. エ blocks even valuable, controlled changes.
All questions are original. No IPA past-exam question was used, translated, or adapted.
Quick sheet and review
- Forward merge=
max(EF); backward split=min(LS); total float=LS-ES=LF-EF. - PERT expected duration=
(O+4M+P)/6; variance=((P-O)/6)^2. SV=EV-PV,CV=EV-AC,SPI=EV/PV,CPI=EV/AC.- Day 1: recall terms and formulas. Day 3: recalculate the network. Day 7: retake Q1–Q5 under time pressure.
Official sources and notice
- IPA, Applied Information Technology Engineer Examination (Level 3) Syllabus Ver.7.2 — checked 2026-10-21
- IPA, examination syllabus overview — checked 2026-10-21
- IPA, syllabus revision information — checked 2026-10-21
This material is not affiliated with or endorsed by IPA. It does not guarantee learning, passing, or examination results.