Some good news first: the current exam has relatively few pure calculation questions. More often a question gives you a ready-made number, such as a cost performance index of 0.85, and asks what it means or what to do next. So understanding what a number means matters more than calculating fast. Even so, it is worth memorizing a short sheet and practicing writing it from memory until it is automatic, which saves time and stress on exam day. The exam usually provides an on-screen calculator.
Schedule formulas: the PERT three-point estimate = (optimistic + 4 × most likely + pessimistic) ÷ 6, or (O+4M+P)/6, and the standard deviation = (P − O) ÷ 6; the larger it is, the less certain the estimate. Example: O = 4 days, M = 6, P = 14, so the estimate is (4 + 24 + 14) ÷ 6 = 42 ÷ 6 = 7 days, and the standard deviation is (14 − 4) ÷ 6 ≈ 1.67 days. Float = late start − early start (LS − ES) = late finish − early finish (LF − EF), and an activity with zero float sits on the critical path.
Earned value (EVM) formulas, which you met in Level 2: cost variance CV = EV − AC, schedule variance SV = EV − PV, cost performance index (CPI) = EV ÷ AC, and schedule performance index SPI = EV ÷ PV. The rule: a positive variance and an index above 1 are good news; a negative variance and an index below 1 are a warning. Then the forecasts: estimate at completion EAC = BAC ÷ CPI; estimate to complete (ETC) = EAC − AC, the spending still ahead; and variance at completion (VAC) = BAC − EAC, where a negative value means an expected overrun. The to-complete performance index (TCPI) = (BAC − EV) ÷ (BAC − AC); above 1, the team must work more efficiently than planned to stay within budget.
Three more short formulas: expected monetary value (EMV) = probability × impact, negative for a threat and positive for an opportunity. Communication channels = n(n − 1) ÷ 2, where n is the number of people including the PM; a team of 8 has 28 channels, and at 10 people it has 45, an increase of 17. In agile projects: iterations remaining = remaining story points ÷ average velocity, rounded up; with 120 points left and an average velocity of 30, that is 4 more iterations.
💡 Key points
- PERT = (O + 4M + P) ÷ 6, and standard deviation = (P − O) ÷ 6.
- Float = LS − ES = LF − EF; zero float means the critical path.
- CV = EV − AC, SV = EV − PV, CPI = EV ÷ AC, SPI = EV ÷ PV; above 1 or positive is good.
- EAC = BAC ÷ CPI, ETC = EAC − AC, VAC = BAC − EAC; a negative VAC is an expected overrun.
- TCPI = (BAC − EV) ÷ (BAC − AC); above 1 means harder performance than planned.
- EMV = probability × impact, channels = n(n − 1) ÷ 2, iterations = remaining points ÷ average velocity.
🌍 Real-life example
An office renovation project has a budget at completion BAC = $200,000. After four months: planned value PV = 80,000, earned value EV = 80,000, and actual cost AC = 100,000. The math: CV = 80,000 − 100,000 = −20,000 (over budget), and SV = 80,000 − 80,000 = 0 (exactly on schedule). CPI = 80,000 ÷ 100,000 = 0.8, and SPI = 80,000 ÷ 80,000 = 1.0. If performance continues: EAC = 200,000 ÷ 0.8 = 250,000, ETC = 250,000 − 100,000 = 150,000, and VAC = 200,000 − 250,000 = −50,000. To finish within the original budget: TCPI = (200,000 − 80,000) ÷ (200,000 − 100,000) = 120,000 ÷ 100,000 = 1.2. What it means: the schedule is fine, but each dollar produces only 80 cents of work, and the team would have to lift its efficiency to 1.2, which is hard. So the PM analyzes the cause of the overrun and discusses with the sponsor either corrective actions or approving a new estimate.
📖 Key terms
| English | العربية |
|---|---|
| PERT (Three-Point Estimate) | تقدير PERT ثلاثي النقاط |
| Standard Deviation | الانحراف المعياري |
| Cost Performance Index (CPI) | مؤشر أداء التكلفة |
| Estimate to Complete (ETC) | التقدير حتى الإنجاز |
| Variance at Completion (VAC) | الانحراف عند الإنجاز |
| To-Complete Performance Index (TCPI) | مؤشر الأداء المطلوب للإنجاز |