AS 91576 Critical Path Analysis: How to Approach the Quiz Evening Report
Quick answer: To pass AS 91576 you draw the precedence network, run a forward and backward pass, name the critical path and its minimum time, then explain what the numbers mean for the real project. Merit and Excellence come from that explanation and from testing the plan against changes, not from extra arithmetic.
This guide is for Level 3 students working on the Te Kura “Quiz Evening” activity (MXO3042Y1) or a similar critical path task. You can see the brief on our MXO3042Y1 question page, and a reference-only extract on the AS 91576 critical path sample.
If the maths is fine but the written report is the problem, our report writing help page shows the support available.
What does AS 91576 actually ask you to do?
AS 91576 is Mathematics and Statistics 3.4, worth 2 credits, assessed internally. The standard is short: use critical path analysis in solving problems. What changes between grades is the thinking type, and NZQA describes it in plain terms.
| Grade | Thinking required | What markers look for |
|---|---|---|
| Achieved | Use critical path analysis | Correct network, times, critical path and a workable allocation |
| Merit | Relational thinking | Logical steps connected to the context, with findings related to the situation |
| Excellence | Extended abstract thinking | A strategy devised and justified, reasoning developed, insight communicated |
Most students stop once the numbers are right. That is an Achieved answer at best. Every sentence you add should answer “so what does this mean for the committee?”
Where do the marks sit in a quiz evening report?
The activity has two tasks. Task 1 is the planning report: network, critical path, minimum time, start and finish for each task, and an allocation to the fewest people. Task 2 asks what happens when the plan changes, which is where Merit and Excellence are decided.
Markers tend to see the same pattern. The network and forward pass are usually fine. The allocation is shaky, because students allocate tasks without checking the rules they were given, such as who may check answers. Task 2 is often a single line of “it takes longer”.
How do you approach critical path analysis, step by step?
- List every activity with its duration and immediate predecessors. Strike out dependencies already implied by a longer chain.
- Draw the activity-on-node diagram with a clear start and end. Check that no box is left hanging.
- Do the forward pass: earliest start is the largest earliest finish among predecessors.
- Do the backward pass from the project finish: latest finish is the smallest latest start among successors.
- Calculate float for each activity. Zero float marks the critical path.
- Add the durations along the critical path and confirm they equal the minimum time.
- Allocate tasks to people, then test the schedule for clashes and rule breaches.
- Write the recommendation in the language of the committee, not of a textbook.
For the underlying method, Hillier and Lieberman cover project scheduling with PERT/CPM, and Kelley and Walker (1959) is the paper that introduced critical path planning. You do not need to cite them in a Level 3 report, but reading how they describe float helps.
How do you find the minimum number of people?
Add up the work, then compare it with the time available. If every member must take part in the first and last activities, those two sit at the ends of the schedule, and everything else has to fit in the window between them.
Divide the total person-weeks of the middle activities by the weeks in that window and round up. That gives a lower bound. Then try to build a schedule that reaches it. If you cannot, say why, because precedence constraints can force a higher number than the arithmetic suggests.
Always show the check for the rule about who verifies the questions. It is easy to break in a clean-looking table.
What separates Merit from Excellence in Task 2?
Merit explains the effect of a change using the network: which activities move, by how much, and why. Excellence goes a step further and devises a strategy. For a delay on a critical activity, ask what could be done in parallel, whether another activity becomes critical after the change, and what the committee should do first.
For a smaller team, compare available person-weeks with the work needed. State a lower bound, test it against precedence, and then give the new minimum time. Tie the result to the event: fewer weeks for ticket sales or prize hunting changes what the committee can promise donors.
A reasonable opinion is better than silence. If you think the best fix is to start the question writing earlier and share it, say so and show why it works.
What do students struggle with in this assessment?
From the questions students ask about critical path tasks, the same worries come up repeatedly.
- Dummy or redundant dependencies. Students draw every listed predecessor and end up with a tangled diagram. Trim to the immediate ones.
- Confusing duration with path length. A long single task is not automatically critical.
- Backward pass errors. The latest finish of an activity with several successors is the smallest latest start, not the largest.
- Allocation without checking. A tidy table can hide a person doing two tasks in one week.
- Writing for the marker, not the committee. The brief asks for a report to organisers, so plain recommendations count.
The same ideas appear in tertiary scheduling tasks. Our blog on the SARC 321 Gantt chart and critical path shows how float is explained in a construction setting.
Mark-maximising checklist
- Network has one start, one end and no unexplained arrows.
- Every ES, EF, LS, LF and float value is shown in a table.
- Critical path is named by activity letters, with the total time stated.
- Start and finish times are given for every task, as asked.
- Allocation respects every rule in the brief and names the number of people.
- Each Task 2 answer compares before and after.
- Every result is linked back to the quiz evening in a sentence.
- The report is addressed to the organisers.
If you want the working checked before you hand it in, you can submit your assignment details and ask for guidance on the structure.
Common mistakes to avoid
Stopping at the arithmetic is the big one. The second is treating float as decoration. Float is the evidence for almost every recommendation: it shows which tasks can slip and which cannot.
Other slips include forgetting that a time of 8 weeks means finish at week 8, mixing up “start at week 5” with “start of week 5”, and giving an allocation that quietly needs an extra person. Keep the convention you use, and say it at the top of your tables.
Finally, do not copy a worked solution from a different version of the task. The activity times in each version differ, and a marker will notice answers that do not match the resource.
Frequently asked questions
What is AS 91576?
AS 91576 is the Level 3 internal achievement standard Mathematics and Statistics 3.4, Use critical path analysis in solving problems. It is worth 2 credits, and the grade depends on the type of thinking shown.
How do I find the critical path?
Run a forward pass and a backward pass, then work out float for each activity. The activities with zero float form the critical path, and their durations add up to the minimum project time.
What is float in critical path analysis?
Float is the time an activity can be delayed without delaying the project. It equals the latest start minus the earliest start. Critical activities have zero float.
How do I decide how many people are needed?
Compare the total work with the time available between the shared first and last tasks, round up, and then check a real schedule. Precedence rules sometimes require more people than the arithmetic suggests.
What does Excellence need in Task 2?
Excellence needs a strategy, not just a new number. You should compare the plan before and after the change, justify a fix, and communicate the insight in terms of the event.
Can I use a sample answer for my own submission?
No. Samples are for reference and learning only. Your submission must be your own work, in line with Te Kura and NZQA rules. Use the sample to see the method, then work on your own data.
If you would rather have a specialist look over a draft or explain a step, our maths assignment help team can talk through your options, and you can read what other students say on our reviews page.
About the expert
Olivia Hart holds a Master’s in Applied Mathematics from the University of Otago, New Zealand, and works on mathematics and technical science assignments covering statistics, calculus and applied problem-solving.
References
- Hillier, F. S., & Lieberman, G. J. (2021). Introduction to operations research (11th ed.). McGraw-Hill Education.
- Kelley, J. E., Jr., & Walker, M. R. (1959). Critical-path planning and scheduling. Papers presented at the December 1–3, 1959, Eastern Joint IRE-AIEE-ACM Computer Conference, 160–173. https://doi.org/10.1145/1460299.1460318
- New Zealand Qualifications Authority. (2017). Achievement standard 91576, version 2: Use critical path analysis in solving problems. https://www.nzqa.govt.nz/nqfdocs/ncea-resource/achievements/2019/as91576.pdf
- New Zealand Qualifications Authority. (n.d.). Standard 91576: Use critical path analysis in solving problems. https://www.nzqa.govt.nz/ncea/assessment/view-detailed.do?standardNumber=91576
