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MOE/SEAB Primary Syllabus | PSLE AL Score Calculator 2027: AL1–AL8, Foundation Grades, Posting Groups and Worked Examples

Three students in blue pinafores sit together at a classroom table, smiling and looking at an open book.

How do you calculate a PSLE score for 2027? Add the Achievement Levels (ALs) for English Language, Mathematics, Science and Mother Tongue Language. Each Standard subject receives AL1 to AL8; the best possible four-subject total is 4 and the largest is 32. If a child takes Foundation subjects, convert Foundation Grade A, B or C to the equivalent Standard-level AL for Secondary 1 posting. A lower total is better; it is not a percentage and must not be compared with the old T-score.

The basic calculation is simple, but parents need more than a calculator. They need to understand the mark boundaries, why a school preliminary AL is not a guaranteed PSLE outcome, how a Foundation grade contributes to the total, and what the total means for the child’s Secondary 1 Posting Group. The tables below use MOE’s published AL scoring and Full Subject-Based Banding posting arrangements as understood on 12 November 2026. Always check the final rules and school-choice materials that apply to the 2027 candidate cohort.

  • AL1: 90 marks or above in a Standard-level subject; AL8: below 20.
  • PSLE Score: four subject ALs added together, e.g. 2 + 3 + 4 + 5 = 14.
  • Foundation A: maps to AL6; Foundation B to AL7; Foundation C to AL8 for posting.
  • Posting Group 3: broadly PSLE Score 4–20; 21–22 offers a PG2/PG3 choice.
  • Posting Group 2: scores 23–24; 25 offers a PG1/PG2 choice.
  • Posting Group 1: scores 26–30 only when English and Mathematics meet the AL7-or-better condition.
  • Important: a score is an eligibility indicator, not a promise of admission to any particular school.

Standard-subject AL1–AL8 table: the marks that matter

AL Standard-level raw mark range What the band means
AL1 90–100 Achievement in the highest published band.
AL2 85–89 One AL point below AL1.
AL3 80–84 A distinct band; 84 and 85 fall on opposite sides of a boundary.
AL4 75–79 Upper-mid achievement band.
AL5 65–74 A 10-mark-wide band.
AL6 45–64 A 20-mark-wide band; pupils within it receive the same AL.
AL7 20–44 A 25-mark-wide band.
AL8 Below 20 Lowest published band.

The numbers in the left column are the AL grades. They are not percentages. A Mathematics mark of 91 maps to AL1; a mark of 84 maps to AL3. A child with 88 in English receives AL2, not AL1, because the AL1 threshold is 90. The use of broader bands is deliberate: the system measures performance against learning standards rather than producing a fine relative ranking on every individual mark.

One meaningful consequence is that improvement in raw marks does not always change a subject AL. Moving from 46 to 63 keeps a pupil within AL6. By contrast, moving from 84 to 85 crosses from AL3 to AL2. This does not make the first improvement worthless: greater mastery matters for later learning even when the published AL remains unchanged.

Common threshold examples

Raw mark AL What students often misunderstand
89 AL2 Very close to 90, but not AL1.
90 AL1 At the AL1 boundary.
84 AL3 Not yet AL2.
85 AL2 Exactly the AL2 threshold.
74 AL5 A mark below 75 remains in AL5.
75 AL4 Crosses into AL4.
64 AL6 Still AL6.
65 AL5 Crosses into AL5.
44 AL7 A mark below 45 stays AL7.
45 AL6 Crosses into AL6.
19 AL8 Below the AL7 boundary.
20 AL7 Crosses into AL7.

These boundary examples help pupils check a practice score, but a school assignment mark must not be treated as a definitive national PSLE grade. Different assessment tasks can have different difficulty, topic coverage and marking objectives. A school report may use AL reporting for familiarity; it does not follow that the next PSLE subject mark will be identical.

How to add four AL grades correctly

Use the simple formula: English AL + Mathematics AL + Science AL + Mother Tongue AL = aggregate PSLE Score. For students with an approved Mother Tongue exemption or special arrangement, use MOE’s specified method rather than inventing a fourth grade. For Foundation subjects, replace the Foundation letter with its corresponding AL for posting before adding.

Case English Maths Science MTL PSLE Score
A: strong and balanced AL2 AL3 AL2 AL3 10
B: mixed strengths AL2 AL5 AL3 AL4 14
C: all AL4 AL4 AL4 AL4 AL4 16
D: edge of PG3 AL5 AL5 AL5 AL5 20
E: option band 21 AL5 AL5 AL5 AL6 21
F: option band 22 AL5 AL5 AL6 AL6 22
G: PG2 AL6 AL6 AL6 AL6 24
H: option band 25 AL6 AL6 AL6 AL7 25
I: PG1 threshold AL6 AL7 AL6 AL7 26
J: possible no PG1 eligibility AL8 AL6 AL6 AL7 27

Important for Case J: A PSLE Score of 27 does not by itself establish eligibility for Posting Group 1. The published PG1 rule for scores 26–30 includes AL7 or better in both English and Mathematics. Because Case J’s English is AL8, the ordinary PG1 eligibility condition is not met. Families in such circumstances should discuss the available progression and support pathways directly with the primary school rather than apply a score-only table.

All examples are fictional. They are arithmetic illustrations, not predictions of actual results, school places or which subjects a child will be offered at secondary school.

Foundation grades A, B and C: what they mean in the PSLE Score

Foundation subjects use letter grades, but those letters are not equivalent to Standard AL1, AL2 and AL3. MOE maps the Foundation grades to Standard-level ALs for the purpose of calculating the PSLE Score used in Secondary 1 posting. It is incorrect to add an ‘A’ as 1 or assume a Foundation A is identical to a Standard A-grade concept.

Foundation grade Foundation raw mark range Equivalent Standard AL for posting
A 75–100 AL6
B 30–74 AL7
C Below 30 AL8

Worked example: English AL5, Foundation Mathematics A, Science AL5 and Mother Tongue AL6 yields 5 + 6 + 5 + 6 = 22. The Foundation Mathematics A counts as six points for posting, not one. The aggregate 22 falls into a Posting Group choice band under the current published arrangement, but the pupil’s actual combination and possible school options must be confirmed through the S1 posting rules.

Second example: English AL6, Foundation Mathematics B, Foundation Science A and Mother Tongue AL7 gives 6 + 7 + 6 + 7 = 26. Because English is AL6 and Mathematics maps to AL7, the child meets the two-subject condition quoted for PG1 scores 26–30. But meeting a Posting Group range does not guarantee any particular school’s place.

A parent may ask why a Foundation A maps to AL6 when the child may have done very well in that subject. The reason is that Standard and Foundation assess different curricular scopes. The score mapping is an administrative way to support Secondary 1 posting; it is not a judgment that the child’s effort was less worthy. The child may have made substantial progress in important foundational skills.

Posting Groups 1, 2 and 3: what each score normally allows

PSLE Score Published Posting Group eligibility What to remember
4–20 Posting Group 3 PG3 guides the starting level for most subjects.
21–22 Posting Group 2 or 3 This is a choice band; the family selects one eligible PG for the S1 posting exercise.
23–24 Posting Group 2 PG2 guides the starting subject level for most subjects.
25 Posting Group 1 or 2 This is another choice band.
26–30 with AL7 or better in English and Mathematics Posting Group 1 Both the aggregate and English/Maths condition must be met.
31–32, or 26–30 without the specified EL/Maths condition No routine PG1/2/3 eligibility in that table Consult the school and MOE’s published pathways; do not assume a guaranteed secondary posting.

Secondary schools under Full Subject-Based Banding do not use the old Express, Normal (Academic) and Normal (Technical) streams as separate identities. Posting Groups are used for admission and to guide initial subject levels. Once enrolled, pupils can take some subjects at different G1, G2 or G3 levels according to their strengths, eligibility and school assessment. The letter ‘G’ stands for General; PG is a posting category, not the lifelong label of the child.

Example: A child with AL5 English, AL6 Mathematics, AL5 Science and AL5 Mother Tongue has a total of 21. Under the published arrangement, the family may be eligible to select PG2 or PG3 for the S1 posting process. This requires consideration of the child’s readiness and school choices. It is not simply a question of choosing the highest sounding number. Once the choice is made, the posting-group selection applies to the submitted S1 school choices.

Why a child with a PSLE Score of 22 may face a real decision

At a boundary such as 21–22, the child may have an option between two Posting Groups. Families should look at the student’s subject-specific achievement, workload, learning preferences, available school programmes, travelling time and support options. A school with an appealing name is not necessarily the best fit for a child whose learning needs and daily travel would make the arrangement difficult.

The sensible question is not simply ‘Which Posting Group looks more prestigious?’ It is ‘Which environment, available schools and starting subject levels will allow this pupil to learn confidently and make progress?’ Parents should discuss the options with the primary school and consult the official MOE S1 Posting portal before finalising preferences.

The difference between an AL score and a secondary school cut-off point

A PSLE Score is calculated from the child’s own grades. A secondary school Cut-Off Point (COP) reflects the score of the last pupil posted to that school in an earlier exercise, under the relevant category and conditions. The two are related but not the same. COPs can vary because each cohort’s results, preferences and vacancies differ. Meeting a historical COP does not reserve a future place.

For example, suppose a family sees that a school previously admitted a candidate with PSLE Score 14 and their child scores 14. That is not a guarantee of posting. Other applicants’ choices, citizenship priority, capacity, school programme eligibility and tie-breakers can influence the eventual result. Use historical COPs as a reference for creating a balanced list, not as a promise.

MOE’s posting system ranks pupils by academic eligibility and includes tie-breakers, notably citizenship, choice order and computerised balloting when applicants share a score at the allocation boundary. That makes genuine ranking of school choices important. Reversing a preferred school’s order based on fear rather than actual preferences can be counterproductive.

What to consider before submitting six schools

  • Whether the student meets the relevant Posting Group and any programme requirements.
  • The family’s actual preference order, rather than copying a popular online ranking.
  • School location, travel time, start/end times and feasible daily transport.
  • Available subject options, programmes, CCAs and learning support.
  • Whether the list includes realistic choices rather than only aspirational historical COPs.
  • Any affiliation, DSA or special admission arrangements and the official conditions.
  • The student’s own voice: strengths, interests and concerns about the transition.

A historical school score range cannot replace the official MOE allocation rules. For up-to-date information, use MOE’s Secondary 1 posting guidance and the MOE PSLE scoring microsite.

How parents should interpret P5 and P6 school-based AL results

P5 and P6 school assessments help pupils and parents become familiar with AL reporting. However, a school Mathematics paper may focus on specific taught topics, whereas the national PSLE has its own assessment scope. A mark on an internal paper is a signal of current performance on that task, not a fixed future national AL.

If a P5 pupil is around the AL4/AL5 boundary, it may be more useful to examine the child’s actual misunderstandings than to calculate dozens of hypothetical PSLE totals. Ask which questions required fractions, ratio, percentage or interpretation of data. Then work on those concepts with delayed retests. A pupil who can solve unfamiliar problems independently is developing a more durable advantage than one who merely knows a threshold table.

What if a raw school mark rises but the AL does not?

Suppose a pupil improves from 51 to 61 in a school subject. Both numbers fall within AL6 if the published Standard band is applied, but the child has gained 10 marks and may have repaired several gaps. It would be a mistake to say there was no progress. Look at concept mastery, independence, ability to explain answers, and how reliably the improvement appears on fresh tasks.

Similarly, a one-mark change crossing an AL boundary has obvious scoring significance, but the pupil should not conclude that a single mistake defines their overall ability. Encourage careful work, meaningful checking and progress across subjects instead of becoming fixated on a narrow percentage point.

Why the PSLE Score is not the same as four raw percentages

It is tempting to add percentages or take an average. That produces a number with no official PSLE aggregate meaning. For example, raw marks of 90, 85, 80 and 75 average 82.5, but those marks correspond to AL1, AL2, AL3 and AL4. The PSLE Score is 1 + 2 + 3 + 4 = 10. That total cannot be reconstructed by simply dividing 82.5 by a constant.

The opposite mistake is converting a subject AL into a raw mark. AL5 could represent a mark anywhere from 65 to 74. You cannot infer that a pupil received exactly 70 just because the result slip says AL5. The published bands intentionally contain multiple raw marks, and the national score reports the band rather than every exact mark.

Higher Mother Tongue and Mother Tongue exemption: keep them separate

Some students take Higher Mother Tongue Language, and some may have officially approved Mother Tongue exemptions or substitute language arrangements. Those circumstances must be handled according to MOE’s specific scoring and school-admission instructions. Do not simply add Higher Chinese as a fifth AL. The standard illustration of PSLE Score as four subject ALs does not mean there are no additional rules for language-related school eligibility and pathways.

Higher Mother Tongue can matter in certain school admission contexts, including specified considerations related to Special Assistance Plan schools under official MOE rules. Parents should read the current detailed conditions instead of using an internet claim that Higher Chinese always ‘subtracts bonus points’ from the main four-subject PSLE Score.

If a child has Mother Tongue exemption, consult MOE’s applicable assigned-score approach rather than entering an arbitrary AL. Use the official MOE PSLE Score Calculator and school guidance when the child has a non-standard language combination.

Eight mistakes to avoid when estimating a PSLE Score

  1. Adding raw marks instead of Achievement Levels.
  2. Assuming Foundation Grade A means AL1.
  3. Calling a lower aggregate worse, when the PSLE uses a lower-is-better total.
  4. Treating a P5 weighted-assessment AL as a guaranteed national PSLE grade.
  5. Ignoring the English and Mathematics condition for Posting Group 1 at scores 26–30.
  6. Believing the score alone guarantees admission to a school with a historical COP.
  7. Assuming the old Express/N(A)/N(T) streaming labels are still the new Full SBB posting system.
  8. Treating a child’s score as a measure of character, creativity, future potential or personal value.

The correct scoring method matters for administrative decisions, but the best educational support focuses on what the child has learned and where the next breakthrough can occur. An AL table is useful for understanding results. It should not become the only language in which parents discuss learning.

Four practical revision priorities by current subject performance

Current situation Study focus Better evidence of progress
Strong marks with avoidable slips Check instructions, units, copied values, question demands and time control. Fewer recurring execution errors on fresh mixed questions.
Good conceptual skills, weak application Translate unfamiliar stories into models, explanations and evidence. Can explain a novel question without hints.
Unstable prerequisites Revisit number sense, fractions, reading comprehension and Science processes from earlier years. Correct independent performance on simpler prerequisites and later transfer.
Low confidence or anxiety around testing Short achievable sessions, supportive feedback, realistic targets and school discussion. Greater willingness to attempt new tasks and explain working.

For Mathematics, a pupil repeatedly misreading 100% as the discounted price needs concept repair more than ten rapid-fire model papers. For English, a pupil missing inference questions needs practice linking evidence to an unstated idea, not only memorising vocabulary. For Science, ‘state’ versus ‘explain’ matters because the command word determines the type of reasoning expected. These improvements are useful whether or not the child’s next marks cross an AL threshold.

How to interpret the same PSLE Score when subject strengths differ

Two children can obtain the same aggregate even with very different strengths. This is a feature of a four-subject total: it summarises achievement but does not explain every subject’s learning profile. Secondary schools and families should still look at individual subject performance, interests, readiness and learning needs. A total of 18 does not tell us whether the child finds Mathematics challenging or is particularly strong in Mother Tongue.

Illustrative pupil English Mathematics Science MTL Total
Pupil A AL2 AL7 AL4 AL5 18
Pupil B AL5 AL3 AL5 AL5 18
Pupil C AL4 AL4 AL6 AL4 18
Pupil D AL6 AL6 AL3 AL3 18

For Pupil A, the Mathematics AL7 suggests a greater need to examine numerical foundations than the English AL2. Pupil B may be relatively confident in Mathematics while benefiting from targeted language practice. Pupil C may need support in Science inquiry and explanation. Pupil D’s comparatively stronger Science and Mother Tongue grades can be recognised as genuine strengths even though the total matches the others.

The correct educational response therefore depends on the pupil, not only the aggregate. A family planning Secondary 1 should ask which subject-specific programmes, teaching levels and support are suitable. Choosing a school purely by an aggregate score risks overlooking both strengths and barriers.

A step-by-step parent worksheet for a PSLE result slip

Read the actual printed or official digital result and confirm its subject entries. Do not transcribe the grades from a remembered conversation or social-media message. List English, Mathematics, Science and Mother Tongue in a table. Identify any Foundation or approved special arrangements. Convert any Foundation letter grades using the published mapping and sum the four contributing AL values.

Next, review the resulting Posting Group eligibility and relevant conditions. At 21, 22 and 25, the school choice includes an option between groups, so the family must understand the consequences. At 26–30, the English and Mathematics AL7-or-better requirement is not optional. Finally, consult the actual Secondary 1 posting instructions and the school options for that year. This process protects families from using a single table out of context.

Step Question to answer Source to check
1 Are all four subject entries and their levels correct? Official result record and primary school.
2 Do any Foundation A/B/C grades need conversion? MOE Foundation-to-AL mapping.
3 What is the four-subject total? Add the four counted ALs.
4 What Posting Group(s) apply? Current MOE S1 posting rules and any English/Maths conditions.
5 Does the family have a posting-group choice? MOE rules for 21/22 or 25, if applicable.
6 Which school choices best match the pupil? Official school information, programmes, travel, interests and historical ranges.
7 Have choices and special circumstances been verified? The school’s guidance and current S1 posting portal.

Worked boundary study: why one mark can matter but is not everything

Consider a child whose practice scores include Mathematics 84 and Science 85. Under the published Standard AL boundaries, 84 is AL3 while 85 is AL2. If every other subject grade were identical, the resulting aggregate would differ by one point. It is therefore sensible to check avoidable errors around a boundary. But a single mark on a school paper is not a guaranteed national result, and an entirely different question could reveal another strength or weakness.

The appropriate response is to improve the child’s reliable method rather than attempt to predict which one mark will appear on examination day. If the child often rounds incorrectly, practise place value and checking. If the child chooses a correct method but drops a step, rehearse clear working. If the child misunderstands a question, read it aloud, identify the unknown and discuss why the alternative interpretation fails.

A good retest changes the story while keeping the underlying mathematical principle. For example, a pupil who misreads a 15% discount should also practise a different question about attendance or population change. If the child succeeds only when a question resembles the last example, the skill remains fragile.

How to handle unusual score combinations without making assumptions

Not every theoretical combination of AL1–AL8 yields eligibility for one of the ordinary Posting Groups. For example, a total of 31 or 32 is not represented in the standard eligibility bands. Similarly, a total of 26–30 with AL8 in English or Mathematics fails the English/Maths threshold stated for PG1. In these situations the family needs specific guidance from the school and MOE about the appropriate pathways. It would be misleading to say that every student with a four-subject total automatically qualifies for PG1.

The purpose of naming this exception is to help families act correctly, not to create fear. The primary school can explain available support and progression arrangements. Parents should ask for the current official guidance rather than rely on advice extrapolated from another student’s result.

Three Foundation Grade examples that often cause confusion

Foundation A is not equivalent to Standard AL1

A Foundation A indicates performance within the highest Foundation grade band, which has its own curriculum scope. For the four-subject aggregate used in posting, MOE maps it to AL6. This is not a mistake in arithmetic and not a penalty invented by a school. Families should keep the distinction between achievement within the Foundation course and the administrative Standard-equivalent conversion.

A Foundation B may still represent real progress

A Foundation B covers a substantial range of raw marks. A pupil may improve meaningfully while remaining in that grade, just as a Standard pupil can improve within AL6. Track the errors that disappeared, the concepts gained and whether the child can apply knowledge in new contexts. The outcome of good teaching is improved understanding, even when a broad grading band has not changed.

One Foundation subject does not determine the entire total

For example, English AL3, Mathematics AL4, Foundation Science A and Mother Tongue AL5 yield 3 + 4 + 6 + 5 = 18. The total reflects four contributions, not a single Foundation label. Each subject should be discussed independently. A child taking a Foundation subject may have substantial strengths in another.

How to explain the AL system to a child

Use simple, accurate language: ‘An AL describes a broad range of marks in one subject. Your PSLE Score adds the four ALs. We use it to understand school entry options, but it does not describe all the things you can do.’ Younger pupils do not need to spend hours calculating their future score. Older pupils can learn the rules so that result-day information feels understandable.

Avoid saying ‘You are an AL5 student’ as if a grade were an identity. The child has particular results in particular subjects at a particular point in time. Their ability to learn, develop interests, build relationships and make decisions extends beyond an exam. The best next step is to identify a suitable learning environment and a manageable plan for growth.

A useful conversation after disappointing results can begin with the child’s experience: What questions felt manageable? Which type was unexpectedly difficult? What has improved during the year? What help would make Secondary 1 easier? The parent can then turn that discussion into concrete plans about school choice, transition skills and study habits.

A seven-day plan for understanding results and choosing schools

Day Family task What should be completed
1 Check official results and explain the individual ALs. A correct total and awareness of any special arrangements.
2 Understand the eligible Posting Group(s). Clear knowledge of whether there is an option band.
3 Identify the child’s interests, support needs and travelling constraints. A short list of non-score priorities.
4 Review the available secondary schools and their programmes. A broad shortlist based on real fit.
5 Compare historical cut-off information without treating it as a guarantee. A balanced preference order and awareness of uncertainty.
6 Discuss choices with the child and consult the school where needed. A genuine ranked list reflecting the family’s priorities.
7 Complete and verify the official S1 posting submission within the real deadline. Confirmed choices and retained official confirmation.

This is an illustrative family workflow, not a claim that MOE provides exactly seven working days for the posting process. Follow the year-specific official opening and closing dates. Begin school exploration earlier where possible, so that the result-day period is used for decisions rather than discovering every school’s location from scratch.

What a score calculator cannot tell you

  • Whether a particular school’s future cut-off point will exactly match its historical value.
  • Whether a child will thrive with a school’s daily schedule, culture and programmes.
  • How a pupil will respond to more demanding algebra, longer reading tasks or independent learning.
  • Whether one weak school assessment will persist after targeted intervention.
  • Which co-curricular activities, friendships or teachers will shape the child’s experience.
  • Whether an unusual subject combination requires a special official interpretation.

A calculator should be used to perform arithmetic and illustrate eligibility. It cannot replace conversation with the pupil, the school’s professional guidance or the actual allocation rules. For planning, combine the numerical result with practical concerns: travel, wellbeing, access to appropriate academic levels and the student’s interests.

The value of the AL system for learning decisions

The AL framework creates broader reporting categories rather than turning every raw mark into a unique rank. This can allow families to focus more on meaningful improvement. Nevertheless, because certain boundaries affect the aggregate, many parents still watch them closely. It is reasonable to understand the thresholds, but unhelpful to treat every practice paper as a verdict on a child’s future.

For a child in P5, a 30-day routine targeting a specific misconception can create more lasting value than another evening spent comparing school cut-offs. For a child who has already received PSLE results, numerical calculation should be followed by a balanced Secondary 1 choice process. At both stages, accurate information is a tool for better decisions, not an end in itself.

Frequently asked questions

What is the best possible PSLE Score?

The lowest and best possible four-subject aggregate is 4, achieved when the four counted subject grades are all AL1. A higher total indicates lower performance bands in one or more subjects.

Is AL1 90 marks or 91 marks?

For a Standard-level subject, AL1 begins at 90. It includes 90 and above.

Why can 84 and 85 receive different AL grades?

They fall on opposite sides of the AL3/AL2 boundary. AL3 is 80–84; AL2 is 85–89. Not every one-mark change crosses a boundary.

What does Foundation A count as?

For the PSLE Score used in Secondary 1 posting, a Foundation A corresponds to AL6. Foundation B maps to AL7 and Foundation C to AL8.

Does a PSLE Score of 25 mean Posting Group 1 or 2?

The current published arrangement gives an option between Posting Group 1 and 2. The family should examine the official posting guidance, child’s readiness and available school choices before selecting.

Does a PSLE Score of 29 always qualify for PG1?

Not necessarily. For 26–30, the published PG1 range requires AL7 or better in both English and Mathematics. Verify the current official rule with the school.

Can school cut-off points be predicted exactly?

No. Historical COPs depend on the previous cohort’s preferences, results and vacancies. A previous COP is a useful reference, not a guaranteed entry threshold for a later exercise.

Does a Foundation subject permanently lock a child into G1 secondary subjects?

No. Primary Standard/Foundation arrangements and secondary G1/G2/G3 subject levels are not one permanent label. Full Subject-Based Banding provides subject-level flexibility subject to school rules, strengths and readiness.

What is the official calculator?

Use MOE’s PSLE Score Calculator, and refer to MOE’s PSLE/Full SBB microsite for accompanying explanations.

Sources, review date and next reading

Reviewed 12 November 2026. Published MOE AL bands, Foundation conversions and the Posting Group framework are used as the planning reference. Check the official 2027 Secondary 1 posting exercise and updated MOE notices for applicable cohort details, admissions changes or exceptional subject arrangements.