O-Level Elementary Mathematics · Singapore

29 years of papers, one forecast for 2026

Every mark of 27 yearly papers (1997–2025), sorted into 22 topics, re-checked against the real papers, and read for what it says about the paper coming in 2026.

27exam years
57papers
1,312question parts coded
180marks a year (90 + 90)
4052the syllabus sat in 2026

Six things the data say

Averages use the 2023–25 papers (the current syllabus) unless stated; marks are out of 180.

36/180

Algebra + equations is the engine

Together they averaged 36 marks (20%) in 2023–25. Algebra alone has more than doubled: 9 marks in 1997–2006 → 18 now.

58%

Seven anchors fill the paper

Algebra, equations, trig/Pythagoras, mensuration, graphs, statistics and the real-world problem appeared every single year of 2016–25 and took 58% of the marks in 2023–25.

10 marks

Paper 2 always ends the same way

Since 2016 the last Paper 2 question is one integrated real-world problem (9–11 marks): money, graphs, a model, then a justified decision.

10/10

Small topics are guaranteed

Sets (3 marks) and matrices (4 marks) have appeared in all ten recent papers. Short, predictable, and easy marks.

8→3

Some topics are fading

Speed & rates fell from 7.6 to 2.7 marks; construction from 5.0 to 1.0; circle properties and similarity are drifting down.

15·13·2·0

No topic is ‘due’

Sequences scored 15, 13, 2, 0 in 2019, 2023, 2024, 2025 (about 6, 10, 2, 0 under an independent re-coding: still wild). The data show no rotation: one year’s mark tells you almost nothing about the next.

The heatmap marks per topic, every year, 1997–2025

Darker = more marks. Read across for a topic’s history; read down for what a whole paper looked like. The right-hand column compares the last ten years with 2009–15.

4017 · old syllabus401640484052 · currentno papers’97’98’99’00’01’02’03’04’05’06’07’08’09’10’11’12’13’14’15’16’17’18’19’20’21’22’23’24’252026fcstavg ’16–’25vs ’09–’15ALGEBRA & GRAPHSAlgebra & formulae98156889571113191614181111191413111416161922141715.8● +1.2Equations & inequalities18920212218182616122016171617162113181891112171319211615.1▼ -2.5Functions & graphs141113201720151416121115171215111216176151412111411171313.3● +0.0Sequences & patterns1169·834138112·33949951115384132·57.0▲ +2.7GEOMETRY & MEASURESPythagoras, trig & bearings262320232020152317202818181316161711152415106121322141514.2▼ -3.8Mensuration11121316111217424131412816172726181410121714141716111414.3▼ -2.8Vectors765311843116761067861048121012596377.9● +0.8Coordinate geometry3·5356476751041145449·4611699676.4● +0.3Congruence & similarity2351349812315127573998888961413877.3● -0.1Circle properties773684888453610966485646663355.1● -1.3Angles & polygons36233266644664633934·625·3944.1● -0.5Construction5458466545·543···13·3··4··311.4● -0.3DATA & CHANCEStatistics81611159148121091010141511121291516141315131116131413.5● +1.5Probability7117610763867678598855713610741087.5● +0.4Sets222·······3334332232433222432.7● -0.3Matrices121·······7324354455467655355.0● +1.0NUMBER & MONEYNumbers & indices12141491612161010141181610693489711108791098.3● -0.7Ratio & proportion2·7247954835886436239833861075.8● +0.5Percentages658104288599442574592668292655.5● +0.5Financial arithmetic3616·12726441045981553155351157266.1● -1.8Speed & rates813561174887514891175525437·22433.4▼ -5.0APPLIEDReal-world problem10101110101111101191010.3new in ’16RETIREDRetired topics (pre-2009)171711686117550.0droppedmarks out of 18003691215182124+1997–2006 scaled from 192 offered marks to 180 · hatched = no yearly papers supplied for 2007–08 · dashed gold = 2026 forecast
Read it like this. The dark band across algebra, equations, graphs, trig, mensuration and statistics never breaks. That is the paper’s spine. The pale rows (sets, construction, travel graphs) are small, and some are fading.
Syllabus breaks matter. Sets and matrices arrive with 4016 (2009); the real-world problem arrives with 4048 (2016); the old 4017 papers carried retired topics worth about 9 marks a year (the grey row).

Trends mean marks by era: 1997–2006 → 2009–15 → 2016–22 → 2023–25

RISING

more marks than before

Algebra & formulae9 → 15 → 15 → 18from 8 to 18: the biggest climber
Ratio & proportion5 → 5 → 5 → 8doubled in the latest 3 papers
Coordinate geometry4 → 6 → 6 → 8up from 4 to 8, mostly in Paper 2
Statistics11 → 12 → 14 → 13steady rise; now 13 marks

FADING

less than they used to be

Speed & rates8 → 8 → 4 → 3from 8 to 3: travel graphs shrinking
Pythagoras, trig & bearings21 → 18 → 13 → 1620 → 16: still big, no longer huge
Congruence & similarity7 → 7 → 9 → 4fell to 4 in 2023–25
Circle properties6 → 6 → 6 → 4slow slide to 4
Construction5 → 2 → 2 → 1nearly gone: 0–4 marks

STEADY CORE

same weight, year after year

Mensuration13 → 17 → 14 → 1514 marks, never below 10
Functions & graphs15 → 13 → 13 → 1413 marks, every year
Equations & inequalities18 → 18 → 14 → 1815–18, rock solid
Probability7 → 7 → 8 → 77 marks, 4–13 range
Matrices0 → 4 → 5 → 43–7, every year

WILD CARDS

swing a lot: never bank on them

Sequences & patterns7 → 4 → 8 → 50 to 15 swings (0–10 on a strict coding)
Financial arithmetic4 → 8 → 7 → 52 to 15
Angles & polygons4 → 5 → 4 → 40 to 9, absent in 2019 & 2023
Vectors6 → 7 → 9 → 63 to 12, lower lately
Numbers & indices13 → 9 → 8 → 94 to 11

Bars, left to right:1997–062009–152016–222023–25

Myth check is a topic ever “due”?

Sequences: 15, 13, 2, 0

9’165’1711’1815’193’208’214’2213’232’240’25

Marks for sequences, 2016–25. After two quiet years it is tempting to expect a big sequences question in 2026. The numbers do not support that.

One year says little about the next

−0.09correlation between a topic’s deviation this year and next, 2016–25
−0.24 to +0.02range pure chance gives (shuffled years)

The real value sits inside the chance range: there is no sign of rotation. A topic that was light last year was not more likely to be heavy this year, and vice versa. Over the longer run (2009–25) topics are slightly sticky, because real shifts such as algebra’s climb persist.

So: treat gaps as noise. Prepare for sequences because it is on the syllabus and can score big, not because it is owed.

Where the marks sit Paper 1 vs Paper 2, average 2023–25

Paper 1 marksPaper 2 marks
Algebra & formulae14 + 4
Equations & inequalities8 + 10
Pythagoras, trig & bearings10 + 7
Mensuration6 + 9
Statistics9 + 5
Functions & graphs4 + 10
Real-world problem0 + 10
Numbers & indices6 + 3
Probability2 + 5
Coordinate geometry1 + 7
Vectors5 + 1
Congruence & similarity2 + 2
Ratio & proportion4 + 4
Financial arithmetic5 + 0

What this tells you

Paper 1 only: financial arithmetic (about 5 marks) and constructions. They live in the short questions.

Paper 2 only: the real-world problem (10), and coordinate geometry is almost entirely Paper 2 (about 7 of 8 marks).

Paper 1 heavy: algebra (14 of 18), trigonometry, statistics and vectors.

Paper 2 heavy: graphs (10 of 14), equations and modelling, probability and mensuration.

Question types that keep coming back in how many of the 10 papers, 2016–25

Hover over a chip (or tap it) to see a real past-year example of that question type.

Counted from the concept label of every coded question part, so it shows how the question is asked, not just which topic it belongs to. “Explain / justify / comment” appears every year: reasoning is marks, not decoration.

Do I agree with the analysis? yes, with three caveats

Eight papers (2009, 2012, 2016, 2019, 2022, 2023, 2024, 2025: the 4016, 4048 and 4052 syllabuses) were re-coded from scratch by independent reviewers who never saw the analyst’s ledger, reading every printed mark from the page images, then compared. The 1997–2006 papers were not re-checked. On average 94% of marks landed in the same topic. Every paper reconciled to its printed total.

Marks in the same topic as the ledger

2009401697%RAT +4
2012401693%EQ +5, SPD -5, NUM +3
2016404888%MEN -6, ALG +5, SPD -5
2019404893%SEQ -9, EQ +6, NUM +3
2022404898%no gap over 2 marks
2023405297%ALG +3, SEQ -3
2024405293%ALG +6, TRI -6, CIR +3
2025405297%ALG +3, GRF -3, TRI -3

Gaps are the re-coded marks minus the ledger’s, for the three biggest topic disagreements of 3+ marks.

Where we differ, and why it matters

1. Boundary calls, not errors. Nearly every disagreement is a part that sits between two topics: an algebraic proof that ends in Pythagoras, a speed problem that is really a quadratic, a number-grid proof (sequence or algebra?). The ledger’s rule (“the skill driving the work”) is sensible and applied consistently.

2. Sequences are less wild than they look. The ledger gives 2019 a 15-mark sequences load; the reviewers code 6 (the number-grid parts go to equations and algebra). The real swing is more like 0–10 than 0–15. The ‘0 in 2025’ and ‘2 in 2024’ are confirmed.

3. In the 2023–25 papers, algebra looks even heavier. The re-coding gives algebra + equations 40 marks (ledger 36) and trigonometry 13 (ledger 16), because proofs that use Pythagoras count as algebra there. The conclusion is the same, only louder: algebra and equations are the single biggest block.

Also: travel-graph (speed) marks come out lower in the re-coding for 2012 and 2016 (by 5 each), so that topic’s fade is, if anything, steeper than shown.

The 2026 forecast expected marks out of 180

Method: recency-weighted average of 2016–25 (each year counts 80% as much as the next one), rescaled to 180, with the real-world problem fixed near 10. The bar shows the middle 80% of what each topic scored in those ten years. It is a planning guide, not a probability: three papers of the 4052 syllabus are too few to fit anything stricter. It uses the ledger’s coding; on the stricter re-coding expect algebra 2–4 marks higher and trigonometry 2–3 lower. Note on the practice pack: the ChatGPT specimen papers carry more graphs (20 marks vs 13 forecast) and travel graphs (8 vs 3), and fewer ratio, finance, percentage and similarity marks than this forecast, so use them with that tilt in mind.

TOPICMARKS: dot = expected, bar = usual range (0–25 scale)EXPECTTIERSEEN
Algebra & formulae17 (14–19)ANCHOR10/10 yrs
Equations & inequalities16 (12–18)ANCHOR10/10 yrs
Pythagoras, trig & bearings15 (11–16)ANCHOR10/10 yrs
Mensuration14 (12–17)ANCHOR10/10 yrs
Statistics14 (13–15)ANCHOR10/10 yrs
Functions & graphs13 (11–16)ANCHOR10/10 yrs
Real-world problem10 (10–11)ANCHOR10/10 yrs
Numbers & indices9 (7–10)REGULAR10/10 yrs
Probability8 (5–10)REGULAR10/10 yrs
Coordinate geometry7 (4–9)WILD CARD9/10 yrs
Vectors7 (5–10)REGULAR10/10 yrs
Congruence & similarity7 (5–8)REGULAR10/10 yrs
Ratio & proportion7 (3–8)REGULAR10/10 yrs
Financial arithmetic6 (3–8)REGULAR10/10 yrs
Sequences & patterns5 (3–11)WILD CARD9/10 yrs
Percentages5 (2–8)REGULAR10/10 yrs
Matrices5 (4–6)REGULAR10/10 yrs
Circle properties5 (4–6)REGULAR10/10 yrs
Angles & polygons4 (2–7)WILD CARD8/10 yrs
Speed & rates3 (2–5)WILD CARD9/10 yrs
Sets3 (2–3)REGULAR10/10 yrs
Construction1 (0–3)WILD CARD5/10 yrs

THE SHAPE OF THE PAPER

  • Paper 1: 90 marks, about 26 short questions, mostly 2–4 marks. Expect algebra, numbers, ratio, finance, sets and matrices here.
  • Paper 2: 90 marks, 9–10 longer questions of about 10 marks, linked parts. Expect a graph-plotting question, an equation-modelling question, coordinate geometry, probability or statistics, and mensuration.
  • Last question: an integrated real-world problem (about 10 marks) asking for a justified decision.

BET ON

  • Heavy algebra: factorising, algebraic fractions, completing the square, proof.
  • A quadratic or fractional equation modelling a situation.
  • A curve question: plot, tangent, line intersection.
  • Trig with bearings or 3-D, plus sine or cosine rule.
  • Data with a comparison: cumulative frequency, standard deviation, a misleading graph.
  • A short matrices question and a short sets question.

COIN-FLIPS, BUT DO NOT SKIP

  • Sequences (0 to 15 marks), angles and polygons, construction.
  • Financial arithmetic as a stand-alone question: it may sit inside the real-world problem instead.

WOULD SURPRISE US

  • A paper with under 20 marks of algebra and equations combined (the lowest since 2016 is 20, in 2019).
  • A paper with no matrices, no sets or no real-world problem.
  • A big travel-graph question (more than 6 marks): last seen in 2021.