PYQ Vault

Strategy

Score 66+ by choosing what to attempt

100 questions × 1 mark = 100 marks in 120 minutes, and a third of a mark lost for each wrong answer. That makes two decisions matter: which chapters to prepare first, and on the day, which questions to attempt and which to leave.

marks out of 100
66+
questions attempted
90/100
accuracy on those
80%
total prep time
~143 h

The arithmetic of 66+

90 attempts at 80% accuracy is 72 right and 18 wrong: 72 − 18/3 = 66 marks. The 10 you leave are the ones you could not narrow down. Attempting them blind would add nothing on average — and attempting them after ruling out an option would add a little.

Expected marks from guessing a CDS Maths question, by how many options are still in play
Options still in playExpected marks from a guessVerdict
40A blind guess gains nothing on average and adds risk. Leave it.
3+1/9 of a markWorth it: one option ruled out makes the guess pay.
2+1/3 of a markClearly worth it.

So a guess is a tool, not a gamble. Ruling out one option on sight — a value out of range, the wrong units, the wrong sign — is what turns a question you cannot solve into one worth attempting. And at 1.2 minutes a question, the questions you leave should be the ones you could not open, not the ones you ran out of time for. The three strands below are ordered for both.

Cornerstone — Trigonometric Ratios and Identities · Number System · Mensuration 2D · Mensuration 3D · Triangles (969 q · 46% of bank)

Five chapters carry 46.1 questions a paper — nearly half of a 100-question paper. Trigonometry and Number System have each risen to 13 a paper on 2024-2026 papers. No score is possible without these five, and four of them cherry-pick: the HARD sits in one or two pages you can leave for last.

The approach

  • Do these five first in prep, and in this order of return: Trigonometry and Number System (13 a paper each recently), then the two mensurations, then Triangles.
  • All five have teaching notes at /notes/cds-maths. Read a chapter's notes once, then drill subtopic by subtopic.
  • Four of the five cherry-pick. In Trigonometry, maximum/minimum and eliminating θ hold 29 of 46 HARD questions; in Mensuration 2D, touching circles and shaded regions are where wrong answers come from. Bank the cheap pages before the pools.
  • Number System does not cherry-pick: its HARD is spread across remainders, factorisation and HCF laws. Own the whole chapter.

Trigonometric Ratios and Identities

227 questions · 20% hard

Split pass — cheap pages first

227 q · 20% HARD · 13 a paper on 2024-2026 papers, up from 8.8. Eight of its ten subtopics are cheap; maximum/minimum (37 q, 35% HARD) and eliminating θ (34 q, 47%) hold 29 of its 46 HARD questions. Bank the eight first, then take the two pools with timed reps.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

10.81 q/paper · about 11 marks16h study time

Number System

223 questions · 16% hard

Own outright — HARD spread through it

223 q · 16% HARD · 13 a paper recently, up from 9.8. The HARD is spread across remainders, factorisation, HCF laws and division rather than pooled, so there is no page to leave out; primes, HCF/LCM applications and irrationals have never set a HARD question.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

10.62 q/paper · about 11 marks16h study time

Mensuration 2D

197 questions · 23% hard

Split pass — cheap pages first

197 q · 23% HARD · about 9.4 a paper. Wheels, arcs and re-bent wires are nearly free; touching circles (62% HARD) and shaded regions (40%) are where the wrong answers come from. Attempt those two only on a clean solve.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

9.38 q/paper · about 9 marks14h study time

Mensuration 3D

171 questions · 17% hard

Split pass — cheap pages first

171 q · 17% HARD · falling from 8.1 to 6.7 a paper. Eight of ten subtopics are under 20% HARD; solids inside solids (53%) is the one page to attempt only when the set-up is clear.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

8.14 q/paper · about 8 marks12h study time

Triangles

151 questions · 20% hard

Split pass — cheap pages first

151 q · 20% HARD · about seven a paper. The altitude to the hypotenuse is 27 questions with no HARD at all; triangle inequalities and the sine and cosine rules are half HARD but only 16 questions between them.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

7.19 q/paper · about 7 marks12h study time

Quick-Win — Statistics · Ratio, Proportion and Variation · Time, Speed and Distance · Percentage, Profit and Loss · Data Interpretation · Averages · Time and Work · Simple and Compound Interest (460 q · 22% of bank)

Eight arithmetic and data chapters carry 21.9 questions a paper at 2-15% HARD. This is where a steady candidate makes the difference: almost every question here is one you should attempt and get right.

The approach

  • Drill these for speed as much as accuracy — at 1.2 minutes a question, the time you save here pays for the cornerstone pools.
  • Every chapter here has at least one subtopic that has never set a HARD question. The only real risk is a careless base: the percentage of the wrong number, the average of the averages.
  • Statistics is rising (3.8 to 5.0 a paper); Data Interpretation and Time and Work are falling. Weight your hours accordingly, but do not skip any of the eight.

Statistics

80 questions · 8% hard

Attempt all — cheap chapter

80 q · 8% HARD · rising from 3.8 to 5.0 a paper. The cheapest chapter of any size: four of its six subtopics have never set a HARD question. Every question here is one to attempt.

Drill — in this order

3.81 q/paper · about 4 marks5h study time

Ratio, Proportion and Variation

76 questions · 9% hard

Attempt all — cheap chapter

76 q · 9% HARD · about 3.6 a paper. Ratio and proportion and variation have no HARD at all; partnership and mixtures carry the little there is.

Drill — in this order

3.62 q/paper · about 4 marks5h study time

Time, Speed and Distance

75 questions · 13% hard

Attempt all — cheap chapter

75 q · 13% HARD · about 3.5 a paper. Average speed is 22 questions at 5%; races and speed changes are the only pages with any real cost.

Drill — in this order

3.57 q/paper · about 4 marks5h study time

Percentage, Profit and Loss

50 questions · 6% hard

Attempt all — cheap chapter

50 q · 6% HARD · about 2.4 a paper — three HARD questions in the whole chapter. The only way to lose a mark is the wrong base.

Drill — in this order

2.38 q/paper · about 2 marks3h study time

Data Interpretation

52 questions · 2% hard

Attempt all — cheap chapter

52 q · 2% HARD · falling from 2.6 to 1.7 a paper. One HARD question in 52: the work is reading a table or chart carefully and dividing by the right total.

Drill — in this order

2.48 q/paper · about 2 marks3h study time

Time and Work

46 questions · 7% hard

Attempt all — cheap chapter

46 q · 7% HARD · falling from 2.7 to 1.3 a paper. Work in rates or man-days, never in days directly, and the chapter is free marks.

Drill — in this order

2.19 q/paper · about 2 marks3h study time

Simple and Compound Interest

34 questions · 15% hard

Attempt all — cheap chapter

34 q · 15% HARD · about two a paper recently. Simple interest is nearly free; compound interest holds most of the HARD.

Drill — in this order

1.62 q/paper · about 2 marks3h study time

Selective — Algebraic Identities and Simplification · Quadratic Equations · Surds, Indices and Simplification · Polynomials · Circles · Quadrilaterals · Heights and Distances · Logarithms · Linear Equations (585 q · 28% of bank)

Nine chapters of algebra and the remaining geometry carry 27.9 questions a paper at 19-39% HARD. Here the one-third penalty decides the score: attempt what you can solve cleanly, and leave the rest rather than guess blind.

The approach

  • Algebraic Identities is the hardest chapter in the bank (39% HARD) but cherry-picks: its conditional and symmetric pages are the pool.
  • Heights and Distances (34%) and Logarithms (24%) each have one expensive page and one or two cheap ones — bank the cheap ones.
  • Linear Equations has faded to one question in six papers; keep it for the word-problem fluency the arithmetic chapters use, not for its own weight.

Algebraic Identities and Simplification

98 questions · 39% hard

Split pass — cheap pages first

98 q · 39% HARD · the hardest chapter in the bank, about 4.7 a paper. It cherry-picks: conditional identities (69% HARD) and symmetric expressions (6 of 6 HARD) are the pool; three-variable sums and the cube identity are cheap.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

4.67 q/paper · about 5 marks8h study time

Quadratic Equations

89 questions · 24% hard

Own outright — HARD spread through it

89 q · 24% HARD · about 4.2 a paper, the HARD spread thinly across nine subtopics. Common roots, maximum/minimum and word problems have never set a HARD question.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

4.24 q/paper · about 4 marks6h study time

Surds, Indices and Simplification

82 questions · 22% hard

Split pass — cheap pages first

82 q · 22% HARD · falling from 4.6 to 3.0 a paper. Equations with surds are 71% HARD; fractions, exponential equations and square roots of surds are almost free.

Drill — in this order

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

3.90 q/paper · about 4 marks5h study time

Polynomials

79 questions · 19% hard

Own outright — HARD spread through it

79 q · 19% HARD · about 3.8 a paper. The factor theorem has never set a HARD question; HCF and LCM of polynomials is the largest page and holds the most HARD.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

3.76 q/paper · about 4 marks5h study time

Circles

69 questions · 26% hard

Own outright — HARD spread through it

69 q · 26% HARD · about 3.3 a paper. Tangents from an external point have never set a HARD question; the HARD is spread over the chord, circumcircle and touching-circle pages.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

3.29 q/paper · about 3 marks5h study time

Quadrilaterals

54 questions · 20% hard

Own outright — HARD spread through it

54 q · 20% HARD · rising from 2.4 to 3.7 a paper. Rhombus and kite has no HARD; the general-quadrilateral page is the expensive one at 36%.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

2.57 q/paper · about 3 marks4h study time

Heights and Distances

41 questions · 34% hard

Split pass — cheap pages first

41 q · 34% HARD · about two a paper. Towers on plane figures is 5 of 7 HARD; one line of sight and two points of observation are the pages to bank.

Drill — in this order

HARD-target

These subtopics carry the chapter’s HARD questions. Timed reps with a HARD-only filter are what turn them from questions you leave into questions you attempt.

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

1.95 q/paper · about 2 marks4h study time

Logarithms

33 questions · 24% hard

Split pass — cheap pages first

33 q · 24% HARD · about 1.6 a paper. The equations page holds 5 of the 8 HARD; the laws and digit counting are cheap.

Drill — in this order

The HARD pool — last

Last in prep, and first to drop if your hours run out. On the paper, attempt one of these only if you can see the solution; otherwise rule out what you can and apply the guessing rule.

1.57 q/paper · about 2 marks3h study time

Linear Equations

40 questions · 20% hard

Own outright — HARD spread through it

40 q · 20% HARD · fading: 2.7 a paper in 2016-2020, one question in the six 2024-2026 papers. Learn it for word-problem fluency, which the arithmetic chapters use, not for its own weight.

Drill — in this order

1.90 q/paper · about 2 marks3h study time

The 4 chapters below the playbook line

These average under 1.5 questions a paper, so none ships a playbook. They are listed so the 26-chapter bank is accounted for. Each still has full teaching notes.

Tail chapters with lifetime question count, questions per paper, percentage HARD and a note
ChapterQuestionsq/paper% HARD
Sets1.3 a paper, falling from 1.9 to 0.8. Mostly Venn-diagram counting at 14% HARD — worth a short drill with the quick-wins.281.3314%
Lines, Angles and Polygons1.05 a paper, falling from 1.8 to 0.8, and the only chapter with no HARD question. Revise the angle-sum rules once; they are free when they appear.221.050%
Sequence and Series19 questions in 21 papers at 11% HARD. Know the AP and GP sums and the three means so a question is recognisable.190.911%
Inequalities13 questions in 21 papers, mostly data-sufficiency items on signs. Read the notes once.130.6215%

Time investment plan

Study hours by strand, summed from each strand’s chapters
StrandChaptersBank shareHours
Cornerstone5969 q · 46%70
Quick-Win8460 q · 22%30
Selective9585 q · 28%43
Total222014 q143

Prepare in strand order — Cornerstone, then Quick-Win, then Selective. On the paper, take two passes: first everything you can solve in about a minute, from any chapter; then the marked questions, closest first. Whatever is left at the end gets an answer only if you can rule out an option.

Start with the 5 cornerstone chapters

969 questions — 46% of the bank — across 5 chapters. No good score is possible without them.

Drill the 969 cornerstone questionsBrowse all CDS Maths