FAA Mathematics — Analysis & Syllabus Mapping (2022 + 2024)
🔢 FAA MATHEMATICS — Analysis & Mapping
Section: Mathematics · 10 of 120 marks · 10 syllabus topics Papers analysed: 2024 (Q81–Q90) and 2022 (Q32, Q37 only — see the caveat below)
🚨 THE HEADLINE FINDING
The same structure as the Statistics section. Two sections, same design: 10 topics, 10 marks, one question each, sequentially.
| Q | Syllabus topic | Asked |
|---|---|---|
| 81 | (i) Simple / Compound interest | Simple interest on a 9-month loan |
| 82 | (ii) Linear equations in two variables | Restaurant word problem |
| 83 | (iii) Permutations / Combinations & Binomial | Four statements to judge |
| 84 | (iv) Limits & Derivatives | Four statements to judge |
| 85 | (v) Set Theory | Interval sets, find D |
| 86 | (vi) Relations and Functions | Matching pairs |
| 87 | (vii) Matrices & Determinants | Matching pairs |
| 88 | (viii) Probability | Order four events by probability |
| 89 | (ix) Coordinate & 3-D Geometry | Area of a triangle in 3-D |
| 90 | (x) Vectors | Unit vector, opposite direction |
What this means
Maths is as predictable as Statistics. You know exactly how many questions come from each topic — one — and probably in what order. No topic can be skipped; no topic needs depth beyond one question.
⚠️ 1. Read this before using the 2022 paper
The uploaded 2022 paper is an Accounts Assistant (PANCHAYAT), Series A booklet — a different post with a different structure. Its actual layout is:
| Q1–30 | Q31–40 | Q41–50 | Q51–80 | Q81–110 | Q111–120 |
|---|---|---|---|---|---|
| GK | Statistics + a little Maths | Economics | Computers | Accountancy | Science |
There is no Q81–90 maths block in it — Q81–110 is Accountancy. Only two genuine maths questions exist in the whole paper, both buried in the Q31–40 block: Q32 (Set Theory) and Q37 (Coordinate Geometry).
2022-paper-distribution.md does NOT describe the 2022 paper — do not trust it for Maths.That file's own header says it maps a "2020 Question Booklet (Set C, Series 68)". It claims Statistics = Q71–80 and Mathematics = Q81–90.
Proof it is a different paper: it lists Q80 as "Consumer Price Index features", but Q80 in the actual 2022 booklet is "What does IMAP stand for?" (a computers question).
This is the second time this distribution file has been found wrong — see PROJECT-LOG Section 3.5, which recorded the same problem for Accountancy.
✅ Useful side-effect: if that file really does describe a 2020 paper, then a 2020 paper also ran Maths as Q81–90, one question per topic — which independently supports the headline finding.
2. The 10 syllabus topics
| # | Topic |
|---|---|
| (i) | Simple / Compound interest |
| (ii) | Linear equations with two variables |
| (iii) | Permutations / Combinations & Binomial Theorem |
| (iv) | Limits & Derivatives |
| (v) | Set Theory — basic concepts and applications |
| (vi) | Relations and Functions |
| (vii) | Matrices & Determinants |
| (viii) | Probability |
| (ix) | Coordinate & Three-dimensional Geometry |
| (x) | Vectors |
Limits, derivatives, matrices, determinants, 3-D geometry and vectors are +2 level. There is no percentage / profit-loss / time-and-work / ratio content at all. Prepare from NCERT Class 11 and 12, not from a general aptitude book.
3. Mapping — 2024 paper (Q81–Q90) ✅ the real FAA paper
| Q | Topic | Question | Ans |
|---|---|---|---|
| 81 | (i) Interest | Interest on ₹54,000 for 9 months at 8% p.a. | C 3240 |
| 82 | (ii) Linear equations | 2 burgers + 1 drink = ₹70; 1 burger + 2 drinks = ₹50 | B ₹30 / ₹10 |
| 83 | (iii) P & C / Binomial | Which statements are correct (PEPPER, C(20,3), (2+x)³, 3B+3G) | C a and b |
| 84 | (iv) Limits & Derivatives | Which statements are correct | D c and d |
| 85 | (v) Set Theory | A = |x|<1, B = |x−1|≥1, A∪B = ℝ∖D. Find D | A [1, 2) |
| 86 | (vi) Relations & Functions | Match relations to properties | D a-4, b-5, c-1, d-2 |
| 87 | (vii) Matrices & Determinants | Match matrices to determinant values | A a-3, b-1, c-4, d-5 |
| 88 | (viii) Probability | Order four events by increasing probability | C b, a, d, c |
| 89 | (ix) Coordinate & 3-D | Area of triangle A(1,2,3) B(3,2,1) C(2,4,5) | ⚠️ see Section 6 |
| 90 | (x) Vectors | Unit vector opposite to (1, −1) | B −(1/√2)(1,−1) |
Coverage: 10 / 10 topics. Perfect one-to-one. All ten answers were independently re-solved and verified — see Maths-Tagged-Answers.
4. Mapping — 2022 paper (only 2 maths questions)
| Q | Topic | Question | Ans |
|---|---|---|---|
| 32 | (v) Set Theory | Symmetric difference of {1,2,3,4} and {3,4,5,6,7} | D {1,2,5,6,7} |
| 37 | (ix) Coordinate Geometry | Length of segment A(2,2) to B(9,11) | B 11.4 |
Genuine maths coverage: 2 / 10 topics.
5. Combined topic frequency
| # | Topic | 2022 | 2024 | Total |
|---|---|---|---|---|
| (v) | Set Theory | 1 | 1 | 2 ⭐ |
| (ix) | Coordinate & 3-D Geometry | 1 | 1 | 2 ⭐ |
| (i) | Simple / Compound interest | — | 1 | 1 |
| (ii) | Linear equations | — | 1 | 1 |
| (iii) | Permutations / Combinations & Binomial | — | 1 | 1 |
| (iv) | Limits & Derivatives | — | 1 | 1 |
| (vi) | Relations & Functions | — | 1 | 1 |
| (vii) | Matrices & Determinants | — | 1 | 1 |
| (viii) | Probability | — | 1 | 1 |
| (x) | Vectors | — | 1 | 1 |
⭐ Set Theory and Coordinate Geometry are the only two topics that appeared in BOTH papers — the two safest bets.
Probability appears in BOTH syllabi — Statistics topic (vi) and Maths topic (viii) — and both papers asked it in both sections:
- 2024: Q76 (statistics) and Q88 (maths)
- 2022: Q34 (statistics)
One body of theory, two marks. It is the highest marks-per-hour topic in either section. Study it once, get paid twice. See Notes-Statistics.md Topic (vi).
6. ⚠️ Two errors found in the 2024 paper
Area of the triangle with A(1,2,3), B(3,2,1), C(2,4,5): AB = (2, 0, −2) · AC = (1, 2, 2) · AB × AC = (4, −6, 4) |AB × AC| = √68 → Area = ½√68 = √17 ≈ 4.123
| Option | Value |
|---|---|
| A) √20 | 4.472 |
| B) √23 | 4.796 |
| C) √26 | 5.099 |
| D) √29 | 5.385 |
√17 is not among them. The answer key in 2024-paper.md says "D) √29" but hedges it as "as per matching patterns in the official exam set approximations" — i.e. it was guessed, not solved. Treat this question as void. If a question like it appears in 2026, compute ½|AB × AC| and pick the nearest option.
Option a is F = {(x,y): x² + y = 2}, i.e. y = 2 − x², whose range is (−∞, 2]. It is matched to statement 4: "Range of F = [−2, ∞)", which is the range of y = x² − 2 — almost certainly the intended relation.
Answer D is still right by elimination, because b-5, c-1 and d-2 are all certain:
- b) x² + y² = 25 → a circle → not a function (5) ✓
- c) y = 2x + 1 → F∘F = 4x + 3 (1) ✓
- d) y = x² → increasing on (0,∞) but not on ℝ (2) ✓
7. What kind of questions are asked
| Format | 2024 | Note |
|---|---|---|
| Direct calculation | 4 | Q81, Q82, Q85, Q90 |
| ⭐ Multi-statement "which are correct" | 3 | Q83, Q84 — judge four claims independently |
| ⭐ Matching pairs | 2 | Q86, Q87 |
| ⭐ Ordering / ranking | 1 | Q88 — arrange by increasing probability |
Every individual fact tested is easy — simple interest, a 2×2 linear system, det(I) = 1, the derivative of 1/x. But 6 of the 10 questions make you evaluate FOUR separate claims before you can answer. One question = four mini-questions. That is what eats the clock, and it is exactly the same design as the Statistics section. Practise judging statements one at a time. In Q83 and Q84, spotting a single false claim eliminates two options.
Difficulty
| Tier | Questions | Why |
|---|---|---|
| 🟢 Easy (4) | Q81, Q82, Q90, and 2022 Q32 | One-step formula or a 2-variable solve |
| 🟡 Moderate (4) | Q85, Q87, Q88, and 2022 Q37 | Needs a definition applied carefully |
| 🔴 Slow (2) | Q83, Q84, Q86 | Four claims each, spanning several sub-topics |
| ⚫ Void (1) | Q89 | No correct option — see Section 6 |
8. 🔮 Prediction for 15 November 2026
| Topic | Most likely question |
|---|---|
| (i) Interest | ⭐ Simple interest for a part-year (the 9-month form came in 2024); or CI for 2 years |
| (ii) Linear equations | Two-item word problem (prices, ages, digits); condition for no / infinite solutions |
| (iii) P & C / Binomial | Arrangements of a word with repeated letters · ⁿCᵣ committee · a binomial expansion term |
| (iv) Limits & Derivatives | Standard limits (⭐ (eˣ−1)/x → 1, (xⁿ−aⁿ)/(x−a)), the first-principles definition, derivative of 1/x |
| (v) Set Theory ⭐ | Symmetric difference · interval sets with modulus · De Morgan |
| (vi) Relations & Functions | One-one / onto · domain and range · composition f∘f |
| (vii) Matrices & Determinants | ⭐ det(I)=1 · identical rows → 0 · diagonal = product · det(AB)=det(A)det(B) · det(Aᵀ)=det(A) |
| (viii) Probability ⭐ | Cards, dice, coins — also revise this for the Statistics section |
| (ix) Coordinate & 3-D ⭐ | Distance formula (2022) · area of a triangle by ½|AB × AC| (2024) · collinearity |
| (x) Vectors | Unit vector = a/|a|, and the opposite direction is its negative |
Two safest bets: ⭐ Set Theory and ⭐ Coordinate Geometry — the only topics asked in both papers. The one to drill hardest: ⭐ Matrices & Determinants — five separate determinant rules were tested in a single question (Q87), and all five are pure recall.
🔗 Related
- Solved questions with working: Maths-Tagged-Answers
- Probability theory (shared with maths):
Notes-Statistics.md→ Topic (vi) - Statistics equivalent: Statistics-Analysis-and-Mapping
- Papers: 2022-paper · 2024-paper · Overall: FAA-MASTER-PLAN · Home