The IITM qualifier maths important questions come from six topics: polynomials, quadratic functions, straight lines, relations, three-set Venn counting and best-fit lines (SSE). We tagged every question in the five past Maths I qualifier papers on BTechi (63 questions, 240 marks). Polynomials alone carry about a quarter of the marks. The top three topics carry more than 60%. Some questions even come back word for word. Every paper below is also a free Maths 1 qualifier PYQ PDF with the answer key.
This post shows the data, the question types that repeat, four real past-year questions solved step by step (checked against the official answer key), and the exact practice sheet for each topic.
If you are new to the qualifier itself, read our IITM BS qualifier exam guide first. It covers the process, the cut-offs and the four-week plan.
What the Maths I qualifier tests#
Maths I is "Mathematics for Data Science I" (course code BSMA1001). The qualifier covers weeks 1 to 4 only. The official Maths I course page on study.iitm.ac.in lists the full syllabus. For the qualifier, these are the four weeks:
Limits, derivatives, integration and graph theory are also in Maths I. But they come after week 4. In our tagging, not one qualifier question came from those topics. They show up only in Maths I Quiz 1, Quiz 2 and the Maths I end term exam. So do not spend qualifier time on them.
To pass, a General-category candidate needs at least 40% in Maths I and at least 50% average across all four courses. Check the current rules on the official IITM BS admissions page.
The 5 Maths I qualifier papers we analysed#
BTechi has five past Maths I qualifier papers. Each one has the official answer key, and you can sit each one in a timed exam portal.
Across these papers there are 27 numerical answer (NAT) questions, 24 multiple-select (MSQ) questions and 12 single-correct (MCQ) questions. That mix matters. NAT and MSQ make up 51 of 63 questions. You cannot guess your way through them. You must actually solve.
For all Maths I papers in one place (qualifier, quiz and end term), see the Maths I PYQ page. For a full list of qualifier papers for all four courses, see our post on the IITM qualifier previous year question paper with answer key.
Topic weightage: where the marks go#
We tagged each question to one topic. Then we added up the marks per topic across the five papers.
What this tells you:
- Weeks 3 and 4 are worth the most. Quadratics plus polynomials give 107 of 240 marks (about 45%). Many students spend too long on sets in week 1 and rush the last two weeks. Do the opposite.
- Polynomials are mostly graph reading. You get a graph and must judge statements about roots, multiplicity, turning points and end behaviour. This is a skill, not a formula. It needs practice on many graphs.
- No topic is safe to skip. Even the smallest real topic (SSE) has 17 marks. That is a lot when you need 40% to pass.
The most repeated question types#
Topics tell you what to study. Question types tell you what the examiner will actually ask. These are the types that came up in two or more of the five qualifier papers.
The Maths I most repeated PYQs sheet puts every repeated type in one printable sheet. It has 112 questions (377 marks) from all 11 Maths I papers on BTechi, with the official answer key at the end. Print it and solve it on paper.
Solved IITM qualifier maths important questions#
These are four real questions from past qualifier papers. Each final answer matches the official answer key in the paper data on BTechi.
Solved example 1: three-set Venn counting (May 2024, Q6, 4 marks)#
Question. 500 candidates applied for a data analyst post. 285 know Python, 195 know C, 115 know Java. 45 know Python and Java, 70 know C and Python, 50 know C and Java. 50 candidates know none of the three. How many know exactly one language?
Solution.
- At least one language = 500 − 50 = 450.
- Use inclusion-exclusion: 450 = (285 + 195 + 115) − (45 + 70 + 50) + x, where x = all three.
- 450 = 595 − 165 + x = 430 + x, so x = 20.
- Exactly two: Python and C only = 70 − 20 = 50. Python and Java only = 45 − 20 = 25. C and Java only = 50 − 20 = 30.
- Exactly one: Python only = 285 − 50 − 25 − 20 = 190. C only = 195 − 50 − 30 − 20 = 95. Java only = 115 − 25 − 30 − 20 = 40.
- Answer: 190 + 95 + 40 = 325. The official key says 325.
Why students lose marks here: they add 285 + 195 + 115 and subtract the pair counts, but forget that each pair count already includes the "all three" group. Always fill the centre first.
Try more on the sets and Venn diagram topic sheet. The January 2024 paper has a two-part version (60 grocery customers; answers 11 and 2).
Solved example 2: relations (May 2024, Q1 to Q3)#
Question. A is the set of even positive integers up to 20. B is the set of positive integers less than 20 that are divisible by 6. Two relations from A to B:
- R₁ = {(a, b) : a is a factor of b}
- R₂ = {(a, b) : (a + b) mod 10 = 0}
Find the cardinality of R₁ ∩ R₂ (3 marks), the cardinality of R₁ (2 marks), and which statements are true (3 marks): R₁ is transitive; R₂ is transitive; R₂ is not symmetric; (2, 18) is in R₂.
Solution.
- Write the sets first. A = {2, 4, 6, ..., 20}. B = {6, 12, 18}.
- List R₁. For b = 6: a = 2, 6. For b = 12: a = 2, 4, 6, 12. For b = 18: a = 2, 6, 18. So |R₁| = 9.
- List R₂. For b = 6: a = 4, 14. For b = 12: a = 8, 18. For b = 18: a = 2, 12. So R₂ has 6 pairs.
- R₁ ∩ R₂. The only pair in both lists is (2, 18). So |R₁ ∩ R₂| = 1.
- Statements. R₁ is transitive, because "is a factor of" is transitive. R₂ is not transitive: (2, 18) and (18, 12) are in R₂, but (2, 12) is not, since 2 + 12 = 14. R₂ is not symmetric: (2, 18) is in R₂ but (18, 2) is not, since 2 is not in B. And (2, 18) is in R₂ because 20 mod 10 = 0.
- Correct statements: R₁ is transitive, R₂ is not symmetric, (2, 18) is in R₂.
Official key: 1, 9, and options 1, 3 and 4. All match.
The habit that wins: write every relation as a list of pairs. Then test each property against the list. Reasoning from the rule alone is where mistakes happen. Practise this on the relations and functions topic sheet.
Solved example 3: straight lines (January 2024, Q6 and Q7, 3 marks each)#
Question. Lines L₁ and L₂ have x-intercepts 2 and −1, and y-intercepts −3 and 2. Find where they meet, and find tan θ, where θ is the angle between them.
Solution.
- Intercepts are points. L₁ passes through (2, 0) and (0, −3). Slope m₁ = (−3 − 0) / (0 − 2) = 3/2. Equation: y = 1.5x − 3.
- L₂ passes through (−1, 0) and (0, 2). Slope m₂ = (2 − 0) / (0 + 1) = 2. Equation: y = 2x + 2.
- Intersection: 1.5x − 3 = 2x + 2, so −0.5x = 5 and x = −10. Then y = 2(−10) + 2 = −18. The point is (−10, −18).
- tan θ = |(m₂ − m₁) / (1 + m₁m₂)| = |(2 − 1.5) / (1 + 3)| = 0.5 / 4 = 1/8.
Official key: (−10, −18) and 1/8. Both match.
The May 2024 paper asked the same two types with different numbers (its tan θ answer is 5/7). The straight lines topic sheet has 16 questions like this.
Solved example 4: polynomial word problem (January 2023, Q8, 5 marks)#
Question. A company starts in 2010. Its yearly profit (in lakhs) is p(x) = 0.1x²(x − 1)(x − 2)(x − 3)²(x − 4)(x − 9), where x is years since 2010. Loss means negative profit. Which are correct?
- (a) Including the launch year, it made neither profit nor loss six times in 12 years.
- (b) It made profit in years x ∈ {7, 8, 10, 11}.
- (c) It made loss in years x ∈ {5, 6, 7, 8}.
- (d) In 2022 (x = 12) it made profit.
Solution.
- Zeros. p(x) = 0 at x = 0, 1, 2, 3, 4, 9. That is six values, all within the 12 years. So (a) is true.
- Sign. x² and (x − 3)² are never negative. So the sign of p(x) depends only on (x − 1)(x − 2)(x − 4)(x − 9).
- For x = 5, 6, 7, 8: the first three brackets are positive and (x − 9) is negative. So p(x) < 0, a loss. (c) is true, and (b) is false, because 7 and 8 are loss years.
- For x = 12: every bracket is positive. Profit. (d) is true.
Official key: (a), (c) and (d). It matches.
The shortcut: squared factors never change the sign. Ignore them when you check profit or loss. This "sign of each bracket" method also solves most graph-reading questions on the polynomials topic sheet.
Download IITM qualifier maths PYQ PDF with answer key#
- Open the question sheet of the paper you want (links below).
- Click the Save PDF button at the top of the sheet. You can also press P on your keyboard.
- In the print window, choose Save as PDF as the destination, then save.
The PDF has every question and figure, and the official answer key at the end. It is free. Print it, or keep it on your phone or tablet.
Want only the important questions as one PDF? Save the Maths 1 most repeated questions PDF. Each full paper as a PDF:
- Maths 1 qualifier May 2024 PDF with answer key
- Maths 1 qualifier January 2024 PDF with answer key
- Maths 1 qualifier September 2023 PDF with answer key
- Maths 1 qualifier May 2023 PDF with answer key
- Maths 1 qualifier January 2023 PDF with answer key
Formulas to know cold for Maths I#
Check the "exactly one" formula on example 1: 595 − 2(165) + 3(20) = 595 − 330 + 60 = 325. Same answer, one line.
The full formula list with more worked examples is in our free Maths I cheat notes for the qualifier.
How to practise these important questions#
A plan that uses the data above. It fits in the four qualifier weeks, or in two weeks before the exam if you are revising.
- Read the notes for one week's topics. Use the Maths I cheat notes and your lecture notes.
- Solve the matching topic sheet on paper. Sets in week 1, lines in week 2, and so on. Use the topic sheet links in the table above.
- Check with the answer key at the end of the sheet. For every wrong answer, write one line: what was the mistake?
- After week 4, solve the most repeated sheet. The Maths I most repeated PYQs sheet is your best single revision document.
- Sit full papers under time. Start with the January 2023 Maths I qualifier paper and end with the May 2024 Maths I qualifier paper. BTechi gives each Maths I paper 60 minutes. You can also pick papers from the qualifier practice portal for Maths I.
- Finish with a full four-course paper. The real exam has all four courses in one sitting. Try the full May 2024 qualifier paper or the January 2024 full qualifier paper, then the qualifier mock test 1 and mock test 2.
If you like printing by year instead of by topic, use the Maths I 2023 PYQ sheet and the Maths I 2024 PYQ sheet. All printable sheets for the course are on the Maths I sheets page.
Mistakes that cost marks in Maths I#
Common ways students lose marks in the Maths I papers:
- MSQ partial thinking. In multiple-select questions, judge each option alone, as true or false. Do not stop after you find one true option.
- Relations across two sets. When R is from A to B, symmetry needs (b, a) to be a valid pair too. If b is not in A, the pair cannot exist.
- Intercept confusion. "x-intercept 2" means the point (2, 0). "y-intercept −3" means (0, −3). Write the point down first.
- Even multiplicity. A root with an even power touches the x-axis and turns back. It does not cross. Graph questions test this almost every time.
- Numerical answer format. Some NAT questions ask you to type option numbers joined together (May 2023 Q1 and Q2 did this). Read the instruction twice.
Where Maths I fits in the qualifier#
Maths I is one of four courses. You need 40% in each and 50% average. A strong Maths I score helps your average, but it cannot save a weak course. Our companion post on IITM qualifier stats important questions does the same analysis for Stats I. To see every course and level in one place, read the IIT Madras BS data science PYQ guide or browse the Foundation level PYQs.
Planning to join the next batch? The IIT Madras BS admission guide for January 2027 has the dates. Applications for the January 2027 batch close on 29 January 2027.
Frequently asked questions#
What are the most important topics for the IITM qualifier maths exam?#
Polynomials (25.4% of marks), quadratic functions (19.2%) and straight lines (17.1%), based on our tagging of five past Maths I qualifier papers. Relations, three-set Venn diagrams and best-fit lines (SSE) come next. All six appear in almost every paper.
Where can I download the IITM qualifier maths important questions PDF?#
BTechi gives every Maths I qualifier paper as an online paper with the official answer key. It also gives printable sheets: open any Maths I PYQ sheet click Save PDF (or press P) and choose Save as PDF. For the important questions only, save the Maths I most repeated questions sheet as a PDF. The answer key is at the end of each sheet.
Are IITM qualifier maths questions repeated?#
Yes. Question types repeat often: three-set counting, polynomial graphs and relation properties each appeared in four of five papers. One full question (the 500-candidates Python, C and Java problem) appeared in both May 2023 and May 2024 with the same numbers.
Do I need calculus for the IITM qualifier?#
No. The qualifier covers weeks 1 to 4 only: sets, relations, functions, straight lines, quadratics and polynomials. In five past qualifier papers, no question came from limits, derivatives or integrals. Those topics come later in Maths I.
How many questions are in the Maths I qualifier paper?#
The five papers on BTechi have 10 to 14 Maths I questions each, worth 40 to 50 marks. Most are numerical answer or multiple-select questions. The exact count and marking can change, so read the instructions on exam day.
Is the answer key for the Maths I qualifier PYQ official?#
Yes. The answers on BTechi are from the official answer keys of the IIT Madras BS papers. Where a numerical answer accepts a range, the range is shown.
How many days should I spend on Maths I important questions?#
There is no fixed number. A practical approach: solve one topic sheet after each week's lectures, then the most repeated sheet and two full papers in the last week. Spend more time on polynomials and quadratics, since they carry the most marks.