The polytechnic maths question paper in BTEUP means two subjects: Mathematics-I in the first semester and Mathematics-II in the second. Each is a 60-mark, 3-hour theory paper with 40 internal marks. Because these papers are common to all branches, a strong maths score lifts every diploma student’s first-year percentage.
This guide breaks down both papers using the revised 2024-25 syllabus. You will find unit weightage, a formula table, practice questions and a simple plan for scoring well.
Key Takeaways
- Two papers: Mathematics-I (Semester 1) and Mathematics-II (Semester 2).
- Marks: 60 external theory + 40 internal = 100 for each paper.
- Top unit in Maths-I: Differential Calculus, about 25% of the marks.
- Top unit in Maths-II: Differential Equations and Numerical Methods, about 25%.
- Common to all branches: the same paper for Civil, Mechanical, Electrical and CS.
- Step marks matter: always show working, even for short questions.
Polytechnic Maths Question Paper — Marks at a Glance
The BTEUP study and evaluation scheme gives both maths subjects 3 lecture periods and 1 tutorial period every week. Each subject also carries 4 credits.
| Detail | Mathematics-I | Mathematics-II |
|---|---|---|
| Semester | 1st | 2nd |
| Periods per week | 3 lecture + 1 tutorial | 3 lecture + 1 tutorial |
| Credits | 4 | 4 |
| External theory paper | 60 marks, 3 hours | 60 marks, 3 hours |
| Internal assessment | 40 marks | 40 marks |
| Practical | None | None |
| Total | 100 | 100 |
Since there is no practical, your entire maths score rests on the theory paper and internal tests. So a weak internal score is hard to recover later.
Mathematics-I Units and Weightage
The table converts the syllabus percentages into approximate marks out of 60.
| Unit | Topic | Periods | Weight | Approx. marks |
|---|---|---|---|---|
| I | Trigonometry | 10 | 15% | 9 |
| II | Differential Calculus | 14 | 25% | 15 |
| III | Partial Fractions | 10 | 20% | 12 |
| IV | Permutations, Combinations and Binomial Theorem | 10 | 20% | 12 |
| V | Complex Numbers | 12 | 20% | 12 |
What Each Mathematics-I Unit Covers
- Trigonometry: angle measurement in degrees, grades and radians; allied angles; sum, difference and product formulae; multiple and sub-multiple angles (2A, 3A, A/2); graphs of |x|, sin x, cos x, tan x and eˣ.
- Differential Calculus: functions and limits, four standard limits, derivatives from first principles, sum, product and quotient rules, chain rule, inverse trigonometric functions and logarithmic differentiation.
- Partial Fractions: proper and improper fractions with non-repeated linear, repeated linear and irreducible quadratic factors.
- Permutations, Combinations and Binomial Theorem: ⁿPᵣ and ⁿCᵣ problems, binomial expansion for positive integral index, general term and expansion for any index.
- Complex Numbers: real and imaginary parts, Cartesian and polar forms, conjugate, modulus and amplitude, and De Moivre’s theorem.
Mathematics-II Units and Weightage
Mathematics-II builds directly on calculus from the first semester.
| Unit | Topic | Periods | Weight | Approx. marks |
|---|---|---|---|---|
| I | Determinants and Matrices | 10 | 20% | 12 |
| II | Integral Calculus | 12 | 20% | 12 |
| III | Differential Equations and Numerical Methods | 15 | 25% | 15 |
| IV | Two-Dimensional Coordinate Geometry | 10 | 20% | 12 |
| V | Vector Algebra | 9 | 15% | 9 |
What Each Mathematics-II Unit Covers
- Determinants and Matrices: properties up to third order, Cramer’s rule, matrix operations and the inverse method for linear equations.
- Integral Calculus: substitution, integration by parts and by partial fractions, definite integrals, plus area and volume of revolution.
- Differential Equations and Numerical Methods: order and degree, variable-separable equations, the trapezoidal rule and Simpson’s rule. The syllabus also introduces MATLAB.
- Coordinate Geometry: straight lines, circles and conic sections.
- Vector Algebra: vector notation, resolution, dot product, cross product and simple applications such as work done.
Section Pattern of the Polytechnic Maths Question Paper
BTEUP’s evaluation strategy suggests three sections for end-term theory papers. The actual paper may differ slightly, but this blueprint matches the guideline.
| Section | Question type | Suggested share | Approx. marks | Choice |
|---|---|---|---|---|
| I | Objective — MCQ, matching, fill in the blanks | About 20% | 12 | None |
| II | Short-answer problems | About 40% | 24 | None |
| III | Two to three long problems | About 40% | 24 | Internal choice in about half |
As a result, every unit can appear in Sections I and II. Section III then rewards the long, multi-step topics: calculus, matrices and differential equations.
Must-Know Formulas for Polytechnic Maths
Keep this table on your desk during revision. These formulas appear again and again in each polytechnic maths question paper.
| Area | Formula |
|---|---|
| Trigonometry | sin 2A = 2 sin A cos A; cos 2A = cos²A − sin²A |
| Trigonometry | sin 3A = 3 sin A − 4 sin³A; cos 3A = 4 cos³A − 3 cos A |
| Limits | lim (x→0) sin x / x = 1; lim (x→0) (aˣ − 1)/x = logₑ a |
| Derivatives | d/dx (xⁿ) = n xⁿ⁻¹; d/dx (eˣ) = eˣ; d/dx (log x) = 1/x |
| Product rule | d/dx (uv) = u v′ + v u′ |
| Combinations | ⁿCᵣ = n! / [r! (n − r)!]; ⁿPᵣ = n! / (n − r)! |
| Complex numbers | (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ (De Moivre) |
| Integration by parts | ∫u v dx = u ∫v dx − ∫[u′ ∫v dx] dx |
| Simpson’s 1/3 rule | (h/3)[y₀ + yₙ + 4(odd ordinates) + 2(even ordinates)] |
| Straight line | Slope-intercept form: y = mx + c |
| Vectors | a · b = |a| |b| cos θ |
Practice Questions for the Polytechnic Maths Question Paper
We wrote these practice questions from the official unit list. They are not copied from a board paper. Solve them in exam conditions to check your speed.
Mathematics-I Practice Set
- Convert 150° into radians.
- Prove that sin 3A = 3 sin A − 4 sin³A.
- Evaluate lim (x→0) (sin 5x)/x.
- Differentiate y = x² sin x with respect to x.
- Resolve (x + 3)/[(x − 1)(x + 2)] into partial fractions.
- Find the value of ⁸C₃ and ⁶P₂.
- Write the general term in the expansion of (2x + 3)⁶.
- Express 1 + i√3 in polar form.
Mathematics-II Practice Set
- Solve by Cramer’s rule: x + y = 5 and 2x − y = 1.
- Evaluate ∫ x eˣ dx.
- Find the area under y = x² between x = 0 and x = 3.
- Solve dy/dx = x/y.
- Use the trapezoidal rule with four strips to estimate ∫₀¹ x² dx.
- Find the equation of the circle with centre (2, −3) and radius 5.
- Find the dot product of a = 2i + 3j − k and b = i − j + 4k.
Six-Week Plan to Score in the Maths Papers
Maths needs daily practice rather than a final-week rush. This plan follows the unit weightage.
| Week | Mathematics-I focus | Mathematics-II focus |
|---|---|---|
| 1 | Trigonometry formulae | Determinants and Cramer’s rule |
| 2 | Limits and derivatives | Matrices and inverse method |
| 3 | Partial fractions | Integration methods |
| 4 | Permutations, combinations, binomial | Differential equations and numerical methods |
| 5 | Complex numbers and De Moivre | Coordinate geometry and vectors |
| 6 | Three full timed papers | Three full timed papers |
Additionally, solve ten mixed problems every day from your weakest unit. Mark every mistake in a separate notebook and revisit it on Sundays.
Common Mistakes in the Maths Paper
- Skipping steps: examiners give step marks, so write every line of working.
- Sign errors in integration: check the sign after every substitution.
- Wrong mode on the calculator: switch between degree and radian mode carefully.
- Ignoring units: area and volume answers need square or cubic units.
- Leaving Section I blank: objective items are quick marks, so attempt all of them.
Where to Find Previous Polytechnic Maths Papers
Start with the official revised first-year syllabus PDF on bteup.ac.in, so you know the exact topic list. Next, ask your institute library and maths faculty for recent papers.
You can also read our guide to BTEUP previous year question papers for more sources. Moreover, URISE e-content sometimes includes question banks; our URISE student login guide shows how to access them.
How Maths Fits Into Your First-Year Result
Mathematics-I sits beside Applied Physics-I, Applied Chemistry and the polytechnic English question paper in Semester 1. In Semester 2, Mathematics-II joins Applied Physics-II and Engineering Mechanics.
Because maths has no practical cushion, it often decides your overall division. After results, check your marks on the BTEUP 1st semester result page. You can also convert grades with the BTEUP CGPA to percentage converter.
Final Word on the Polytechnic Maths Question Paper
The polytechnic maths question paper rewards steady practice. Calculus, complex numbers and differential equations carry the biggest share across both semesters. So learn the formulas, show every step and finish at least three timed papers before the exam.
For more exam help, browse BTEUP student help or visit the BTEUP.net homepage.
Source: BTEUP NEP-aligned first-year curriculum (2024-25), approved by the CDC on 3 September 2024. Always confirm the latest notices on bteup.ac.in.
Frequently Asked Questions
How many marks is the polytechnic maths question paper?
Both Mathematics-I and Mathematics-II carry a 60-mark external theory paper of 3 hours. Each subject also has 40 internal marks, so the total for each paper is 100 marks. Neither subject has a practical.
Which chapters are in Mathematics-I for polytechnic 1st semester?
Mathematics-I has five units: Trigonometry, Differential Calculus, Partial Fractions, Permutations-Combinations with the Binomial Theorem, and Complex Numbers. Differential Calculus carries the highest share at about 25% of the marks.
Which chapters are in Mathematics-II for the 2nd semester?
Mathematics-II covers Determinants and Matrices, Integral Calculus, Differential Equations with Numerical Methods, Two-Dimensional Coordinate Geometry and Vector Algebra. Differential Equations and Numerical Methods carry about 25% of the marks.
Is the polytechnic maths question paper the same for all branches?
Yes. Under the BTEUP curriculum revised from session 2024-25, the first and second semesters are common to all engineering and technology branches. Therefore, Civil, Mechanical, Electrical and Computer Science students write the same maths papers.
Which book is best for the polytechnic maths question paper?
The official syllabus recommends B.S. Grewal’s Higher Engineering Mathematics, Reena Garg’s Engineering Mathematics and S.S. Sabharwal and Sunita Jain’s Applied Mathematics. Start with your class notes and then practise extra problems from one of these books.
How can I score 50+ in the polytechnic maths question paper?
Master differentiation and integration first, because they appear across several units. Next, revise a formula sheet daily. Finally, solve at least three full timed papers and show every step, since examiners award step marks.
Are old polytechnic maths papers still useful?
Yes, mostly. Topics like trigonometry, calculus, determinants and coordinate geometry have stayed stable. However, check each question against the revised unit list, because some older chapters have moved or changed.
