BCS 12 Solved Guess Paper 2026 is a 25-page answer booklet built for students sitting the Basic Mathematics Term-End Examination. It holds 13 questions with complete worked solutions, drawn from a session-by-session reading of five past IGNOU papers. Five of those 13 questions are printed in full on this page, solutions included, so you can judge the working before you enquire about the rest.
Basic Mathematics is the paper that decides how many BCA first-semester students clear their semester in one attempt. The syllabus is not difficult, but it is wide, and the marks sit in the steps rather than the final number. This booklet is written for that reality: every answer carries the definition line, the substitution, the intermediate algebra and the closing statement an evaluator looks for.
BCS 12 Basic Mathematics: key facts at a glance
- Course code: BCS-012, commonly written as BCS 12
- Course title: Basic Mathematics
- Programme: Bachelor of Computer Applications (Revised), BCA, Semester 1
- Syllabus size: 4 blocks, 16 units
- Exam duration and marks: 3 hours, 100 marks
- Paper pattern: Question 1 compulsory, then any three from Questions 2 to 5
- Questions in this booklet: 13 solved, of which 5 are shown on this page and 8 are in the file
- Booklet length: 25 pages
- Prepared for: December 2026 Term-End Examination
- Enquiry number: WhatsApp 9899436384
What the BCS 12 Solved Guess Paper Covers for Basic Mathematics
The booklet contains 13 solved questions spread across all four blocks of Basic Mathematics, printed over 25 pages, with full working shown for every one. There are no hints, no half-answers and no "refer to the textbook" lines. Whatever the question asks for, the answer supplies it in the order an evaluator reads it.
Coverage is deliberately weighted rather than even. Block 1 and Block 2 take the largest share because Question 1 of the BCS 12 paper is compulsory and historically leans on determinants, matrices, induction, progressions and quadratic roots. Calculus and vectors follow, since those blocks feed the 20-mark questions you choose between. Nothing in the booklet sits outside the official syllabus.
Each answer is set out the same way. The relevant definition or formula opens on its own line, the given values are substituted next, the algebra runs step by step, and a one-line conclusion closes it. That structure exists because BCS 12 is marked on method. A correct method with a slipped sign still earns most of the marks, while a correct number with no visible working often does not.
The same editorial standard runs through every course code in our IGNOU Solved Guess Paper collection, so if you are taking more than one paper this semester the format will already be familiar to you.
Sample Questions With Answers From the BCS 12 Basic Mathematics Guess Paper
Five of the 13 questions are reproduced below in full, with their complete solutions, one from each block plus the compulsory determinant question. Read the working rather than the answers. The point of these samples is to let you check the depth of the solutions before you ask for the file.
Properties of determinants, area of a triangle and the collinearity condition
Question: (a) State any five properties of determinants. (b) Using determinants, find the area of the triangle whose vertices are A(1, 4), B(2, 3) and C(-5, -3). Also derive the condition for three points to be collinear.
Answer.
(a) Five properties. One, if any two rows or columns are interchanged, the sign of the determinant changes. Two, if two rows or two columns are identical, the determinant is zero. Three, if every element of a row or column is multiplied by a constant k, the determinant is multiplied by k.
Four, if each element of a row or column is written as the sum of two terms, the determinant splits into the sum of two determinants. Five, adding a multiple of one row or column to another leaves the value unchanged.
(b) For vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃), the area is one half the modulus of the determinant with rows (x₁ y₁ 1), (x₂ y₂ 1) and (x₃ y₃ 1). Substituting A(1, 4), B(2, 3) and C(-5, -3) and expanding along the first row gives Β½[1(3 + 3) - 4(2 + 5) + 1(-6 + 15)] = Β½(6 - 28 + 9) = Β½(-13).
Taking the modulus, the area of the triangle is 13/2 square units.
For collinearity, three points that lie on one straight line enclose a triangle of zero area. Setting the same expression to zero gives the condition: the determinant with rows (x₁ y₁ 1), (x₂ y₂ 1) and (x₃ y₃ 1) equals 0. That single determinant equation is the collinearity condition, and stating it in this form is what the 20-mark version of this question is looking for.
Proving a summation identity for powers of 2 by induction
Question: Use the principle of mathematical induction to show that 1 + 2 + 2Β² + ... + 2βΏβ»ΒΉ = 2βΏ - 1 for every natural number n.
Answer.
Let P(n) be the statement 1 + 2 + 2Β² + ... + 2βΏβ»ΒΉ = 2βΏ - 1.
Base step. For n = 1, the left side is 1 and the right side is 2ΒΉ - 1 = 1. The two sides agree, so P(1) is true.
Induction hypothesis. Assume P(k) is true for some natural number k, that is, 1 + 2 + 2Β² + ... + 2α΅β»ΒΉ = 2α΅ - 1.
Inductive step. Add the next term 2α΅ to both sides. The left side becomes 1 + 2 + 2Β² + ... + 2α΅β»ΒΉ + 2α΅, which by the hypothesis equals (2α΅ - 1) + 2α΅ = 2Β·2α΅ - 1 = 2α΅βΊΒΉ - 1. That is exactly P(k + 1).
Since P(1) holds and P(k) implies P(k + 1), by the principle of mathematical induction the result is true for every natural number n. Note that the marks here sit in naming the three steps explicitly. Students who merge the hypothesis into the inductive step routinely lose two to three marks even with correct algebra.
A.P. term relation and the sum of an infinite G.P.
Question: (a) If 7 times the 7th term of an A.P. equals 11 times its 11th term, show that the 18th term of the A.P. is zero. (b) Find the sum of an infinite G.P. whose first term is 15 and fourth term is 3/25.
Answer.
(a) Let the first term be a and the common difference d, so Tβ = a + (n - 1)d. Then Tβ = a + 6d and Tββ = a + 10d. The given condition is 7(a + 6d) = 11(a + 10d), which expands to 7a + 42d = 11a + 110d, so 4a + 68d = 0, and dividing by 4 gives a + 17d = 0.
Now Tββ = a + (18 - 1)d = a + 17d = 0. Hence the 18th term is zero, as required.
(b) For the G.P., a = 15 and Tβ = arΒ³ = 3/25. So 15rΒ³ = 3/25, giving rΒ³ = 3/375 = 1/125 and therefore r = 1/5. Since the modulus of r is less than 1, the infinite sum exists.
Sβ = a/(1 - r) = 15/(1 - 1/5) = 15/(4/5) = 75/4. The sum of the infinite G.P. is 75/4. A frequent error here is solving for r without checking that its modulus is under 1, which is the condition that makes the infinite sum formula usable at all.
Local maxima and minima of a cubic
Question: Determine the points of local maxima and local minima of f(x) = xΒ³ - 6xΒ² + 9x + 100.
Answer.
Differentiating, f'(x) = 3xΒ² - 12x + 9 = 3(xΒ² - 4x + 3) = 3(x - 1)(x - 3). Setting f'(x) = 0 gives the critical points x = 1 and x = 3.
Differentiating again, f''(x) = 6x - 12.
At x = 1, f''(1) = 6 - 12 = -6, which is negative, so f has a local maximum there. The value is f(1) = 1 - 6 + 9 + 100 = 104, giving the local maximum point (1, 104).
At x = 3, f''(3) = 18 - 12 = 6, which is positive, so f has a local minimum there. The value is f(3) = 27 - 54 + 27 + 100 = 100, giving the local minimum point (3, 100).
Write both as coordinate pairs, not as bare x values. The question asks for points, and answers that stop at x = 1 and x = 3 are routinely marked down by half even though the calculus is correct.
Formulating and solving a two-variable LPP
Question: Kiaan wants to buy colour boxes and books to donate to an orphanage. He wishes to buy at least 4 books and 4 colour boxes. A colour box costs βΉ200 and a book costs βΉ400. How many of each should he buy so that expenditure does not exceed βΉ4000 and he buys the maximum number of items?
Answer.
Let x be the number of colour boxes and y the number of books. The constraints are x β₯ 4, y β₯ 4 and 200x + 400y β€ 4000, which simplifies on dividing by 200 to x + 2y β€ 20. Also x β₯ 0 and y β₯ 0. The objective is to maximise Z = x + y, the total number of items.
The feasible region is bounded by x = 4, y = 4 and x + 2y = 20, giving corner points A(4, 4), B(12, 4) and C(4, 8).
Evaluating Z at each corner: at A(4, 4), Z = 8; at B(12, 4), Z = 16; at C(4, 8), Z = 12. The maximum value of Z is 16 at the point (12, 4).
Kiaan should buy 12 colour boxes and 4 books. Checking the budget, 200(12) + 400(4) = βΉ4000, which meets the limit exactly. The corner point table is worth around 3 marks on its own, so write it out even when the graph makes the answer obvious.
Those five give you a fair view of the booklet's standard. The remaining 8 solved questions cover matrix operations, the inverse by elementary row operations, cube roots of unity with De Moivre's theorem, quadratic root formation, modulus inequalities, limits and higher-order derivatives, integration with area and arc length, and vectors with shortest distance in three dimensions.
Want the other 8 solved answers? WhatsApp 9899436384 with your course code and session.
Enquire on WhatsApp 9899436384Complete Question Index of the BCS 12 Basic Mathematics Guess Paper Booklet
Here is the full index of all 13 questions in the booklet, with the 5 shown above marked as samples and the 8 remaining marked as inside the file. Nothing is hidden from the index. You can see the exact topic list before deciding whether the paper suits your revision.
| Q. No. | Topic covered | Block and unit | Marks | Status |
|---|---|---|---|---|
| Q1 | Five properties of determinants, area of a triangle from vertices, collinearity condition | Block 1, Unit 1 | 20 | Sample shown above |
| Q2 | Verifying that A satisfies AΒ² - 4A - 5Iβ = Oβ for a 3Γ3 matrix, Cayley-Hamilton style | Block 1, Unit 2 | 10 | Inside the file |
| Q3 | Finding the inverse of a 3Γ3 matrix using elementary row operations on the augmented form | Block 1, Unit 3 | 10 | Inside the file |
| Q4 | Proving a summation identity for powers of 2 by mathematical induction | Block 1, Unit 4 | 10 | Sample shown above |
| Q5 | Products involving cube roots of unity, plus De Moivre's theorem applied to (β3 + i)Β³ | Block 2, Unit 2 | 5 + 5 | Inside the file |
| Q6 | A.P. term relation proving the 18th term is zero, and sum of an infinite G.P. | Block 2, Unit 1 | 10 + 10 | Sample shown above |
| Q7 | Forming a new quadratic whose roots are Ξ±Β²/Ξ² and Ξ²Β²/Ξ± from a given equation | Block 2, Unit 3 | 10 | Inside the file |
| Q8 | Solving a modulus inequality and representing the closed solution set on a number line | Block 2, Unit 4 | 10 | Inside the file |
| Q9 | Formulating and solving a two-variable LPP by the graphical corner point method | Block 4, Unit 4 | 10 | Sample shown above |
| Q10 | Evaluating a limit by rationalisation, and proving a second-order derivative identity | Block 3, Unit 1 | 10 + 10 | Inside the file |
| Q11 | Locating local maxima and minima of a cubic using the second derivative test | Block 3, Unit 2 | 10 | Sample shown above |
| Q12 | Integration by substitution, and finding the length of a straight-line curve between two points | Block 3, Units 3 and 4 | 10 + 10 | Inside the file |
| Q13 | Scalar and vector products, coplanarity to find Ξ», and shortest distance between two skew lines | Block 4, Units 2 and 3 | 10 + 10 | Inside the file |
Note that BCS 12 is a theory paper with no practical file or lab record attached to it. The lab component in BCA Semester 1 sits under BCSL-013, a separate course code with its own submission. Anything you read elsewhere about a BCS 12 practical file is a mix-up between the two codes.
BCS 12 Basic Mathematics Syllabus Blocks and Units at a Glance
BCS 12 Basic Mathematics is organised into 4 blocks holding 16 units in total, and the guess paper draws from every one of the four blocks. The table below lists each unit with its actual content and shows where that unit surfaces in the booklet.
| Block | Unit | Key topics in this unit | Guess paper question |
|---|---|---|---|
| Block 1: Algebra-I | Unit 1: Determinants | Determinants of order 2 and 3, properties, evaluation, area of a triangle, Cramer's rule | Q1 |
| Block 1: Algebra-I | Unit 2: Matrices-I | Definition and equality of matrices, addition and multiplication, adjoint and inverse of a matrix | Q2 |
| Block 1: Algebra-I | Unit 3: Matrices-II | Homogeneous and non-homogeneous systems, elementary row operations, rank of a matrix | Q3 |
| Block 1: Algebra-I | Unit 4: Mathematical Induction | Principle of induction, base and inductive steps, summation and divisibility proofs | Q4 |
| Block 2: Algebra-II | Unit 1: Sequence and Series | A.P., G.P., H.P. and A.G.P., nth term and sums, sum to infinity, limit of a sequence | Q6 |
| Block 2: Algebra-II | Unit 2: Complex Numbers | a + ib form, conjugate and modulus, cube roots of unity, De Moivre's theorem | Q5 |
| Block 2: Algebra-II | Unit 3: Equations | Quadratic equations, nature of roots, relation between roots and coefficients, forming equations | Q7 |
| Block 2: Algebra-II | Unit 4: Inequalities | Linear and quadratic inequalities, modulus inequalities, solution sets on the number line | Q8 |
| Block 3: Calculus | Unit 1: Differential Calculus | Limits, continuity at a point, differentiation rules, parametric functions, second-order derivatives | Q10 |
| Block 3: Calculus | Unit 2: Simple Application of Differential Calculus | Increasing and decreasing functions, maxima and minima, rate of change and related rates | Q11 |
| Block 3: Calculus | Unit 3: Integration | Integration by substitution and by parts, standard forms, definite integrals | Q12 (a) |
| Block 3: Calculus | Unit 4: Application of Integral Calculus | Area under a curve, area between two curves, length of a curve | Q12 (b) |
| Block 4: Vectors and Three Dimensional Geometry | Unit 1: Vectors-I | Vectors and scalars, magnitude and direction, scalar multiplication, position vector, section formula | Q13 (a) basis |
| Block 4: Vectors and Three Dimensional Geometry | Unit 2: Vectors-II | Dot product, cross product, scalar triple product, vector triple product, coplanarity test | Q13 (a) |
| Block 4: Vectors and Three Dimensional Geometry | Unit 3: Three Dimensional Geometry-I | Distance formula, direction cosines and ratios, equation of a line, skew lines and their distance | Q13 (b) |
| Block 4: Vectors and Three Dimensional Geometry | Unit 4: Linear Programming | Constraints and objective function, mathematical formulation, graphical method, feasible region | Q9 |
The block and unit names above follow the official self-learning material hosted on IGNOU's eGyanKosh repository for BCS-012. If you have not yet downloaded the four block PDFs, do that first and keep them beside the guess paper while you revise.
How This BCS 12 Solved Guess Paper Was Built From Past Basic Mathematics Papers
Five Term-End papers were read question by question, every topic was tallied session by session, and only topics that recurred or filled a recent gap were carried into the booklet. Nothing was picked on instinct and nothing was copied from another publisher's list.
The process ran in four stages. First, each past paper was split into its compulsory Question 1 sub-parts and its optional Questions 2 to 5. Second, every sub-part was tagged to a block and unit. Third, the tags were counted across the five sessions to produce a frequency table. Fourth, topics that scored four or five appearances, and topics that had gone missing for two consecutive sessions, were shortlisted for solving.
That second category matters more than students expect. A topic absent from the last two papers is often overdue rather than dropped, and BCS 12 rotates within a fairly small pool. Determinant area questions, matrix inverse by row operations and De Moivre's theorem all behave this way. The booklet includes them for exactly that reason.
The solving itself was done against the IGNOU textbook, not against a general mathematics reference. Symbols, formula statements and the order of steps follow the block PDFs, because an evaluator marking hundreds of scripts recognises the house notation quickly. If you want to test that claim yourself, pull any IGNOU Previous Year Question Paper for BCS 12 and compare the phrasing against Sample 1 above.
BCS 12 Basic Mathematics Exam Pattern and Marking Scheme Explained
BCS 12 is a 3-hour, 100-mark Term-End paper in which Question 1 is compulsory and you attempt any three of Questions 2 to 5. That structure has held steady across the papers analysed, and understanding it changes how you should revise.
Question 1 carries 40 marks, usually split into short sub-parts of 5 marks each, and it samples widely across the syllabus. You cannot skip a block and still expect to clear Question 1. Questions 2 to 5 carry 20 marks each and are themselves split into sub-parts, so choosing three of the four gives you some room to avoid your weakest topic, but not much.
On length, a workable target inside the answer book is roughly 450 words for a 20-mark answer, 250 words for a 10-mark answer and 150 words for a 5-mark answer. In a mathematics paper those word counts are mostly working, not prose. Budget about five minutes per 5-mark sub-part and hold back the last 15 minutes for re-checking arithmetic, which is where most avoidable marks are lost.
Two practical points. Diagrams for LPP graphs and inequality number lines may be drawn in pencil while the rest stays in pen. And partial credit is real: showing AΒ², 4A and 5I as three separate displayed matrices before subtracting scores better than a single condensed line, even when both reach the same result. Students working across the wider BCA Guess Paper set will find the same marking logic applies to the other mathematics-heavy codes in the programme.
BCS 12 Basic Mathematics Important Questions Ranked by Repeat Frequency
Across the five papers analysed, nine topics appeared in every single session and a further group appeared in four of five. Those are the topics the booklet solves first, and the ones your revision should reach before anything else.
| Topic | Block | Sessions appeared (out of 5) | Priority |
|---|---|---|---|
| Determinants, proving identities | Block 1 | 5 | High |
| Matrices, showing A satisfies a polynomial | Block 1 | 5 | High |
| Mathematical induction proofs | Block 1 | 5 | High |
| Quadratic equations, roots and formation | Block 2 | 5 | High |
| Linear programming, graphical method | Block 4 | 5 | High |
| Maxima and minima of a function | Block 3 | 5 | High |
| Geometric progression and sum to infinity | Block 2 | 4 | High |
| Linear and modulus inequalities | Block 2 | 4 | High |
| Integration by substitution or parts | Block 3 | 4 | High |
| Area between curves | Block 3 | 4 | High |
| Cube roots of unity | Block 2 | 4 | High |
| Vectors, dot, cross and coplanarity | Block 4 | 4 | High |
| Determinants, area and collinearity | Block 1 | 2 | High, recent gap |
| Matrix inverse by elementary row operations | Block 1 | 2 | High, recent gap |
| Limits by rationalisation | Block 3 | 3 | High |
| Higher-order derivatives | Block 3 | 3 | High |
| Length of a curve | Block 3 | 3 | High |
| Shortest distance between two lines | Block 4 | 3 | High |
| Cramer's rule and systems of equations | Block 1 | 3 | Medium |
| Roots in A.P. or G.P. | Block 2 | 3 | Medium |
| Direction cosines and equation of a line | Block 4 | 3 | Medium |
| Complex numbers, modulus and real or imaginary parts | Block 2 | 3 | Medium |
| Series sum and sum to infinity variants | Block 2 | 3 | Medium |
| Matrix rank and normal form | Block 1 | 2 | Medium |
| De Moivre's theorem | Block 2 | 2 | Medium |
| Rate of change and related rates | Block 3 | 2 | Medium |
| Harmonic progression | Block 2 | 1 | Low |
| Continuity at a point | Block 3 | 1 | Low |
The booklet also carries a short skip list, which is arguably as useful as the priority list in the last week before the exam. Long proofs of complex conjugate properties, stand-alone triple vector product proofs, Cramer's rule with awkward fractional 3Γ3 systems and the full derivation of the quadratic formula have all stayed out of the papers analysed. Read those once for understanding and spend the time you save on the high-priority rows above.
Who Should Use This BCS 12 Basic Mathematics Guess Paper
This booklet suits BCA students who have read the blocks at least once and now need to convert that reading into exam-ready answers. It is a revision and answer-writing tool, not a replacement for the self-learning material.
It works well for students returning to mathematics after a gap, for those repeating BCS 12 after a previous attempt, and for anyone whose difficulty is presentation rather than concept. If you can follow a solution but freeze when asked to produce one under time pressure, seeing 13 answers written the way they should appear on paper fixes more than another read of the theory will.
It is a weaker fit if you have not opened the blocks at all. The solutions assume you recognise the formulae being applied, and a guess paper cannot teach determinant expansion from scratch in the space it has. In that situation, work through the BCS 12 Study Material first and come back to the booklet once the notation looks familiar.
One more group it serves: students who have already collected question papers but do not know which topics to trust. The frequency table alone answers that, and it is what most people tell us they used first.
How to Get the Complete BCS 12 Basic Mathematics Guess Paper With Answers
Message 9899436384 on WhatsApp with your course code, and the complete 25-page booklet with all 13 solved questions is shared with you after enquiry. Five of those questions are already on this page; the other 8 come with the file.
Send the code BCS 12 along with your programme and the session you are appearing in, and you will get a straight answer on availability, format and cost. There is no form to fill and no account to create. If you are taking several papers this semester, mention all the codes in one message and we will tell you which of them we currently have solved booklets for.
Get the complete BCS 12 Basic Mathematics booklet with all 13 solved answers. WhatsApp 9899436384 with your course code and session.
Enquire on WhatsApp 9899436384Unnati Educations works only on IGNOU, NIOS and B.Ed. study support, which is why a first-semester BCA mathematics paper gets this level of attention rather than a generic template. Students already following IGNOU's Bachelor of Computer Applications (BCA) course listings on our site will find the rest of the semester's codes there as they are published.
BCS 12 Basic Mathematics Guess Paper Questions Answered
What is included in the BCS 12 Basic Mathematics guess paper for 2026?
The BCS 12 booklet includes 13 questions with complete worked solutions across 25 pages, covering all four blocks of Basic Mathematics. It also carries a block-wise question map, a topic frequency table built from five past Term-End papers, a skip list of rarely tested topics, and answer-writing tips. Five of the 13 questions are shown on this page as samples, and the other 8 come with the file.
How many questions in the BCS 12 guess paper are shown on this page?
Five of the 13 questions are printed in full on this page with their complete solutions, one drawn from each of the four blocks plus the compulsory determinant question. That leaves 8 questions inside the file. The samples were chosen to show working across different answer types, including a proof, a numerical, an optimisation problem and a calculus application, so you can judge the standard fairly.
Which sessions were analysed to prepare the BCS 12 guess paper?
Five consecutive Term-End sessions were analysed, running from June 2023 through to June 2025 and covering both the June and December cycles. IGNOU conducts BCS 12 only in these two sessions each year. Every sub-part of each paper was tagged to a block and unit, then counted, which is how the frequency table and the high, medium and low priority ratings in the booklet were produced.
Is the BCS 12 guess paper enough to pass Basic Mathematics on its own?
It is a strong revision aid rather than a substitute for the blocks. Students who have read the self-learning material once and then work through these 13 solved answers tend to walk in far better prepared, because the booklet fixes presentation and step order. Someone opening the subject for the first time should read the four block PDFs first, then use the guess paper to practise writing full answers.
Does BCS 12 have a practical file or lab record to submit?
No. BCS 12 Basic Mathematics is a theory course with no practical file, lab record or viva component. The practical course in BCA Semester 1 is BCSL-013, which is a separate code with its own lab submission requirements. Any listing that mentions a BCS 12 practical file has confused the two codes, so check the course code on the document before you spend time on it.
What is the exam pattern and total marks for BCS 12?
BCS 12 is a 3-hour Term-End paper carrying 100 marks. Question 1 is compulsory and worth 40 marks, usually as short sub-parts of 5 marks each sampled across the syllabus. Questions 2 to 5 carry 20 marks each and you attempt any three of them. Because Question 1 samples every block, skipping an entire block is not a workable strategy in this paper.
Are the BCS 12 answers written in IGNOU textbook notation?
Yes. Every solution follows the symbols, formula statements and step order used in the official BCS 12 block PDFs on eGyanKosh rather than a general mathematics reference. This matters because evaluators mark quickly and recognise the house notation. Answers that state the formula on its own line before substituting, in the textbook's own form, read faster and tend to hold their method marks better.
How do I receive the complete BCS 12 guess paper after enquiry?
Message 9899436384 on WhatsApp with the course code BCS 12, your programme and the session you are appearing in. You will get a direct reply covering availability, the file format and cost, with no form to fill or account to create. The booklet is shared as a PDF once the enquiry is confirmed, so you can begin revising the same day you get in touch.
All 13 solved answers for BCS 12 Basic Mathematics, December 2026 session
Message 9899436384 on WhatsApp