Test Of Mathematics At The 10 2 Level Solutions Pdf

How to prepare for CMI and ISI Entrance Exams? Candidates preparing for UG entrance exam should know what and how to prepare for CMI and ISI exams. Both exams are Mathematical aptitude tests for Class 12 students to get admission in UG courses. CMI entrance exam is conducted by Chennai Mathematical Institute, whereas ISI entrance exam is held by Indian Statistical Institute, Kolkata. CMI UG entrance exam is a 3-hour duration test that comprises 16 subjective questions. Similarly, the ISI entrance exam comprises MCQs and descriptive-type questions. ISI UG entrance exam will be held in 2 sessions, each of 2 hours. To qualify the CMI and ISI Entrance Exams, candidates will need more conceptual clarity rather than time-pressured problem-solving. These tests are conducted once a year by the respective institutions. Read more to find CMI and ISI exam preparation tips, syllabus, exam pattern, suggested reading material, time- table, sample papers and previous years' question papers.

How to prepare for CMI and ISI Entrance Exams?

CMI and ISI entrance exams are primarily based on Class 12 Mathematics. Any student who wishes to join any of these institutes should ideally have a deep interest and genuine aptitude for the subject. Below are some CMI and ISI exam preparation tips that might be helpful for aspirants:

CMI & ISI Exam Preparation Tip 1- Understand the syllabus thoroughly

Aspirants must go through the syllabus carefully, and analyse which areas might need them to put relatively more effort. Accordingly, they may decide on how to allocate time to different components of the syllabus.

CMI and ISI entrance exam syllabus

Algebra : Arithmetic and geometric progressions, arithmetic mean, geometric mean, harmonic mean and related inequalities, polynomial equations, roots of polynomials, Matrices and Determinants, linear equations, solvability of equations, binomial theorem and multinomial theorem, Permutations And Combinations, mathematical induction, prime numbers and divisibility, GCD, LCM, modular arithmetic logarithms, probability.

Geometry : Vectors, triangles, two dimensional geometry of Conics - straight lines, parabola, hyperbola, ellipses and circles, tangents, measurement of area and volume, Co-ordinate Geometry.

Trigonometry : addition, subtraction formulas, double-angle formulas

Calculus: Limits, continuity, derivatives, integrals, indefinite and definite integrals, maxima and minima of functions in a single variable, series and sequences, convergence criterion, Complex numbers, roots of unity.

ISI Entrance Test- Exam Pattern

Part	Duration
Part 1- UGA - Multiple Choice Questions	2 hours
Part 2- UGB- Descriptive Questions	2 hours

CMI Entrance Test- Exam Pattern

Course

Pattern of Exam

Maximum Marks

Duration

B. Sc (Hons) Mathematics & Computer Sc.

Part A- 40 marks, 10 questions

Part B- 60 marks- 6 questions

100

3 hours

B.Sc (Hons) Mathematics & Physics

Part A- 30 marks, 10 questions

Part B- 70 marks, 7 questions

100

3 hours

CMI & ISI Exam Preparation Tip 2- Make exam preparation time table

Carefully understanding the syllabus and evaluating the question papers of the past few years may help an aspirant to figure out how to allocate the appropriate amount of time to each topic. A time- table helps a student bring about structure to their preparation while maintaining a sense of stability. It also may help them identify achieved and missed targets more clearly, thereby fuelling preparation better. Below is a suggested time- table for CMI and ISI entrance exam preparation, based on a topic- wise analysis of the past five years' papers of the Institute.

ISI & CMI Exam Preparation Time Table

	No. of days suggested for each topic
Algebra	46.25
Geometry	17.5
Calculus	27.5
Trigonometry	5
Complex numbers	3.75

Please note, the above is only a suggested time- table. Students might choose to study as per any other alternative which they find more suitable.

CMI & ISI Exam Preparation Tip 3- Solve Sample Papers and Previous Years' Question Papers

Solving the previous year's papers help in understanding the important topics, weightage of topics and level of difficulty. After covering the entire syllabus do solve the sample papers or previous year paper to check the preparation level. Below are the links to CMI and ISI exam preparation papers PDF

CMI Previous years question papers

Year	CMI Question Paper with Solutions PDF
CMI 2020 Question Paper with Solutions	Click Here
CMI 2019 Question Paper with Solutions	Click Here
CMI 2018 Question Paper with Solutions	Click Here
CMI 2017 Question Paper with Solutions	Click Here
CMI 2016 Question Paper with Solutions	Click Here
CMI 2015 Question Paper with Solutions	Click Here

ISI Previous year's papers

Year	ISI Question Paper with Solutions PDF
ISI 2020 Question Paper with Solutions	Click Here
ISI 2019 Question Paper with Solutions	Click Here
ISI 2018 Question Paper with Solutions	Click Here
ISI 2017 Question Paper with Solutions	Click Here
ISI 2016 Question Paper with Solutions	Click Here
ISI 2015 Question Paper with Solutions	Click Here

CMI & ISI Exam Preparation Tip 4- Research and choose appropriate resources for preparation

Aspirants must do thorough research on the recommended books, online resources, and if required, then formal coaching for preparation and then choose the most suitable and relevant ones. The right resources can help bring a structure to prepare and facilitate it.

ISI and CMI entrance exam preparation books

Students may refer to the following reading material for CMI UG entrance exam preparation:

The following books are suggested, in addition to the Class XI and XII Mathematics Textbooks of the National Council of Educational Research and Training, New Delhi.

1. V. Krishnamoorthy, C.R. Pranesachar, K. N. Ranganathan, B.J.Venkatachala: Challenge and Thrill of Pre-College Mathematics, New Age International Publishers.

2. M.R. Modak, S.A. Katre, V.V. Acharya: An Excursion in Mathematics, Bhaskaracharya Pratishtan (Pune).

3. D. Fomin, S. Genkin, I. Itenberg: Mathematical Circles: Russian experience, Universities Press (Hyderabad) 1998.

4. H.S. Hall, S.R. Knight: Higher Algebra.

For ISI entrance exam preparation, a recommended reading is Test of Mathematics at the 10+ 2 level, which is a book of rigorous Mathematics compiled by the ISI, and also contains sample papers and previous years' question papers from the Institute.

CMI & ISI Exam Preparation Tip 5- Set your goals right

Students may spend some time introspecting and putting in place their short-term, intermediate and long-term goals. A good facilitating question they might ask themselves can be, "Where do I see myself x years down the line?". Setting these goals and getting back to them after short time lapses may work as a positive motivator and fuel performance.

CMI & ISI Exam Preparation Tip 6- Take care of physical and mental health

To reap the best possible results, it is essential that students ensure a balance of physical and mental health. A healthy diet, combined with light physical exercise and some amount of mindfulness, may help students remain in good spirits and work towards their entrance with more zeal.

CMI & ISI Exam Preparation Tip 7- Plan in advance and allow yourself enough time to prepare

Maths is a hands- on subject that requires repeated practice, for concepts to settle in one's mind and speed to pick up, rather than one which can be read overnight and written in the exam the next day. Hence, planning about appearing for the entrances, and thereby formulating a time table wherein adequate time is devoted to each component, is likely to give the student a sense of comfort and predictability, and enhance preparation quality.

CMI- Direct admission to B. SC through Olympiads

Students who perform exceedingly well in the Indian Mathematical Olympiad conducted by Homi Bhabha Centre for Science Education (HBCSE) need not write the CMI entrance exam for B. Sc. Specifically, students in the following categories are exempted from the written entrance test at CMI:

Those who have qualified for the International Mathematical Olympiad Training Camp (IMOTC) in Class 11 or Class 12
Those who have qualified for the Orientation Cum Selection Camp (OCSC) in Physics in Class 11 or Class 12
Those who have qualified for the International Olympiad in Informatics Training Camp (IOITC) in Class 11 or Class 12

Those students who are exempted from writing the CMI entrance examination for B. Sc are required to fill out the online application form, and send an email to the admissions department of CMI, along with suitable proof of qualification.

ISI- Waiver of written tests for INMO awardees

The written ISI entrance examination is waived off for applicants who have been selected as INMO AWARDEES to participate in the International Mathematics Olympiad Training Camp (IMOTC) are usually called directly for interviews.

However, such candidates are also required to apply in the prescribed online application form for admission to the programme.