NTSE Practice

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To enhance the potential and to motivate the students for cracking National Level Competitive Exams by means of more & more real time practice.

Achiever’s Competitive Edge

“There is no glory in practice, but without practice, there is no glory”

Mission: To enhance the potential and to motivate the students for cracking National Level Competitive Exams by means of more & more real time practice.

Vision: Provide opportunity to every single student of this country to give them a chance to explore their potential a and achieve their Dream Career through systematic practice.


Achiever’s Competitive Edge (ACE) is a single platform for a student where they can practice thousands of questions of different difficulty levels which ultimately excel their Speed & Accuracy in NTSE and also gives a Confidence to achieve their desired goal. With the help of Question Bank which is designed & Curated skillfully under the guidance of various NTSE teaching experts to help students to get a comprehensive understanding of the various subjects and topics covered in the NTSE exam.

ACE will also give you a real time experience of NTSE exam through the Sample Papers of previous years. These sample papers are designed on online exam format where student will attempt the exam just like the real exam of NTSE with proper marking system and Time duration. Through this experience you will feel more prepared and also learn to manage the time effectively, which comes handy when you are in the Examination hall.

ACE is not just a place where you can only do the practice through Question bank and get the real time exam experience through Online Sample Papers test but it also give you a proper or detailed analysis of your practice. This way you can figure out your strength & Weakness and form the right exam strategy  With the help of this analysis any student can evaluate his/her level of preparation for NTSE.

NTSE Exam Details

NTSE stand by National Talent Search Examinations, NTSE is conducted by the National Council of Educational Research and Training (NCERT) for identifying talented student who want to pursue higher education in Science and social streams.

The test is performed at two stages, i.e. first the examination of talent at the state level and then the examination of talent at the national level. The students who qualify for the State Level Talent Search Examination are eligible to appear for NCERTs NTSE Stage II exam.

Other way to understand what is NTSE:
  • Exam name – NTSE (National Talent Search Examinations)
  • Levels of NTSE exam NTSE exam is divided in 2 stages the 1st  stage is State level conducted by states/UTs, and 2nd   stage is national level conducted by NCERT 
  • Class level – NTSE is the 10th class level examination.
  • Exam duration 2 hours at each level for each paper (MAT and SAT), ie. 240 minutes in all. MAT stands for Mental Aptitude Test and SAT stands for Scholastic aptitude test. 
  • NTSE scholarship detail
  • Scholarship amount for class 11 and 12 1200rs per month.
  • Scholarship amount for UG  and PG  2000 rs per month.
  • Scholarship for PHO as per UGS norms
Stages of NTSE examination

NTSE is divided into Stage 1 and Stage 2. In both the stages, subjects, and syllabus are the same. But there is a little bit difference between stage 1 and stage 2 and it depends on the pattern and organizing factors.

So it is essential to have a clear understanding of both the tiers. Thereby the students who clear both the stages are offered scholarships and are called NTSE Scholars.

Stage I

Stage 1 is a state level exam conducted by respective state boards in the month of November every year. NTSE Stage 1 is a process through which students are selected state wise.

In the first tier or Stage 1, there is no time gap between MAT and SAT paper. Providing students the liberty to devote less to one subject and devote more time to other subjects.

Eligibility Criteria for Stage-I:

  • Only Indian students are eligible to appear in this level.
  • The students studying in Class X are eligible for appearing in this test.
  • Minimum 60% marks for General Category and 55% for SC, ST and PH category candidates, in their Class IX (last academic year).
  • Candidate must be a student in a recognized school in the respective State or Union Territory
Stage II

The second tier is a national level exam and is conducted by NCERT in the month of May in the succeeding year.

  NTSE Stage 2 is a selection process wherein best students out of the best are selected across the nation. So, the level of competition is high, hence one must be adequately prepared for it.

In Stage 2, the questions are analytically based and are of higher difficulty level.

Eligibility Criteria for Stage-II:

  • Based on Stage I, students recommended by state, are eligible for the Stage-II to be held by NCERT at National level.
  • All the students, who secure the minimum required marks at Stage-II, are eligible for the scholarship program. All the eligible students, who wish to appear in the scholarship programme, are required to register for the same. After the scrutiny of the applications, only eligible candidates are allowed to appear in the exam.
How to prepare for NTSE

Students who are preparing fer NTSE exam should be aware of how to prepare for NTSE exam and what to prepare for NTSE exam to obtain good marks. The NTSE exam will be conducted in two stages, stag1 (statelevel) and Stage 2 (nationallever) to award scholarshipto deserving students.

Here, are some usefuland simplNTSE preparation tipto make students ready for the finadayNTSE exam preparation tips includhow and what to preparfor the NTSE examthese NTSE exam preparation tips and tricks aruseful for stage and stage Iexams.

  • It is a must for all the aspirants tknow what are their strong and weak aspectsA proper and accurate preparation strategy can be formed only after that. Soknowing which areas arthe weakest section and provide a proper concentrate more on them whilpreparing for the exam.
  • The only method ttrack your performance itattempt sample papers or mock test .Solve as many sample papers or mock testtkeep checking your progress. Also helps you in speeding up the calculations. Solve online as welas offline samplpapers.

As the NTSE syllabuibased on the NCERT class 9 and 10th syllabusyou can prepare for thNTSE exam alonwith regular classes.

  • Students will havto understand thbasic concepts weland know how to implement them to differenissues rather than simply mugginthe truth. The coveted scholarshiwill only be gained by thpractical use of knowledgeLearning the test habits and syllabus of both levelis important because learnercan maka proper plan of study
  • When candidates prepare notes to learn formulas. definitionsand equationsNTSE preparation can bvery beneficial. Logicallymakinthese equations written will help us understand them quicklyIts also a convenient way to carry notes wherever you want rather than dragging thheavy booksYou dont have tread the entirchapter at thtime of the review. just qo through these notes carefully
  • Revision ian important part of any method of planningStudents can easily forget important facts without revision. iIt is also advised that the previously studied syllabus be revised beformoving to a new section. This will help you tstay connected with the important topics anto stop the lastminute problems
  • As applicanthavto study for stage 1 of thNTSE along with the syllabus of the 10th board and subsequently for stage 2. they will not have much timto research on a subject that inot knownApplicant should ask a friend or someone whis sufficiently qualified texplaiand go on.
Tips to Become an NTSE Scholar
  • Understanding your strengths and weaknesses is necessaryEgif youre strong in mathematics and science, but language is average and social science weakthen you can turn your weaknesses into strengths for a good overall score.
  • Follow class Iand X NCERT books for preparation for NTSELearninthsocial studies NCERT book for NTSE idetail is essential.
  • lot of samplpaperand mock testmust be solved at least three days a weekThere are several practice questions & mock tests on this site. Within the stipulated timyou will try tsolvthese papersthat you can increase your speeand learn the partwhich take mortime.
  • Make sure you access minutely what you could dand what it was hard for you to doWas it the lack of understanding of the subjectOr havyou missed the scores due to silly mistake;? Whatever it is,  just critically analyzthperformance.
  • decent amount of selfstudy iimportant for clearing any test. Becoming an NTSE scholar ione of the most basic and important of all the tips. At least 34 hourof self­ learninshould be dedicated to solving this competitivexamination.
  • Solve as many mental ability questions as possible and you wont be surprised on thday of thtest. Takthhelp of seniorand teacherfrom your class. Yowill alshavgreater confidence iyour speed,  subject  knowledgeand accuracy with practice.
  • Read reference books carefullto train for NTSE. The handbook oR.5.Aggarwais extremelhelpful in planning for the MAT exams. For mocksyou can refer to books analso do rigorous practice of question bank on ACE website. 
Advantage of being an NTSE Scholar

NTSE is a  scientificalldeveloped evaluation systefor class X graduates. Based on the principles taught in classit tests the strengths and weaKnesses of thstudent Ithis scholarship review, approximatel300,000 applicants (a largelselfselective group of studentsparticipate each year and 2,000 scholarshiparawarded, of whic775 are noreservedAn NTSE scholar has severathings tlook forward tihigschooand beyond from an exciting and wonderful preparation journey besides a significant standout iyoucurriculum vitaesome of the advantages of being an NTSE scholar are:

  • NTSE scholararawarded by the Central Government to pursue studies in sciences and social sciences up tthe doctoral levelThe scholarship is awarded up to thpostgraduatlevel in the case of a professional course such as engineering or medicine..
  • Being an NTSE scholar produces supreme confidence in the futurtcrack such competitivexams. Nearly every one of your classmates at llT is a topper or scholar of NTSEStudyintbecome a scholar in NTSiabout simply knowinthe definitionsSuch traininwould certainly be useful if you take competitivexams such as NEET ,JEECLATetc.
  • If you aspire to optout of the country for advanced studiesthen aan NTSE scholaryohavaedge over others. Tchoose whether tapply for M/ MBA. it also acts as a Differentiator. Those who apply for US scholarshipreceive additional points to qualify for NTSE. NTSE is familiar tuniversities abroad and gives preference tcandidates whhave qua lified for thexamination.
  • Somof Indiacolleges have seatreserved for NTSE scholronly Thiprestigioutest is your gateway in thfuture to an excellenuniversity you may surpass collegadmission testto gain direcentry to your preferred class.
  • Whether applying fojobs or interviews,NTSE scholar” on the resume ian added advantage. In government jobs as well, an NTSE scholar igiven preference. It ihelpful tappear for IFS,IA S,IRS,IPS, etc. interviews.
  • At thhigh school levelNTSE scholarcan enjoy discounts on course materialand books so they can purchassome very important and expensive booksI f a student ieligiblto apply for entry tanother school. NTSE scholarwill always be chosen.
NTSE Exam day Instructions

Students appearing for the exam shouId follow some dos and dontfor the exam day

  • Reach thexamination center 4minutes before the scheduled time.
  • Candidates reaching after 1minutes of thgiven time arnot allowed to enter thexam hall.

Students need to bring their admit cardphoto identity proofand ball pen to the enter.

  • No gadgets are allowed including watches. calculatorsetc.
  • Focus in  time management and maintain your speed accordingly.

Try to attempall the questions as therinnegative marking.

Reference books for NTSE

Before starting NTSE preparation, very first question that arises in aspirant’s mind is, “Which is the best book for NTSE Preparation?” During any competitive exam preparations, students seem attracted towards different reference books to have more study material and knowledge of different topics. We strongly believes that

“There is no ideal book for NTSE preparations. Some are too easy and some are having too tough content for NTSE preparation.”

Students tend to look for a book that visibly has a lot study material. They do not realize that some books consist of preparation and practice material which is too easy for the students and some books include material which is really difficult. Moreover, some topics included in these books are not even a part of the syllabus. Students believe that solving really difficult questions would leave them well prepared for the exam. They do not realize that spending hours on irrelevant study material is a waste of time. Your study material must match the standards of your exam syllabus.

NTSE Stage I paper is based on state board syllabus, so students must stick to their state board books for the proper preparation. Whereas, NTSE Stage II paper is based on NCERT syllabus, so students should prepare well from their NCERT books.

Best Books For NTSE SAT

Subjects like Maths, Physics, and Chemistry require a lot of practice for which you must solve each and every question given at the back of each chapter. The number of questions in the State board books and NCERT books are not enough for the preparation. So, once you’re done with all the State board and NCERT questions you must look out for practice sheets. These practice sheets give you enough material to practice from.

Best Book For NTSE MAT

Moreover, for the preparation of MAT, State Board and NCERT books do not provide anything. MAT is a quintessential part and requires consistent practice. To prepare for the MAT section, you must understand the verbal and non- verbal concepts first and then you must solve practice sheets to cover as many questions as you can.

When you are done with your school books and practice sheets, you should invest your time on sample papers and previous years’ question papers. This is one of the most effective ways to prepare for NTSE or any competitive exam in general. There’s no point splurging your parents’ money on irrelevant books that do not even help you reach your potential. State board books, NCERT books, and a standard study material is all you need for your NTSE preparation. Deeper understanding of the subjects and consistent practice is the key to ace NTSE.

NTSE Books for Class 10

If you still wish to study from a reference book, you can refer to the following NTSE books but remember, ‘Over-reliance on any books is suicidal in case of NTSE preparation.’

NTSE Books

  • Study Package for NTSE class X (1st & 2nd edition)- Mcgraw Hill
  • Pearson Guide to NTSE Class 10 1st edition – Saurabh Priyadarshini & Navin C. Joshi
  • Study Guide for NTSE for Class 10 – Disha Publication
  • Maths Class X – R.D Sharma
NTSE Syllabus & Pattern

NTSE Exam Pattern

The pattern of the written examination remains same for stage I and stage II and is mentioned below. The written examination involves two different papers (MAT and SAT) of 100 marks each.

Paper I: Mental Ability Test (MAT)

Paper I MAT

No. of Questions


Exam duration




2 hours

Paper II: Scholastic Ability Test (SAT) which includes Maths, Science and Social science.

Paper II SAT


No. of Questions


Exam duration





2 hours






Social Science








NTSE Syllabus – MAT

Mental ability test (MAT) is conducted to analyse the overall potential of a student in terms of problem solving and logical reasoning skills. It challenges their presence of mind within a specific time frame. These skill sets are scanned through a variety of questions related to data analytics, verbal and non-verbal reasoning, figure related problems etc. It overall analyses the approach of a student to map and solve a particular problem and puts their thinking process to test. It is one of the major parameters to screen the candidates on the basis their understanding and ability to comprehend.

NTSE has been conducting MAT to identify bright minds in the following domains:

Chapters in MAT

(1) Series

(2) Coding & Decoding

(3) Clocks & Calendar

(4) Alphabet Test

(5) Mathematical Operator 06_Blood Relation

(6) Blood Relation

(7) Number and Ranking

(8) Analogy

(9) Classification

(10) Water and Mirror Image

(11) Cube & Dice

(12) Puzzle Test

(13) Missing Character

(14) Direction Sense

(15) Venn Diagram

(16) Incomplete Figures

(17) Embedded Figures

(18) Paper Folding

(18) Paper Folding

(20) Non-verbal classification

(21) Non-verbal Analogy

(22) Non-verbal Figure partition

NTSE Syllabus – SAT

Scholastic ability test (SAT): This section is designed to test the academic skills of a student and includes Mathematics, Science and Social science.

NTSE Exam Syllabus for Science – Refer your state books for phase 1

The NCERT prescribed syllabus for class IX and X is generally asked in NTSE stage I along with the topics that are specifically included in the state board syllabus of a particular state. Most of the states in India run NCERT books as a part of their IX and X curriculum but some states have their own state specific books. You can get the state specific content from ntseguru.in. It is important for an aspirant to acquaint himself with the preparation of the state specific topics in order to crack NTSE stage I with a good score.

A vigorous and relevant study material made by experts for NTSE stage I including the detailed question bank specific to particular state is available at ACE for your help. Every minute detail is covered so as to provide the students a complete preparation package and giving an extra edge to their ambitions.

However, stage II of NTSE completely emphasises on the topics given in NCERT and deals with detailed and deeper understanding of topics on a conceptual level.

Class IX

  • Motion
  • Force and Newton’s laws of Motion
  • Gravitation
  • Floatation
  • Sound
  • Matter in our surroundings
  • Is matter around us pure?
  • Atoms and molecules
  • Structure of atom
  • CELL: Fundamental unit of life
  • The tissues
  • Diversity in living organisms
  • Why do we fall ill?
  • Natural resources
  • Improvement in food resources

Class X

  • Electricity
  • Magnetic effects of current
  • Sources of energy
  • Chemical reactions
  • Acids, bases and salts
  • Metals and nonmetals
  • Carbon and its compounds
  • Periodic classification of elements
  • Life processes
  • Control and co-ordination in animals and plants
  • Control and co-ordination in animals
  • How do organisms reproduce?
  • Heredity and Evolution
  • Our environment
  • Sustainable management of natural resources

NTSE Exam Syllabus for Social Science – Refer your state books for phase 1


  • Unit 1: India and the Contemporary World –
  • I. The French Revolution
  • III. Nazism and the Rise of Hitler
  • Any one theme of the following
  • IV. Forest Society and Colonialism
  • V. Pastoralists in the Modern World
  • Unit 2: Contemporary India – I
  • 1. India
  • 2. Physical Features of India
  • 3. Drainage
  • 4. Climate
  • 5. Natural Vegetation and Wild Life
  • 6. Population
  • Unit 3: Democratic Politics –
  • 1. What is Democracy? Why Democracy?
  • 2. Constitutional Design
  • 3. Electoral Politics
  • 4. Working of Institutions
  • 5. Democratic Rights
  • Unit 4: Economics
  • 1. The Story of Village Palampur
  • 2. People as Resource
  • 3. Poverty as a Challenge
  • 4. Food Security in India


  • Unit 1: India and the Contemporary World – II
  • 1. The Rise of Nationalism in Europe
  • 2. Nationalism in India
  • Any one theme of the following:
  • 3. The Making of a Global World
  • 4. The Age of Industrialization
  • 5. Print Culture and the Modern World
  • Unit 2: Contemporary India – II
  • 1. Resources and Development
  • 2. Forest and Wildlife
  • 3. Water Resources
  • 4. Agriculture
  • 5. Minerals and Energy Resources
  • 6. Manufacturing Industries
  • 7. Life Lines of National Economy
  • Unit 3: Democratic Politics
  • 1. Power Sharing Case Studies of Belgium and Sri Lanka
  • 2. Federalism What is Federalism?
  • 3. Democracy and Diversity
  • 4. Gender, Religion and Caste
  • 5. Popular Struggles and Movements
  • 6. Political Parties
  • 7. Outcomes of Democracy
  • 8. Challenges to Democracy
  • Unit 4: Understanding Economic Development
  • 1. Development
  • 2. Sectors of the Indian Economy
  • 3. Money and Credit
  • 4. Globalization and the Indian Economy

NTSE Exam Syllabus for Maths – Refer your state books for phase 1

NTSE 2020 Syllabus for Class 10

       1. Review of representation of natural numbers, integers, rational numbers, terminating / non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
       2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers, and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
       3. Definition of nth root of a real number. Rationalization (with precise meaning) of real numbers of the type and (and their combinations) where x and y are natural number and a and b are integers.
       4. Laws of exponents with integral powers. Rational exponents with positive real
       Definition of a polynomial in one variable, with examples .Coefficients, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. The Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax 2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities, factorization of polynomials.
    Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax+by+c=0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables.
  • COORDINATE GEOMETRY : The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.
  • 1. INTRODUCTION TO EUCLID’S GEOMETRY :History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example: (Axiom)
       1. Given two distinct points, there exists one and only one line through them.
       2. Two distinct lines cannot have more than one point in common.
       1. If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.
       2. If two lines intersect, vertically opposite angles are equal.
       3. Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
       4. Lines which are parallel to a given line are parallel.
       5. The sum of the angles of a triangle is 180O .
       6. If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.
       1. Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
       2. Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
       3. Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
       4. Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)
       5. The angles opposite to equal sides of a triangle are equal.
       6. The sides opposite to equal angles of a triangle are equal.
       7. Triangle inequalities and relation between ‘angle and facing side’ inequalities in triangles.
       1. The diagonal divides a parallelogram into two congruent triangles.
       2. In a parallelogram opposite sides are equal, and conversely.
       3. In a parallelogram opposite angles are equal, and conversely.
       4. A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
       5. In a parallelogram, the diagonals bisect each other and conversely.
       6. In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and its converse.
  • 5. AREA
       Review concept of area, recall area of a rectangle.
       1. Parallelograms on the same base and between the same parallels have equal area.
       2. Triangles on the same base (or equal bases) and between the same parallels are equal in area.
  • 6. CIRCLES
       Through examples, arrive at definition of circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.
       1. Equal chords of a circle subtend equal angles at the center and its converse.
       2. The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
       3. There is one and only one circle passing through three given non-collinear points.
       4. Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
       5. The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
       6. Angles in the same segment of a circle are equal.
       7. If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
       8. The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.
       1. Construction of bisectors of line segments and angles of measure 60o, 90o, 45o etc., equilateral triangles.
       2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
       3. Construction of a triangle of given perimeter and base angles.
  • 1. AREAS
       Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.
       Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.
       Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency polygons. Mean, median and mode of ungrouped data.
       Repeated experiments and observed frequency approach to probability. Focus is on empirical probability.

NTSE 2020 Syllabus for Class 9

  • 1. REAL NUMBER : Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements Proofs of irrationality of Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.
  • 1. POLYNOMIALS : Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.
       2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES : Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.
       3. QUADRATIC EQUATIONS :Standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.
       4. ARITHMETIC PROGRESSIONS : Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.
  • 1. Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.
       Definitions, examples, counter examples of similar triangles.
       1. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
       2. If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
       3. If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
       4. If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
       5. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
       6. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
       7. The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
       8. In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
       9. In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle.
  • 2. CIRCLES :
       Tangent to a circle at, point of contact
       1. The tangent at any point of a circle is perpendicular to the radius through the point of contact.
       2. The lengths of tangents drawn from an external point to a circle are equal.
       1. Division of a line segment in a given ratio (internally).
       2. Tangents to a circle from a point outside it.
       3. Construction of a triangle similar to a given triangle.
  • 1. INTRODUCTION TO TRIGONOMETRY : Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); Values of the trigonometric ratios of 00 300 , 450 and 600 , 900. Relationships between the ratios.
  • 2. TRIGONOMETRIC IDENTITIES :Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.
       Trigonometric ratios of complementary angles.
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