DIRECT ADMISSION provides you the best courses specially designed by best faculties of Kota for 8^{th}, 9th and 10th class students who want to score good marks in their future coming examinations like KVPY, NTSE, JEE, NEET and various Olympiads. KOCP courses are sketched for the students to lay the strong foundation for entrance exams by providing them with best and advanced level of content, questions and concepts, so that they do not face any problem in their preparation for higher classes and which will help you to enhance your strength and know your weakness.

KOCP offers courses for various Competitive Exams and Olympiads for the students of classes 8th to 10th. It fosters Creativity, Scientific Thinking, Competitive Temperament and Divergent Aptitude in the students by means of our Classroom Contact Programs and Workshops.

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School Integrated Pre Foundation Course to develop Mathematical aptitude, Scientific and reasoning skills, and preparation for various scholarship exams like NTSE, Science & Maths Olympiads and Foundation course for other future competitive examination like IIT-JEE and Pre-Medical. Courses help students to take early lead, prepare them in gradual and systematic manner for high level competitive exams and avoid stress and time pressure in subsequent years.

KOCP Career Foundation courses have been specially designed with a view to prepare students of class 8th to 10th by building a firm foundation of every concept for SA-I and SA-II conducted by CBSE. We gradually transforms a student’s learning from the foundation to the excellent level and ensures a concrete conceptual base which helps the students emerge successful in formal school academics and competitive examinations. The periodic tests of the program are planned in such a manner which evaluates the profundity of student’s learning and the multidimensional analysis reports of the test give a microscopic feedback to student on areas or subjects which need to be worked upon and improved. We work towards utilizing the complete potential of our students. Our comprehensive study material, periodic tests and multidimensional analysis ensure the sound academic development of our 8th to 10th class students.

Along with the school level studies, KOCP Career Foundation students are thus geared up for competitive examinations like NTSE, various National/International Olympiads and nationally recognized awards like Balshree, National Child Award etc. We bring concrete changes in the persona of students and powerfully install all essentials of success in their minds to prepare them for the competitive environment in studies and in life.

There is no fixed syllabus for IIT Foundation Course. Generally, IIT Foundation syllabus covers subjects such as Arithmetic, Chemistry, Physics, Reasoning and Communication skills. The IIT Foundation Course covers all basic Math, Chemistry and Physics concepts taught in VII, VIII, IX and X standard. For excelling in the IIT Foundation Course, students must acquaintance themselves with Math, Chemistry and Physics topics covered in – State Board, CBSE and ICSE syllabus for Class VIII–X.

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Yes, coaching centres have their pros. But if this is the case, then why do many people flunk the competitive exams even after joining these coaching institutes?

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**Kota Online Coaching Program**(KOCP).

#### KOCP

KOCP is an educational tool developed by Direct Admission featuring education faculty of KOTA which possess an experience of more than 30 years. The KOCP kit includes video lectures that are accessible online. This

was an initiative taken by the company in aid of students who intend to crack national level competitive exams inclusive of JEE, NEET and CBSE. To dodge the problem of inefficient internet connectivity, the video lectures are also made available offline in the form of DVD, USB, SD card and Tablet. Kota Online Coaching Program (KOCP) combines the best faculty of Kota, their teaching methodologies, their experience and bring it to the comfort of your own home. You can access it via CD Rom, USB Drives, Pen drives and watch it at your own fixed schedule. You are also provided with the contact number of the concerned authorities to clear your doubts the very same day via telephonic discussion or other electronic correspondences.

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We all have know that making our academic base strong helps in career building at a later stage. To make one’s foundation strong, the need to study diligently always tops the list. In fact, from childhood we were told to learn tables, BODMAS etc., to clear our doubts in Maths and make it strong or to understand vowels to make grammar our strong subject. Exactly the same applies when one is preparing for IIT JEE, a student starts covering and understanding the syllabus from Class 9th, at times even from Class 8.

But do you think it’s justified or worth to start preparing for one of the most difficult competitive exam IIT-JEE from such an early stage? Since there are chances that you might hamper either school or preparation process, in an attempt to excel the latter! Well, there are definitely more reasons as why preparation for IIT JEE should start from Class 9 or 10, rather than from later stage.

**Deciding Career Path-**It has been seen that many students are very unclear which career they want to pursue after their academic years. But as for the one who start preparing for IIT JEE from their Foundation or to be more precise from Class 9-10, seems to have their target set, and give their full attention and concentration towards Engineering.**Common Syllabus –**The syllabus for Foundation and the IIT JEE’s core subject are quite similar in many aspects. In fact, even if the IIT JEE syllabus is a bit notch higher, it is helpful because in this way the students learn to prepare for the toughest exam as well. During the course of their school, they can easily cover the major scoring core subjects.**Ahead in covering Syllabus-**since the IIT aspirants start preparing for the exam well in advance. They are left only with revision after the boards’ exam is over, they definitely have an edge over their peers who don’t start Foundation Course.**No year gap-**The biggest advantage of preparing for the exam from Class 9-10 is the fact that you don’t have to take a year gap or so, to sit back at home for preparation or joining classes. There are many students who prefer taking a year gap or so, to improve their marks, or to learn through coaching classes in order to seek a seat in a reputed institute.

Pre foundation courses deals with the varied potential of the students of class 9th & 10th. While taking care of school & board syllabus these courses are designed to develop a strong foundation which helps to crack competitive exams. An early beginning is essential for success in future competitive examinations like JEE, NEET, NTSE, KVPY, OLYMPIADS. The basics of science, mathematics and mental ability increase student’s IQ and emphasize on understanding each concept from GRASS ROOT LEVEL.

These courses are designed to develop Mathematical aptitude, Scientific and reasoning skills, Logical thinking and Problem solving skills of the student at early stage and prepare them for future competitive exams. These courses are synchronized with school education hence prepare for both school and competitive exams Courses help students to take early lead, prepare them in gradual and systematic manner for high level competitive exams and avoid stress and time pressure in subsequent years.

Pre foundation courses deals with the varied potential of the students of class 9th & 10th. While taking care of school & board syllabus these courses are designed to develop a strong foundation which helps to crack competitive exams. An early beginning is essential for success in future competitive examinations like JEE, NEET, NTSE, KVPY, OLYMPIADS. The basics of science, mathematics and mental ability increase student’s IQ and emphasize on understanding each concept from GRASS ROOT LEVEL.

These courses are designed to develop Mathematical aptitude, Scientific and reasoning skills, Logical thinking and Problem solving skills of the student at early stage and prepare them for future competitive exams. These courses are synchronized with school education hence prepare for both school and competitive exams Courses help students to take early lead, prepare them in gradual and systematic manner for high level competitive exams and avoid stress and time pressure in subsequent years.

Course Target:

Excellence in School Examination

This Programme lay strong foundation & prepare the students for Competitive Examinations organized at state or National Level like NTSE, IJSO, NSTSE & Various Olympiads like NSO, IMO, IEO, UIEO, UCO etc & also ensure excellence in school exams.

#### Class 10^{th} mathematics syllabus

### UNIT I: NUMBER SYSTEMS

**REAL NUMBERS**

- Review of representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification. Rational numbers as recurring/terminating decimals.
- Examples of non-recurring / non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.
- Existence of √x for a given positive real number x (visual proof to be emphasized).
- Definition of nth root of a real number.
- Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/(√x+√y) (and their combinations) where x and y are natural number and a and b are integers.
- Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

### UNIT II: ALGEBRA

**POLYNOMIALS**

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, 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. Motivate and State 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:

(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2zx

(x ± y)^{3} = x^{3} ± y^{3} ± 3xy (x ± y)

x³ ± y³ = (x ± y) (x² ± xy + y²)

x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z) (x^{2} + y^{2} + z^{2} – xy – yz – zx) and their use in factorization of polynomials.

**LINEAR EQUATIONS IN TWO VARIABLES**

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. Prove 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. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

### UNIT III: COORDINATE GEOMETRY

**COORDINATE GEOMETRY**

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

### UNIT IV: GEOMETRY

**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.
- (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

**LINES AND ANGLES**

- (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse.
- (Prove) If two lines intersect, vertically opposite angles are equal.
- (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
- (Motivate) Lines which are parallel to a given line are parallel.
- (Prove) The sum of the angles of a triangle is 180°.
- (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

**TRIANGLES**

- (Motivate) 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).
- (Prove) 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).
- (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
- (Motivate) 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.
- (Prove) The angles opposite to equal sides of a triangle are equal.
- (Motivate) The sides opposite to equal angles of a triangle are equal.
- (Motivate) Triangle inequalities and relation between ‘angle and facing side’ inequalities in triangles.

**QUADRILATERALS**

- (Prove) The diagonal divides a parallelogram into two congruent triangles.
- (Motivate) In a parallelogram opposite sides are equal, and conversely.
- (Motivate) In a parallelogram opposite angles are equal, and conversely.
- (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
- (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
- (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse.

**AREA**

Review concept of area, recall area of a rectangle.

- (Prove) Parallelograms on the same base and between the same parallels have the same area.
- (Motivate) Triangles on the same (or equal base) base and between the same parallels are equal in area.

**CIRCLES**

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, secant, sector, segment subtended angle.

- (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
- (Motivate) 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.
- (Motivate) There is one and only one circle passing through three given non-collinear points.
- (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
- (Prove) 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.
- (Motivate) Angles in the same segment of a circle are equal.
- (Motivate) 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.
- (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

**CONSTRUCTIONS**

- Construction of bisectors of line segments and angles of measure 60°, 90°, 45° etc., equilateral triangles.
- Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
- Construction of a triangle of given perimeter and base angles.

### UNIT V: MENSURATION

**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**

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

### UNIT VI: STATISTICS & PROBABILITY

**STATISTICS**

Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data.

**PROBABILITY**

History, Repeated experiments and observed frequency approach to probability.

Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real – life situations, and from examples used in the chapter on statistics).

#### Course Highlights

- Well Designed Exercise Sheets & Theoretical Notes prepared by most experienced faculty.
- Regular self assessment through Daily Practice Problems (DPP’s).
- Clearance of Doubts.
- Periodic Tests on Saturday to nurture academic skills & appreciation award to toppers.
- Personal care and support of administration and Faculty team.

**Teaching Methodology**

Our foundation course has been designed in such a manner that it will focus on:

Imparting a thorough understanding of core concepts & fundamentals |

Sharpening Analytical Skills |

Building an inter disciplinary approach |

Thus our course design and conduct is such that it enables the students to build a strong conceptual base & eventually helps them to prepare successfully for Exams like –

School/Board Exam | NTSE | IMO | KVPY |

NSEJS | IIT JEE | NEET |

Course Details for 10^{th} Standard:

These courses are designed to develop Mathematical aptitude, Scientific and reasoning skills, Logical thinking and Problem solving skills of the student at early stage and prepare them for future competitive exams. These courses are synchronized with school education hence prepare for both school and competitive exams Courses help students to take early lead, prepare them in gradual and systematic manner for high level competitive exams and avoid stress and time pressure in subsequent years.

Pre foundation courses deals with the varied potential of the students of class 9th & 10th. While taking care of school & board syllabus these courses are designed to develop a strong foundation which helps to crack competitive exams. An early beginning is essential for success in future competitive examinations like JEE, NEET, NTSE, KVPY, OLYMPIADS. The basics of science, mathematics and mental ability increase student’s IQ and emphasize on understanding each concept from GRASS ROOT LEVEL.

Course Target:

Excellence in School Examination

The Programme prepares students for NTSE & build strong foundation which leads Excellent performance in Engineering & Medical Examinations along with excellence in school studies.

Course Syllabus:

Science: Chemical Substances – Nature and Behaviour, World of living, Natural Phenomenon, Effects of Current, Natural Resources.

### Unit I: Chemical Substances – Nature and Behaviour

**Chemical reactions:** Chemical equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction.

**Acids, bases and salts:** Their definitions in terms of furnishing of H+ and OH- ions, General properties, examples and uses, concept of pH scale(Definition relating to logarithm not required), importance of pH in everyday life; preparation and uses of sodium hydroxide, Bleaching powder, Baking soda, Washing soda and Plaster of Paris.

**Metals and non metals:** Properties of metals and non-metals, reactivity series, formation and properties of ionic compounds, basic metallurgical processes, corrosion and its prevention.

**Carbon compounds:** Covalent bonding in carbon compounds. Versatile nature of carbon. Homologous series Nomenclature of carbon compounds containing functional groups (halogens, alcohol, ketones, aldehydes, alkanes and alkynes), difference between saturated hydrocarbons and unsaturated hydrocarbons. Chemical properties of carbon compounds (combustion, oxidation, addition and substitution reaction). Ethanol and Ethanoic acid (only properties and uses), soaps and detergents.

**Periodic classification of elements:** Need for classification, Modern periodic table, gradation in properties, valency, atomic number, metallic and non-metallic properties.

### Unit II: World of Living

**Life processes:** “living being”. Basic concept of nutrition, respiration, transport and excretion in plants and animals.

**Control and co-ordination in animals and plants:** Tropic movements in plants; Introduction to plant hormones; control and co-ordination in animals : nervous system; voluntary, involuntary and reflex action, chemical co-ordination: animal hormones.

**Reproduction:** Reproduction in animal and plants (asexual and sexual) reproductive health-need for and methods of family planning. safe sex vs HIV/AIDS. Child bearing and women’s health.

**Heredity and evolution:** Heredity; Mendel’s contribution- Laws for inheritance of traits: Sex determination: brief introduction; Basic concepts of evolution.

### Unit III: Natural Phenomenon

Reflection of light at curved surfaces, Images formed by spherical mirrors, centre of curvature, principal axis, principal focus, focal length, mirror formula (Derivation not required), magnification.

Refraction; laws of refraction, refractive index.

Refraction of light by spherical lens, Image formed by spherical lenses, Lens formula (Derivation not required), Magnification. Power of a lens.

Functioning of a lens in human eye, defects of vision and their corrections, applications of spherical mirrors and lenses.

Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life.

### Unit IV: Effects of Current

Electric current, potential difference and electric current. Ohm’s law; Resistance, Resistivity, Factors on which the resistance of a conductor depends. Series combination of resistors, parallel combination of resistors and its applications in daily life. Heating effect of electric current and its applications in daily life. Electric power, Inter relation between P, V, I and R.

**Magnetic effects of current:** Magnetic field, field lines, field due to a current carrying conductor, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming’s left hand rule. Electromagnetic induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule, Direct current. Alternating current : frequency of AC. Advantage of AC over DC. Domestic electric circuits.

### Unit V: Natural Resources

**Sources of energy:** Different forms of energy, conventional and non-conventional sources of energy: fossil fuels, solar energy; biogas; wind, water and tidal energy; nuclear energy. Renewable versus non-renewable sources.

**Our environment:** Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and non-biodegradable substances.

**Management of natural resources:** Conservation and judicious use of natural resources. Forest and wild life; Coal and Petroleum conservation. Examples of people’s participation for conservation of natural resources. Big dams: advantages and limitations; alternatives, if any. Water harvesting. Sustainability of natural resources.

## Practicals

- Finding the pH of the following samples by using pH paper / universal indicator:

- a) Dilute Hydrochloric Acid
- b) Dilute NaOH solution
- c) Dilute Ethanoic Acid Solution
- d) Lemon juice
- e) Water
- f) Dilute Hydrogen Carbonate solution

Studying the properties of acids and bases (HCl & NaOH) by their reaction with:

- a) Litmus solution (Blue/Red)
- b) Zinc metal
- c) Solid sodium carbonate

- Performing and observing the following reactions and classifying them into:

- a) Combination reaction
- b) Decomposition reaction
- c) Displacement reaction
- d) Double displacement reaction
- (i) Action of water on quick lime
- (ii) Action of heat on ferrous sulphate crystals
- (iii) Iron nails kept in copper sulphate solution
- (iv) Reaction between sodium sulphate and barium chloride solutions

OR

- Observing the action of Zn, Fe, Cu and Al metals on the following salt solutions:

- a) ZnSO
_{4}(aq) - b) FeSO
_{4}(aq) - c) CuSO
_{4}(aq) - d) Al
_{2}(SO4)_{3}(aq)

Arranging Zn, Fe, Cu and Al (metals) in the decreasing order of reactivity based on the above result.

- Studying the dependence of potential difference (V) across a resistor on the current (I) passing through it and determine its resistance. Also plotting a graph between V and I.
- Determination of the equivalent resistance of two resistors when connected in series and parallel.
- Preparing a temporary mount of a leaf peel to show stomata.
- Experimentally show that carbon dioxide is given out during respiration.
- Study of the following properties of acetic acid (ethanoic acid):

- i) odour
- ii) solubility in water
- iii) effect on litmus
- iv) reaction with sodium Hydrogen Carbonate

- Study of the comparative cleaning capacity of a sample of soap in soft and hard water.
- Determination of the focal length of:

- i) Concave mirror
- ii) Convex lens

by obtaining the image of a distant object.

- Tracing the path of a ray of light passing through a rectangular glass slab for different angles of incidence. Measure the angle of incidence, angle of refraction, angle of emergence and interpret the result.
- Studying (a) binary fission in Amoeba, and (b) budding in yeast with the help of prepared slides.
- Tracing the path of the rays of light through a glass prism.
- Finding the image distance for varying object distances in case of a convex lens and drawing corresponding ray diagrams to show the nature of image formed.
- Identification of the different parts of an embryo of a dicot seed (Pea, gram or red kidney bean).

### CBSE Class 10 Physics Syllabus

The search of class 10 students to find class 10 Physics syllabus has come to an end, as Byju’s – the learning app brings comprehensive material for cbse students to help improve their performances in class 10 board exams. Students must be updated with the latest cbse syllabus and compare with the previous years syllabus to know which are the chapters and units that are added and whether any concepts are eliminated.

Here is the list of Units included in class 10 Physics syllabus:

- Light reflection and refraction
- Electricity
- Human eye and colorful world
- Magnetic effect of electric current
- Sources of energy
- Management of Natural Resources

CBSE class 10 Biology syllabus

- Life Processes
- How Do Organism Reproduce
- Heredity and Evolution
- Control and Coordination

CBSE class 10 Chemistry syllabus is mentioned below.

- Chemical Reactions and Equations
- Metal and Non-metals
- Periodic Classification of Elements
- Acid, Bases and Salts
- Carbon and its Compounds
- Our Environment

Mathematics: Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics & Probability.

### UNIT I: NUMBER SYSTEMS

**REAL NUMBERS**

Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results – irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

### UNIT II: ALGEBRA

**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.

**PAIR OF LINEAR EQUATIONS IN TWO VARIABLES**

Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/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 must be included. Simple problems on equations reducible to linear equations.

**QUADRATIC EQUATIONS**

Standard form of a quadratic equation ax^{2}+bx+c=0, (a ≠ 0). Solution of the quadratic equations (only real roots) by factorization, by completing the square 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.

**ARITHMETIC PROGRESSIONS**

Motivation for studying Arithmetic Progression Derivation of the n^{th} term and sum of the first n terms of A.P. and their application in solving daily life problems.

### UNIT III: COORDINATE GEOMETRY

**LINES (In two-dimensions)**

Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

### UNIT IV: GEOMETRY

**TRIANGLES**

Definitions, examples, counter examples of similar triangles.

- (Prove) 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.
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- (Motivate) 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.
- (Motivate) 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.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- (Prove) 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 triangle.

**CIRCLES**

Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.

- (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- (Prove) The lengths of tangents drawn from an external point to circle are equal.

**CONSTRUCTIONS**

- Division of a line segment in a given ratio (internally).
- Tangent to a circle from a point outside it.
- Construction of a triangle similar to a given triangle.

### UNIT V: TRIGONOMETRY

**INTRODUCTION TO TRIGONOMETRY**

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

**TRIGONOMETRIC IDENTITIES**

Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

**HEIGHTS AND DISTANCES**

Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, 60°.

### UNIT VI: MENSURATION

**AREAS RELATED TO CIRCLES**

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).

**SURFACE AREAS AND VOLUMES**

(i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

(ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).

### UNIT VII: STATISTICS AND PROBABILITY

**STATISTICS**

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

**PROBABILITY**

Classical definition of probability. Simple problems on single events (not using set notation).

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