VYAPAM / PEB (Professional Examination Board) Bhopal

Pre- Polytechnic Test (PPT) - 2020

MP Pre Polytechnic Test (PPT) 2020 Exam stages- 

                          1)   Online  Examination     –     Objective type(MCQ)   

S.NO EXAM STAGES NAME OF PAPER TIME QUESTION MARKS
1 Online Exam Physics 2 Hours 50 50
    Chemistry 50 50
    Maths 50 50
      Total 150 150

 

MP Pre Polytechnic Test (PPT) Exam 2020 Syllabus- 

 

Online Exam

Online Exam Syllabus In Hindi Download Now

Online Exam Syllabus In English Download Now

       

COURSE STRUCTURE CLASS –X

MATHEMATICS

UNIT I: NUMBER SYSTEMS 1. REAL NUMBER (15) Periods  

Euclid’s division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √ √ √ Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

UNIT II: ALGEBRA

1. POLYNOMIALS(7) Periods

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 (15) Periods  

Pair of linear equations in two variables and graphical solution, consistency/inconsistency.  method of their 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(15) Periods

Standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). Solutions of 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.

4. ARITHMETIC PROGRESSIONS            (8) Periods Motivation for studying 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.  

UNIT III: COORDINATE GEOMETRY  

1. LINES (In two-dimensions)(14) Periods

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

UNIT IV: GEOMETRY  

1. TRIANGLES(15) Periods  

Definitions, examples, counter examples of similar triangles.

1. (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.

2. (Motivate)   If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.  

3. (Motivate) I f in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.  

4. (Motivate). If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.  

5. (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.

6. (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.  

7. (Prove)   The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.  

8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.  

9. (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 angle.

  2. CIRCLES ( 8) Periods  

Tangent to a circle at, point of contact  

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2. (Prove)   The lengths of tangents drawn from an external point to a circle are equal..

3. CONSTRUCTIONS (8) Periods  

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.  

UNIT V: TRIGONOMETRY  

1. INTRODUCTION TO TRIGONOMETRY(10) Periods  

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o . Values (with proofs) of the trigonometric ratios of 300 , 450 and 600 . Relationships between the ratios.  

2. TRIGONOMETRIC IDENTITIES(15) Periods  

Proof and applications of the identity sin2 A + cos 2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.  

3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression.(8) Periods  

Simple 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  

1. AREAS RELATED TO CIRCLES(  12) Periods  

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.)  

2. SURFACE AREAS AND VOLUMES(12) Periods

  1. 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.  

2. 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  

1. STATISTICS(18) Periods  

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

2. PROBABILITY(10) Periods  

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

     

COURSE STRUCTURE CLASS –X

MATHEMATICS

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER(15) Periods

Euclid’s division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √ √ √ Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

       

UNIT II: ALGEBRA

 

1. POLYNOMIALS(7) Periods

 

    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 (15) Periods    

Pair of linear equations in two variables and graphical solution, consistency/inconsistency.  method of their 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(15) Periods

Standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). Solutions of 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.  

4. ARITHMETIC PROGRESSIONS(8) Periods

Motivation for studying 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.  

UNIT III: COORDINATE GEOMETRY

  1. LINES (In two-dimensions)(14) Periods

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

UNIT IV: GEOMETRY

  1. TRIANGLES (15) Periods  

Definitions, examples, counter examples of similar triangles.

1. (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.

2. (Motivate)   If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

  3. (Motivate) I f in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.  

4. (Motivate).   If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.  

5. (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.

6. (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.  

7. (Prove)   The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

  8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

  9. (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 angle.  

2. CIRCLES(8) Periods

  Tangent to a circle at, point of contact  

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2. (Prove)   The lengths of tangents drawn from an external point to a circle are equal.  

3. CONSTRUCTIONS(8) Periods  

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.      

UNIT V: TRIGONOMETRY  

1. INTRODUCTION TO TRIGONOMETRY (10) Periods  

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o . Values (with proofs) of the trigonometric ratios of 300 , 450 and 600 . Relationships between the ratios.  

2. TRIGONOMETRIC IDENTITIES(15) Periods  

Proof and applications of the identity sin2 A + cos 2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.  

3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression.(8) Periods

Simple 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  

1. AREAS RELATED TO CIRCLES (  12) Periods  

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.)  

2. SURFACE AREAS AND VOLUMES(12) Periods  

1. 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.  

2. 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  

1. STATISTICS(18) Periods  

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

2. PROBABILITY(10) Periods  

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

COURSE STRUCTUR CLASS X

Science

(Annual Examination)

  Theme: Materials(55 Periods)    

 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 nonmetals: 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, Early attempts at classification of elements (Dobereiner’s Triads, Newland’s Law of Octaves, Mendeleev’s Periodic Table), Modern periodic table, gradation in properties, valency, atomic number, metallic and non-metallic properties.  

Theme: Natural Phenomena(23 Periods)  

Unit II: Natural Phenomena Reflection of light by 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 oflightthrough a prism, dispersion oflight, scattering oflight, applic ations in daily life.  

Theme: How Things Work(32 Periods)  

Unit III: 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, Interrelation 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, Electric Motor, Electromagnetic induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule, Electric Generator, Direct current. Alternating current : frequency of AC. Advantage of AC over DC. Domestic electric circuits.

Theme: Natural Resources(20 Periods)  

Unit IV: Natural Resources Sources of energy: Different forms of energy, conventional and nonconventional sources of energy: Fossil fuels, solar energy; biogas; wind, water and tidal energy; Nuclear energy. Renewable versus non-renewable sources of Energy.

Our environment: Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and nonbiodegradable 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.  

 

                                               

 

       

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