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Test Papers of Class 10 MathematicsIndian Education system primarily consists of two parts one being studying the subjects and the other one is appearing for exams and tests. All these exams are conducted by schools for various classes to gauge how much the students have understood , learned and what is their capability score in any particular subject. But sometimes even after understanding the topics fully there are chances the students don’t do well in exams because of lack of preparation from the examination perspective. The reason being that one needs to prepare for exams in a particular way and for that previous question papers, sample papers, worksheets and unit test papers play a major role.

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Number Systems (6 Marks)

Algebra (20 Marks)

Coordinate Geometry (6 Marks)

Geometry (15 Marks)

Trigonometry (12 Marks)

Mensuration (10 Marks)

Statistics & Probability (11 Marks)

Chapter 1 : 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 irrationality of 12, /3, 15. Decimal representation of rational numbers in terms of terminating / non-terminating recurring decimals.

Chapter 2 : 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. Also covered topics include Polynomial of nth Degree, HCF of polynomial , methods of finding HCF and LCM of polynomials, Relation among LCM and HCF of the production of polynomial, Rational Expressions in lowest terns, addition and subtraction of rational expressions, multiplication of rational expressions, division of rational expressions.

Chapter 3: Coordinate Geometry

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

Chapter 3: 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. Solutions 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.Also covered advance topics include Transposition, simultaneous linear equations, elimination by cancellation, elimination by substitution, adding two equations and subtracting one equation from the other, cross multiplication method, graphical method, nature of solutions, word problems and applications of simultaneous equations

Chapter 4: Quadratic Equations

Standard form of a quadratic equation ax2 + 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. Advance topics include roots of equation, finding the roots by factorisation, finding the roots by using the formula , sum and products of roots of a quadratic equation, nature of the roots, signs of the roots, constructing a quadratic equation, finding the roots of a quadratic equation by graphical method, equation of higher degree, maximum or minimum value of a quadratic expression, quadratic in-equations.

Chapter 5: Arithmetic Progressions

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 Some more advanced topics include Arithmetic Mean (A.M), Geometric Progression (G.P), Infinite geometric progression, Harmonic Progression ( H.P), Harmonic mean, inserting n harmonic means between two numbers, relationship between A.M, H.M, and G.M of two numbers.

Chapter 6: 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 of their corresponding sides.
- (Prove) In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- (Prove) In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, the angle opposite to the first side is a right angle.

Chapter 7: Coordinate Geometry

Lines (In two-dimensions)

Review: Concepts of co-ordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.Advance topics included are convention of signs, applications of distance formula, collinearity of three points, straight lines, inclination of a line, slope of gradient of a line, intercepts of a straight line, equation of line in general form, equation of some standard lines, oblique line, different forms of equations of oblique lines, areas of triangle, area of quadrilateral, section formulae, mid point, centroid, equation of a line parallel or perpendicular to the given line, median of a triangle, altitude of a triangle.

Chapter 14: Statistics

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.More advanced topics include data, types of data, tabulation or presentation of data, class interval, class boundaries, class size, class mark of mid value, statistical graphs, bar graph, histograms, frequency polygon, frequency curve, cumulative frequency curves, arithmetic mean for raw data, weighted arithmetic mean, median, mode, properties of mode, measure of central tendencies for grouped data, mean of grouped data, median of grouped data, mode of grouped data, range, calculation of variance and standard deviation of raw and grouped data, coefficient of variation, quartiles, estimation of mode from histogram.

Chapter 15: Probability

Classical definition of probability. Simple problems on finding the probability of an event. Sub topics include sample space, events, probability of an event, probability of non occurrence of an event.

Chapter 15: Probability

Classical definition of probability. Simple problems on finding the probability of an event. Sub topics include sample space, events, probability of an event, probability of non occurrence of an event,

Note: 1. Topic “Solutions of quadratic equations by completing the square method.” of chapter 4 will be deleted as per CBSE curriculum 2019-20.

Chapter 8: 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^{0} and 90^{0}. Values of the trigonometric ratios of 30^{0}, 45^{0} and 60^{0}. Relationships between the ratios.

Proof and applications of the identity sin^{2} A + cos^{2}A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles. Sub topics include angle, systems of measurement of angle, trigonometric ratios, pythagorean triplets, trigonometric identities, standard position of an angle, coterminal angles, signs of trigonometric ratios, trigonometric tables

Chapter 9: Some Applications of Trigonometry

Heights and distances: Angle of elevation, Angle of Depression. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30, 45^{0}, 60^{0}

Chapter 10: Circles

Tangent to a circle at point of contact

- (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 a circle are equal.

Chapter 11: Constructions

Division of a line segment in a given ratio (internally). Tangents to a circle from a point outside it.

Construction of a triangle similar to a given triangle.

Chapter 12: Area 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 the area of the segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)

Chapter 13: Surface Areas and Volumes

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.

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

Suggested Mathematics Question Paper Design - Class 10

Typology of Questions

**Remembering:** Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.

Number of Questions Asked that are Objective type Questions = 6

Number of Questions Asked that are Short Answer Type Questions = 4

Number of Questions Asked that are Long Answer Type Questions = 1

Total Marks = 20

Total Weightage = 25%

Typology of Questions

**Understanding:** Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions and stating main ideas

Number of Questions Asked that are Objective type Questions = 6

Number of Questions Asked that are Short Answer Type Questions = 2

Number of Questions Asked that are Long Answer Type Questions = 3

Total Marks = 23

Total Weightage = 29%

Typology of Questions

**Applying:** Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.

Number of Questions Asked that are Objective type Questions = 5

Number of Questions Asked that are Short Answer Type Questions = 4

Number of Questions Asked that are Long Answer Type Questions = 1

Total Marks = 19

Total Weightage = 24%

Typology of Questions

**Analysing:** Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations

**Evaluating:** Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.

**Creating:** Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions

Number of Questions Asked that are Objective type Questions = 3

Number of Questions Asked that are Short Answer Type Questions = 4

Number of Questions Asked that are Long Answer Type Questions = 1

Total Marks = 18

Total Weightage = 22%

Internal Assessment = 20 Marks

Pen Paper Test and Multiple Assessment (5+5) = 10 Marks

Portfolio = 5 Marks

Lab Practical (Lab activities to be done from the prescribed books) = 5 Marks

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