## JKBose Syllabus class 10th – Mathematics

Syllabus for the Mathematics subject of Class 10th, PDF file, The state board of School Education Jammu and Kashmir Syllabus:

## JKBose 10th Maths Subject and Marks

### Unit 1: NUMBER SYSTEMS

Real Numbers 05 Marks

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, decimal expansions of rational numbers in terms of terminating / non terminating recurring decimals.

### UNIT 2: ALGEBRA

• Polynomials 05 Marks

Zeros of a Polynomial. Relationship between zeros and Coefficients of a Polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

• Pair of Linear Equations in Two variables 07 Marks

Pair of Linear equations in two variables. Geometric representations of different possibilities of solutions/ inconsistency. Algebraic conditions for a number of solutions. Solutions of pair of linear equations in two variables algebraically – by substitution, by elimination, and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included

Standard form of a quadratic equations ax2 + bx + c = 0 ( a # 0 ). Solutions of quadratic equations ( only real roots ) by factorization and by completing the square i.e. by using the quadratic formula. Relationship between discriminant and nature of roots. Problems related to day to day activities to be incorporated.

• Arithmetic Progressions(AP) 07 Marks

Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.

### UNIT 3: TRIGONOMETRY

• Introduction to Trigonometry 07 Marks

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

Trigonometric Identities: Proof and applications of the identity sin 2 A + cos2 A + 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

• Heights and Distances 07 Marks

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 degree.

### UNIT 4: COORDINATE GEOMETRY

Lines ( in two- dimensions) 08 Marks

Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representations of quadratic polynomials. Distance between two points and section formula ( internal ). Area of a triangle.

## UNIT 5: GEOMETRY

• Triangles 09 Marks

Definitions, examples, counterexamples 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.

## JKBose Class 10th Maths Geometry Syllabus

( 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 to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.

### Also check JKBose Class 10th English Syllabus

( 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 the sum of the squares on the other two sides, the angles opposite to the side is a right triangle.

• Circles 06 Marks

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 a circle are equal.

• Constructions 07 Marks

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 6: MENSURATION

• Areas Related to Circles 04 Marks

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 a segment of a circle, problems should be restricted to the central angle of 60, 90, and 120 degrees only. Plane figures involving triangles, simple quadrilateral, and circle should be taken).

• Surface Areas and Volumes 07 Marks

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 cone.

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 7: STATICS AND PROBABILITY

• Statics 07 Marks

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

• Probability 04 Marks

Classical definition of Probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.