HPBOSE Class 10 Maths Syllabus 2023-2024: HP Board Exam Pattern and Marking Scheme

HP Board 10th Maths Syllabus and Marking Scheme 2024: Himachal Pradesh Board of School Education (HPBOSE) has published its 10th class Maths syllabus 2023-24 on the official website of the board at hpbose.org. The syllabus enlists the objectives of the curriculum, the complete course content with division of marks and the names of prescribed books. The marking scheme is also given. The theory exam will be conducted for 80 marks. In this article, we have provided the HP 10th maths marking scheme and the complete syllabus of HPBOSE Matric Maths for 2024.

HPBOSE Class 10 Maths Syllabus Course Structure 2024

Check the unit-wise course structure here:

HP Board Class 10 Maths Marking Scheme 2024

Check the marking scheme here:

HPBOSE Class 10 Maths Syllabus 2024

Check the complete course content here:

UNIT I : NUMBER SYSTEMS

1. REAL NUMBERS ( 6 Marks) 

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

UNIT II : ALGEBRA 

1. Polynomials ( 3 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. 

2. Pair of Linear Equations in Two Variables. ( 6 Marks) 

Pair of linear equations in two variables. Geometric representation of different possibilities of solutions inconsistency. Algebraic conditions for number of solutions. Solution 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. 

3. Quadratic Equations ( 3 Marks) 

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

4. Arithmetic Progression ( 5 Marks) 

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

UNIT III : TRIGONOMETRY : 

1. Trigonometric Ratios ( 7 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 00 & 900 . Values (with proofs) of the trigonometric ratios of 300 , 450 , & 600 . 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. 3. Heights and Distances ( 5 Marks) Simple and believable problems on heights and distances. Problems should not involve more than two right triangle. Angles of elevation/ depression should be only 300 , 450 , 600 . 

UNIT IV: COORDINATE GEOMETRY 

1. Lines (In two-dimensions) ( 6 Marks) 

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

UNIT V : GEOMETRY 

1. TRIANGLES ( 9 Marks) 

Definitions, examples, counter examples of similar triangles. 

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect to 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) If 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. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides. 
7. (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. 
8. (Prove) In a right triangle, the square of the hypotenuse is equal to the sum of the squares of 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 triangle. 

CIRCLES ( 4 Marks) 

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

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 circle are equal. \

CONSTRUCTIONS ( 3 Marks) 

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

UNIT VI MENSURATION 

AREAS OF PLANE FIGURES ( 6 Marks) 

The area of circle; area of sectors and segments of a circle. Problems bases 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 600 , 900 , & 1200 only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).

SURFACE AREAS AND VOLUMES ( 7 Marks) 

1. 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. 
2. Problems involving concerting 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 ( 5 Marks) 

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

2. PROBABILITY ( 5 Marks) 

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

HPBOSE Class 10 Maths Prescribed Books 2023-24

1. Ganit Published by H.P. Board of School Education.