Mathematics Class X Syllabus
ExamÂ Structure
Units | Marks | |
I | Number Systems | 06 |
II | Algebra | 20 |
III | Coordinate Geometry | 06 |
IV | Geometry | 15 |
V | Trigonometry | 12 |
VI | Mensuration | 10 |
VII | Statistics & Probability | 11 |
Â | Total | 80 |
UNIT I: NUMBER SYSTEMS
1. REAL NUMBERS
Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustratingÂ and motivating through examples, Proofs of results – irrationality of âˆš2, âˆš3, âˆš5, decimal expansions of rational numbers inÂ terms of terminating/non-terminating recurring decimals.
UNIT II: ALGEBRA
1. POLYNOMIALS
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problemsÂ on division algorithm for polynomials with real coefficients.
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities ofÂ solutions/inconsistency.
Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution,Â by elimination and by cross multiplication method. Simple situational problems must be included. Simple problems on equationsÂ reducible to linear equations.
3. QUADRATIC EQUATIONS
Standard form of a quadratic equation ax^{2}+bx+c=0, (a â‰ Â 0). Solution of the quadratic equationsÂ (only real roots) by factorization, by completing the square and by using quadratic formula. Relationship betweenÂ discriminant and nature of roots.
Situational problems based on quadratic equations related to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS
Motivation for studying Arithmetic Progression Derivation of the n^{th}Â 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)
Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.
UNIT IV: GEOMETRY
1. 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 twoÂ 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 theÂ triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the twoÂ triangles are similar.
- (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles areÂ 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 trianglesÂ 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 oppositeÂ to the first side is a right traingle.
2. 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.
3. 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
1 . INTRODUCTION TO TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios,Â whichever are defined at 0Â° and 90Â°. Values (with proofs) of the trigonometric ratios of 30Â°, 45Â° and 60Â°. RelationshipsÂ between the ratios.
2. TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities to be given. Trigonometric ratios ofÂ complementary angles.
3. HEIGHTS AND DISTANCES
Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles ofÂ elevation / depression should be only 30Â°, 45Â°, 60Â°.
UNIT VI: MENSURATION
1. AREAS RELATED TO CIRCLES
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter /Â circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restrictedÂ to central angle of 60Â°, 90Â° and 120Â° only. Plane figures involving triangles, simple quadrilaterals and circle should beÂ taken).
2. SURFACE AREAS AND VOLUMES
(i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids,Â 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 withÂ combination of not more than two different solids be taken).
UNIT VII: STATISTICS AND PROBABILITY
1. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
2. PROBABILITY
Classical definition of probability. Simple problems on single events (not using setÂ notation).