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First Term Exam Syllabus for Grade X
UNIT I : NUMBER SYSTEMS
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 results - irrationality of √2, √3, √5, decimal
- expansions of rational numbers in 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 problems 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 of solutions/inconsistency
- 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
- Simple situational problems must be included
- Simple problems on equations reducible to linear equations may be included
UNIT III : 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 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 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 opposite to the first side is a right traingle
UNIT IV : 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
- whichever are defined at 0o & 90o
- Values (with proofs) of the trigonometric ratios of 30o, 45o & 60o. Relationships between the ratios
2. TRIGONOMETRIC IDENTITIES
- Proof and applications of the identity sin2 A + cos2A = 1. Only simple identities to be given
- Trigonometric ratios of complementary angles
UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS
- Mean
- median
- mode of grouped data
- Cumulative frequency graph
Second Term Exam Syllabus for Class X
UNIT II : ALGEBRA (Contd.)
3. QUADRATIC EQUATIONS
- Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0)
- Solution of the quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula
- Relationship between discriminant and nature of roots
- Problems related to day to day activities to be incorporated
4. ARITHMETIC PROGRESSIONS
- Motivation for studying AP
- Derivation of standard results of finding the nth term
- sum of first n terms
- their application in solving daily life problems
UNIT III : GEOMETRY (Contd.)
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
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 IV : TRIGONOMETRY
3. HEIGHTS AND DISTANCES
- Simple and believable problems on heights and distances
- Angles of elevation / depression should be only 30o, 45o, 60o
UNIT V : STATISTICS AND PROBABILITY
2. PROBABILITY
- Classical definition of probability
- Connection with probability as given in Class IX
- Simple problems on single events, not using set notation
UNIT VI : COORDINATE GEOMETRY
1. LINES (In two-dimensions)
- 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 VII : MENSURATION
1. AREAS RELATED TO CIRCLES
- the area of a circle
- area of sectors and segments of a circle
- Problems based on areas, perimeter, and circumference of the above said plane figures (In calculating area of segment of a circle, problems restricted to central angle of 60o, 90o & 120o only
2. SURFACE AREAS AND VOLUMES
- 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
- Problems involving converting one type of metallic solid into another and other mixed problems
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