The Grade X Mathematics syllabus is divided into four compulsory units. Each unit carries separate marks and together they form a 3-hour examination of 100 marks.
Total Marks: 100Time: 3 HoursAll four units are compulsory. Separate marks are given with each unit.
Instructions: This syllabus is divided into four units. All units are compulsory and separate marks are indicated with each unit as given below.
Across all units, learners build: strong foundations in real numbers, algebra, trigonometry, coordinate geometry, Euclidean geometry, mensuration, statistics and probability, with applications connected to real-life situations.
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 and non-terminating recurring decimals.
ALGEBRA - POLYNOMIALS
Zeros of a polynomial.
Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials.
Statement and simple problems on the division algorithm for polynomials with real coefficients.
ALGEBRA - PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Pair of linear equations in two variables.
Geometric representation of different possibilities of solutions: consistency and 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 based on pairs of linear equations.
ALGEBRA - QUADRATIC EQUATIONS
Standard form of a quadratic equation: ax² + bx + c = 0, (a ≠ 0).
Solution of quadratic equations (only real roots) by factorisation 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.
ALGEBRA - ARITHMETIC PROGRESSIONS
Motivation for studying Arithmetic Progressions (AP).
Derivation of standard results for finding the nth term and the sum of first n terms of an AP.
Grade X · Mathematics · Unit 2
TRIGONOMETRY & COORDINATE GEOMETRY (30 Marks)
30 Marks
INTRODUCTION TO TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle.
Proof of the existence (well-defined nature) of trigonometric ratios.
Motivate the ratios which are defined at 0° and 90°.
Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°.
Relationships between the trigonometric ratios.
TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin²A + cos²A = 1.
Only simple identities are to be given.
Trigonometric ratios of complementary angles.
HEIGHTS AND DISTANCES
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° and 60°.
COORDINATE GEOMETRY - 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 division).
Area of a triangle using coordinates.
Grade X · Mathematics · Unit 3
GEOMETRY & MEASUREMENT (30 Marks)
30 Marks
TRIANGLES
Definitions, examples and 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 (Pythagoras theorem).
(Prove) In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.
CIRCLES
Tangents to a circle motivated by chords drawn from points coming closer and closer to the 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.
CONSTRUCTIONS
Division of a line segment in a given ratio (internally).
Construction of a tangent to a circle from a point outside it.
Construction of a triangle similar to a given triangle.
MEASUREMENT - AREAS 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 plane figures.
In calculating area of the segment of a circle, problems should be restricted to central angles of 60°, 90° and 120° only.
Plane figures involving triangles, simple quadrilaterals and circles should be taken.
MEASUREMENT - SURFACE AREAS AND VOLUMES
Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinder/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 should be taken.
Grade X · Mathematics · Unit 4
STATISTICS & PROBABILITY (10 Marks)
10 Marks
STATISTICS
Mean, median and mode of grouped data (bimodal situations to be avoided).
Cumulative frequency graph.
PROBABILITY
Classical definition of probability.
Connection with probability as given in Class IX.
Simple problems on single events, not using set notation.
