|Unit 1||Number System and Number Sense||05||read more|
|Unit 2||Algebra (core)||10||read more|
|Unit 3||Coordinate Geometry (core)||15||read more|
|Unit 4||Lines, Angles and Triangles (core)||20||read more|
|Unit 5||Quadrilaterals and Area of Parallelograms & Triangles (core)||05||read more|
|Unit 6||Circle (core)||15||read more|
|Unit 7||Area of Plane Figures and Solid Shapes (core)||10||read more|
|Unit 8||Volume of Solids (core)||05||read more|
|Unit 9||Introduction to Trigonometry (core)||10||read more|
|Unit 10||Introduction to Statistics and Probability (core)||05||read more|
|Total Marks||100||Time: 3 Hours|
Variable, constant, algebraic expression, equation.
Definition of polynomial, degree of polynomial, No. of terms in a polynomial of degree n, Types of polynomial based on number of terms-monomial, binomial, trinomial etc.
Types of polynomial based on degree of polynomial- linear, quadratic etc.
Sum, difference, product and division of polynomial.
Factor theorem, Remainder theorem and their applications
Difference between polynomial, equation and identity, proving identities using manipulative or otherwise:(a+ b + c)2, a4,– b4 , a3,– b3 , a3 + b3
Factorizing polynomial using common factors.
Factorizing polynomial by splitting middle terms
Factorizing using algebraic identities: a2 – b2, (a+ b + c)2, a4,– b4 , a3,– b3 , a3 + b3
Linear equation in one variable, solution of linear equations and its representation on number line, expressing word statements into linear equations.
Linear inequalities in one variable and their representation on number line.
Quadratic equation in one variable, to verify the solution of given quadratic equation.
Number patterns and geometric patterns.
Introduction of terms like axes, quadrants, origin, abscissa, ordinate, ordered pair, Cartesian coordinates, Cartesian independent and dependent variables plane.
Representation of a given point in Cartesian plane in the form of ordered pair. Plotting of a given point in the plane.
Point of intersection of simultaneous straight line equations drawn in same plane and that the point of intersection represents the solution of two equations.
Real life situation graphs including travel graphs and conversion graphs; graphs of quantities that vary against time.
Plot of two independent variables (scatter diagram) and examination by eye for positive or negative correlation
Point, Line, line segment, collinear points, non collinear points; Angle: right angle, acute angle, obtuse angle, straight angle, reflex angle, supplementary angles, complementary angles; Parallel lines, perpendicular lines, transversal; Triangle: scalene, isosceles, equilateral, acute angled, obtuse angled, right angled; Median, altitude, bisector of an angle, perpendicular bisector of a line segment.
Pair of angles: adjacent angles, linear pair, vertically opposite angles; Linear pair axiom; Parallel lines and transversal: exterior angles, interior angles, corresponding angles, alternate interior angles, interior angles on the same side of transversal; corresponding angle axiom and converse, if a transversal intersects two parallel lines then each pair of alternate interior angles are equal and converse, if a transversal intersects two parallel lines then each pair of interior angles on the same side of the transversal is supplementary and converse; Proof: sum of interior angles of a triangle is 180 degrees, exterior angle property of triangle.
Congruence criteria: SSS, SAS, ASA, RHS; Properties: angles opposite to equal sides of an isosceles triangle are equal and converse; all angles of an equilateral triangle are 60 degrees.
Polygon, convex and concave polygons, quadrilateral, vertices, diagonal, adjacent sides, adjacent angles, opposite sides, opposite angles, types of quadrilaterals: square, rectangle, parallelogram, rhombus, trapezium, isosceles trapezium, and kite. Base and altitude of parallelogram.
Exploration of following properties of parallelogram:
Investigation into following results:
Definition of circle, centre, radius, diameter, Interior of circle, circular region, exterior of circle ,arc, chord, minor segment, major segment, minor arc, major arc, sector of circle, minor sector, major sector, semicircular region, circumference of circle, angle subtended by the chord at a point on the circle, angle subtended by the arc at the centre of circle, concentric circles, intersecting circles, congruent circles, concyclic points.
Equal chords of a circle (or of congruent circles) subtend equal angles at the centre; If the angles subtended by the chords of a circle (or of congruent circles) at the centre are equal, then the chords are equal.
The perpendicular from the centre of a circle to a chord bisects the chord; The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
Perimeter & area of plane figures, curved surface area and total surface area of solids.
Area of right triangle, isosceles triangle, equilateral triangle, rectangle, square, parallelogram, rhombus, trapezium.
Area of triangle using Heron's formula and its application in finding area of quadrilateral.
Surface Area of cube, cuboids, curved surface area and total surface area of cylinder, cone, sphere and hemisphere.
Applications in finding the area of field, land etc.
Volume as product of area of base and height.
Formulae for finding volume of cube and cuboid of given dimension.
Volume of a hollow right circular cylinder. Volume of metal required to cast a solid right circular cylinder. volume of cylindrical pipe of given thickness. volume of a right circular cone, relation between volume of right circular cylinder and right circular cone of given radius and given height.
Volume of sphere and hemisphere of given radius.
Trigonometry as study of right angle triangle using relation between its sides and angles.
Primary data and secondary data.
Ungrouped data and grouped data class interval, class-marks, upper limit, lower limit, frequency, range, cumulative frequency, class-size, discrete data and continuous data.
Measure of central tendency: Mean, median, mode of ungrouped data Interpretation of Bar graph, histogram of uniform width and frequency polygon for a given data.
Probability as chance of occurrence of an event Basic terms: random experiment, sample space, event, favourable and unfavourable events, sure event and impossible event.
Probability of an event E is P(E)= n/N, where n is number of favourable events and N is total number of events in a sample space