Syllabus of Higher Secondary
Standard 8-9-10
Implemented From June - 2004 in Standard - 8,
Implemented From June - 2005 in Standard - 9,
Implemented From June - 2006 in Standard - 10

Standard 8
Maths

Standard - 9 | Standard - 10

Number Sets

(1) Set operations

• Universal set

• Properties of Union

• Properties of intersection

• Distributive property

• Properties of complementation

(2) Cartesian Product

• Cartesian product of two sets

• Equality of ordered pairs

• Graph in the plane

• Cartesian coordinate system

• One to one correspondence between the plane and R x R

• Quadrant

• Graph of Cartesian product Arithmetic

(3) Percent

• Discount and commission

• Successive discount

• Cost of living index

• Sales tax

(4) Banking

• Different types of bank accounts

• Cheque and its types

• Calculation of interest from passbook of savings account passbook

• Calculation of interest on fixed deposit

• Algebra 

(5) Factorization

• Revision of factorization of Std. Vill( maximum degree -3)

• Ax2 + bx + c (a ¹ O)and factors by splitting the middle term in a,bc.

• (x+y)(x2+xy+y2) - Expansion

• factors of x3+y3

• factors of x3+y3+z3 - 3xyz

• if x+y+z = 0 then x3+y3+z3= 3xyz

• factorization with the help of remainder theorem

(6) properties of ratio and proportion

• laws of ratios (laws - alternendo , invertendo , componendo,dividendo,

• equality of ratios componendo & dividendo)

(7) Variation

• Direct variation

• Inverse variation

• Compound variation

• Partial variation

(8) Linear equations of two variables

• Explanation of two variable linear equation

• Solution of a linear equation of two variables

• Method of elimination

• Graphical method Geometry

(9) Triangle and conditions of congruence

• Triangle and its elements

• Interior of triangle

• Correspondence

• Congruence of triangles

• SAS postulate

• Theorem:- If two angles and included side of one triangle are congruent to the corresponding elements of the other triangle then those two triangles are congruent (ASA) (with proof)

• Theorem:- If two sides of a triangle are congruent then their opposite angles are congruent. (with proof)

• Theorem:- If two angles of a triangle are congruent then their opposite sides are congruent. (without proof)

• Corollary:- Every equilateral triangle is equiangular

• Corollary:- Every equiangular triangle is equilateral.

• Theorem (SSS):- If three sides of one triangle are congruent to the corresponding three sides of the other triangle then triangles are congruent. (without proof)

• Theorem (RHS):- Given a correspondence between two right triangles, if the hypotenuse and leg (side) of one triangle are congruent with the corresponding elements of the other trangle, then correspondence is congruence.

(10) Inequalities of triangles

• Theorem:- If the measures of two sides of a triangle are unequal, the measure of an angle opposite to the side of greater measure is greater. (with proof)

• Theorem:- If a triangle has two angles unequal, the side opposite to the greater angle is greater than the side opposite to the smaller angle. (with proof)

• Theorem:- Sum of lengths of any two sides of a triangle is greater than the length of the third side. (with proof)

• Theorem:- Given a line and a point external to it, of all the line segments joining to that point to any point of the line the perpendicular line segment is of the least measure.

• Definition:- Exterior angle and its remote interior angles.

• Characterized point set
  (1) The point set of the set of points of a plane which are equidistant from two given points in the plane is the perpendicular bisector of the line segment joining the points.
  (2) The point sets of points in a plane equidistant from two intersecting lines is a pair of bisectors of the angles formed by these lines.

• Theorem:- Measure of an exterior angle of a triangle is greater than measure of each of the remote interior angles of that angle. (without proof)

(11) Parallel lines in a plane

• Postulate of parallel lines

• Theorem:- Angles of every pair of corresponding angles, formed by the transversal of two parallel lines are congruent and its converse is also true. (without proof)

• If a transversal intersects two parallel lines, angles of every pair of alternate angles are congruent. (with proof)

• Theorem:- converse of the theorem mentioned above (without proof)

• Theorem:- If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal so formed are supplementary. (with proof)
  Converse of the theorem mentioned above. (without proof)

• Theorem:- Lines parallel to a given line are parallel (without proof)

• Theorem:- Measure of an exterior angle is equal to the sum of measure of the remote interior angles. (without proof)

• Sum of measure of three angles of a triangle is 180o (with proof)

(12) Properties of parallelogram (Plane quadrilateral and convex quadrilateral definition)

• Parallelogram (definition)

• Properties of parallelogram

• Diagonals of parallelogram, divides it into two congruent triangles (without proof)

• Opposite sides of parallelogram are congruent. Its converse is true. (without proof)

• Opposite angles of parallelogram are congruent. Its converse is true (without proof)

• Theorem:- If one pair of opposite sides of a quadrilateral is parallel and congruent, it is a parallelogram. (with proof)

• Theorem:- Diagonals of a parallelogram bisect each other. Its converse is also true. (without proof)

• Theorem:- If the diagonals of parallelogram are congruent then it is a rectangle (without proof)

• Theorem:- Its converse is also true.

• Theorem:- If the diagonals of a parallelogram are perpendicular then lit is a rhombus.

• Converse of it is also true. (without proof)

• Theorem:- If the diagonals of a parallelogram are congruent and perpendicular then it is a square. Its converse is also true. (without proof)

• Theorem:- The line segment joining the mid points of any two sides of a triangle is parallel to its third side and of measure equal to half its measure (with proof)

• Theorem:- If three or more parallel lines make congruent intercepts on one transversal, then they make congruent intercepts on other transversal also. (with proof)

(13) Concurrent lines:-

• Theorem:- The bisectors of angles of a triangle are concurrent (without proof)

• Theorem:- The perpendicular bisectors of the sides of a triangle are concurrent (without proof)

• Theorem:- The medians of a triangle are concurrent and centroid divides the median in ratio 2:1 (with poof)

• Theorem:- The altitudes of a triangle are concurrent (without proof)

(14) Area

• Triangular and quadrilateral regions

• Postulates of area
  1) Postulate of area :- To every triangular gegion there corresponds a unique positive number which is said to be the area of the region.
  2) Postulate of congruence (Area):- If two triangles are congruent the areas of their triangular regions are equal.
  3) Postulate of addition of area :- D* ABC = area of D* ABD + area of D* ADC.
  4) Postulate of the area of a rectangle:- The area of a rectangular region is equal to the product of the lengths of any two consecutive sides of the rectangle.

• Area of triangle

• Area of parallelogram

• Equivalent figures

• Theorem:- Parallelograms on the same base and between the same pair of parallel lines are equivalent (with proof)

• Theorem :- Triangles on the same base and between the same pair of parallel lines are equivalent. (without proof)

(15) Practical and Constructive geometry (constructions)

• Construction 1:- Base of triangle , one base angle and sum of length of two sides.

• Construction 2:- Base , right angle on base and difference of length of two sides.

• Construction 3:- Perimeter of triangle and both the angles on base.

• Construction 4:- Two sides of triangle and one median.

• Construction 5:- Triangle which is equivalent to a given parallelogram. (Proof is not required in all constructions. Use scale and compass)

• Construction of quadrilateral: (length of sides in integers and angles in multiple of 50

• Construction 6:- four sides and diagonals.

• Construction T- Three sides and two diagonals.

• Construction 8:- Two adjacent sides and three angles.

• Construction 9:- Three sides and two included angles.

(16) Area:

• To find area of triangle using Hero's formula.

• Area of quadrilateral.

• Area of sector and segment of acircle.

• Area of triangle and problems based on perimeter.(To find area of segment of a circle, angles subtended at the centre to be taken of measure 60°, 90°, & 120°)
  (In coplanar figures , rectangle , square , triangle , trapezium quadrilateral, parallelogram, rhombus and circle should be taken)

(17) Solid figures:- To explain solid figures.

(1) Prism (2) Pyramid (cuboidal) (square pyramid)
(3) Introduction of octagonal pyramid , octahedron)
(17.2) Surface areas and volume of the following figures:-
(1) Right angle and triangular prism.
(2) Equilateral triangle whose base is rectangular.
(3) Volumes and surface area of the figures obtained above and simple problem sums based on it.

• Statistics (Observations not exceeding 30 , no. of observation's for X , m and z not
  exceeding 10 i.e. maximum 10)

(18) Statistics

• Classification of data and graphical representation

• Classification frequency, frequency table, cumulative frequency, to take equal class length.

• Measures of central tendency of ungrouped data and sums
  X, m and z - properties and uses.

• Trigonometry

(19) Trigonometric ratios

• Similar triangles

• Trigonometrical ratios

• The invariant natural of the trigonometric ratios.

• The inter relationship of the trigonometrical ratios.

• Identity sin2 q + COS2 q = 1 (with proof)

• Sums of finding values of special angles.(30°, 45°, 60°)

• To accept values in tabular form.

Standard - 9 | Standard - 10

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