Syllabus

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1. Number System

• Terminating and non-terminating decimals, definition of rational and irrational numbers, recurring decimals into rational number.
• Rational numbers, representation on number line, rational numbers between two numbers.
• Irrational numbers, decimal number on number line, square root number on number line.
• Exponents and powers (surds), Properties on exponents.
• Problems based on exponents and power.
• Rationalisation of irrational denominator.
• Problems based on irrational number and rationalisation.

2. Polynomials

• Definition and Classification of polynomials, zeroes of polynomials.
• Remainder theorem, problems based on remainder theorem.
• Factor theorem, problems based on factor theorem.
• Derivation of algebraic identities in whole square form and its application.
• Derivation of algebraic identities in whole cube form and its application.
• Simplification using identities.
• Factorization of quadratic polynomial using splitting middle term.
• Factorization using identities.
• Miscellaneous problems on polynomials.

3. Coordinate Geometry

• Representation of points on coordinate axes, Meaning of abscissa and ordinate.
• Problems based on coordinate geometry, to find image  of a point and distance between two points.

4. Linear Equations in Two Variables

• Linear equation in two variables and their graphical representation.
• Word problems and application of Linear equations in two variables.

5. Introduction to Euclid's Geometry

• Postulates of Euclid, relationship between axiom and theorem.

6. Lines and Angles

• Adjacent Angles, Complementary Angles, Supplimentary Angles.
• Linear pair, vertically opposite angles and problems based on intersecting lines.
• Corresponding angles, alternate angles, problems based on parallel and transversal lines.
• Problems on parallel and transversal lines.
• Angle sum property and problems based on angle sum.
• Problems on angle sum and exterior angle properties.

7. Triangles

• Congruent figures definition, congruency of two triangles.
• SAS, SSS, ASA, AAS and RHS congruency theorem in a triangle and its basic application, CPCT.
• Problems based on Congruent Triangles.
• Theorem and problems on inequalities of triangles.
• Miscellaneous problems on triangles.

8. Quadrilaterals

• Types of quadrilaterals and their properties.
• Properties of a paralleogram and their proof.
• Problems on parallelograms.
• Problems on parallelograms and other quadrilaterals.
• Mid-point theorem proof and applications.
• Problems on mid-point theorem and its converse.
• Intercept theorem proof and applications.
• Miscellaneous problems based on parallelogram , mid-point theorem and intercept theorem.

9. Areas of Parallelograms and Triangles

• Proof of theorem on areas of parallelograms and triangles.
• Problems on areas of parallelograms and triangles.

10. Circles

• Proof of theorems on chords and arcs of a circle.
• Proof of theorems in two congruent circles.
• Problems on theorems on chords and arcs.
• Proof of theorems on angles in the same segment.
• Application on angles in the same segment theorems.
• Proof of theorems related to cyclic quadrilateral.
• Problems on cyclic quadrilateral.

11. Constructions

• Construction of line and angle bisector, construction of equilateral triangle.
• Construction of triangles if sum and difference of two sides are given.
• Construction of triangles if sum of all the three sides is given.

12. Heron's Formula

• Area of triangle formula derivation.
• Heron's formula application.
• Application of Heron's formula to find the area of quadrilaterals.
• Application of Heron's formula in different shapes.
• Miscellaneous problems on areas.

13. Surface Areas and Volumes

• Surface areas and volumes of cuboid and cube concepts and applications
• Problems on surface areas and volumes of cuboid and cube
• Problems on water flow in cubiodal pipe
• Surface areas and volumes of solid cylinder and hollow cylinder concepts and applications
• Problems on surface areas and volumes of cylinder
• Problems on water flow in cylindrical pipe
• Surface areas and volumes of cone concepts and applications
• Problems on surface areas and volumes of cone
• Surface areas and volumes of sphere and hemisphere
• Problems on combination of two or more than two figures

14. Statistics

• Collection and representation of data in tabular form.
• Drawing bar graph and histogram and problems based on given bar graph and histogram.
• Problems based on frequency polygons.
• Mean of ungrouped data.
• Properties of mean and problems on properties of mean.
• Median of ungrouped data.
• Mode of ungrouped data, emperical relation between mean, median and mode.

15. Probability

• Some terms related to probability, formula and properties of probability.
• Problems on probability.

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