Syllabus
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.