Syllabus
1. Real Numbers
- Terminating and non-terminating decimals, recurring decimals.
- To prove a square root number is irrational.
- To find HCF and LCM by prime factorization method and Properties of HCF and LCM.
- Word problems on HCF and LCM.
2. Polynomials
- Types of polynomial, geometrical representation of polynomial, zeroes of the polynomial.
- Quadratic polynomials, its zeroes and coefficients.
- Problems on zeroes and coefficient of quadratic polynomials.
- To find the quadratic polynomials, when zeroes are given.
- Division algorithm for polynomials and its application.
- Cubic polynomials, its zeroes and coefficients.
- Find the zeroes of cubic and biquadratic polynomials, Miscellaneous problems on polynomials.
3. Pair of Linear Equations in Two Variables
- Substitution method to solve a pair of linear equations
- Elimination method to solve a pair of linear equations
- Important problems on elimination method
- Higher order thinking skills (HOTS) on cross-multiplication method
- Graphical method to solve a pair of linear equations
- Unique solution, no solution and infinite solutions of a pair of linear equations. Consistency and inconsistency
- Word problems based on numbers, fraction, ratio and two digit numbers
- Word problems based on age of the person and geometry
- Word problems on time, distance and speed
- Word problems based on areas and perimeter, fexed and variable charges
- Word problems on time and work, profit, loss and discount and Miscellaneous problems
4. Quadratic Equations
- To solve the quadratic equations by factorization method
- Problems based on factorization method
- Quadratic formula derivation, solution of equation by formula method and nature of roots
- Problems based on nature of roots
- Word problems on numbers and consecutive numbers
- Word problems on two digit numbers and fraction
- Word problems on speed, distance and time
- Word problems on speed, distance and time and upstream, downstream
- Word problems on ages of person
- Word problems on areas and perimeter
- Word problems on time and work and cost
5. Arithmetic Progressions
- Sequences, introduction of arithmetic progressions
- nth term of and AP, derivation and application of formula
- Problems based on nth term of an AP, Word problems on nth term
- Sum of n terms of an AP (derivation and application of formula)
- Problems on sum of n terms of an AP
- Word problems on sum of n terms of an AP
6. Triangles
- Basic proportionality theorem (Thales theorem) and its converse (Proof of theorem)
- Application on Thales theorem and its converse
- AAA, AA, SSS and SAS similarity theorem (Proof)
- Problems based on similarity of triangles
- Pythagoras theorem and its converse proof
- Problems based on Pythagoras theorem
7. Coordinate Geometry
- Introduction to coordinate geometry, derivation of distance formula
- Problems based on distance formula
- Derivation of section formula and mid-point formula
- Problems based on section formula
- Centroid of triangle
8. Introduction to Trigonometry
- Trigonometric ratios of acute angles of a right angled triangle
- Application on trigonometric ratios
- Application based problems on trigonometric ratios
- Trigonometric ratios of some particular angles and its derivation
- Problems based on some particular angles
- Trigonometric identities derivation
- Problems based on trigonometric identities
- Problems based on trigonometric identities, some HOTS problems
- Problems based on elimination of trigonometric ratios
9. Some Applications of Trigonometry
- Angle of elevations, angle of depressions, basic problems
- Problems on heights and distances with two or more than two right angled triangles
- Prove that type problems on heights and distances
- Higher order thinking skills (HOTS) Problems on Heights and Distances
10. Circles
- Tangents and secant to the circle introduction, proof of theorems
- Problems based on tangents to the circle
11. Areas Related to Circles
- Areas of sector and segment and its application, basic formulae of two dimensional figures
- Problems on areas related to circles
12. Surface Areas and Volumes
- Revision of formulae of cuboid, cube, cylinder, cone, sphere and hemisphere
- Combination of two or more figures
13. Statistics
- Mean of ungrouped and grouped data by direct method, missing frequency problems
- Mean of grouped data by assumed mean and step deviation method
- Problems based on assumed mean and step deviation method
- Median of ungrouped data
- Median of grouped data, to find the missing frequencies
- Mode of ungrouped and grouped data, emperical relation between mean, median and mode
14. Probability
- Basic concepts of probability, properties of probability, sure event, impossible event
- Problems on probability