IntroductionMathematics is the language of all sciences. The subject at the secondary level has great importance in a progressive country like India as it develops various living skill. It is important to note that the subject itself has a separate identity in the life of a man. The challenges due to the tremendous growth in the population, globalization, pollution, competition between countries, natural disasters emphasise the need to develop the curriculum in Mathematics at the secondary level. Knowledge of the subject and skills acquired while learning Mathematics develop the ability to execute, manage, plan with precision. This could be effectively inculcated at the secondary level and is hence a decisive factor in according Mathematics an important place in the scheme of studies of secondary education in the state of Maharashtra.
Mathematics at the primary stage of education develops the skill of quantification of experiences in learners. It helps to develop decision making which is applicable to real life situations in future. In addition, it helps enormously in the development of other disciplines which involves analysis, reasoning and qualification of ideas.
The study of Mathematics has to be graded at different levels viz. primary, higher primary and secondary, higher secondary levels. At the primary stage the focus is on understanding of various concept and fundamentals and on developing the basic skills of calculation. At the secondary level the emphasis is on the capacity of students to apply mathematics in solving problems. Secondly a systematic study of Mathematics as a discipline has to be started and continued for the use of algebraic methods, arithmetical skills. A study of the different applications of mathematics in various fielda like science, geography, economics, social science etc. gives the student a comprehensive and global prespective.
In the beginning of the 21st century, man has developed new disciplines like Information Technology, Genetic Engineering, Biotechnology, etc. on the basis of Mathematics. Thus a supplementary study of Mathematics is necessary to develop in students the skills essential for these new disciplines. We are confident that enriching these skills at the secondary level, will meet the basic and allied needs and fulfil the requirements in future. So, it has become necessary for every student to study and to develop a modicum of mathematical skills at the secondary level.
Objectives
To enable the students to-

• Introduction to Sequence
• Arithmetic progression ( A.P.) and Geometric Progression (G.P)
• General terms of an A.P. and G.P.
• Sum of the first ‘n’ terms of an A.P. and G.P.
• Arithmetic Mean and Geometric Mean

• Introduction to quadratic equations
• Solutions of quadratic equations
• Nature of roots based on discriminant
• Relation between roots of the equation and coefficient of the equation
• Equations reducible to quadratic form

• System of linear equations in two variables
• Algebraic methods of solving linear equations in two variables
• Graphical representation of different possibilities of solutions / inconsistency
• Graphical method of solving a system of linear equations
• Determinant of order two
• Cramer rule
• Consistency of pair of linear equations

• Introduction to probability and related terms
• Classical definition of probability
• Types of events
• Equally likely outcomes
• Probability of an event
• Properties of Probability
• Addition theorem ( without proof)

• Brief revision of Tabulation of data, inclusive and exclusive type of tables
• Mean median and mode of grouped data
• Histograms, frequency polygon, frequency curve, pie digram
• Ogives ( Cumulative frequency graphs)
• Applications ogives in determination of median
• Relation between measures of central tendency
• Introduction to normal distribution
• Properties of normal distribution

• Properties of ratios of area of two triangles
• Basic proportionality theorem
• Introduction to similarity
• Similar triangles
• Areas of two similar triangles
• Similarity in right angled triangles
• Pythagoras theorem and its converse
• 30⁰ – 60⁰ – 90⁰ theorem and 45⁰ – 45⁰ – 90⁰ theorem
• Application of Pythagoras theorem in acute and obtuse angle.
• Appolonius theorem

• Tangents and its properties
• Theorem – Tangent at any point to the circle is perpendicular to the radius and it converse
• Number of tangents from a point to a circle
• Theorem – The length of two tangent segments drawn from a point outside the circle are equal
• Touching circles
• Introduction to an arc
• Angle subtended by the are to the centre and to the point on the circle
• Cyclic quadrilateral
• Tangent – Secant theorem

• Slope of a line
• Intercepts made by a line
• Standard forms of equation of a line
• General equation of a line

• Division of line segment in a given ratio
• Basic geometric constructions
• Construction of tangent to the circle from the point on the circle and outside the circle.
• Construction of tangent without using centre
• Construction of triangle 0 If the base, angle apposite to it and either median or altitude is given
• Construction of a triangle similar to given triangle

• Angles in standard position
• Trigonometric ratios in terms of coordinates of point
• Trigonometric Identities ( with proof) Sin (0) = -Sin 0 ; Cos (-0) = Cos 0
• Use of basic identities and their applications
• Problems on height and distance

• Length of an area
• Area of the sector
• Area of a Circular Segment
• Euler’s formula
• Surface area and volume of cuboids Spheres, hemispheres, right circular cylinders, cones, frustum of a cone.
• Problems based on area and perimeter / circumference of circle, sector and segment of a circle.
• Problems on finding surface area and volumes of combinations of any two of the following : cuboids, spheres, hemispheres and right circular cylinders/ cones.
• Problems involving converting one type of metallic solid and into another

The National curriculum Framework 2005 (NCF 2005) is one of the most comprehensive documents published in the last decade. It suggests radical changes in curricula for the country and offers an excellent framework for preparing need based curricula. While revising the syllabi for Science and Technology, the position paper on science ( NCF 2005) has selected ‘’Learning without burden” as the main theme. It also recommends a pedagogy which is hand-on and inquiry based.
The present syllabus of Science and Technology for STD IX and X is based on the principles and themes suggested in NCF 2005. The Themes are cross – disciplinary in nature : Food, Materials, The world of the Living, How things work, Moving things; people and ideas; Natural phenomena and Natural Resources. Some themes have been merged to consolidate content.
As suggested in NCF 2005, unnecessary focus on enumeration has been avoided. More importance has been given to the processes in science rather than focusing on only factual information.
Since the themes are inter-linked to each other, the entire syllabus has been integrated into one paper. This will facilitate better understanding of the subject across disciplinary boundaries and at the same time expose students to many topics in Biology, physics and Chemistry.
The Objectives are :

1. To enable the students to ‘’Learn without Burden”.
2. To expose the students to a “hand-on way of learning science.
3. To correlate scientific principles to the student’s experience.
4. To involve students in exploring topics through discussion and activity.
5. To imbibe the spirit of enquiry in students through valuable learning experiences through experiment.
6. To help the students become autonomous learners.