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Syllabus for Std-X Maths SSC :

Organisation : Maharashtra State Board of Secondary & Higher Secondary Education
Announcement : Std-X Maths SSC Syllabus

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Std. X : Mathematics
1. Arithmetic Progression :
** Introduction to Sequence
** Arithmetic Progression (A.P.) and Geometric Progression (G.P.)
** General term 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.

2. Quadratic Equations
** Introduction to quadratic equations
** Solutions of quadratic equations
** Nature of roots based on discriminant
** Relation between roots of the equation and coefficient of the terms in the equation Equations reducible to quadratic form

3. Linear equations in two variables
** 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
** Determinantof order two
** Cramer’s rule
** Consistency of pair of linear equations

4. Probability :
** 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)

5. Statistics :
** 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 diagram
** Ogives (Cumulative frequency graphs)
** Applications of ogives in determination of median
** Relation between measures of central tendency
** Introduction to normal distribution
** Properties of normal distribution

Geometry :
1. Similarity :
** Properties of ratios of areas 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
** 30o-60o-90o theorem and 45 o-45 o- 90 o theorem
** Application of Pythagoras theorem in acute and obtuse angle.
** Appolonius theorem

2. Circle :
** Tangents and its properties
** Theorem – Tangent at any point to the circle is perpendicular to the radius and its 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 arc to the centre and to the point on the circle
** Cyclic quadrilateral
** Tangent – Secant theorem

3. Co-ordinate Geometry :
** Slope of a line
** Intercepts made by a line
** Standard forms of equation of a line
** General equation of a line.

4. Geometric Constructions :
** Division of line segment in a given ratio
** Basic geometric constructions
** Construction of tangent to the circle from the point on the circle and out side the circle.
** Construction of tangent without using centre
** Construction of triangle If the base, angle apposite to it and either median altitude is given
** Construction of a triangle similar to a given triangle

5. Trigonometry :
** Angles in standard position.
** Trigonometric ratios in terms of coordinates of point
** Trigonometric Identities (with proof)
** Use of basic identities and their applications
** Problems on height and distance

6. Menstruation :
** Length of an arc
** 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 areas and perimeter/circumference of circle, sector and segment of a circle.
** Problems on finding surface areas 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 into another.

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