Maharashtra Board SSC Mathematics Syllabus for Board Exam 2020
The Maharashtra Board SSC students can get here complete syllabus of Mathematics subject including detailed topics for each paper and latest evaluation scheme.
Maharashtra Board SSC Syllabus for Mathematics Subject is available here for Class 9^{th} and Class 10^{th}. The syllabus of Mathematics subject is provided here with latest pattern including evaluation scheme which will be implemented in the upcoming SSC Examinations 2020.
Evaluation Scheme for Maharashtra Board SSC Mathematics subject:
There are two papers of Maharashtra Board SSC Mathematics subject i.e. Algebra and Geometry.
The theory paper of Maharashtra Board SSC Mathematics will carry 80 marks weightage and the practical/project/viva are allotted 20 marks.
The 80 marks of theory paper have been divided equally in two parts; 40 marks for Algebra and 40 marks for Geometry.
The questions in both papers of Maharashtra Board SSC Mathematics subject will be as under –
Type of Questions
Marks without options
Marks with options
One mark based questions
5
6
Two marks based questions
8
12
Three marks based questions
9
15
Four marks based questions
8
12
Five marks based questions
10
15
Total
40
60
Maharashtra Board SSC Mathematics Syllabus –
Maharashtra Board Class 9th Mathematics Syllabus –
Part A: Algebra Chapters
Detailed Topics
Chapter 1: Sets
Introduction
Methods of writing sets
Types of sets
Subset - Proper, Improper subset
Super set
Universal set
Venn diagrams
Operations on sets
Relations between various operations
Number of elements in the set and related results
Chapter 2: Real Numbers
Revision of natural numbers, integers, rational numbers and irrational numbers
Existence of irrational numbers and their representations on the number line
Every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number
Properties of real numbers
Definition of nth root of a real number
Surds - Definition
Forms of surds
Operations and Laws of surds
Rationalization of Surds
Absolute value of real numbers
Euclid's division Lemma
Fundamental theorem of Arithmetic
Chapter 3: Algebraic Expressions
Introduction to algebraic expression
Operations on algebraic expressions
Methods of factorization of algebraic expression
Introduction to polynomials
Operations on polynomials Value of polynomials
Zeros/roots of polynomial
Relation between zeros and coefficient of polynomials
Remainder theorem
Factor theorem
Chapter 4: Graphs
Cartesian coordinate system
Understanding of graphs of lines parallel to axes
Graph of line ax + by + c = o
Chapter 5: Linear equations in two variables
System of linear equations
Solution of system of linear equations in two variables(Algebraic methods)
Chapter 6: Ratio, proportion and variation
Introduction to ratio
Properties of ratio
Properties of equal ratios
Theorem on equal ratios
Percentage as a ratio
Introduction to proportion
Introduction to variation
Revision of concepts based on Direct variation, Inverse variation
Mixed variation
Real life problems based on ratio, proportion and variation
zero angle, straight angle, co-terminal angle · Relation between angles
Introduction to mathematical proofs
Parallel lines
Results on parallel lines and transversal
Tests of parallel lines
Results on perpendicular lines
Distance of a point from a line
Chapter 2: Triangles
Types of triangles
Terms related to triangle
Properties of triangle
Exterior angles and corresponding interior opposite angles
Results involving exterior angle and corresponding interior opposite angles
Similar triangles
Chapter 3: Congruence of triangles
Criteria of congruent triangles
Theorem of an isosceles triangle and its converse
Perpendicular bisector theorem
Angle bisector theorem
Properties of triangles based on inequalities
Property of perpendicular drawn from a point outside the line
Chapter 4: Circle
Introduction to circle and related terms
Circle passing through the given points
One and only one circle passes through the three non collinear points
Congruence of circles
Properties of chords of the circle
Chapter 5: Quadrilateral
Properties of quadrilateral
Properties of parallelogram
Properties of rectangle
Properties of a trapezium
Properties of a rhombus
Properties of a square
Kite
Tests for particular quadrilateral
Theorem on midpoints of two sides of a triangle and its converse
Chapter 6: Coordinate Geometry
Distance formula
Section formula
Area of a triangle
Chapter 7: Geometric constructions
Basic construction - perpendicular bisector of given segment
Construction of a triangle – Sum/difference of two sides and base angles is given – Perimeter and base angles are given
Chapter 8: Trigonometry
Introduction to trigonometric ratios
Trigonometric Ratios of angles 0o, 30 o, 45 o, 60 o, 90 o
Trigonometric identities for complementary angles
Chapter 9: Mensuration
Area of triangle
Area of regular hexagon, polygon
Area of quadrilaterals
If two parallelograms lie between two parallel lines and have the same base then they have the same area
If a triangle and a parallelogram have the same base and lie between the same parallel lines, then the area of the triangle is half the area of the parallelogram
Perimeter of triangle and quadrilateral · Area of circle
Maharashtra Board Class 10^{th} Mathematics Syllabus –
Part A: Algebra Chapters
Detailed Topics
Chapter 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
Chapter 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
Chapter 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
Determinant of order two
Cramer's rule
Consistency of pair of linear equations
Chapter 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)
Chapter 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
Application of Pythagoras theorem in acute and obtuse angle
Apollonius theorem
Chapter 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
Chapter 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
Chapter 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 outside 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
Chapter 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
Chapter 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
Chapter-wise marking scheme for Maharashtra Board Class 10^{th} Mathematics–
Part A: Algebra
Chapters
Marks with options
Chapter 1: Arithmetic Progression
12
Chapter 2: Quadratic Equations
12
Chapter 3: Linear equations in two variables
12
Chapter 4: Probability
10
Chapter 5: Statistics
14
Total
60
Part B: Geometry
Chapters
Marks with options
Chapter 1: Similarity
12
Chapter 2: Circle
10
Chapter 3: Co-ordinate Geometry
10
Chapter 4: Geometric Constructions
10
Chapter 5: Trigonometry
8
Chapter 6: Menstruation
10
Total
60
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