# Mathematics (M 1007) - Grade 10

Unit Area Covered Marks
Unit 1 Real Numbers 05 Read more
Unit 2 Polynomials (core) 10 Read more
Unit 3 Pair of Linear Equations in Two Variables (core) 10 Read more
Unit 4 Quadratic Equations (core) 05 Read more
Unit 5 Arithmetic Progression and Geometric Progression (core) 20 Read more
Unit 6 Coordinate Geometry and Transformations (core) 10 Read more
Unit 7 Trigonometry and its Applications (core) 10 Read more
Unit 8 More on Statistics and Probability (core) 10 Read more
Unit 9 Similar Triangles (core) 10 Read more
Unit 10 Circles and Constructions (core) 10 Read more
Total Marks 100

# Unit 1

Revisit the Number System

• Recapitulation of all number systems- Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers

Expression of Integers as product of prime integers

• Euclid's Division Lemma,.
• Euclid's Division Algorithm to find HCF (highest common factor) of two given positive integers.

Prime factorization of composite number

• Composite No., Prime No., Prime factorization, HCF and LCM of numbers using prime factorization. Fundamental Theorem of Arithmetic.
• Application problem.

Rational numbers as decimal expansion

• Express rational number as either terminating decimal or non-terminating, recurring decimal.

# Unit 2

Polynomial

• Recapitulation of vocabulary of polynomials in one variable - coefficient, terms, degree, constant, linear, quadratic, cubic polynomial.

Zeroes of polynomial

• Zero of linear polynomial, zeroes of quadratic polynomial, zeroes of cubic polynomial.
• Relation between zeroes and coefficients.
• Geometrical representation of zeroes of polynomial, reading zeroes of linear and quadratic polynomial from graph

Division algorithm

• Dividend= divisor x quotient + remainder.
• Division of linear polynomial by a linear polynomial, division of quadratic polynomial by linear polynomial , division of cubic polynomial by linear polynomial.

# Unit 3

Graphical representation of linear equations

• Plotting the lines representing two linear equations on the same plane Algebraic interpretation of graphs of simultaneous equations as following:
• intersecting lines with common point means linear equation with unique solution.
• parallel lines with no common point means linear equations with no solution.
• coinciding lines with all point common means linear equations with infinite solutions.
• Define: consistent system and inconsistent system

Nature of system of linear equations

• Relation between the coefficients of pair of linear equations to predict about the given system of linear equations.

Algebraic method of solving system of linear equations

• Substitution method and elimination method, cross multiplication method.

Application in daily life problems

• Number problems, age problems, work ratio problems,dimensional problems.

# Unit 4

Introduction to Quadratic Equation

• Quadratic Equation are of the form ax 2+ bx + c=0, a 0, a, b, c are real numbers.

Methods to solve quadratic equations

• Factorisation,using discriminant (D = b2 – 4ac ) formula , to solve Equation ax2 + bx + c = 0.

Nature of roots

• Nature of roots when D=0, D 0, D 0 Sum of roots, product of roots, conjugate roots Writing quadratic equation when roots are known.

Application in daily life

• Number problems, age problems, work ratio problems, distance time problems.

# Unit 5

Introduction to arithmetic progression(A.P.) and geometric progression (G.P.)

• Recalling number patterns and geometrical patterns, Illustration of arithmetic progression from daily life situations, terms of A.P., first term, common difference terms of G.P., first term, common ratio.

General term of an A.P.

• nth term of A.P.as an = a+(n-1)d, where "a‟ is first term and "d‟ is common difference, n is total number of terms

General term of G.P.

• nth term of G.P.as an =arn-1, where "a‟ is first term and "r‟ is common ratio and is the required term finding unknown when any three of a, n, r, an are given.

Sum of first n terms of A.P.

• Sn = (n/2)(2a+(n-1)d) finding unknown when any three of a, n, d, Sn are given

# Unit 6

Revisit coordinate geometry

• Location of a point in plane as (x, y), representation on line as y= m x + c, where m is gradient and c is y- intercept.

Distance between two points in a coordinate plane

• Distance of a point P(x, y) from origin(0,0) as
• OP= √(a 2 + b 2 )P(x, y) O(0,0)
• Distance formula to find distance between points A (X1,Y1) and B(X2,Y2) as
• AB = √((X2–X1) 2 +(Y2-Y1) 2 )

Section formula

• point of internal division

Transformations

• Translation as transformation that slides figure, translation of a point from P(x, y)to Q(x+a, y+a), Translation of a line, Reflection as transformation that flips everything over, reflection across x-axis, reflection across y- axis, reflection across the lline x=constant, reflection across the line y = constant

# Unit 7

Revision of trigonometric facts

• All T- ratios, values of T-ratios at 0 0 ,30 0 ,45 0 ,60 0 ,90 0 TrigonSSometric ratios and the relation between them at complementary angles

Trigonometric identities

• sin2θ + cos2θ = 1, sec 2 θ – tan 2 θ = 1, cosec 2 θ - cot 2 θ = 1, Problems based on values of trigonometric ratios and trigonometric identities

Angle of elevation and angle of depression Application problems

• Describing angle of elevation and angle of depression for a given point Simple Problems involving one triangle and angle measure of 30 0 , 45 0 , 60 0 .

# Unit 8

Introduction to volume

• Volume as product of area of base and height.

Volume of cubes and cuboids

• Formulae for finding volume of cube and cuboid of given dimension.

Volume of right circular cylinder and right circular cone

• Volume of a hollow right circular cylinder. Volume of metal required to cast a solid right circular cylinder. volume of cylindrical pipe of given thickness. volume of a right circular cone, relation between volume of right circular cylinder and right circular cone of given radius and given height.

Volume of sphere

• Volume of sphere and hemisphere of given radius.

# Unit 9

Introduction to Trigonometry

• Trigonometry as study of right angle triangle using relation between its sides and angles.

Defining trigonometric ratios in a right angle triangle

• Right angle triangle: hypotenuse, side containing angles of observation and right angle as adjacent side, side opposite to bearing as perpendicular side.
• Define sine, cosine and tangent of angle as ratio of sides of right triangle.
• Values of T-ratios for 30⁰, 45⁰, 60⁰

Angle of elevation and angle of depression

• Describing angle of elevation and angle of depression for a given point.
• Drawing of figure for given problems involving one right angle triangle.

# Unit 10

Introduction to Trigonometry

• Trigonometry as study of right angle triangle using relation between its sides and angles.

Defining trigonometric ratios in a right angle triangle

• Right angle triangle: hypotenuse, side containing angles of observation and right angle as adjacent side, side opposite to bearing as perpendicular side.
• Define sine, cosine and tangent of angle as ratio of sides of right triangle.
• Values of T-ratios for 30⁰, 45⁰, 60⁰

Angle of elevation and angle of depression

• Describing angle of elevation and angle of depression for a given point.
• Drawing of figure for given problems involving one right angle triangle.