# 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 =ar
^{n-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.**

- S
_{n}= (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 + b2 )P(x, y) O(0,0) - Distance formula to find distance between points A (X
_{1},Y_{1}) and B(X_{2},Y_{2}) as - AB = √((X
_{2}–X_{1})2 +(Y_{2}-Y_{1})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 ,300 ,450 ,600 ,900 TrigonSSometric ratios and the relation between them at complementary angles

**Trigonometric identities**

- sin2θ + cos2θ = 1, sec
2 θ – tan2 θ = 1, cosec2 θ - cot2 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 , 450 , 600 .

# 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.