The Mathematics Springboard 10th, 1st Edition

Book description

The Springboard Series containing titles on Science (Physics/Chemistry/Biology) and Mathematics both for class 9th and 10th, are thoughtfully designed to tread seamlessly along with the flow of the NCERT curriculum. This foundation series prepares students to gear up for the Board exams and various talent search examinations like NTSE, Olympiads, KVPY, etc. Comprising of 15 chapters on Mathematics, this series caters to students of classes IX. The core objective of the series is to help aspiring students understand the basic concepts with more clarity, in turn, developing a problem-solving approach. It also encourages students to attempt various competitive examinations from an early age.

1. the concepts are explained in a well structured and lucid manner, using simple language and ample number of examples
2. Each chapter has a good number of sample questions along with a separate section on Solved Problems at the end of each chapter
3. Different levels of questions have been included in the Practice Exercises Sections
4. a complete section on Competitive Examinations: Competition Corner which will help students to check their examination readiness
5. Previous year CBSE papers and NTSE papers are also included

Book Contents –

1) Real Numbers
2) Polynomials
3) Pair of Linear Equations in Two Variables
4) Quadratic Equations
5) Arithmetic Progression
6) Triangles
7) Coordinate Geometry
8) Introduction to Trigonometry
9) Some Applications of Trigonometry
10) Circles
11) Constructions
12) Areas Related to Circles
13) Surface Areas and Volumes
14) Statistics
15) Probability

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents (1/2)
  5. Contents (2/2)
  6. About the Series
  7. Chapter Insight
  8. Chapter 1 Real Numbers
    1. 1.1 Introduction
    2. 1.2 Algorithm
    3. 1.3 Euclid’s Division Lemma
      1. 1.3.1 Euclid’s Division Algorithm
    4. 1.4 The Fundamental Theorem Arithmetic
    5. 1.5 Rational and Irrational number
      1. 1.5.1 Rational Number
      2. 1.5.2 Irrational Number
    6. 1.6 Decimal Expansion of Rational Numbers (1/2)
    7. 1.6 Decimal Expansion of Rational Numbers (2/2)
  9. Chapter 2 Polynomial
    1. 2.1 Introduction
      1. 2.1.1 Definition
    2. 2.2 Degree of a Polynomial
    3. 2.3 Geometric Meaning of Zeros of A Polynomial
      1. 2.3.1 Graph of Polynomials
      2. 2.3.2 Graph of a Linear Polynomial
      3. 2.3.3 Graph of a Quadratic Polynomial
    4. 2.4 Relationship between the Zeroes and Coefficient of a Polynomial
    5. 2.5 Relationship between Zeroes and Coefficients of a Cubic Polynomial
    6. 2.6 Division Algorithm for Polynomials
      1. 2.6.1 Division Algorithm
  10. Chapter 3 Pair of Linear Equations in Two Variables
    1. 3.1 Introduction
    2. 3.2 Graphical Representation of Linear Equations
    3. 3.3 Graphical Method of Solving Simultaneous Linear Equations
      1. 3.3.1 Algorithm
    4. 3.4 Algebraic Methods of Solving Simultaneous Linear Equations in Two Variables
      1. 3.4.1 Substitution Method
    5. 3.5 Method of Elimination by Equating the Coefficients Elimination Method
      1. 3.5.1 Algorithm
    6. 3.5.2 Cross Multiplication Method
    7. 3.6 Equations Reducible to a Linear Pair in Two Variables
      1. 3.6.1 Condition for Solvability 3.9
      2. 3.6.2 Algorithm 3.10 (1/3)
      3. 3.6.2 Algorithm 3.10 (2/3)
      4. 3.6.2 Algorithm 3.10 (3/3)
  11. Chapter 4 Quadratic Equation
    1. 4.1 Introduction
    2. 4.2 Quadratic Equation
    3. 4.3 Solving a Quadratic Equation by Factorization
    4. 4.4 Solution of the Quadratic Equation by Discrimination Method
    5. 4.5 Roots of a Quadratic Equation
      1. 4.5.1 Algorithm 4.5
    6. 4.5 Solution of a Quadratic Equation by Completing the Square
    7. 4.6 Application of Word Problem Involving Quadratic Equation
  12. Chapter 5 Arithmetic Progression
    1. 5.1 Introduction
      1. 5.1.1 Definition 5.1
    2. 5.2 nth Term of an A.P.
      1. 5.2.1 nth Term of an A.P. from the End 5.3
      2. 5.2.2 Selection of Terms in an A.P. 5.3
    3. 5.3 Sum of First ‘n’ Terms of an A.P. (1/2)
    4. 5.3 Sum of First ‘n’ Terms of an A.P. (2/2)
  13. Chapter 6 Triangles
    1. 6.1 Introduction
      1. 6.1.1 Definition 6.1
      2. 6.1.2 Similarity of Triangles 6.4
      3. 6.1.3 Areas of Similar Triangles 6.8
      4. 6.1.4 Pythagoras Theorem 6.10 (1/3)
      5. 6.1.4 Pythagoras Theorem 6.10 (2/3)
      6. 6.1.4 Pythagoras Theorem 6.10 (3/3)
  14. Chapter 7 Coordinate Geometry
    1. 7.1 Introduction
      1. 7.1.1 Distance Formula 7.2
      2. 7.1.2 Section Formula 7.3
      3. 7.1.3 Centroid of a Triangle 7.5
      4. 7.1.4 Mid-Point Formula 7.7
      5. 7.1.5 Area of the Triangle 7.8
      6. 7.1.6 Area of the Triangle 7.8
      7. 7.1.7 Collinearity 7.9
    2. 7.2 Summary (1/2)
    3. 7.2 Summary (2/2)
  15. Chapter 8 Introduction to Trigonometry
    1. 8.1 Introduction
    2. 8.2 Trigonometry Ratios
      1. 8.2.1 To Find Trigonometry Ratios if Two Sides of a Right Triangle are Given 8.4
      2. 8.2.2 To Find Trigonometry Ratios if One of the Ratio is Given 8.6
      3. 8.2.3 Relation between Trigonometry Ratios 8.8
    3. 8.3 Trigonometry Ratios of Some Specific Angles
      1. 8.3.1 Trigonometric Ratios of 45° 8.9
      2. 8.3.2 Trigonometric Ratios of 30° and 60° 8.10
      3. 8.3.3 Trigonometric Ratios of 0° and 90° 8.11
      4. 8.3.4 Table for the Different Trigonometric Ratios for 0°, 30°, 45°, 60° and 90° 8.12
    4. 8.4 Trigonometry Ratios of Complementary Angles
    5. 8.5 Trigonometry Identities
      1. 8.5.1 Definition of Identity 8.15
      2. 8.5.2 Definition of Trigonometry Identities 8.15
      3. 8.5.3 Theorem 1 8.15
      4. 8.5.4 Theorem 2 8.16
      5. 8.5.5 Theorem 3 8.16
  16. Chapter 9 Some Applications of Trigonometry
    1. 9.1 Introduction
    2. 9.2 Height and Distance
  17. Chapter 10 Circles
    1. 10.1 Introduction
    2. 10.2 Secant of a Circle
    3. 10.3 Tangent of a Circle
      1. 10.3.1 Point of Contact 10.2
      2. 10.3.2 Length of the Tangent 10.2
      3. 10.3.3 Some Properties of Tangents to a Circle 10.2
    4. 10.4 Important Results
    5. 10.5 Number of Tangents from a Point on a Circle (1/3)
    6. 10.5 Number of Tangents from a Point on a Circle (2/3)
    7. 10.5 Number of Tangents from a Point on a Circle (3/3)
  18. Chapter 11 Constructions
    1. 11.1 Introduction
    2. 11.2 Division of a Line Segment
      1. 11.2. 1 Alternative Method for Division of a Line Segment Internally in a Given Ratio
    3. 11.3 To Construct a Triangle Similar to a Given Triangle as Per Given Scale Factor
    4. 11.3 Construction of Tangents to a Circle
      1. 11.3. 1 To Construct the Tangents to a Circle from a Point Outside it
  19. Chapter 12 Areas Related to Circles
    1. 12.1 Introduction
    2. 12.2 Circle
    3. 12.3 Terms of Circle
    4. 12.4 Formula’s of Circumference and Area of a Circle
      1. 12.4.1 Finding the Area of Segment of a Circle
    5. 12.5 Rotating Wheels
    6. 12.6 Area Enclosed by Two Concentric Circles
    7. 12.7 Touching Circles
    8. 12.8 Area of a Sector
    9. 12.9 Area of Combinations of Plane Figures
  20. Chapter 13 Surface Area and Volume
    1. 13.1 Introduction
      1. 13.1.1 Cuboid 13.2
      2. 13.1.2 Cube 13.2
      3. 13.1.3 Right Circular Cylinder 13.2
      4. 13.1.4 Right Circular Hollow Cylinder 13.3
      5. 13.1.5 Right Circular Cone 13.3
      6. 13.1.6 Sphere 13.3
      7. 13.1.7 Hemi-Sphere 13.4
      8. 13.1.8 Spherical Shell 13.4
    2. 13.2 Surface Area of a Combination of Solids
    3. 13.3 Volume of a Combination of Solids
    4. 13.4 Conversion of Solid from One Shape to another
    5. 13.5 Frustum of a Cone
      1. 13.5 1 Derive the Formula for the Curved Surface Area and Total Surface Area of the Frustum of Cone 13.15
  21. Chapter 14 Statistics
    1. 14.1 Introduction
    2. 14.2 Statistics
    3. 14.3 Mean of Grouped Data
      1. 14.3.1 Direct Method 14.2
      2. 14.3.2 Assumed-mean Method 14.3
      3. 14.3.3 Step-deviation Method 14.4
    4. 14.4 Median of the Grouped Data
    5. 14.5 Mode of the Grouped Data
    6. 14.6 Inter-relation Between Mean, Median and Mode
    7. 14.7 Graphical Representation of Cumulative Frequency Distribution
      1. 14.7.1 For Less Than Type Cumulative Frequency Distribution 14.9
      2. 14.7.2 For More Than Type Cumulative Frequency Distribution 14.11 (1/3)
      3. 14.7.2 For More Than Type Cumulative Frequency Distribution 14.11 (2/3)
      4. 14.7.2 For More Than Type Cumulative Frequency Distribution 14.11 (3/3)
  22. Chapter 15 Probability
    1. 15.1 Introduction
    2. 15.2 Probability
    3. 15.3 Terms Related to Probability
    4. 15.4 Rules of Probability (1/2)
    5. 15.4 Rules of Probability (2/2)
  23. Competition Corner (1/8)
  24. Competition Corner (2/8)
  25. Competition Corner (3/8)
  26. Competition Corner (4/8)
  27. Competition Corner (5/8)
  28. Competition Corner (6/8)
  29. Competition Corner (7/8)
  30. Competition Corner (8/8)
  31. Summative Assessment (2016–2012) (1/13)
  32. Summative Assessment (2016–2012) (2/13)
  33. Summative Assessment (2016–2012) (3/13)
  34. Summative Assessment (2016–2012) (4/13)
  35. Summative Assessment (2016–2012) (5/13)
  36. Summative Assessment (2016–2012) (6/13)
  37. Summative Assessment (2016–2012) (7/13)
  38. Summative Assessment (2016–2012) (8/13)
  39. Summative Assessment (2016–2012) (9/13)
  40. Summative Assessment (2016–2012) (10/13)
  41. Summative Assessment (2016–2012) (11/13)
  42. Summative Assessment (2016–2012) (12/13)
  43. Summative Assessment (2016–2012) (13/13)
  44. National Talent Search Examination (2015–2013) (1/30)
  45. National Talent Search Examination (2015–2013) (2/30)
  46. National Talent Search Examination (2015–2013) (3/30)
  47. National Talent Search Examination (2015–2013) (4/30)
  48. National Talent Search Examination (2015–2013) (5/30)
  49. National Talent Search Examination (2015–2013) (6/30)
  50. National Talent Search Examination (2015–2013) (7/30)
  51. National Talent Search Examination (2015–2013) (8/30)
  52. National Talent Search Examination (2015–2013) (9/30)
  53. National Talent Search Examination (2015–2013) (10/30)
  54. National Talent Search Examination (2015–2013) (11/30)
  55. National Talent Search Examination (2015–2013) (12/30)
  56. National Talent Search Examination (2015–2013) (13/30)
  57. National Talent Search Examination (2015–2013) (14/30)
  58. National Talent Search Examination (2015–2013) (15/30)
  59. National Talent Search Examination (2015–2013) (16/30)
  60. National Talent Search Examination (2015–2013) (17/30)
  61. National Talent Search Examination (2015–2013) (18/30)
  62. National Talent Search Examination (2015–2013) (19/30)
  63. National Talent Search Examination (2015–2013) (20/30)
  64. National Talent Search Examination (2015–2013) (21/30)
  65. National Talent Search Examination (2015–2013) (22/30)
  66. National Talent Search Examination (2015–2013) (23/30)
  67. National Talent Search Examination (2015–2013) (24/30)
  68. National Talent Search Examination (2015–2013) (25/30)
  69. National Talent Search Examination (2015–2013) (26/30)
  70. National Talent Search Examination (2015–2013) (27/30)
  71. National Talent Search Examination (2015–2013) (28/30)
  72. National Talent Search Examination (2015–2013) (29/30)
  73. National Talent Search Examination (2015–2013) (30/30)

Product information

  • Title: The Mathematics Springboard 10th, 1st Edition
  • Author(s): Pearson Education
  • Release date: December 2024
  • Publisher(s): Pearson India
  • ISBN: 9789332585133