Mathematics Class 10 Important Formulas And Theorems
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Mathematics - Class 10 Important Formulas and Theorems
This book is very important for the students appearing for 10th std STATE / CBSE / ICSE Board through out INDIA. It has all important Definitions , Important Formulas, Solved Important and all Theorems, Diagrams, MCQ’s , Terminology, Key points of every lesson and topics to make student understand and to clear Basic Fundamental concepts of Mathematics. All important formulas relevant to each and every topic which are very important and useful for the board ( 10th STD Exam ) Brief and each and every steps are given as per the requirement of the proof of the Theorems
Mathematics class 10 Based on NCERT Guidelines
Author: Dr. Ram Dev Sharma
language: en
Publisher: SBPD Publications
Release Date: 2022-07-12
1. Real Number : Euclid’s division lemma, Fundamental Theorem of Arithmetic-statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals. Unit II : Algebra 1. Polynomials : Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients. 2. Pair of Linear Equations in Two Variables: Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically-by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equation reducible to linear equations. 3.Quadratic Equations : Standard form of a quadratic equation ax2 + bx + c = 0, (a ¹ 0). Solutions of quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula. Relationship between discriminate and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated. 4. Arithmetic Progressions: Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. their application in solving daily life problems. Unit III: Coordinate Geometry 1. Lines (In two-dimensions) : Review : Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle. Unit IV: Geometry 1.Triangles: Definition, examples, counter examples of similar triangles 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line in parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides proportional and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and two triangles are similar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar. 6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other. 7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. 8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle. 2. Circles Tangent to a circle at, point of contact : 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to a circle are equal. 3.Constructions : 1. Division of a line segment in a given ratio (internally) 2. Tangents to a circle from a point outside it. 3. Construction of a triangle similar to a given triangle. Unit V : Trigonometry 1. Introduction of Trigonometry : Trigonometric ratios of an acute angel of a right-angled triangle. Proof of their existence (well defined) ; motivate the ratios whichever are defined at 0 and 90. Values (with proofs) of the trigonometric ratios of 30º, 45º and 60º. Relationship between the ratios. 2.Trigonometric Identities : Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles. 3. Heights and Distances : Angle of elevation, Angle of Depression. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30º, 45º, 60º. Unit VI : Mensuration 1.Areas Related to Circles : Motivate the area of a circle ; area of sectors and segments of a circle. Problems based on area and perimeter/circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60º, 90º and 120º only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.) 2. Surface Areas and Volumes : 1. Surface areas and volumes of combination of any two of the following : cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone. 2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken.) Unit VII : Statistics and Probability 1.Statistics : Mean, median and mode of grouped data (bimodal situation to be avoided) cumulative frequency graph 2.Probability : Classical definition of probability. Simple problems on single events (not
Class 10 Math MCQ (Multiple Choice Questions)
The Class 10 Math Multiple Choice Questions (MCQ Quiz) with Answers PDF (10th Grade Math MCQ PDF Download): Quiz Questions Chapter 1-13 & Practice Tests with Answer Key (Math Questions Bank, MCQs & Notes) covers review tests for competitive exams with solved MCQs. Class 10 Math MCQ with Answers PDF book covers basic concepts, analytical and practical assessment tests. "Class 10 Math MCQ" PDF book helps to practice test questions from exam prep notes. The Class 10 Math MCQs with Answers PDF eBook includes revision guide with verbal, quantitative, and analytical past papers, solved MCQs. Class 10 Math Multiple Choice Questions and Answers (MCQs) PDF: Free download chapter 1, a book covers solved quiz questions and answers on chapters: Introduction to trigonometry, 3rd, 4th, mean and continued proportion, algebraic formulas and applications, algebraic manipulation, basic statistics, factorization, geometry, linear equations and inequalities, matrices and determinants, ratio, proportions and variations, roots of quadratic equations, sets and functions tests for school and college revision guide. Class 10 Math Quiz Questions and Answers PDF, free download eBook’s sample covers beginner's solved questions, textbook's study notes to practice online tests. The book Grade 10 Math MCQs Chapter 1-13 PDF includes high school question papers to review practice tests for exams. Class 10 Math Multiple Choice Questions (MCQ) with Answers PDF digital edition eBook, a study guide with textbook chapters' tests for NEET/Jobs/Entry Level competitive exam. 10th Grade Math Mock Tests Chapter 1-13 eBook covers problem solving exam tests from Math textbook and practical eBook chapter wise as: Chapter 1: 3rd, 4th, Mean and Continued Proportion MCQ Chapter 2: Algebraic Formulas and Applications MCQ Chapter 3: Algebraic Manipulation MCQ Chapter 4: Basic Statistics MCQ Chapter 5: Factorization MCQ Chapter 6: General Math Questions MCQ Chapter 7: Geometry MCQ Chapter 8: Introduction to Trigonometry MCQ Chapter 9: Linear Equations and Inequalities MCQ Chapter 10: Matrices and Determinants MCQ Chapter 11: Ratio, Proportions and Variations MCQ Chapter 12: Roots of Quadratic Equations MCQ Chapter 13: Sets and Functions MCQ The 3rd, 4th, Mean and Continued Proportion MCQ PDF e-Book: Chapter 1 practice test to solve MCQ questions on Continued proportional, fourth proportional, mean proportional, and third proportional. The Algebraic Formulas and Applications MCQ PDF e-Book: Chapter 2 practice test to solve MCQ questions on Algebraic expressions, Math formulas, surds and surds applications. The Algebraic Manipulation MCQ PDF e-Book: Chapter 3 practice test to solve MCQ questions on Basic operations on algebraic fractions, square root of algebraic expression, HCF, and LCM. The Basic Statistics MCQ PDF e-Book: Chapter 4 practice test to solve MCQ questions on Construction of frequency polygon, construction of histograms, frequency distribution, measures of central tendency, and measures of dispersion. The Factorization MCQ PDF e-Book: Chapter 5 practice test to solve MCQ questions on Factorization of expressions, and Math theorems. The General Math MCQ PDF e-Book: Chapter 6 practice test to solve MCQ questions on Basic concepts, circle's basic concepts, fraction, improper fraction, proper fraction, rational fraction, Math theorems, parallel lines, relation between roots, and coefficients. 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