FACTORS AND MULTIPLES


 Ami Short
 3 years ago
 Views:
Transcription
1 FACTORS AND MULTIPLES.(A) Find the prime factors of : (i) (ii) (iii) Ans. (i) (ii) (B.) If P n means prime  factors of n, find : (i) P (ii) P (iii) P (iv) P Ans. (i) F =,,, P (Prime factor of ) = and. (ii) F =,,,,,,, P = and. (iii) F =,,,,,,,, P = and. (iv) F =,,,,,,, P =, and. (C.) List the elements of each of M() and M(). Hence, find the least element in the set M() M(). Is it the L.C.M. of and? Ans. M() = {,,,,,,...} M() = {,,,,,...} Set of common multiples of and = M() M() = {, } The smallest element of this set is. Hence, the LCM of and =. Yes, it is LCM of and. (D). List the elements of each of M() and M(). Hence find the LCM of and. Ans. M() = {,,,,,..} M() = {,,,... } Set of commom multiples of and = M() M() = {, } The smallest element of this set is Hence, the LCM of amd =. List the elements of P and P. Hence, find : (i) P P (ii) P P Ans. We have: = =
2 P = {,, } and P = {, } P (i) (ii) P P P = {,, } {, } = {} = {,, } {, } = {,,, }. (i) If P P = Pn, find the value of n. (ii) If P(n) P() = P(), find the n given that n <. Ans. (i) We have : =, = P = {, } and P = {, } P P = {,} {, } = {} = P Hence, n =. (ii) P(n) P() = P(), P(n) P{,,, } = P{, } P(n) =. Express each one of the following as a product of prime factors : (i) (ii) (iii) (iv) (v) Ans. (i) = (ii) = (iii) = (iv) = (v) =. Find the H.C.F. of (i), (ii), (iii),, (iv),, Ans. (i) (ii) and
3 =, =, =, =, HCF = =. HCF = =. (iii),, =, =, =, HCF = =. (iv),, =, =, =, HCF =.. Find the HCF of the following numbers using prime factorisation method : (i), (ii), (iii), (iv), (v), (vi),, Ans. (i), (ii), =, =, =, =, HCF = =. HCF = =
4 (iii), (iv), =, =, =, =, HCF = =. HCF = =. (v), (vi),, =, =, =, =, HCF = = = HCF = =. Find the HCF of the following numbers using long division method : (i), (ii), (iii), (iv), (v), (vi),, Ans. (i), (ii), HCF of and = HCF of and =
5 (iii), (iv), HCF of and = HCF of and = (v), (vi),, HCF of and =. Now, find the HCF of and HCF of, and =.. Find the greatest number that exactly divides and. Ans. Find the HCF of and The required number =.
6 . Find the greatest number that exactly divides, and. Ans. Now, find the HCF of and The required number =.. Two vessels contain litres and litres of milk. Find the measure of a bucket of maximum capacity which can measure the milk of either vessel an exact number of times : Ans. Required capacity of bucket = litres.. Find the LCM of the following number using prime factorisation method: (i), (ii), (iii), (iv),, (v),, Ans. (i), (ii), = = = = = = = = LCM = = = LCM = = = (iii), (iv),,
7 = = = = = = LCM = = = = = (v),, LCM = = = = = ; = ; = LCM = = =. Find the L.C.M. of the following using common division method: (i),,, (ii),,, (iii),,, (iv),,, (v),,,, (vi),, Ans. (i),,, (ii),,, LCM = = LCM = = (iii),,, (iv),,, LCM = =. LCM = =
8 (v),,,, (vi),, LCM = =. LCM = =. The HCM of two numbers is and their LCM. is. If one of the number is, find the other. Ans. Let the other number be x Product of two numbers = HCF LCM x = x = =. The other number is.. The HCF of two numbers is and their LCM is. If one of number is, find the other. Ans. Let the other number be x. Product of two numbers = HCF LCM x = x = = =. The other number is.. The product of two numbers is and their HCF is. Find their LCM. Ans. HCF LCM = Product of two numbers LCM = LCM = =.. The product of two numbers is and their LCM is. Find their HCF. Ans. HCF LCM = Product of two numbers HCF = LCM = =. The H.C.F. and the L.C.M of two numbers are and respectively. If one of the numbers is, find the other number. Ans. HCF = and LCM =, One number = Product of LCM and HCF = =
9 The other number = Product of LCM and HCF One number = =. The product of two numbers is and their LCM is. Find their HCF. Ans. Product of two numbers = Product of their LCM and HCF Here, product of two number = LCM = HCF = =. Can there be two numbers with HCF and LCM? Give reasons in support of your answer. Ans. No, because HCF of two numbers always divides their LCM.. An electronic device makes a beep after every minutes. Another device makes a beep after every minutes. They beeped together at a.m. At what time will they make the next beep together? Ans. LCM of and = = The next beep will be after minutes i.e. + minutes = a.m.. Six bells commence tolling together and toll at intervals of,,,, and minutes respectively. After what interval of time will they toll together again? Ans. Find the LCM of,,.,,. LCM = =. The six bells toll together again after minutes, i.e. after hours.. Find the least number which when divided by,,, and leaves no remainder. Ans. The least number which is exactly divisible by each given numbers is their LCM. Required number = LCM of,,, and. LCM = least required number
10 ,,,,,,,,,,,, = =,,,,,,,, Hence, the least required number =.. Find the least number which when increased by one is exactly divisible by,,, and.,,,, Ans.,,,,,,,,,,,,,,,, LCM = = The required number = =.
HCF & LCM Solved Sums
HCF & LCM Solved Sums 1. The least common multiple of 24, 36, and 40 is A ) 340 b ) 360 c) 230 d) 400 2 24 36 40 => 2 X 2 X 2 X 3 X 1 X 3 X 5 2 12 18 20 => 360 2 6 9 10 3 3 9 5 1 3 5 Ans : 360 2. The LCM
More information1 Paid Copy Don t Share With Anyone
HCF & LCM Solved Sums 1. The least common multiple of 24, 36, and 40 is A ) 340 b ) 360 c) 230 d) 400 2 24 36 40 => 2 X 2 X 2 X 3 X 1 X 3 X 5 2 12 18 20 => 360 2 6 9 10 3 3 9 5 1 3 5 Ans : 360 2. The LCM
More informationCHAPTER 1 REAL NUMBERS KEY POINTS
CHAPTER 1 REAL NUMBERS 1. Euclid s division lemma : KEY POINTS For given positive integers a and b there exist unique whole numbers q and r satisfying the relation a = bq + r, 0 r < b. 2. Euclid s division
More informationand LCM (a, b, c) LCM ( a, b) LCM ( b, c) LCM ( a, c)
CHAPTER 1 Points to Remember : REAL NUMBERS 1. Euclid s division lemma : Given positive integers a and b, there exists whole numbers q and r satisfying a = bq + r, 0 r < b.. Euclid s division algorithm
More informationGive (one word answer) and Take (one mark in future):
Star Sums: Give (one word answer) and Take (one mark in future): 1. If is a rational number, what is the condition on q so that the decimal representation of is terminating. 2. Find the (H.C.F X L.C.M)
More informationREAL NUMBERS. Any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b.
REAL NUMBERS Introduction Euclid s Division Algorithm Any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b. Fundamental
More informationDownloaded from
Topic : Real Numbers Class : X Concepts 1. Euclid's Division Lemma 2. Euclid's Division Algorithm 3. Prime Factorization 4. Fundamental Theorem of Arithmetic 5. Decimal expansion of rational numbers A
More informationnot to be republished NCERT REAL NUMBERS CHAPTER 1 (A) Main Concepts and Results
REAL NUMBERS CHAPTER 1 (A) Main Concepts and Results Euclid s Division Lemma : Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 r < b. Euclid s Division
More informationRevision papers for class VI
Revision papers for class VI 1. Fill in the blanks; a. 1 lakh=ten thousand b. 1 million=hundred thousand c. 1 Crore=million d. 1 million=1 lakh 2. Add the difference
More informationNumber Theory and Divisibility
Number Theory and Divisibility Recall the Natural Numbers: N = {1, 2, 3, 4, 5, 6, } Any Natural Number can be expressed as the product of two or more Natural Numbers: 2 x 12 = 24 3 x 8 = 24 6 x 4 = 24
More informationDownloaded from
MODEL TEST PAPER SUMMATIVE ASSESSMENTI SOLVED Time : 3 hrs. Maximum Marks: 80 General Instructions. SectionA consists of 8 parts carrying 1 mark each SectionB Q2 to Q11 carry 2 marks each SectionC
More informationCLASS  X Mathematics (Real Number)
CLASS  X Mathematics (Real Number) 1. 7 11 13 15 + 15is a (a) Composite number (c) Prime number (b) Whole number (d) None of these. For what least value of n a natural number, ( 4) n is divisible by 8?
More informationQuantitative Aptitude
WWW.UPSCMANTRA.COM Quantitative Aptitude Concept 1 1. Number System 2. HCF and LCM 2011 Prelims Paper II NUMBER SYSTEM 2 NUMBER SYSTEM In Hindu Arabic System, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7,
More informationDiscrete Structures Lecture Primes and Greatest Common Divisor
DEFINITION 1 EXAMPLE 1.1 EXAMPLE 1.2 An integer p greater than 1 is called prime if the only positive factors of p are 1 and p. A positive integer that is greater than 1 and is not prime is called composite.
More informationSection 34: Least Common Multiple and Greatest Common Factor
Section : Fraction Terminology Identify the following as proper fractions, improper fractions, or mixed numbers:, proper fraction;,, improper fractions;, mixed number. Write the following in decimal notation:,,.
More informationGrade 10 Real Numbers
ID : ww10realnumbers [1] Grade 10 Real Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) In a seminar, the number of participants in German, English and French are 378,
More informationMasters Tuition Center
1 REAL NUMBERS Exercise 1.1 Q.1. Use Euclid s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution. (i) In 135 and 225, 225 is larger integer. Using Euclid
More informationSlide 1 / 69. Slide 2 / 69. Slide 3 / 69. Whole Numbers. Table of Contents. Prime and Composite Numbers
Slide 1 / 69 Whole Numbers Table of Contents Slide 2 / 69 Prime and Composite Numbers Prime Factorization Common Factors Greatest Common Factor Relatively Prime Least Common Multiple Slide 3 / 69 Prime
More informationEDULABZ INTERNATIONAL NUMBER SYSTEM
NUMBER SYSTEM 1. Find the product of the place value of 8 and the face value of 7 in the number 7801. Ans. Place value of 8 in 7801 = 800, Face value of 7 in 7801 = 7 Required product = 800 7 = 00. How
More information6 SQUARES AND SQUARE ROOTS
6 SQUARES AND SQUARE ROOTS Exercise 6.1 Q.1. What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796
More informationClass 10 Real Numbers
ID : in10realnumbers [1] Class 10 Real Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) The LCM of two numbers is 760 and their product is 6080. Find their HCF. (2)
More informationpreface It is hoped that this book will help students to gain confidence in the subject and be better equipped to face the examinations.
preface Secondary 1 Mathematics Tutorial 1A and 1B are designed to prepare Secondary 1 students in their understanding and application of mathematical concepts, skills and processes. What s covered in
More informationDivisibility, Factors, and Multiples
Divisibility, Factors, and Multiples An Integer is said to have divisibility with another nonzero Integer if it can divide into the number and have a remainder of zero. Remember: Zero divided by any number
More information81 Factors and Greatest Common Factors 81. Factors and Greatest Common Factors
81 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 81 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.
More informationMATHEMATICS X l Let x = p q be a rational number, such l If p, q, r are any three positive integers, then, l that the prime factorisation of q is of t
CHAPTER 1 Real Numbers [N.C.E.R.T. Chapter 1] POINTS FOR QUICK REVISION l Euclid s Division Lemma: Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 r
More informationSection 4. Quantitative Aptitude
Section 4 Quantitative Aptitude You will get 35 questions from Quantitative Aptitude in the SBI Clerical 2016 Prelims examination and 50 questions in the Mains examination. One new feature of the 2016
More information5.1. Primes, Composites, and Tests for Divisibility
CHAPTER 5 Number Theory 5.1. Primes, Composites, and Tests for Divisibility Definition. A counting number with exactly two di erent factors is called a prime number or a prime. A counting number with more
More informationGrade 6 Natural and Whole Numbers
ID : pk6naturalandwholenumbers [1] Grade 6 Natural and Whole Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Along the highway, there are electric poles on one side
More informationN= {1,2,3,4,5,6,7,8,9,10,11,...}
1.1: Integers and Order of Operations 1. Define the integers 2. Graph integers on a number line. 3. Using inequality symbols < and > 4. Find the absolute value of an integer 5. Perform operations with
More informationArithmetic, Algebra, Number Theory
Arithmetic, Algebra, Number Theory Peter Simon 21 April 2004 Types of Numbers Natural Numbers The counting numbers: 1, 2, 3,... Prime Number A natural number with exactly two factors: itself and 1. Examples:
More informationmep MEP: Feeder Primary Project: Year 4 YEAR 4 Copy Masters CIMT, University of Exeter
YEAR 4 Copy Masters a) How many circles are in the diagram? b) What is the total amount? c) Nine hundred and thirty seven d) 3 100 + 1 10 + 9 1 e) 6 hundreds + 8 tens + 3 units 10 10 10 10 1 1 1 1 1 100
More informationNumber Theory. Number Theory. 6.1 Number Theory
6.1 Number Theory Number Theory The numbers 1, 2, 3, are called the counting numbers or natural numbers. The study of the properties of counting numbers is called number theory. 2 2010 Pearson Education,
More information{ independent variable some property or restriction about independent variable } where the vertical line is read such that.
Page 1 of 5 Introduction to Review Materials One key to Algebra success is identifying the type of work necessary to answer a specific question. First you need to identify whether you are dealing with
More information( ) y 2! 4. ( )( y! 2)
1. Dividing: 4x3! 8x 2 + 6x 2x 5.7 Division of Polynomials = 4x3 2x! 8x2 2x + 6x 2x = 2x2! 4 3. Dividing: 1x4 + 15x 3! 2x 2!5x 2 = 1x4!5x 2 + 15x3!5x 2! 2x2!5x 2 =!2x2! 3x + 4 5. Dividing: 8y5 + 1y 3!
More informationMath Ed 305 Defining Common Divisors and Multiples. 1. From a partitive perspective, to say that X is a divisor of Y is to say that:
Defining Common Divisors and Multiples Part A. 1. From a partitive perspective, to say that X is a divisor of Y is to say that: 2. From a measurement perspective, to say that X is a divisor of Y is to
More informationMATHEMATICS IN EVERYDAY LIFE 8
MATHEMATICS IN EVERYDAY LIFE Chapter : Square and Square Roots ANSWER KEYS EXERCISE.. We know that the natural numbers ending with the digits,, or are not perfect squares. (i) ends with digit. ends with
More informationFour Basic Sets. Divisors
Four Basic Sets Z = the integers Q = the rationals R = the real numbers C = the complex numbers Divisors Definition. Suppose a 0 and b = ax, where a, b, and x are integers. Then we say a divides b (or
More informationAngles on a Point. Always add up to 360º. a + b + c = 180º.
Angles on a Point Always add up to 360º a + b + c = 180º a b c Area of a Trapezium Add the parallel sides, multiply by the perpendicular height, then divide by 2. Formula is ½(a+b)h a Perpendicular Height
More information1 Adda247 No. 1 APP for Banking & SSC Preparation Website: bankersadda.com sscadda.com store.adda247.com
1 Adda247 No. 1 APP for Banking & SSC Preparation S46. Ans.(d) Sol. Let width of the path = x cm So, length of the park will be = (x + 4) cm So, 4 3 (Area of path) = Area of the park Solutions => 4 [x(x
More information4. A rectangular courtyard is 18m72cm long and 13m20cm broad. it is to be paved
1 1. he LCM and HCF of the following pairs of integers and verify that LCM X HCF product of integers (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54 Solution 26) 91 ( 3 13 26  91 78 2  7 13 26 2 26
More informationThe numbers 1, 2, 3, are called the counting numbers or natural numbers. The study of the properties of counting numbers is called number theory.
6.1 Number Theory Number Theory The numbers 1, 2, 3, are called the counting numbers or natural numbers. The study of the properties of counting numbers is called number theory. 2010 Pearson Education,
More informationUNIT 10 NUMBER SYSTEMS, NUMBER THEORY, EXPONENTS AND LOGARITHMS
UNIT 10 NUMBER SYSTEMS, NUMBER THEORY, EXPONENTS AND LOGARITHMS Number Systems, Number Theory, Exponents and Logarithms Structure 10.1 Introduction 10.2 Objectives 10.3 Number Systems 10.3.1 Sets of Numbers
More informationNumeric Reasoning. Robert Lakeland & Carl Nugent. Contents
Year 11 Mathematics IAS 1.1 Numeric Reasoning Robert Lakeland & Carl Nugent Contents Achievement Standard.................................................. 2 Prime Numbers.......................................................
More informationExercises Exercises. 2. Determine whether each of these integers is prime. a) 21. b) 29. c) 71. d) 97. e) 111. f) 143. a) 19. b) 27. c) 93.
Exercises Exercises 1. Determine whether each of these integers is prime. a) 21 b) 29 c) 71 d) 97 e) 111 f) 143 2. Determine whether each of these integers is prime. a) 19 b) 27 c) 93 d) 101 e) 107 f)
More informationMaths Scheme of Work. Class: Year 10. Term: autumn 1: 32 lessons (24 hours) Number of lessons
Maths Scheme of Work Class: Year 10 Term: autumn 1: 32 lessons (24 hours) Number of lessons Topic and Learning objectives Work to be covered Method of differentiation and SMSC 11 OCR 1 Number Operations
More informationKey Stage 3 Subject: Maths Foundation Year: Year 7 Year 8 Year 9 Topic/Module: Geometry
Subject: Foundation Topic/Module: Geometry Time Geometry 1 234 Metric Units Angles/Polygons Bearings Transformations watch Clips N21 N7 N7 N7 N7 N7, R2, 112 112 G10, 46 G16, 122 G14 G13, G17, 45, 121 G23
More informationTenth Bit Bank Mathematics Real Numbers
Tenth Bit Bank Mathematics Real Numbers 1. The rational number among the following is... i) 4.28 ii) 4.282828... iii) 4.288888... A) i) & ii) B) ii) & iii) C) i) & iii) D) All the above 2. A rational number
More informationNCERT Solutions. 95% Top Results. 12,00,000+ Hours of LIVE Learning. 1,00,000+ Happy Students. About Vedantu. Awesome Master Teachers
Downloaded from Vedantu NCERT Solutions About Vedantu Vedantu is India s biggest LIVE online teaching platform with over 450+ best teachers from across the country. Every week we are coming up with awesome
More informationSAMPLE PAPER, TERM  1 SESSION MATHEMATICS CLASSVI Time Allowed 3 hrs M.M.  80
SAMPLE PAPER, TERM  1 SESSION 201718 MATHEMATICS CLASSVI Time Allowed 3 hrs M.M.  80 General Instructions: 1. All questions are compulsory. 2. The question paper consist of 27 questions, divided
More informationDownloaded from
CLASS VI Mathematics (Knowing our Numbers) Worksheet01 Choose correct option in questions 1 to 7. 1. Which is greatest? a. 234 b. 543 c. 657 56 2. Which is smallest? a. 4567 b. 3456 c. 2345 d. 1234 3.
More informationIn the ratio a : b, a and b are called the terms of ratio, `a' is the antecedent and `b' is the consequent.
Ratio: The number of times one quantity contains another quantity of the same kind is called ratio of the two quantities. The ratio of a to b is written as a : b a b a b In the ratio a : b, a and b are
More informationIntroduction to Number Theory
Introduction to Number Theory Number theory is about integers and their properties. We will start with the basic principles of divisibility, greatest common divisors, least common multiples, and modular
More informationSAMPLE QUESTION PAPER ClassX ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80
SAMPLE QUESTION PAPER ClassX (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided
More informationPRINCIPLE OF MATHEMATICAL INDUCTION
Chapter 4 PRINCIPLE OF MATHEMATICAL INDUCTION 4.1 Overview Mathematical induction is one of the techniques which can be used to prove variety of mathematical statements which are formulated in terms of
More informationQUESTION 1 50 FOR JSS 1
QUESTION 1 5 FOR JSS 1 1. The LCM of, 3 and 4 is A. 14 B. 1 C. 1 D. 16. Estimate 578.6998 to 3 decimal places. A. 578.7 B. 578.79 C. 578.8 D. 579. 3. Express 111 two as a number in base ten. A. 15 B. 18
More informationIntermediate Math Circles Number Theory II Problems and Solutions
WWW.CEMC.UWATERLOO.CA The CENTRE for EDUCATION in MATHEMATICS and COMPUTING Intermediate Math Circles Number Theory II Problems and Solutions 1. The difference between the gcd and lcm of the numbers 10,
More informationILLUSTRATIVE EXAMPLES
CHAPTER Points to Remember : POLYNOMIALS 7. A symbol having a fied numerical value is called a constant. For e.g. 9,,, etc.. A symbol which may take different numerical values is known as a variable. We
More informationA number that can be written as, where p and q are integers and q Number.
RATIONAL NUMBERS 1.1 Definition of Rational Numbers: What are rational numbers? A number that can be written as, where p and q are integers and q Number. 0, is known as Rational Example:, 12, 18 etc.
More informationSample Question Paper Mathematics First Term (SA  I) Class X. Time: 3 to 3 ½ hours
Sample Question Paper Mathematics First Term (SA  I) Class X Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided
More informationReal Number. Euclid s division algorithm is based on the above lemma.
1 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius Basic Concepts 1. Euclid s division lemma Given two positive integers a and b, there exist unique integers q and r
More informationMATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 3 X 6 = 18 3 X 7 = 21 3 X 8 = 24 3 X 9 = 27
LEARNING PAPERS FOR CLASS V TABLE 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 2 X 6 = 12 2 X 7 = 14 2 X 8 = 16 2 X 9 = 18 2 X 10 = 20 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 3 X 6 =
More informationCHAPTER 3. Number Theory
CHAPTER 3 Number Theory 1. Factors or not According to Carl Friedrich Gauss (17771855) mathematics is the queen of sciences and number theory is the queen of mathematics, where queen stands for elevated
More informationANSWER KEY & SOLUTIONS
PREHALFYEARLY ASSESSMENT [PHA MATHS SYLLABUS] ANSWER KEY & SOLUTIONS General Instructions:. The question paper comprises of four sections, A, B, C & D.. All questions are compulsory. 3. Section A Q
More informationMATH 2112/CSCI 2112, Discrete Structures I Winter 2007 Toby Kenney Homework Sheet 5 Hints & Model Solutions
MATH 11/CSCI 11, Discrete Structures I Winter 007 Toby Kenney Homework Sheet 5 Hints & Model Solutions Sheet 4 5 Define the repeat of a positive integer as the number obtained by writing it twice in a
More informationKENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32. SECTION A Questions 1 to 6 carry 1 mark each.
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER TEST 09 (201819) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions
More informationCBSE CLASS10 MARCH 2018
CBSE CLASS10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four sections
More informationNumber Tree LCM HCF Divisibility Rules Power cycle Remainder Theorem Remainder of powers a n b n Last and Second last digit Power of Exponents Euler s
Vedic Numbers Number Tree LCM HCF Divisibility Rules Power cycle Remainder Theorem Remainder of powers a n b n Last and Second last digit Power of Exponents Euler s Theorem Fermet s Theory Wilson Theorem
More information2. In an AP. if the common difference (d) = 4, and the seventh term (a7) is 4, then find the first term.
CBSE Board Class X Set 3 Mathematics Board Question Paper 2018 Time: 3 hrs. Marks: 80 Note: Please check that this question paper contains 11 printed pages. Code number given on the right hand side of
More informationCalculate angle y. Reflect shape B using x = 4 as the mirror line
1st August Calculate angle y Describe fully the single transformation that maps shape A onto shape B. Reflect shape B using x = 4 as the mirror line There are three colours of beads in a bag. The ratio
More informationExpressions that always have the same value. The Identity Property of Addition states that For any value a; a + 0 = a so = 3
Name Key Words/Topic 2.1 Identity and Zero Properties Topic 2 Guided Notes Equivalent Expressions Identity Property of Addition Identity Property of Multiplication Zero Property of Multiplication The sum
More informationPark Forest Math Team. Meet #2. Number Theory. Selfstudy Packet
Park Forest Math Team Meet #2 Number Theory Selfstudy Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements
More information1. y is directly proportional to the square of x. When x = 4, y = 25. (a) Find an expression for y in terms of x. ... (3) (b) Calculate y when x = 2.
1. y is directly proportional to the square of x. When x = 4, y = 25. (a) Find an expression for y in terms of x.... (3) (b) Calculate y when x = 2. (1) (c) Calculate x when y = 9. (Total 6 marks) 2. (a)
More informationNotes on Systems of Linear Congruences
MATH 324 Summer 2012 Elementary Number Theory Notes on Systems of Linear Congruences In this note we will discuss systems of linear congruences where the moduli are all different. Definition. Given the
More informationMathematics Challenge 2014
Mathematics Challenge 014 5 th January 014 YEAR 7 Model Answers We provide these model answers of our CWN: Mathematics Challenge 014 exam to help parents. Please note that for some problems there are more
More informationRange: The difference between largest and smallest value of the. observation is called The Range and is denoted by R ie
TNPSC GROUP 2 APTITUDE AND MENTAL ABILITY TEST IMPORTANT FORMULAS 1 Page Range: The difference between largest and smallest value of the observation is called The Range and is denoted by R ie R = Largest
More informationANSWERS. CLASS: VIII TERM  1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)
ANSWERS CLASS: VIII TERM  1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) 21/24 (ii) 4/7 < 4/11 (iii)16/19 (iv)11/13 and 11/13 (v) 0 2. Answer True or False:
More informationBasic Algebra. CAPS Mathematics
Basic Algebra CAPS Mathematics 1 Outcomes for this TOPIC In this TOPIC you will: Revise factorization. LESSON 1. Revise simplification of algebraic fractions. LESSON. Discuss when trinomials can be factorized.
More informationArithmetic. Integers: Any positive or negative whole number including zero
Arithmetic Integers: Any positive or negative whole number including zero Rules of integer calculations: Adding Same signs add and keep sign Different signs subtract absolute values and keep the sign of
More informationQ 1 Find the square root of 729. 6. Squares and Square Roots Q 2 Fill in the blank using the given pattern. 7 2 = 49 67 2 = 4489 667 2 = 444889 6667 2 = Q 3 Without adding find the sum of 1 + 3 + 5 + 7
More informationMath League SCASD. Meet #2. Number Theory. Selfstudy Packet
Math League SCASD Meet #2 Number Theory Selfstudy Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements
More informationFIITJEE ALGEBRA2 Pre RMO
FIITJEE ALGEBRA Pre RMO A. AP, GP 1. Consider the sequence 1,,,, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7,... and evaluate its 016 th term.. Integers 1,,,..., n, where n >, are written on a board. Two numbers
More informationSEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION
CHAPTER 5 SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION Copyright Cengage Learning. All rights reserved. SECTION 5.4 Strong Mathematical Induction and the WellOrdering Principle for the Integers Copyright
More informationthen the hard copy will not be correct whenever your instructor modifies the assignments.
Assignments for Math 2030 then the hard copy will not be correct whenever your instructor modifies the assignments. exams, but working through the problems is a good way to prepare for the exams. It is
More informationChapter 3: Section 3.1: Factors & Multiples of Whole Numbers
Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
More informationMATHEMATICS QUESTION BANK. for CLASS X CHAPTER WISE COVERAGE IN THE FORM IMPORTANT FORMULAS & CONCEPTS, MCQ WORKSHEETS AND PRACTICE QUESTIONS
MATHEMATICS QUESTION BANK for CLASS X 017 18 CHAPTER WISE COVERAGE IN THE FORM IMPORTANT FORMULAS & CONCEPTS, MCQ WORKSHEETS AND PRACTICE QUESTIONS Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold
More informationc d d Determine whether a. 5 is a factor of 90580? b. 7 is a factor of 691? 9. Write all factors of: a. 48 b.
Practice Paper Unit7 (Transport and Communication) Decimals 1. Write the fractions as decimals a. b. c. 9 10 38 7 2. Compare the following decimals a. 3.4 3.34 b. 93.44 93.440 d. 295 e. 68 + 8 f. 35 +
More informationSAMPLE QUESTION PAPER ClassX ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80
SAMPLE QUESTION PAPER ClassX (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided
More informationSolutions to Assignment 1
Solutions to Assignment 1 Question 1. [Exercises 1.1, # 6] Use the division algorithm to prove that every odd integer is either of the form 4k + 1 or of the form 4k + 3 for some integer k. For each positive
More informationCM2104: Computational Mathematics General Maths: 2. Algebra  Factorisation
CM204: Computational Mathematics General Maths: 2. Algebra  Factorisation Prof. David Marshall School of Computer Science & Informatics Factorisation Factorisation is a way of simplifying algebraic expressions.
More informationINTRODUCTION TO FRACTIONS
INTRODUCTION TO FRACTIONS MEANING AND PROPERTIES OF FRACTIONS Fractions are used to represent parts of a whole. Example: What is the fraction of the shaded area? onehalf onequarter threeeighths 4 The
More informationELEMENTS OF NUMBER THEORY
ELEMENTS OF NUMBER THEORY Examination corner 1 one mark question in part A 1  two mark question in part B 1 five mark OR 3mark+2 mark question in part C 1 two or four mark question in part E concepts
More informationKENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD32. SECTION A Questions 1 to 6 carry 1 mark each.
KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD32 SAMPLE PAPER TEST 10 (201819) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions
More informationMesaieed International School
Mesaieed International School SUBJECT: Mathematics Year: 10H Overview of the year: The contents below reflect the first half of the twoyear IGCSE Higher course which provides students with the opportunity
More informationPreCalculus: Semester 1 Final Exam Review
Name: Class: Date: ID: A PreCalculus: Semester 1 Final Exam Review Short Answer 1. Determine whether the relation represents a function. If it is a function, state the domain and range. 9. Find the domain
More informationP2 GCSE Maths bestguess paper 2018
P2 GCSE Maths bestguess paper 2018 Name: Class: Date: Time: 90 minutes Marks: 80 marks This is a predicted paper based on topics that have already come up in P1 Comments: This is a best guess paper and
More informationAugust 15, M1 1.4 Common Factors_Multiples Compacted.notebook. Warm Up MI 36. Jun 20 10:53 AM
Warm Up MI 36 8 14 18 Jun 20 10:53 AM 1 Assignment Jun 20 12:36 PM 2 Practice 7 13 A = bh 7 x 13 91 7 7 A = ½bh ½(7 x 7) ½(49) 24.5 Jun 20 12:36 PM 3 Practice 6 4 8 A=½bh 4 6x8 24 A=bh 4x8 32 4 5 8 8 A=bh
More informationCBSE CLASS10 MARCH 2018
CBSE CLASS10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four
More informationPolynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example:
Polynomials Monomials: 10, 5x, 3x 2, x 3, 4x 2 y 6, or 5xyz 2. A monomial is a product of quantities some of which are unknown. Polynomials: 10 + 5x 3x 2 + x 3, or 4x 2 y 6 + 5xyz 2. A polynomial is a
More informationA group of figures, representing a number, is called a numeral. Numbers are divided into the following types.
1. Number System Quantitative Aptitude deals mainly with the different topics in Arithmetic, which is the science which deals with the relations of numbers to one another. It includes all the methods that
More informationMaths Worksheet for class 6 SA1[prepared by Kani Raja]
Maths Worksheet for class 6 SA1[prepared by Kani Raja] Solve the equation using transposition method: 1) b + 6 = 13 ) x 7 = 3) f 0.6 =.4 4) x 4 = 16 5) 14 more than a number equals 18. Find the number.
More information