Maths 7 SB Completed.pdf

Mathematics G r a d e 7 student text book MATHEMATICS G R A D E 7 STUDENT TEXT BOOK South Nations Nationalities and Peoples Regional Education Bureau i  Mathematics G r a d e 7...

Mathematics G r a d e 7 student text book MATHEMATICS G R A D E 7 STUDENT TEXT BOOK South Nations Nationalities and Peoples Regional Education Bureau i  Mathematics G r a d e 7 student text book MATHEMATICS G R A D E 7 STUDENT TEXT BOOK South Nations Nationalities and Peoples Regional Education Bureau ii  Mathematics G r a d e 7 student text book Developed By Addis Ababa Education Bureau and Adapted by South Nations Nationalities and Peoples Regional Education Bureau. Adapted By: Natan Labiso (Msc) Firehiwot Eyuel (Bsc) Meseret Ayenew (MA) First Edition, 2014 E.C. South Nations Nationalities and Peoples Regional Education Bureau iii  Mathematics G r a d e 7 student text book Table of Contents Unit 1..........................................................................................................................1 Basic Concepts of Sets.............................................................................................1 Introduction........................................................................................................1 1.1.Sets and Elements of Sets..............................................................................1 Unit 2........................................................................................................................18 Integers.....................................................................................................................18 2.1.Revision of whole and natural numbers.........................................................18 2.2.Introduction to integer....................................................................................22 2.3.Comparing and Ordering Integers..................................................................29 2.4. Addition and subtraction of Integers.............................................................39 2.5.Multiplication and Division of Integer numbers............................................49 2.6.Even and Odd integers....................................................................................65 Review Exercise for unit 2................................................................................72 Unit 3........................................................................................................................76 Ratio, proportion and percentage.............................................................................76 3.1.Ratio and proportion.......................................................................................76 3.1.2 Proportion.................................................................................................85 3.2.Revision on Percentages.................................................................................95 3.3. Application of Ratio, Proportion and Percentage........................................109 3.3.1. Calculating profit and loss percentage...............................................113 3.3.2. Simple interest.......................................................................................117 3.3.3 Compound interest.................................................................................120 3.3.4 Ethiopian Income Tax, Turn over Tax, VAT....................................123 Summary for unit 3..........................................................................................129 iv  Mathematics G r a d e 7 student text book Review exercise for unit 3...............................................................................131 Unit 4......................................................................................................................135 Linear equations.....................................................................................................135 4.1.Algebraic terms and expressions..................................................................136 4.1.1. Use of Variables in Formula..................................................................136 4.1.2 Variables, Terms and Expressions......................................................139 4.2.Solving linear equations................................................................................144 4.2.1 Linear Equations Involving Brackets.............................................144 4.2.1 Solving linear equation involving fractions........................................155 4.3.Cartesian coordinate system.........................................................................160 4.3.1 The Four Quadrants of the Cartesian coordinate Plane.......................160 4.3.2 Coordinates and graph of linear equations.............................................168 4.4.Applications of linear Equations.................................................................178 Summary for unit 4..........................................................................................184 Review Exercise for unit 4..............................................................................186 Unit 5......................................................................................................................189 Perimeter and Area of Plane figures......................................................................189 5.1.Revision of triangles.....................................................................................190 5.2.Four - sided Figures......................................................................................197 5.4.Perimeters and Areas of four sided figures..................................................218 5.5.Circumference and Area of a crcle...............................................................229 The following activity will help you find the way of calculating the accurate area of a circle.............................................................................................................235 5.6.Applications of Perimeter and Area of Plane Figures..................................238 Summary for unit 5..........................................................................................242 Review exercise for unit 5...............................................................................243 Unit 6......................................................................................................................246 Congruency of plane figures..................................................................................246 6.1.Congruent of Plane Figures..........................................................................246 v  Mathematics G r a d e 7 student text book 6.1.1 Definition and Illustration of Congruent Figures...................................247 6.1.2 Congruency of Triangles........................................................................250 6.1.3 Tests for congruency of triangles (ASA, SAS, SSS).............................254 6.2.Applications..................................................................................................264 Summary for unit 6.......................................................................................269 Review exercise for unit 6...............................................................................269 Unit 7......................................................................................................................273 Data Handling........................................................................................................273 7.1.Organization of data using frequency table..................................................273 7.2. Construction and Interpretation of line graphs and pie charts..................278 7.2.1 Line graphs.............................................................................................279 7.2.2 Pie charts.................................................................................................283 7.3.The Mean, Mode, Median and Range of Data.............................................292 7.4.Application of Data Handling.......................................................................300 Summary for unit 7..........................................................................................305 Review exercise for unit 7.............................................................................305 vi  Mathematics G r a d e 7 student text book Unit 1 Basic Concepts of Sets Learning Outcomes: At the end of this unit, learners will be able to:  Understand the concept of set.  Describe the relation between two sets.  Perform two operations (intersection and union) on sets. Introduction The idea of a set is familiar in everyday life. In your surrounding there are different groups of objects or individuals. For example group of all grade 7 students in your school, group of all teachers in your school is a collection of individuals. In this unit you will learn about some sets and properties of sets. 1.1.Sets and Elements of Sets In our daily life things are grouped together with a certain property in common such as family members, a collection of clothes, fingers of hands, collection of students in a class, a herd of cattle, a flock of sheep, a swarm of bees,etc.all these groups are well defined. Definition: A Set is a well-defined collection of objects or individuals. The objects in the set are called its elements or members of the set. asset is well-define collection of 1 object or individual. the object in the set are called its element or members  Mathematics G r a d e 7 student text book By well-defined, we mean that, given a collection and an object or individual, we have to say that the object or the individual is in the collection or not without any ambiguity. Repeating elements in a set do not add new elements to the set. For Example, {b, b, b} is the same as {b}. Example 1.1 Identify each of the following collections are a set or not a. The collection of whole numbers less than 6. b. The group of short students in a certain school. c. The collection of vowel letters in the English alphabet. d. A group of rich people in Hawassa. Solution: a. The collection of whole numbers less than 5 is a well-defined collection. The whole numbers 1, 2, 3, 4, and 5 are in collection and anything other than these is not in the collection. b. The group of short students in a certain school is not well-defined. It is because shortness is relative someone may be short for some group, but not for others. c. The vowels in the English alphabet are a, e, i, o, u are well-defined; anything other than these five letters is not in the collection. d. The group of rich people in Hawassa is not well-defined because richness is relative Note: 1. Sets are denoted by capital letters like A, B, C, etc, and elements of a set are denoted by small letters like a, b, c, d, x, y, z, etc. [Grade 7student book] Page 2  Mathematics G r a d e 7 student text book 2. The symbol {....} is used to group the members of a set called braces or curly brackets with elements separated by commas. 3. Given a set A and an object x, i. If x is an element of A, then we denote this relation by “x ∈A” and read as “x is an element of set A” or “x belongs to set A”. ii. If x is not an element of A, then we denote the relation by “x ∉ A” and read as “x is not an element of set A” or “x does not belong to set A”. Example 1.2 If A is the set of natural numbers less than5, then A can written as A= {1,2,3,4,} In this case, 1∈A,2∈A,3∈A,and 4∈A,but5∉Aand also 7 ∉A and so on. Every object in a set is unique. The same object cannot be included in the set more than once. For example, if A= {1, 2, 3, 4, 5} then every element of A is included not more than once. We do not write A= {1, 1,2,3,4, 5} or A= {1, 2,2,3,4, 5} or A= {1, 2,3,3,4, 5} and so on. Example 1.3 Determine the set X as the set of all days in a week. Solution: There are seven days in a week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. Therefore= {Monday, Tuesday, Wednesday,Thursday,Friday,Saturday, Sunday}. Example 1.4 [Grade 7student book] Page 3  Mathematics G r a d e 7 student text book Let M be the set of multiples of 2 between 1 and 9; determine the set M and members of the set M. Solution: M = {2, 4, 6, 8,} and 2, 4, 6and 8 are the members of set M. Exercise 1.1 1. Which of the following collections are sets? Justify your answer. a. The beautiful birds in Hawassa. b. The natural numbers less than 1000. c. The prime factors of 2500. d. The months of a year. e. Students in grade 6 that are 12 years of age in Ethiopia. 2. Identify each of the following statements are true or false a. -1∈{ –2, -1,0,1,2 } b. b∈{ a, b, c, d, e, f } c. 6∉{factorsof48} d. 3 ∉ {1, 2, {3}, 4}. e. {3}∈ {3}. 1.1.1. Ways to Describe Sets i.Listing or Roster Method [Grade 7student book] Page 4  Mathematics G r a d e 7 student text book Listing or roster notation also called enumeration method is a list of elements separated by commas enclosed in curly braces. The curly braces are used to indicate that the elements written between them belong to that set. The elements in such types of sets can be completely or partially listed and the elements follow certain pattern. Example 1.5 Let P be the set of all prime numbers less than 9. Write P using listing method. Solution: The prime numbers less than 9 are 2, 3, 5 and 7. Therefore, P= {2, 3, 5, 7} is tabulation or complete listing method. Example 1.6 If A is the set of natural numbers less than 10, then write B using listing or roster method. Solution: The natural numbers less than10 are numbers from1to9. Instead of writing all the 9 numbers, you can list the first three numbers to indicate that the numbers follow a certain pattern followed by three dots to indicate that the numbers are continuing up to the last number, which is 9. Thus, A= {1, 2, 3… 9} is a partial listing method. ii.Verbal Method There are times when it is not practical to list all the elements of a set. In such cases, it is better to describe the set using verbal method. [Grade 7student book] Page 5  Mathematics G r a d e 7 student text book Example 1.7 Describe each of the following sets a. The set of letters in the English alphabet. b. The set of Grade 6 students in Ethiopia in 2014 E.C. Solution: There are 26 letters in the English alphabet and instead of listing all the English alphabets, you can write the set as {the English alphabets}. It is very difficult to list all Grade 6 students in Ethiopia in 2014 E.C. and the better way to write it is as {Grade 6 students in Ethiopia in 2014 E.C.}. ii.Set builder method It is called method of defining property. It is another way to specify a set that enables us to decide whether or not any given objects belong to the set. Example 1.8 a. F is the set of all females who are living in Hawassa can be described as F= {x/x is a female living in Hawassa} which is read as "F is the set of x such that x is a female living in Hawassa". b. Let A={2, 3, 4, 5, 6} can be described as A={x| x∈ and 2