Acme Mathematics 7

Acme Mathematics 7 3016.1 Collection of Data(a) Data Let us suppose that we are interested in knowing about the marks obtained by 30 students of class-7 of third term exam in mathematics. How do we obtain the desired information? We ask each of the 30 students his or her marks in mathematics and note down the marks. Let us suppose that these 30 students obtained the following marks: 35, 40, 45, 50, 35, 40, 50, 35, 25, 45, 35, 50, 40, 25, 30, 45, 35, 30, 30, 35, 45, 25, 30, 50, 35 50, 40, 45, 50, 30 In the above example, each entry is a numerical fact which is called an observation. Such a collection of observations gathered initially is called raw data. Data originally collected for an investigation are known as primary data. The above data is primary data. Data which are not originally collected are known as secondary data. (b) Tabulation of data We may organize the raw data in ascending or descending order. For above example, we organize the data in the ascending order and write it as follows: 25, 25, 25, 30, 30, 30, 30, 30, 35, 35, 35, 35, 35, 35, 35, 40, 40, 40, 40, 45, 45, 45, 45, 45, 50, 50, 50, 50, 50, 50, The above marks show that the highest mark obtained is 50 and the lowest mark is 25. The arrangement of data in descending or ascending order is called an array of data. (c) Frequency Distribution From the above example, 3 students have obtained 25 marks, 5 students have obtained 30 marks and so on. The number of times a particular observation occurs is called its frequency. In the above example, if we rearrange the data in the form of a table starting from lowest to highest observation values then this is called the frequency distribution of the marks obtained by 30 students. A table in which such a frequency distribution is given is called the frequency distribution table or simply frequency table. We thus have the following table. When the number of observation is large, it may not be convenient to find the frequencies simply by counting. In such case, we make

302 Acme Mathematics 7use of tally marks which are quite helpful to find the frequencies. Tallies are usually marked in a bunch of five for ease in counting. The fifth tally in a bunch is usually marked diagonally across the earlier e.g.( ). We shall illustrate the method of tally marks in the following example. Frequency distribution of marks obtained by 30 students in mathematics is given below:Marks obtained Tally Bars Frequency25 ||| 330 535 || 740 |||| 445 550 | 6Total 30Solved ExampleExample 1 : The following marks were obtained by 40 students in a unit exam in mathematics: 2, 3, 7, 5, 6, 5, 4, 2, 3, 5, 6, 4, 5, 7, 8, 9, 10, 10, 7, 8, 7, 2, 3, 5, 9, 8, 4, 5, 3, 4, 9, 2, 2, 3, 4, 5, 7, 6, 6, 8 Prepare a frequency table. Solution: Frequency distribution of marks of 40 students in unit exam in mathematics.Marks Tally marks Frequency2 53 54 55 || 76 |||| 47 58 |||| 49 ||| 310 || 2Total 40

Acme Mathematics 7 303Classwork1. Tabulate the following data: 2, 7, 5, 4, 3, 2, 1, 3, 2, 6, 5, 3, 1, 3, 1, 2, 4, 1, 3, 4, 4, 3, 2, 3, 4, 5, 2, 3, 1, 4 2. Make a frequency table from the following data: 1, 3, 2, 5, 6, 3, 4, 5, 6, 3, 2, 2, 4, 4, 7, 8, 6, 4, 5, 8, 3, 4, 3, 3, 8, 7, 8, 6, 4, 7 3. Prepare frequency table of the following marks obtained by 25 students in a test : 42, 37, 42, 42, 37, 38, 50, 50, 49, 33, 39, 44, 39, 42, 42, 37, 39, 35, 50, 41, 35 38 31 42 394. Fill the missing frequencies:Marks Tally Mark Frequency15 || ......................20 |||| ......................25 ......................30 || ......................35 ||| ......................Exercise 6.11. The weight (in kg) of 10 students of grade seven of a school are as follows: 30, 35, 31, 40, 38, 37, 39, 36, 39. Arrange the data in ascending order and find: (a) The least weight. (b) The highest weight.

304 Acme Mathematics 72. Following are the number of members in 25 families in a village: 6, 8, 6, 3, 2, 5, 7, 8, 6, 5, 5, 7, 7, 8, 6, 6, 7, 7, 6, 5, 3, 4, 2, 4, 3Prepare a frequency distribution table for the data and answer the following questions: (a) What is the smallest family size? (b) What is the most common family size? (c) How many families are of the smallest size? 3. In a study of number of accidents per day the observations for 30 days were obtained as following: 4, 3, 5, 6, 4, 3, 2, 5, 4, 2, 6, 2, 1, 2, 2, 0, 5, 4, 6, 1, 3, 0, 5, 3, 6, 1, 5, 5, 2, 6 Prepare a frequency distribution table. 4. A die was thrown 30 times and the following scores were obtained:5, 4, 3, 2, 1, 1, 2, 5, 4, 6, 6, 3, 2, 1, 4, 3, 2, 1, 5, 6, 4, 3, 2, 1, 5, 6, 5, 2, 1, 3 Prepare a frequency table of the scores. 5. The age in years of 20 students studying in class VII are as follows. Construct its frequency table: 11, 11, 11, 12, 10, 13, 12, 10, 14, 11, 12, 14, 12, 13, 12, 11, 11, 11, 12, 10. 6. The weight in kg of 25 students is given below. Represent it in a frequency table: 30, 32, 35, 38, 30, 35, 38, 32, 30, 30 30, 32, 35, 35, 32, 30, 35, 38, 32, 30 32, 35, 38, 32, 35

Acme Mathematics 7 3056.2 Bar GraphA bar graph is a pictorial representation of the numerical data by a series of bars or rectangles of uniform width erected horizontally or vertically from the same base line with equal spacing between the bars. Each rectangle or bar represents only one value of the numerical data. So, there are as many bars as the number of values in the numerical data. The height or length of each bar represents the value of the numerical data. Some Bar diagrams are : 1. Simple Bar Graph 2. Multiple Bar Graph (a) Simple Bar Graph The diagram that represents the value of only one variable is simple bar graph. The height of a bar represents the value of the variable in the graph. The breadth of bars should be equal and the gaps of the bars to each other should also be equal. Drawing Bar graphs on Graph Paper We now learn to draw a bar graph. We shall use graph paper to construct the bars for ease and accuracy. But it is not necessary to do so. We must keep the following points in mind for drawing a bar graph . 1. It should have a title at the top or a caption below the graph to indicate what it is about. 2. Scale should be mentioned below the graph. 3. All bars should be of the same width. 4. Spaces between the bars should be of the same width. 5. Each bar should be labeled. We shall illustrate the construction of bar graphs through example.Solved ExampleExample 1 : Out of 20 students in class-7, the first term examination result of a school is given below:Year 2079 2080 2081 2082No. of passed students 8 10 12 15051015202079 2080 2081YearsNo. of students2082

306 Acme Mathematics 7Solution: The above graph is the required bar graph.Classwork1. Read the given bar graph and answer the following questions: ClassesNumber of students01030502040601 2 3 4 5YX(a) How many students are there in class-2? (b) How many students are there in class-4? (c) Which class has the highest number of students? (d) Which class has the least number of students? (e) Which classes have the equal number of students? (f) What is the information given by the bar graph? (g) What is the total number of students in the school?Exercise 6.21. Prepare a bar diagram for the given data: Classes VI VII VIII IX X No. of students 100 195 130 140 150 051015202079 2080 2081YearsNo. of students2082First term examination result of a schoolNumber of students of a school

Acme Mathematics 7 3072. The number of books sold by a shopkeeper on six consecutive days is as follows: Daya Sunday Monday Tuesday Wednesday Thursday Friday No. of books sold 10 20 30 50 40 30 Draw a bar graph to represent the above information. 3. Marks obtained in mathematics by 109 students are given in the following table: Marks 40 50 60 70 80 90 100 Number of students 8 10 16 20 30 15 10 Represent the above information by a bar graph. 4. The heights (in cm) of 50 students of class X of a school are given as follows: Height (in cm) 144 150 155 157 164 Number of student 7 8 17 13 5 Represent the above information by a bar graph.5. Represent the following data in a simple bar diagram. (a) Classes III IV V VI VII No. of students 25 20 30 40 35(b) Means of transportation Bus Cycle Pedestrian Motorbike No. of vehicles 30 25 20 506. Study the given diagram and answer the following questions: 5 6 7ClassesNumber of students81030204050Class wise students of a school(a) Which class has the highest number of student? (b) How many students are there in class-7? (c) How many students are there in a school? (d) In which class there are 20 students?

308 Acme Mathematics 77. Represent the following simple bar graph in the table.(a)(b)YXSubjectsMarks0103050204060English Maths Science Social NepaliSubject wise marksDays of MaghDegree Celsius0111315121416YHumla Pokhara Chitwan Jhapa KathmanduXTemperature of the city

Acme Mathematics 7 309(b) Multiple Bar Graph The bar graph representing two or more items together is called a multiple bar graph. The result for drawing them is similar to that of simple bar diagram. But we use different colors or shadings to distinguish bars of one type from the other. Consider the given example.Example 1 : Final result of class-7 of a school is given below : Academic Years Grade A+ Grade A Grade B+ 2080 6 2 4 2081 8 2 2 2082 6 4 2 Represent the data by a multiple bar diagram. Solution: Final result of a school0214365872080 2081Academic YearsNo. of students2082Grade A+Grade AGrade B+SymbolClasswork1. The following data gives the number of boys and girls offering different optional subject in a school. Represent the data by multiple bar diagram: SubjectNumber of studentsBoys GirlsMathematics 90 70 English 20 10 Economics 100 60 Computer Science 80 70

310 Acme Mathematics 72. Colour the graph. 021436572082Academic YearsNo. of studentsGrade A+Grade AGrade B+Symbol3. The table below shows the number of boys and girls in a school. Construct a multiple bar diagram to represent the data. Classes 6 7 8 9 10 Boys 100 70 90 80 90 Girls 70 80 70 80 80 Exercise 6.31. The strength of different years of a school is given below. Represent the data by multiple bar-diagram: (a) YearsNumber of studentsBoys Girls2078 25 8 2079 30 7 2080 80 15 2081 94 19 2082 115 27 (b) YearsNumber of studentsBoys Girls2079 170 802080 235 702081 375 2202082 470 300

Acme Mathematics 7 3112. The academic qualification of teachers of your school is given below. Present the data by multiple diagram: QualificationTeachersMale FemaleSEE Level 2 1+2 Level 13 12Bachelor Level 13 8Masters Level 10 23. Table below shows the number of boys and number of girls in a school. Present the data by multiple bar diagram: Classes VII VIII IX X Boys 80 90 110 100 Girls 60 90 100 1104. The table below shows the income and expenditure (Rupees in thousand) of a family in different years. Present the data by multiple bar diagram: Year 2078 2079 2080 2081 2082 Income 200 300 275 300 325 Expenditure 175 200 175 225 250 5. The literacy rate of male and female of different districts of the year 2058 are given below. Districts Chitwan Kathmandu Kaski Mugu MahottariMale 79% 86% 63% 45% 45%Female 63% 66% 61% 9% 22%Represent the data by multiple diagrams. 6. From the bar diagram alongside. Answer the following questions: (a) Find the total number of boys. (b) Find the total number of girls. (c) Which class has more students and by how much? (d) What is the total number of students?7ClassesNumber of students8103020405060No. of boysNo. of girls

312 Acme Mathematics 77. From the bar diagram alongside. Answer the following questions: 1st Sunday 2nd Sunday 3rd SundayMangsir - 2081Weight in Kg100300200400500600700900800CauliflowerPotatoCabbage(a) In the first Sunday how much kg of cabbage is sold?(b) In which Sunday potato is sold most?(c) On which days are cauliflowers sold in the same quantity?(d) How much cabbage is sold in total?(e) How much cabbage is sold in total?(f) On which day was 400 kg of cabbage sold?8. The given table shows the number of new admission of students from class 6 to 9.Classes 6 7 8 9Boys 10 15 25 20Girls 25 35 10 5(a) Construct a multiple bar graph from the above data.(b) How many total girls admitted from classes 6 to 9? Find it.

Acme Mathematics 7 3136.3 Line GraphIntroduction A data formed by the values of variable at different periods is shown in the line graph. The way of representing the data using lines in a graph is called line graph. This kind of graph is very good for showing the changes that is upward and downward trends. Steps for drawing a line graph: Step 1: Take time along X-axis and values of the variable along Y- axis by assuming appropriate scale. Step 2: Plot the values of the variable. Step 3: Join these points by a straight line. The resulting broken lines gives as a line graph. Note: broken lineSolved ExamplesExample 1 : Present the following price of sugar in a line graph.Years 2078 2079 2080 2081 2082Price (Rs) 60 80 75 70 82Solution : The data is presented in a line graph is given below.207810O305070204060806080757082902080YearsPrice (Rs.)2079 2081 2082

314 Acme Mathematics 7Example 2 : Present the following data in a line graph.Years 2077 2078 2079 2080 2081Production of carrot (in Tones) 8 14 12 6 8Solution: The line graph of production is given below:14106281412681284102077 2078 2079 2080 2081YearsProduction (tones)Example 3 : The following line graph shows that the number of different currency notes with a shopkeeper.052515354510302040502 5 10 20 50 100 500Types of NotesNumber of Notes1000Answer the following questions using the above line graph: (a) How many 20 rupees notes are there ?(b) Which types of currency has greater number of notes ? (c) Which types of currency have equal number of notes ? Solution: From the given line graph we can answer the above questions: (a) The number of 20 rupees notes is 35. (b) 1000 rupees note has greater number. (c) Currency notes of 20 rupees and 50 rupees have equal number.

Acme Mathematics 7 315Classwork1. Draw the line graph for the following data: (a) Monthly income of Mr. Kabindra.Year 2078 2079 2080 2081 2082Income in Thousand 30 40 35 50 45(b) Profit of Mrs. Ujeli in her company:Year 2078 2079 2080 2081 2082Profit (in thousand) 30 40 50 55 25(c) Marks of a student of class - 7Subject English Math Science Social NepaliMarks 60 80 75 65 602. The wages of the workers are given below. Draw its line graph.Wages (Rs) per day 300 400 450 475 500 No. of workers 2 4 10 3 1 3. Draw the line graph of the given data. x 2 4 6 8 10 f 2 5 8 3 2 Exercise 6.41. Draw the line graph for the following data:(a) Price of PetrolYear 2078 2079 2080 2081 2082Price in Rs 130 135 142 162 155(b) Height of NarayanAge (in years) 10 11 12 13 14 15Height (in cm) 110 115 120 125 130 140

316 Acme Mathematics 7(c) Temperature of a townMonths Paush Magh Fagun Chait Baishakh JethTemperature in (°C) 20 25 35 40 42 38(d) Class wise number of students of a school.Class 1 2 3 4 5 6No. of Student 40 35 45 30 35 402. Study the given line graph and answer the following questions. (a) Which class has the least number of students?(b) Which class has the maximum number of students?(c) How many students are there in the all classes? 3. The marks of Kushal in different subjects is shown in the line graph given below. 0 Nepali Math Computer Science HPE English Social103050204060SubjectsMarksAnswer the following questions.(a) Which subject has the least mark? (b) Which subject have the highest mark? (c) How many marks is secured in Social?(d) In which subjects Kushal secured the equal marks?0 1 2 3 4 5 6 7 8 9 10103050204060ClassesNo. of Students

Acme Mathematics 7 3171. The table given below shows the SEE result of a school for last four years.Year (in B.S.) 2079 2080 2081 2082Grade A+ 10 15 12 14Grade A 15 101 18 16Grade B+ 5 11 8 10(a) Draw a multiple bar graph to represent the data.(b) How many students secured A+ in the last three years?2. There are 13 students in class seven and their mass in kg are as follows.30, 32, 36, 35, 45, 41, 35, 32, 32, 40, 33, 35, 36(a) Write the number of students using tally marks.(b) Represent the data in frequency distribution table.3. The given table shows the number of new admission of students from class 6 to 10.Classes 6 7 8 9 10No. of students 10 15 25 10 20(a) Construct a line graph from the above data.(b) How many new students admitted from classes 6 to 10? Find it.4. A line graph showing the marks obtained in mathematics by five students in a class is given.(a) Who got maximum, marks in mathematics?(b) If in an examination system, less than 35 marks is non graded. 35 to below 40 is D grade. How much additional marks is required for Ram to get D grade?RamRitaGitaAayushHariStudentsMarks1002030405060Mixed Exercise

318 Acme Mathematics 75. The table given below shows the daily sales of a shop for six days of a week.Day SUN MON TUE WED THU FRISales (in Rs.) 2000 4000 3000 4500 6000 2500(i) Construct a line graph for the frequency table.(ii) On which day were the sales above Rs. 3000.6. Study the given bar diagram and answer the following questions:01020304050Cricket Football Volleyball BasketballNo. of StudentsGames(i) What is shown in the simple bar graph?(ii) How many students like volleyball?(iii) Which is the most popular game?7. (a) Show the given data in multiple bar diagram.SchoolA B CGirls Boys Girls Boys Girls BoysNo. of Students 250 200 200 300 300 250(b) Which school has the maximum number of students?8. The number of boys and girls studying in various classes of a school are shown in the table below.Classes VI VII VIII IX XNo. of Boys 30 25 20 10 25No. of Girls 20 30 30 30 35(a) Draw a multiple bar diagram to represent the data.(b) How many students are there in class VI to X.

Acme Mathematics 7 3199. The table below shows the number of students in a secondary level school of Bharatpur.Classes 6 7 8 9 10No. of students 40 50 40 60 25(a) What is the total number of students of that school?(b) Represent the above data by simple bar diagram.10. (a) What is the number represented by the following tally bars? (b) Show the following data in a line graph.Classes 6 7 8 9 10No. of students 50 70 80 60 4011. The following graph shows Kushal's height changes. Understand the graph and answer the question given below.60 2 4 6 8Age of Kushal (in year)Height in inches10 12121824303642485460(a) What was Kushal's height when he was 4 years old?(b) What is the changes in Kushal's height from 2 years of age to 8 years of age?(c) When was Kushal 54 inches tall?

320 Acme Mathematics 7EvaluationTime: 36 minutes Full Marks: 151. (a) Represent the following data table in a multiple bar diagram [2] Year (B.S) 2078 2079 2080 2081 2082Male 32 41 36 28 48Female 35 42 36 27 50 (b) In which year, number of male is more than number of female ? [1]2. The number of boys and girls studying in various classes of a school are shown in the table below. Classes VI VII VIII IX XNo. of boys 30 25 20 10 25No. of Girls 20 30 30 30 35(a) Draw a multiple bar diagram to represent the data. [2](b) How many students are there in class VI to X ? [1]3. (a) What is the number represented by the following tally bars? [1] (b) Show the following data in a line graph. [2] Class 6 7 8 9 10No.of students 50 70 80 60 404. (a) Define line graph. [1] (b) Represent the following result in a multiple graph. [2] Grade \\Classes VI VII VIIIA 30 20 20B 10 25 15C 5 10 155. The population of female and male of a town of 5 year is given below.Year (B.S) 2078 2079 2080 2081 2082Male 11 14 15 13 11Female 12 13 14 17 17(a) Define multiple bar diagram [1](b) Represent the given table in a multiple bar diagram [2]

Acme Mathematics 7 321Class – 7 Time – 2 hrs F.M. 50Model Question1. P = {Prime numbers less than 10}, Q = {Odd numbers less than 8}, R = {Prime factors of 6} and S = {cube numbers between 10 and 20} are given :(a) Which of the four sets are equivalence sets? [1U](b) Write the subsets of set R. [1A](c) Is the set S being the proper subset of set P? write with reason. [1HA]2. In a quiz competition held in Saraswoti secondary school, four teams were participated. The rules of quiz competition are given:(a) Team Annapurna answered 20 questions correctly, didn't answer 12 questions and answered 8 questions incorrectly, then how many marks did the team Annapurna secured? [1U](b) The marks secured team Annapurna is a square number or a cube number? Write down. [1K](c) Which one is the greatest number that divides 8, 12 and 20 exactly? Find it. [2A]3. Sabita is working in a cooperative institution. She has spend 26 part of her income in food and 29 part of her income in education:(a) In which title between food and education will she spent more? [1K](b) She has monthly income Rs. 18000. What is her monthly saving? Find it. [2A](c) Write any two rational numbers between 29 and 26 . [2U](d) Which number is added to the numerator and denominator of 29 so that sum is equal to 12 ? Calculate it. [1HA]The rules of quiz competition(i) For each correct answer (+8)(ii) For each incorrect answer (–2)(iii) Not given answer (0)

322 Acme Mathematics 74. Kabita is a wholeseller. She has bought 120 packets of half liters cooking oil in 6 cartons from a dealer. When she reached her shop and opened the cartoon, she got 10 packets were broken:(a) Write the formula to find the loss percent. [1K](b) If she sold each packets in Rs. 180 from unbroken packets she made a loss of 10%. What was her cost price? [1A](c) If 5% profit is to be made then the remaining unbroken packets should be sold more or less than Rs. 200 each? Calculate and write with reason. [2HA]5. A model of a 5 m long cubic block and another cuboidal box made by combining same three cubic blocks is given.(a) Find the total surface area of the given cubical block. [1U](b) Find the volume of the given cuboid. [2A](c) Is the total surface area of the given cuboidal box being three times the total surface area of the cubical block? Write with reason. [1HA](d) Write the relationship between radius and diameter of the circle. [1K]6. The table given below shows the result of class Seven of a school in the subject of Mathematics for last four years :Grade Years(B.S.)2075 2076 2077 2078A+ 12 15 12 14A 18 8 16 11B+ 5 12 7 10(a) Draw a multiple bar graph to represent the data. [2A](b) Which years in exam has the least number of students, who got B+ in Mathematics? [1K]7. A rectangular play ground is shown in the figure with its length (2x+ y) m. and breadth (x+3y) m.(a) What is the area of that play ground? Express in terms of x and y. (b) If x = 4 and y = 1, which one, the length or breadth should be decrease or increase so that a square playground can be made? Write with reason. [2HA]5 cm(x+ 3y) m(2x+ y) m[2A]

Acme Mathematics 7 3238. Give the answer of the follwing questions.(a) Write the expanded form of (a + b)2. [1K](b) Simplify: xa – b × xb – c × xc – a [2A]9. An inequality is represented on a number line.– 4 – 3 – 2 – 1 0 1 2 3 4(a) What does the black circle on the nuber line represents? Write it. [1K](b) Table formed by the linear equation 2x + y = 8 with two variables is given below. Draw the graph on the basis of the given table. [2U]x 4 3 2y 0 2 410. Observe the given graph as given below:(a) Writhe the coordinates of P and Q and also write the length of PQ. [2U](b) Reflect the points P and Q in X- axis and then write the coordinates of their images. [2U](c) When the line segment PQ is transformed, then the image point of the point P becomes Q. What type of transformation is this? Write with reason. [1HA](d) What type of triangle is formed by joining the points P, X and Y? Give reason. [1HA]11. In the given figure straight lines AB and CD are intersecting at the point E.A BDECACEBD Fig. 1 Fig. 2(a) Write the relationship between vertical opposite angles AEC and BED. [1K]OP QX' XY'Y 1 small box = 1 unit

324 Acme Mathematics 7(b) Make the table as given below and fill in the gaps on the basis of above given figure. Also write the conclusion. [2HA]Fig no. ∠AEC ∠BEC Result12Conclusion:(c) Construct the Δ ABC with AB = 7.5 cm, ∠ABC = 75° and ∠BAC = 60°. [3A]12. A sample of Volley ball court having length 18 m and breadth 9 m is given below.18 m9 m(a) Draw the scale of 1 cm = 0.2 m in the volleyball court. Also draw the possible axis of the line symmetry. [3A](b) Write the name of the objects made by the given net. [1K]

Acme Mathematics 7 325Exercise: 1.1 to 1.4Show to your teacher. Mixed Exercise : Show to your teacher.Exercise: 2.11. (a) 196 (b) 324 (c) 729 (d) 1024 (e) 1225 (f) 1521(g) 1849 (h) 2401 (i) 3364 (j) 4225 (k) 4096 (l) 4900 (m)6400 (n) 8464 (o) 12321 (p) 66049 (q) 122500 (r) 2621442. (a) 152 (b) 172 (c) 222 (d) 352 (e) 402 (f) 572(g) 602 (h) 762 (i) 802 (j) 1002 (k) 1122 (l) 15023. (a) Yes (b) No (c) No (d) Yes (e) Yes (f) No (g) No (h) Yes (i) Yes (j) Yes (k) Yes (l) No 4. (a) 3 (b) 5 (c) 7 (d) 3 (e) 2 (f) 5 (g) 6 (h) 35 (i) 2 (j) 3 (k) 15 (l) 30 5. (a) 3 (b) 5 (c) 2 (d) 3 (e) 11 (f) 3 (g) 7 (h) 3 (i) 15 (j) 5 (k) 10 (l) 429 6. (a) 289 m2 (b) Rs. 2401 7. (a) 361 (b) 196 8. (a) 7 (b) 5 (c) 7 9. (a) 2 (b) 7 (c) 3Exercise: 2.21. Show to your teacher.2. (a) 11 (b) 18 (c) 35 (d) 42 (e) 52 (f) 54 (g) 55 (h) 60 (i) 64 (j) 69 (k) 70 (l) 72 3. (a) 8 (b) 40 (c) 70 (d) 72 (e) 171 (f) 420 (g) 660 (h) 416 (i) 630 (j) 1250 (k) 128 (l) 36454. (a) 22 (b) 23 (c) 31 (d) 43 (e) 33 (f) 3 2(g) 12 7 (h) 16 6 (i) 2 119 (j) 52 2 (k) 120 (l) 125 5. (a) 6 (b) 25 (c) 42 2 (d) 14 3 (e) 63 15 (f) 24 15(g) 60 (h) 280 2 (i) 288 26. (a) 6 (b) 313 (c) 1 (d) 7 3 (e) 23 (f) 2217. (a) 5 (b) 83 (c) 1.5 (d) 1.5 (e) 65 (f) 9100(g) 0.25 (h) 316 (i) 112 (j) 0.02 (k) 0.001 (l) 31008. (a) 25 cm (b) 51 cm (c) 57 cm 9. (a) 68 (b) 144 ANSWER

326 Acme Mathematics 710. (a) 37 (b) 75 11. (a) 58 (b) 96 (c) 75 12. (a) 2 (b) 3 13. (a) 3 (b) 5 14. (a) 111 (b) 45 15. 24 16. 99856 17. 880 m 18. 2025 19. 27 20. 1600 m2 21. 51 mExercise: 2.31. (a) 5 (b) 6 (c) 8 (d) 10 (e) 11 (f) 13 (g) 15 (h) 12 (i) 16 (j) 20 (k) 21 (l) 37 (m) 43 (n) 49 (o) 56 (p) 52 2. (a) 67 (b) 810 (c) 911 (d) 1214 (e) 1213 (f) 1519 (g) 2126 (h) 2235 (i) 3133 (j) 1635 (k) 0.6 (l) 0.8 (m) 1.1 (n) 1.2 (o) 1.5 (p) 2.5 (q) 3.5 (r) 2.2 (s) 0.02 (t) 0.01 3. (a) No (b) Yes (c) No (d) Yes (e) No. (f) No (g) Yes (h) No 4. (a) 16 cm (b) 35 cm (c) 1214 cm (d) 0.3 cm 5. 2 and 8 6. 2 and 4 7. 17 m 8. 1000000 lExercise: 2.41. (a) 6 (b) 2 (c) 18 (d) 16 (e) 15 (f) 8 (g) 36 (h) 35 2. (a) 26 (b) 18 (c) 75 (d) 125 (e) 50 (f) 6 (g) 4 (h) 7 (i) 5 (j) 18 (k) 15 (l) 20 3. (a) 18 (b) 11 (c) 24 (d) 24 (e) 48 (f) 19 (g) 31 (h) 124 (i) 25 (j) 7 (k) 17 (l) 20 (m) 5 (n) 18 (o) 1 (p) 48 (q) 133 (r) 33 4. 5 5. 25 students, 3 banana, 4 oranges and 5 apples 6. 12 7. 32 8. 4 9. 2 m 40 cm 10. 18 cm , 94311. 39 12. 72 13. 14 students 14. 1560, 1680, 1800 or 1920 15. 8 16. 10 17. 33 families, 49 kg daal, 129 kg rice, 87 kg potatoExercise: 2.51. (a) 60 (b) 48 (c) 30 (d) 100 (e) 120 (f) 500 (g) 720 (h) 600 2. (a) 72 (b) 105 (c) 90 (d) 150 (e) 120 (f) 216(g) 90 (h) 192 (i) 1050 (j) 320 (k) 5670 (l) 480 3. (a) 180 (b) 120 (c) 630 (d) 3480 (e) 27360 4. 390 5. 420 6. 460 7. 1550 8. 4722 9. 107010. 367 11. 310 12. 11 a.m 13. 14 minutes

Acme Mathematics 7 32714. (a) 180 (b) 15, 10, 9 15. 8 16. 18017. (a) 9 (b) 2 (c) 818. (a) after 6 weeks (b) after 4 weeks (c) after 12 weeks (d) after 12 weeksExercise: 2.61. Show to your teacher. 2. 30 3. 150 4. 131 5. 90 6. 300 7. 900 8. 16 9. 48 10. 225 11. 292 12. 80 13. 476014. 900 15. 900 Exercise: 2.71. (a) 8 (b) – 2 (c) 10 (d) – 5 (e) 20 (f) – 13 2. (a) raised by 70 c (b) loss Rs.700 (c) Going 10 km to north (d) 100 meter below the ground 3. (a) 9 (b) 0 (c) 10 (d) 7 (e) 8 4. (a) – 8, – 7, – 2, 9, 10, 15 and 15, 10, 9, – 2, – 7, – 8(b) – 7, – 5, – 2, – 1, + 4,+ 6, + 12 and 12, + 6, + 4, – 1, – 2, – 5, – 75. 12 units (Km) 6. to 8. Show to your teacher. Exercise: 2.81. Show to your teacher. 2. (a) +8 (b) +9 (c) – 7 (d) – 43. (a) – 3 (b) + 11 (c) – 9 (d) – 14. Show to your teacher.5. (a) +13 (b) + 7 (c) – 13 (d) – 46. (a) + 13 (b) + 9 (c) – 1 (d) 07. + 22 8. + 34 9. – 45 10. + 3 11. + 3 12. to 14. Show to your teacher.Exercise: 2.91. (a) + 12 (b) – 12 (c) – 20 (d) + 20 2. (a) – 70 (b) +56 (c) + 81 (d) – 150 3. (a) – 120 (b) + 192 (c) – 4204. (a) – 96 (b) – 6 (c) + 605. (a) + 15 (b) + 152 (c) – 10 (d) + 65 (e) – 18 (f) – 48 6. (a) + 4 (b) – 3 (c) + 8 (d) – 7 (e) + 4 (f) +5 7. (a) – 8 (b) + 4 (c) + 48. – 8 9. – 21 10. – 10 11. + 11 12. – 15 13. –15 Exercise: 2.101. (a) –132 (b) – 1 (c) 2 (d) 23 (e) 9 (f) 69(g) 6 (h) 35

328 Acme Mathematics 72. 1200 3. 24 4. 1908 5. 1 6. – 3 7. 153 8. 27 minutes 9. Rs. 73630Exercise: 2.111. (a) 8.025 (b) 2.405 (c) 0.882... (d) 4.66… (e) 5.18.. (f) 0.027…(g) 3.14… (h) 0.188… (i) 0.11… (j) 6.66…. (k) 0.183… (l) 0.035. . .2. to 6. Show to your teacher.Exercise: 2.121. (a) 49 (b) 1799 (c) 15299 (d) 318999 (e) 4599 (f) 13(g) 89 (h) 59 (i) 1299 (j) 533 (k) 833 (l) 12299(m) 23399 (n) 53799 (o) 637992. (a) false (b) true (c) true3. (a) 1750 (b) 3190 (c) 19699 (d) 733 (e) 411 (f) 41333(g) 123449999 (h) 44333 4. Show to your teacher.Exercise: 2.131. (a) 17, 27, 37, 47 and 47, 37, 27, 17 (b) 23, 56, 72, and 72, 56, 23(c) 312 , 724, 26, 43 and 43, 26, 724, 3122. (a) 147 (b) 745 (c) 358 (d) 3 316 (e) 734 (f) 20 17100 3. (a) 113 (b) 1 421 (c) – 37700 (d) 1 118 (e) – 233270 (f) 178195 4. (a) 115 (b) 24 217 (c) 2009 (d) 935 (e) 144370 (f) 35128 5. (a) 863 (b) 1 741 (c) 23 (d) 1 (e) 56 (f) 14276. (a) 500 litre (b) 584 m (c) 60 hours (d) Rs. 6000 (e) Rs. 9000 (f) Rs 3636 7. (a) – 27 (b) – 36 (c) – 2627 (d) – 7 (e) 9118. (a) 512 (b) 22328 (c) 2 (d) 3 (e) 23 (f) 2 38(g) 4381 (h) 528 (i) 149 (j) 2 56 (k) 7 1517Exercise: 2.141. 2 m 2. Rs. 350 3. 2.5 kg 4. 19 and 195. (a) 14 (b) 140 6. Rs.80000 7. Rs. 130008. Sulu & 100 m 9. – 613 10. (a) Rs.1080 (b) Rs.1200 11. 15 pieces No left

Acme Mathematics 7 32912. 165 13. No. 14. 300 maths, 140 English, 70 Nepali and 190 ScienceExercise: 2.151. (a) 3012.713 (b) 1050.569 (c) 18.874 (d) 77.133 2. (a) 1.874 (b) 5.801 (c) 64.193 (d) 22.468 (e) 4.2608 (f) 16.068 3. (a) 6.8005 (b) 0.77158 (c) 69.851331 (d) 115.09728 (e) 9250.3085 (f) 17.615 (g) 9.6096 (h) 57.53125 (i) 441.2083088 4. (a) 6.5 (b) 206.8 (c) 2.7 (d) 1.6 (e) 0.075 (f) 127.3(g) 25 (h) 4144 (i) 18000 5. (a) 1262.2267 (b) 54 (c) 0.00225 (d) 70 (e) 0.917 (f) 0.32(g) 1.2453 (h) – 0.2 (i) 2.75 (j) 2.75 (q) 2.5 (l) 1.391896. (a) 191.8 m (b) 2238.36 m2 7. (a) 68.5 m (b) 388.4 m 8. 7500 9. Rs.112.10 10. 6.45 m 11. Rs.140.70 12. 13.41 km13. 157.593 sq. ft.Exercise: 2.161. (a) 33.33% (b) 18.92% (c) 10.31% (d) 10.22% (e) 9.99% (f) 2.5% 2. (a) 90 (b) 150 (c) 33.92 (d) Rs. 300 (e) 1263.5 kg (f)390 m 3. (a) 75 (b) 560 kg (c) 63.75 (d) Rs. 21 (e) 75 (f) 121.254. (a) Rs.5000 (b) 100 5. 500,175 6. (a) Rs.10320 (b) Rs. 10000 and Rs. 40000 (c) 80 7. 16.67% 8. Rs.62.50 9. 83.33% 10. Rs 414 11. (a) 532 pigs (b) (i) Rs 24000 and Rs 16000 (ii) Rs. 40000 (c) Rs. 500, Rs. 8400 Exercise: 2.171. (a) 8 : 3 (b) 4 : 3 (c) 3 : 2 (d) 1 : 20 (e) 1 : 7 (f) 8 : 7 2. Show to your teacher 3. (a) 7:3 (b) 3 : 7 (c) 7 : 10 (d) 3:10 4. (a) 12 and 18 (b) Rs. 100, Rs.120 (c) 150 kg, 120 kg 5. (a) 57 and 76 (b) 32, 28 6. (a) 30 years (b) 18 m 7. (a) 2 : 1 (b) 5 8. (a) 30 (b) 60 9. (a) 2 : 1 (b) 32 : 45 (c) 45 : 22 (d) Opt. Maths10. Show to your teacher. Exercise: 2.181. (a) 3 (b) 18 (c) 42 (d) 30 (e) 2000 (f) 20 2. (a) 10 (b) 3 (c) 1 (d) 24 (e) 9 (f) 8 3. (a) 100 (b) 2 4. (a) 4a3 (b) 72a (c) 7a4

330 Acme Mathematics 75. (a) 4b5 (b) 7b6 (c) 45b 6. (a) 9 (b) 8 7. (a) 12 (b) Rs 48 8. (a) 9 minutes (b) 1m 21sec 9. (a) 24 m (b) 360 m2 (c) 78 m 10. (a) 16 m (b) 192 m2 (c) 56 m 11. (a) 14 m (b) 252 m2 (c) 64 mExercise: 2.191. (a) Rs. 800 (b) Rs. 1200 (c) Rs. 1600 (d) Rs. 1500 (e) Rs.1700 (f) Rs. 25502. (a) Rs. 4800 (b) Rs. 4200 (c) Rs. 3400 (d) Rs. 1400 (e) Rs 3100 (f) Rs. 4000 3. Rs. 6 4. Rs. 36 5. Rs.250 6. Rs. 6 7. Rs. 1440 Exercise: 2.201. (a) 25.69% (b) 4% (c) 11.11% 2. (a) 48.33% (b) 10% (c) 1.11% 3. (a) 1.69% (b) 8.15% (c) 12.5% (d) 10% 4. (a) Rs. 630.43 (b) Rs. 6666.67 5. (a) Rs. 262.50 (b) Rs. 2070 (c) Rs. 27.5 (d) Rs. 105 (e) Rs. 460 (f) Rs.1162.56. 20% 7. 3.57% 8. 1.49% 9. Rs.708.33 10. Rs. 826.3111. Rs. 300 12. Rs. 425 13. (a) Rs. 200 (b) Rs. 220 14. (a) Rs 1888.89 (b) Rs 2266.66 15. profit, 33.33%Exercise: 2.211. Rs. 650 2. 522 km 3. 960 words 4. 960 words 5. 32 m 6. 350 km 7. 12.5 hrs 8. 3.5 hours 9. Rs. 37500 10. 15, 180, 30, 4.5 and show to your teacher11. 45 days 12. 18 13. (a) 4375 IC (b) Rs. 3200 (c) 1IC = 1.6 NC 14. Rs. 3339000 15. Show to your teacher. Exercise: 2.221. 335 hours 2. 120 workers 3. 50 cows 4. 12 weeks 5. 3559 days6. 2623 days 7. 2250 workers 8. 10 farmers 9. 5 hours 10. 2 h 20 min 11. Show to your teacher. 12. Show to your teacher. 13. (a) 10 women (b) 125 (c) 20 (d) 10.67 days (e) 10 hrs and 3 hrs Mixed Exercise :1. (a) STYT (Show to your teacher) (b) 343 (c) 992. (a) STYT (b) 25 (c) 5043. (a) 100 (b) 216 (c) 2 × 3 × 5

Acme Mathematics 7 3314. (a) 12 (b) 12 (c) 725. (a) 81 m2 (b) 25 (c) 6 cm (d) 1, 646. (a) 48 minutes (b) 7:48 am (c) 2:17. (a) 240 (b) 15 Samosa, 3 Packets of noodles, 7 packet of biscuit(c) 152 (d) No8. (a) STYT (b) 1 910 (c) 7789. (a) 27 and 64 (b) 25, 36 and 64 (c) 11 (d) 4210. (a) STYT (b) 12 (c) (+ 44)11. (a) (+ 60) (b) (– 5) (c) (+ 2)12. (a) + 3 (b) 360 (c) 8 m13. (a) (– 4) (b) (+ 10) (c) 115014. (a) – 214 (b) 6 cm (c) 3415. (a) 35 m (b) 4 shirts (c) 2.33 m (d) 1.25 m16. (a) 48:17 (b) 17:48 (c) 48:65 (d) 17:6517. (a) Rs. 60, Rs. 90 (b) Rs. 300 (c) 2310518. (a) Rs. 300 (b) Rs. 12 (c) 619. (a) Rs. 15000 (b) Profit, 20% (c) 12:120. (a) 60% (b) Rs. 55 (c) Profit, 5.45%21. (a) 7, 14 (b) 60 liter22. (a) STYT (b) 320 km23. (a) STYT (b) 48 (c) 80 (d) 86.2524. (a) 14 m (b) 252 m2 (c) 1825. (a) 23499 (b) 71.42%, Profit26. (a) 3140 part and One pipe (b) 25 and 2:327. (a) + 18 (b) 6 (c) 1228. (a) 535 m (b) 525 m (c) 2 710 m29. (a) 8:7 (b) Rs. 450 (c) Rs. 5030. (a) STYT (b) 1 year (c) 16, 25 → Square number, 8 → cube number 31. (a) On food (b) Rs. 7500 (c) STYT (d) – 1432. (a) (– 3) (b) STYT (c) 2 715 (d) Rs. 67.5033. (a) SP – CP (b) Rs. 400 (c) 5%Exercise: 3.11. to 5. Show to your teacher. 6. (a) 100 cm (b) 60 cm (c) 56 cm (d) 80 cm (e) 22 cm (f) 40 cm 7. (a) 20 cm (b) 22 cm (c) 24 cm (d) 28 cm

332 Acme Mathematics 78. (a) 12 cm (b) 8.6 cm (c) 20.5 cm (d) 9.5 cm (e) 21 cm (f) 25 cm 9. (a) 36 cm (b) 55 cm (c) 77.6 cm (d) 81.8 cm 10. 190 m 11. 52 m 12. 19 m 13. 31 cm 14. 13 cm 15. (a) 7 cm (b) 10 cm (c) 9 cm 16. 7 ft. 17. 16 ft. 18. 40 cmExercise: 3.21. (a) face 6 (b) face 5 (c) face 3 2. (a) 340 cm2 (b) 166 cm2 (c) 134.02 cm2 3. (a) 150 cm2 (b) 238.14 cm2 (c) 181.5 cm2 (d) 600m24. 4.625 m2 5. Show to your teacher.6. (a) 42 m2 (b) 130 m2 7. 5 cm 8. 13.54 cm 9. 15 cm 10. (a) 4 cm (b) 6 cm (c) 10 cm (d) 5 cm Exercise: 3.31. (a) 160 cm3 (b) 56.25 cm3 (c) 1139.25 cm32. (a) 125 cm3 (b) 274.63 cm3 (c) 79.5 cm33. 6 m 4. 4 cm 5. 2.27 cm 6. 12 cm 7. 20 cm and 10 cm 8. 680 cm3 9. 1500 lts., 1500 times 10. 0.46 m11. (a) both have equal volume (b) box 'B' uses more (c) box 'A'12. Show to your teacher. 13. (a) 150 cm (b) 20 cm (c) 10 cm 14. Show to your teacher.Exercise: 3.41. Show to your teacher. 2. Show to your teacher.3. (a) 4 cm (b) 7 cm (c) 8 cm (d) 10 cm 4. (a) 4 cm (b) 3.3 cm (c) 35 cm (d) 3.5 cm 5. Show to your teacher 6. Show to your teacherExercise: 3.51. (a) 30.8 cm (b) 132 cm (c) 44 cm (d) 968 cm2. (a) 154 cm (b) 198 cm (c) 4.4 km (d) 88 m3. (a) 12.57 cm, 2 cm (b) 9.43 cm, 3 cm (c) 15 cm, 7.5 cm (d) 6.6 cm, 1.05 cm(e) 44 cm, 14 cm (f) 3 cm, 1.5 cm4. (a) 968 m 5. 484 m 6. 47.7 cm 7. 3.19 m8. 1056 m 9. 21.87 m 10. 13.42 cm11. 18.85 m 12. and 13. Show to your teacher. 14. 1507.2 m15. 72 cm

Acme Mathematics 7 333 Mixed Exercise :1. (a) OC and AB (b) 376 cm2 (c) 88 cm2. (a) 15 cm (b) STYT (c) 54 cm2 (d) 148 cm23. (a) 119 m (b) 44 m (c) 9000 m3 (d) 248 m24. (a) STYT (b) 65 m (c) 390 m (d) Rs. 195005. (a) STYT, 700 m (b) 1032 cm2, 816 cm26. (a) STYT (b) 9.5 cm (c) 48 m7. (a) 292 cm2 (b) 336 cm3 (c) 0.336 liter (d) STYT8. (a) 16 cm, 6 l2 (b) 9 m3, 4500 liter9. (a) STYT (b) 20 cm (c) 2010. (a) 15 cm (b) 50 cm (c) Rs. 300011. (a) 216 cm3 (b) 216 cm3 (c) 5.5 cm (d) 8 times12. and 13. Show to your teacher.Exercise: 4.11. (a) 55 (b) a4 (c) (– 4)5 (d) 26(e) 323(f) 574(g) 3104(h) – 433 2. Show to your teacher. 3. (a) 74 (b) 1 (c) 5 (d) – 57 (e) 1312 (f) 50 (g) 100 (h) 163 (i) 5a5Exercise: 4.21. (a) 216 (b) 256625 (c) 4096 (d) 6415625(e) 14096 (f) 24014096 (g) – 1 (h) 3906251679616(i) 72964 2. (a) 88 (b) 512 (c) 5 (d) 6481(e) 16 (f) a3b23. Show to your teacher.4. (a) (x + y)6 (b) (x – y)2 (c) 128x7y7 (d) x3y3 (e) 2x25. (a) 1 (b) xa + b (c) 16. (a) 1 (b) – 8 (c) 4 (d) 12(e) 4 (f) 19007. (a) 7 (b) 9 (c) 5 (d) 5 (e) 4 (f) 4 (g) 0 (h) 2

334 Acme Mathematics 78. (a) 2 (b) 1 (c) 69. (a) 1 (b) 1 10. (a) STYT (b) 9411. (a) 1 (b) 1 12. (a) 0 (b) (xy )4Exercise: 4.31. (a) 0 (b) 4 (c) 32 (d) – 3432. (a) 32716 (b) –56 (c) – 3 (d) – 97443. (a) 10 (b) – 3 (c) 29 (d) 13914Exercise: 4.41. (a) 15x2 + 4y2 (b) 6x2y (c) – 4x2 – y2 + 12z2 (d) x2 – x3 + 385(e) 8a2 – 3b2 – 12c2 (f) 9b + 2c – 2d + 5 2. (a) 4xy (b) x2 – 7y2 + 3 (c) – 2a2 + 4a – 12 (d) – 5x2 + y2 + 8z2(e) –x2 – 3y2 + 4z2 + 9 (f) a2 + 2b2 – 4c2 + 9 (g) 0 (h) 2x + 3y – z + 2 3. (a) 4x2 – 4y2 (b) 3a2 – b2 (c) 2x + 20y – 12 (d) – 7x + 2y + 3z (e) 37 a2 – 37 b2 – 2 (f) – 13 x2 + 43 y2 – 2z24. (a) – 2x + 7y (b) y + 3z + 5 – x (c) 6x – 11y + 3z Exercise: 4.51. (a) 30a4 + 35a3b (b) 4x5 – 8x3y2 (c) x3 + x2y2 – 2x3y (d) 3x3y + 3xy3 + 3xyz (e) – 48y2z5 – 9y3z5 – 96yz3 (f) 52 x4z3 – 154 x3z2 + 5x2z4(g) x2 + x2y2 – 2x3y (h) 3x3y + 3xy3 + 12xy (i) 4xy2z2 – yz4 + 34y3z4(j) 9x3yz + 9xy3z + 9xyz2 2. (a) 3x sq. units (b) (4x2 + 4xy) sq. units (c) (12x2 + 3xy) sq. units 3. (a) 3x3 + 3xy2 – 2x2 + 18xy (b) x2 – x3 – x (c) 3x5 – 5x4 + 2x3 + x2 – x (d) x5 – x3c2 + 2b2c2 – 2b2x3 + x2c2 – b3c2 (e) a2b3 – 5a3b (f) – 23x5 – 59x4 + 119 x3 (g) ab – a4b (h) x5y + x3y + 6xy2Exercise: 4.61. (a) 4a4 – 13a2b2 + a3b + 10b4 – 2ab3 (b) 9b3 + 4a2b – 6ab2 – a3(c) a3 – ab + 5a2b + a2b2 + 5ab3 – b3 (d) 16xy – 2yz – 8y2 + 8xz + z2(e) 3xy – 12y2 + 11y – 2x – 2 2. (a) x3 + y3 (b) x3 – y3(c) 6a5 – 4a3b – 9a2b2 + 6b3 (d) 12x4 – 3x2y2 – 8x2y + 2y3(e) 3xy2 – 3x2 – xy + y3 (f) 24x3y – 4y4 – 18x5 + 3x2y3(g) 3p3q2 – 5p2q3 + 9p – 15q (h) 2a2b2 + a3b + ab3

Acme Mathematics 7 3353. (a) a3 – a2 – 16a + 16 (b) – x3 + 9x2 – 15x – 25 (c) x3 – 6x2 – 16x + 96 (d) – 4x3 – y3 + 3xy2 4. (a) – 3y2 + 6y (b) 8x2 – 11y2 + xy (c) – 32y2 – 24xy (d) – a2 + 10a + 8 5. (a) (2a2 + ab – b2) Sq. unit (b) (2b2 + 4ac + 4bc + 4ab + 2c2) Sq. unit(c) (2a2 + 5ab + 6ac + 3bc + 2b2) Sq. unit (d) (a2 + 2ab + 5a + 5b + b2 + 6) Sq. unit6. (a) (a2 + 3ab + 9bc + 4ac + 3c2) Sq. unit (b) 104 m2Exercise: 4.71. (a) 4a2 + 12ab + 9b2 (b) 9x2 – 12xy + 4y2(c) p3 + 15p2q + 75pq2 + 125q3 (d) 27m3 – 27m2n + 9mn2 – n3(e) 125x3 + 75x2bc + 15xb2c2 + b3c3 (f) x4 – x22 + 116(g) 4x29 + 2xy + 9y24 (h) m2n24 – 2 + 4m2n22. (a) x2 + 2xy + y2 (b) a2 – 4ab + 4b2(c) 4m2 + 12mn + 9n2 (d) 1x2 +2 + x2(e) x24y2 – 12 + y24x2 (f) x24 + xy2 + y24 (g) 9a2b2 +2 + a2b29 (h) x2y2 – 2 + y2x2 (i) a2+b2+c2+2ab+2bc+2ca (j) a4+b4+c4+2a2b2+2b2c2+2c2a23. (a) 2x2 + 2y2 (b) 4xy (c) 8a2 + 18b2 (d) 2a3 + 6ab24. (a) 40 (b) 52 (c) 14 (d) 18 5. (a) 2xy (b) – 4x + 24 (c) a3 – b3 (d) a3 + b3(e) 0 (f) 2a2 + 2b2 – 4ab 6. (a) 961 (b) 841 (c) 2401 (d) 2601 (e) 9801 (f) 10201 (g) 998001 (h) 1002001 7. (a) 13 (b) 18 (c) 37 (d) 13 (e) 7 (f) 11 8. (a) 8 (b) 8 + 6xy (c) y3 + 3y (d) x3 + 3x 9. (a) 3a2b + 3ab2 (b) – 2a2b + 2ab2 (c) – 5x2y – 2y3 (d) 2y3 + 5x2y10. (a) (x + 2)2 (b) (y – 7)2 (c) (3x + 13x)2 (d) (2a – 5b)2(e) (3x2 + 4y2)2 (f) a + 1a2Exercise: 4.81. (a) 3a – 5b (b) 2a + 3b (c) 3x – 2y (d) 2a – b (e) 7a + 8b (f) 3a2 + b (g) 6a + 7b (h) 2a2 + 1 2. (a) 4xy – 2x + 6 (b) 2x2 – x + 1 (c) 5x2y3 – 4xy – 1 (d) 3x2 + 5x – 1

336 Acme Mathematics 7(e) – 2x4y4 + 4x3y3 – 10xy (f) 2ab + 1 – 10ab (g) z2 + 9z – 14(h) 2a2b2c2 + 5abc – 43. (a) (x + 4) m (b) (x+2y) cm (c) (x2y + x) ft. (d) (7x + 4y + 3) mExercise: 4.91. (a) x – 2 (b) x – 3 (c) a + 5 (d) x – 3 (e) x + 2 (f) x + 2 (g) x + 3 (h) 3x – 2 (i) 2x + 1 (j) x + y (k) x2 – xy + y2 (l) 2a + 12. (a) (x + 4) m (b) (4x + 3y) m (c) (a2 + ab + b2) ft.3. (2 + 3xy) 4. a2 – ab + b25. (a) (2a – 3b + 5) m (b) 13 m, 4 m, 52 m2 6. Show to your teacher.Exercise: 4.101. (a) 2 (b) 14 (c) 3 (d) 3 (e) – 34 (f) – 2312 (g) 0 (h) –6 (i) 2 (j) 0(k) – 343 (l) 0 2. (a) 935 (b) 325 (c) 4 (d) 2 (e) – 5 (f) – 8 (g) 11 (h) 32 Exercise: 4.111. (a) 5 (b) 13 (c) 18 2. (a) 25 and 26 (b) 11 and 13 (c) 22 and 24 3. (a) Rs. 1600 and Rs. 800 (b) 1000 girls and 500 boys(c) 28 boys and 16 girls 4. (a) 100 m and 50 m (b) 9 years, 36 years (c) 47 years and 17 years 5. (a) 16 and 18 (b) 120 and 60 (c) 795 and 705 (d) 9 yearsExercise: 4.121. & 2. Show to your teacher.3. (a) {3, 4, 5, 6, …….} (b) {29, 30, 31, …….} (c) {10, 9, 8, ……….} (d) {– 5, – 4, – 3, …….} (e) {8, 7, 6, 5, ……….} (f) {30, 31, 32, 33, ……} (g) {…..., 0, 1, 2} (h) {6, 7, 8, 9, 10, ....} (i) {– 1, 0, 1, 2, …….} (j) {6, 7, 8, 9, 10} (k) {– 2, – 1, 0, …….., 8} (l) {1, 2, 3, 4, 5} 4. (a) (i) 2x + 7 > 3 (x+12) (ii) x < 0 (iii) 3x ≥ 17(b) (i) x > 0 (ii) x > – 2 (iii) x > – 4 5. l = b + 6, p2 ≤ 50, b ≤ 226. (a) 91 – 9x > 10 (b) {8, 7, 6 …..} (c) Show to your teacher.

Acme Mathematics 7 3377. (a) 4x + 7 < 15 (b) {....., – 1, 0, 1} (c) Show to your teacher.Exercise: 4.131. to 4. Show to your teacher. 5. (a) y = 2x (b) y = 2x + 4 (c) y = x + 36. (a) y = x + 5 (b) y = x – 3 (c) y = x + 107. (a) Show to your teacher. (b) y = 2x8. Show to your teacher. Mixed Exercise :1. (a) (a + b)8 (b) 2a (c) STYT2. (a) 2 (b) (– 2a)2 × (– 3b)33. (a) 19 (b) STYT4. (a) 35x2 – 24xy + 4y2 (b) x + 3 (c) (3x2 + 5xy – 2y2) m25. (a) a2 + 2ab + b2 (b) z2 + 6z + 9 (c) 986. (a) 36° (b) x2 – xy + y27. (a) 15m2 – 16mn – 15n2 (b) (3x2 + 5xy + 2y2) Sq. unit8. (a) a2 + 2ab + b2 (b) 1 m29. (a) (P – 3) bottles (b) 200, 40 people, 5 bottles10. (a) (2x + 3y)2m + 2n (b) 111. (a) 4th degree (b) – 712. (a) (x2 – 7x – 12) sq. unit (b) 513. (a) STYT (b) Trinomial (c) STYT (d) yes14. (a) (9x2 + 24xy + 16y2) cm2 (b) 64 cm2 (c) STYT15. (a) x2 – 5x + 6 (b) 1316. (a) 6 (x2 + 4xy + 4y2) Sq. unit (b) 8 Sq. unit (c) STYT17. (a) x = 4 (b) x = {2, 1, 0, –1, ...................}18. (a) 10 cm (b) STYT (c) x = – 819. (a) x ≥ – 2 (b) 25 boys, 15 girls20. (a) x = 2 (b) 250 boys, 160 girls21. (a) (6x2 + 9xy + 19x + 6y + 10) m2 (b) 96 m2 (c) 822. (a) STYT (b) 3x + 4y23. (a) Second (b) STYT (c) 6x5y – 8x2y4 (d) 2x – 324. (a) 2a (b) x ≤ 6, x + 325. (a) STYT (b) 10 m26. (a) x + 2y = 50 (b) 40 years

338 Acme Mathematics 727. (a) x + y = 48 (b) STYT (c) STYT28. (a) 3x + 7 < 10 (b) x < 1 (c) STYT29. (a) y = 2x (b) y = 2x + 4 (c) y = x + 3Exercise: 5.11. (a) 130° (b) 70° (c) 160°(d) x = 40°, y = 140°, z = 140° (e) 70° (f) x = 55° , y = 55°, a = 55°, z = 70°(g) a = 65° (h) 63.5° (i) x = 70°, y = 110°, a = 120°, b = 120°, c = 50° (j) 38.13° (k) x = 100°, y = 100°, a = 20° (l) 28.63° 2. (a) 10° (b) 37° (c) 17.5° (d) 6.75° 3. (a) 145° (b) 59° (c) 44.5° (d) 13.75° 4. (a) 75° (b) 20° (c) 45° (d) 57° (e) 54° (f) 40° 5. to 13. Show to your teacher. Exercise: 5.2Show to your teacher.Exercise: 5.31. to 5. Show to your teacher.6. (a) 10 cm and 15 cm (b) 2 cm and 3 cm (c) 3 cm and 5 cm (d) 80° and 100° (e) 20° and 30° (f) 60° and 60° (g) 20° and 150° (h) 89.5° and 91.5° (i) 30° and 100° 7. (a) 70° (b) 34.4° 8. (a) 40°, 60°, 130° (b) 52°, 104°, 104° , 100° (c) 136.5°, 91°, 40.5°, 92°9. (a) x = 100°, y = 100°, z = 80°, a = 80° (b) a = 70°, b = 70°. c = 110°, d = 110° (c) x =70°, y = 55°, z = 125°, a = 125°, b = c = 55° (d) x = y = 120°, a = z = 60°, b = c = d = 60° (e) x = 30°, y = 50°, z = 40° (f) x = y = 46°, a =70°, z = 40°10. Show to your teacher. 11. Show to your teacher.Exercise: 5.41. Show to your teacher.2. (a) 10 cm (b) 17 cm (c) 5 cm (d) 61 cm (e) 56 cm(f) 24 cm (g) 30 cm (h) 6.7 (i) 10.5 cm3. Show to your teacher.4. (a) x = 8 cm, y = 12.69 cm (b) x = 97 cm, y = 65 cm (c) x = 12 cm, y = 14.98 cm(d) y = 14.3 cm, x = 13.4 cm (e) x = 15 cm, y = 23.8 cm5. 12 m 6. 19.8 km 7. 36.72 m 8. 14.46 m

Acme Mathematics 7 339Exercise: 5.5 to 5.6Show to your teacher Exercise: 5.71. (a) A (3, 4), B (1, 2), C(4, 1) (b) A (– 2, 5), B (– 4, 2), C (0, 3) (c) A (2, 3), B ( – 2, 1) , C( (1, –2) (d) A(2, 0), B(2, –4), C(5, – 1) (e) A(3, 1), B(–1, – 2), C(4, – 2) (f) A (– 2, 2), B(– 3, –2), C(1,1) 2. Show to your teacher.3. (a) Triangle (b) Triangle (c) Rectangle (d) Rectangle (e) Parallelogram (f) Rectangle (g) Rectangle 4. (a) (–1, 0) (b) (– 2, 3) (c) (– 3, 2) (d) D(1, 3) (e) (1, – 1) (f) (2, 4) (g) (3, 3) (h) (– 1, 2) 5. Show to your teacher. 6. (– 1, 1) 7. (4, 3) 8. (3, 3) 9. (2, 3) 10. Straight line Exercise: 5.81. (a) 13 units (b) 2 units (c) 5 units (d) 2 units2. (a) 2 units (b) 5 units (c) 2 units (d) 34 units 3. (a) 5 2 units (b) 97 units (c) 13 units4. 2 units, 26units and 2 5units5. (a) 5 units (b) 4 units (c) 5 units (d) 4 unitsExercise: 5.9 to 5.13Show to your teacher.Exercise: 5.141. (a) 088º (b) 236º (c) 110º (d) 345º 2. & 3. Show to your teacher.4. - 6. Show to your teacher. Mixed Exercise : 1. (a) STYT (b) STYT (c) x = 30°, y = 20°2. (a) ∠PNO (b) ∠MNP (c) 60°3. (a) STYT (b) STYT (c) 45°4. (a) x = 110°, y = 110°, z = 70° (b) STYT5. (a) 360° (b) a = 25°, b = 30° (c) STYT6. STYT 7. (a) 60° (b) STYT 8. STYT

340 Acme Mathematics 79. (a) STYT (b) 70° (c) 40° and 50°10. (a) STYT (b) a = 135°, b = 72°, c = 135°11. (a) STYT (b) 25 ft (c) STYT12. (a) 12 (b) STYT (c) STYT13. (a) STYT (b) STYT14. (a) A'(–2, 5), B'(3, 1), C'(– 4, 0), yes (b) STYT15. (a) STYT (b) 2 unit (c) STYT16. (a) (iii) (b) 25 cm17. (a) STYT (b) A'(–1, –2), B'(4, –1), C'(1, – 5)18. (a) STYT (b) 10 ft (c) 70°19. (a) STYT (b) 070° (c) STYT20. (a) equal (b) STYT (c) STYT21. (a) STYT (b) equal22. (a) x = 5 cm, y = 7 cm (b) STYT (c) STYT23. (a) STYT (b) STYT (c) 50°24. (a) STYT (b) 12 cm (c) STYT25. (a) ∠AEC + ∠BEC = 180° (b) STYT (c) STYT26. (a) equal (b) STYT (c) STYTExercise: 6.1Show to your teacher.Exercise: 6.21. to 5. Show to your teacher.6. (a) 7 (b) 50 (c) 150 (d) class - 5 7. Show to your teacher. Exercise: 6.3Show to your teacher. Exercise: 6.4Show to your teacher. Mixed Exercise : Show to your teacher.