3012. Tick the correct answer.(a) A rectangle has(i) One line of symmetry(ii) Two lines of symmetry(iii) Multiple lines of symmetry(b) A shape with infinite lines of symmetry is(i) Oval (ii) Circle (iii) Rectangle(c) A line of symmetry makes the shapes on either side(i) Similar (ii) Congruent (iii) Different(d) Letters having a line of symmetry are(i) A, D, H (ii) A, F, B (iii) C, B, K(e) Letters having two line of symmetry are(i) H, I, X (ii) H, M, I (iii) B, N, X(f) The shape with a diagonal line of symmetry is(i) (ii) (iii)Exercise 5.91. Draw the line of symmetry as many as you can.(a) (b) (c) (d)(e) (f) (g) (h)Acme Mathematics 6 301
2. Complete the shape of the given figures, whose line of symmetry are given.(a) (b) (c) (d)(e) (f) (g) (h)3. Find the number of lines of symmetries for each of the following figures.(a) (b) (c)(d) (e) 5555(f)(g) (h) (i)4. Draw any two figures which has no line of symmetry.5. Draw any two figures which has one line of symmetry. 6. Draw any two figures which has two line of symmetry. 7. Draw any two figures which has three line of symmetry.302 Acme Mathematics 6
B. Design of polygonsWe can make attractive design by drawing many triangles, squares, pentagons and hexagons. Look at the following designs.(a) Designs from triangles.(b) Designs from squares.(c) Designs from pentagon and hexagon.(d) Designs from square and straight lines.1098765432100 1 2 3 4 5 6 7 8 9 1010998765432100 1 2 3 4 554321010 9 8 7 6 5 4 3 2 1 06677889 1010Acme Mathematics 6 303
(e) Designs from triangle and straight lines.C TessellationA honeycomb is an example of tessellation, hexagon fit together to cover a frame in the beehive. Here are the some other examples.A tessellation of triangles A tessellation of square A tessellation of rectangleIn all the figures a tessellation is created when a shape is repeated over again covering a surface without any gaps or overlaps. Tessellation is also called tiling. Thus a tessellation is covering of the 'surface with regular congruent geometrical shapes in a repeating without any gaps.It is used in the surface, walls, floor or carpets to make the area more attractive.Exercise 5.101. Draw the following patterns in your copy and colour with different colours and make different designs.(a) (b) (c)304 Acme Mathematics 6
(d) (e) (f)2. Using the regular polygons given below make different tessellations.(a) (b)Rectangle Square3. Find out how many shapes are in the following picture.(a) (b)4. Copy the given tessellation and complete it.(a) (b)(c) (d)Acme Mathematics 6 305
5. Complete the given tessellation (use graph paper).6. Copy the tessellation in your exercise book.(a) (b)(c) (d)306 Acme Mathematics 6
1. Objective : To make symmetrical figures2. Materials required: papers colours scissor gum scale etc.3. Activity:(a) Fold the paper (b) Draw any figure.(c) Cut out the figure (d) Unfold the cut piece.(e) Paste on the A4 size paper. (f) Draw line of symmetry.Activity 1Activity 2Activity 3Project WorkAcme Mathematics 6 307
1. Plot the following points on the graph.A (2, 3) , B (– 3, 4), C (– 3, – 14), D (10, – 4)2. (a) Plot the coordinates of the given points A(2, 2), B(6, 2), C(6, 6) and D(2, 6) in a graph paper. Join the points in order and write the name of figure so formed. Also find its area.(b) By using same measures of square shapes prepare tessellation and fill up the colour.3. In which quadrants do the following points lie.A(2, 3), B(–2, 5)4. Who sits in the following place.Row5 Yam Sita Padam Niranjan4 Roshan Anish Shilpa Yaman3 Anish Amar Roslin Madhu2 Surendra Sanjaya Krishna Rudra1 Raju Bishnu Mahesh DeepakColumn 1 2 3 4(a) (2, 3) (b) (4, 4) (c) (1, 4) (d) (1, 1)5. (a) Define quadrant.(b) A(3, 4), B(1, 4), C(1, 1), D(3, 1) are four given points. Plot these points on a graph paper and join them in order.Mixed Exercise308 Acme Mathematics 6
6. (a) Does the letter given alongside have a line of symmetry?(b) Draw a line symmetry for the figure given below.(i) (ii)(c) Name the list of figures of two lines of symmetry7. (a) Plot the following points in the graph and join them. What do you get?P(2, 3), Q(5, 2) and R(2, 4)(b) A(3, 4), B(1, 4), C(1, 1) and D(3, 1) are four given points. Plot these points on the graph paper and join them in order.(c) In which quadrant do the following points lies?A(–2, –3) and B(2, 4)8. (a) Plot A(2, 3), B(5, 2) and C(2, 4) on the graph paper and join them in order. Also write the name of the figure formed.(b) Draw the line of symmetry for the following figures.(i) (ii)9. (a) List the English alphabets that has line of symmetry.(b) Complete the tessellation given below.AAcme Mathematics 6 309
10. (a) Write the coordinates of the vertices of given figures.OY'X' XYHFDGB CAE(b) Draw three figures that have two lines of symmetry.11. (a) Define axis of symmetry with example.(b) Draw rectangular tessellations by joining the given dots.12. (a) Draw tessellation using square and colour it.(b) (0, 0), (8, 0) and (4, 6) are the vertices of a triangle.(i) Plot the points on the graph.(ii) Name the triangle.(iii) Calculate the area of the triangle.310 Acme Mathematics 6
EvaluationTime: 55 minutes Full Marks: 231. (a) Plot the points A(2, 4),B(6, 4), C(6,–3), and D(2,–3) in a graph paper. [2](b) What figure is formed when all the points are connected in sequence. [1](c) Draw a tessellation using same size triangle and colour it. [2]2. (a) Draw the net of cone. [2](b) Complete the symmetrical figure. [1] (c) Prepare tessellation by same size of square shapes and fill up the colour. [2]3. (a) Write one similarity and one difference between the sphere and cone. [2](b) Write one similarity and one difference between the cylinder and cone. [2](c) Write one similarity and one difference between the cylinder and sphere. [2]4. (a) Draw the cylinder and label its parts. [2](b) Draw the cone and label its parts. [2](c) Draw a line of symmety of given figure. [1]5. Complete the tessellation. [2]mAcme Mathematics 6 311
6Working hour : 10UNIT Statistics6.1 Collection of DataA. IntroductionThe teacher is interested to know about the marks obtained by 30 students of a class - 6 in Mathematics. He ask each of the 30 students his or her marks in mathematics and write down the marks. The marks are given below.30, 35, 50, 30, 35, 35, 50, 30, 10, 40,30, 50, 10, 50, 20, 40, 30, 20, 20, 30,40, 10, 50, 20, 30, 50, 35, 40, 50, 20In the above example, each entry is a numerical fact which is called an observation. Such a collection of observations gathered initially is called data.B. Array of dataWe can organize the data in ascending or descending order. For above example, we organize the data in the descending order and write it as follows:50, 50, 50, 50, 50, 50, 50, 40, 40, 40,40, 35, 35, 35, 35, 30, 30, 30, 30, 30,30, 30, 20, 20, 20, 20, 20, 10, 10, 10From the above data the highest marks obtained by the students is 50 and the lowest marks is 10.The arrangement of data in descending or ascending order is called an array of data.6.2 Frequency TableA. Frequency DistributionFrom the above example, 7 students have obtained 50 marks, 4 students have obtained 40 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 the lowest marks to the highest marks then this is called the frequency distribution of the marks obtained by 30 students.312 Acme Mathematics 6
B. TallyTallies are used to find the frequencies. Tallies are usually mark in a bunch of five for ease in counting. The fifth tally is usually marked diagonally across the four tallies.For example:Mark obtained Tally Mark Frequency10 | 120, 20 || 225, 25, 25 ||| 332, 32, 32, 32 |||| 440, 40, 40, 40, 40 5Solved ExampleExample 1 : The following marks were obtained by 40 students in a unit exam in mathematics:12, 13, 17, 15, 16, 15, 14, 12, 13, 15,16, 14, 15, 20, 18, 19, 10, 10, 17, 18,17, 12, 13, 15, 19, 18, 14, 15, 13, 14,19, 12, 12, 13, 14, 15, 20, 16, 16, 18Prepare a frequency table.Solution: Frequency distribution of marks of 40 students in unit exam in mathematics:Marks Tally Mark Frequency10 || 212 513 514 515 || 716 |||| 417 ||| 318 |||| 419 ||| 320 || 2Total 40Acme Mathematics 6 313
Classwork1. Write the number represented by the given tally mark:(a) || (b) || (c) |||| (d) ||| (e) |2. Write the tally mark represented by the following numbers: (a) 15 (b) 19 (c) 12 (d) 16 (e) 213. Fill the missing frequencies:Marks Tally Mark Frequency15 || ......................20 |||| ......................25 ......................30 || ......................35 ||| ......................4. Write the tally marks with respect to given frequency:(a) Marks Tally Mark Frequency15 ................................. 720 ................................. 925 .................................. 1030 .................................. 1235 ................................... 13(b) Age in years Tally Mark Frequency12 .............................. 813 ............................. 1014 ............................ 915 ............................. 1516 .............................. 6314 Acme Mathematics 6
Exercise 6.11. The age of 21 children are as follows. Construct its frequency table:10, 10, 11, 12, 10, 13, 12, 10, 14, 11, 12, 14, 12,13, 10, 11, 11, 11, 12, 11, 14.2. 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, 35.3. The marks obtained by 24 students of a class are shown in the following data. Represent this raw data in the table by using tally mark:9, 5, 8, 7, 8, 10, 6, 9, 8, 9, 9, 8, 7,5, 8, 5, 6, 7, 8, 9, 9, 5, 5, 9.4. The height of 27 students of a school is given below. Construct the frequency table .120, 121, 122, 123, 124, 125, 125, 124, 123, 122, 121, 120, 120, 120,121, 122, 122, 123, 123, 124, 123, 125, 122, 120, 122, 122, 123.5. Following are the ages of Grade 6 students of a school. Represent this data in a frequency table and answer the questions given below.11, 12, 13, 14, 15, 14, 13, 12, 11, 11, 12, 13, 13,14, 14, 14, 15, 14, 14, 13, 12, 11, 12, 15.(a) How many students are 12 years old ?(b) How many students are more than 10 years old ?(c) How many students are less than 14 years old ?6. Arrange the following data in ascending order and then prepare a frequency table:21, 24, 23, 25, 25, 24, 24, 22, 22, 21, 22, 23, 24, 25,25, 22, 22, 21, 23, 22, 23, 24, 21, 21, 21, 22, 23, 237. Arrange the following data in ascending order and then prepare a frequency table:30, 31, 34, 32, 33, 35, 31, 32, 33, 30, 30, 31, 31, 32,32, 33, 33, 34, 34, 30, 31, 32, 32, 34, 35, 35, 31 30Acme Mathematics 6 315
C. Simple Bar GraphStudy the given picture carefully. No. of passed Students2077 2078 2079 2080 2081 2082SEE Result of a School020601204010080140A bar graph is a pictorial representation of the data. There are many ways to represent the data. The mostly used method of representing data is a bar graph. The bar graph helps us to understand the information easily and quickly. In a bar graph the height or length of the bar shows the quantity of the data.Construction of bar graph is illustrated by the following example.Solved ExampleExample 1 : The frequency table shows the final result of class - 6 of a school.Year 2078 2079 2080 2081 2082No. of passed students 30 50 90 95 60Draw a bar graph.Solution: For drawing a bar graph remember the following steps: (i) Draw two straight lines, one vertical and one horizontal which are perpendicular to each other.(ii) Choose the scale, to represent the data conveniently.(iii) Marks are drawn with bases on horizontal line. (iv) Marks are drawn with equal spacing between them. (v) Width of different marks should be equal.(iv) Put frequencies in the vertical line and variables (data) in the horizontal line.316 Acme Mathematics 6
The final result of class - 6 of a school is shown on the bar graph:2078Number of studentsYears01030507090204060801002079 2080 2081 2082Exercise 6.21. The given bar graph shows the number of students from class-1 to class-4 of a school. Find the total number of students. 2. The given bar graph shows the numbers of students from class 5 to 8 of a school. Answer the following questions. (a) What is the total number of students? (b) Which class has the lowest number of students?3. Study the given bar diagram and answer the following questions given below: (a) Which heading has the highest source of income?(b) Which heading has the least income? (c) What is the total income of the family ?Number of students0 1 2 3 4515253510203040ClassesNumber of students0 5 6Classes7 8515251020Income in thousand0InterestHouse rentIncome HeadingsSalaryOthers51525102030Acme Mathematics 6 317
4. Represent each of the following information in a simple bar diagram:(a) Temperature of five different regions on a day.Dhankuta Kathmandu Pokhara Nepalganja Dipayal20° C 10° C 15° c 30° C 25° c(b) The description of animal in an animal farm house. Animal Sheep Goat Cow BuffaloNumber 20 25 30 15(c) The favorite fruits of 40 students are given below.Orange Apple Banana Mango15 10 5 105. Represent the following data in a simple bar-diagram.(a) Number of class - 6 students in different years.Years 2076 2077 2078 2079 2080No. of Students 15 24 10 49 17 (b) Number of class -10 students in different years.Years 2079 2080 2081 2082No. of Students 100 125 140 150(c) SEE result of a school.Years 2074 2075 2076 2077 2078 2079 2080No. of Passed Students15 20 30 40 65 80 1006. Represent the following data in a simple bar diagram.(a) Monthly expenditure of a familyItems Education House rent Food Clothing OthersAmount (Rs.) 800 1200 1000 400 600(b) The monthly budget of a familyFood Clothing Entertainment Saving MiscellaneousRs. 8000 Rs. 4000 Rs. 3000 Rs. 10000 Rs. 6000318 Acme Mathematics 6
1. Write the numbers represented by the given tally marks.(a) (b)(c) ||| (d) ||2. Write the tally marks for the following numbers.(a) 14 (b) 9(c) 23 (d) 253. Find the average of the given data: 3, 4, 7, 64. Study the given bar graph which shows the number of students of different classes of a school.Answer the following questions:(a) What is the total number of students ?(b) Which class has the lowest number of students ?(c) Which class has the highest number of students ?(d) How many classes are there in all ?5. The ages of 28 children in years are as follows. Construct a frequency table.8, 2, 5, 8, 3, 5, 8, 2, 1, 1, 4, 4, 5, 3,4, 1, 7, 6, 6, 7, 6, 4, 7, 2, 6, 1, 9, 96. Monthly expenditure of a family is given below. Represent the data in a simple bar graph.Items Education House rent Food Clothing OthersAmount (Rs.) 800 1200 1000 400 600 Number of students0 5 6Classes7 851525102030Mixed ExerciseAcme Mathematics 6 319
7. The enrolled students from classes 6 to 10 in Nepal Secondary School in the academic year 2080 is given below: Grade 6 7 8 9 10No. of students 80 60 100 90 70(a) Draw a bar diagram on a graph paper based on above table.(b) What is the total number of students enrolled in the academic year 2080 in Nepal Secondary School from classes 6 to 10?8. The number of students of class 10 in different years of Bishow Prakash Secondary School is given below.Years 2075 2076 2077 2078No. of student 75 90 85 95(a) Draw a bar diagram on a graph based on above table.(b) Find the total number of student of class 10 from 2075 to 2078.(c) Which year has the highest number of student?9. Marks obtained by six students of class four in Maths exam are given below.Name of students Kabir Karna Rajensh Rupa Tripti RakhiMarks 16 12 18 10 14 20This information is the tabulation form. Now fill in the blanks.(a) ............ is the highest marks.(b) ............ is the lowest marks.(c) Marks obtained by Kabir is .............10. (a) Define data.(b) The marks obtained by 20 students of class 6 out of 25 full marks in a class are given below. 20, 15, 22, 24, 19, 15, 20, 24, 19, 24, 22, 19, 20, 24, 15, 20, 24, 19, 20, 22Prepare a frequency table with tally marks.320 Acme Mathematics 6
11. Study the given diagram and answer the questions given below.Name of students081621018412202224614KabirMarksKarna Rajesh Rupa Tripti Rakhi(a) How much marks is obtained by Karna?(b) Who obtained the highest marks?(c) Who obtained the 18 marks?(d) Name the diagram.(e) Who got least mark?(f) Compare the marks of kabir and Tripti.Acme Mathematics 6 321
EvaluationTime: 38 minutes Full Marks: 161. The data if various activities participate by 150 students of grade 6 of Gyanodaya secondary school is given below. Activities Dance Music Art Singing Play instrumentNo. of student 30 40 35 20 25 (a) Show the given data in a simple bar graph. [2](b) In which subject there are more students? [1]2. The age of 15 students of class 6 are as follows. 11, 12, 11, 13, 12, 14, 15, 13, 14, 12, 13, 12, 13, 14, 15 (a) Construct a frequency table. [2](b) Construct a bar graph. [2]3. The student number from class 1 to 5 in Kashirupa Lower Secondary School in academic year 2081 is given below.Class 1 2 3 4 5No. of students 20 25 35 30 40(a) Draw a bar diagram based on above table. [2] (b) Find the total number of students. [1] (c) In which class the number of students is maximum ? [1]4. Study the given bar graph and answer the given questions.(a) Which activities is liked by most of the students ? [1](b) Which activities is liked by fewest of the students ? [1](c) How many students like singing? [1](d) How many students are there in the school? [1](e) What is the heading of the grph ? [1]322 Acme Mathematics 6
1. Answer the following questions based on the given collected numbers:2,3,5,7,11,13,17,19(a) State whether the given collection of numbers is well-defined or not? Writewith reason. [1HA](b) Write the presented collection of numbers in set notation. [1K](c) Write the given set in a set-builder method. [1A]2. (a) The smallest number which is exactly divisible by the given numbers is called....... [1K](b) The drill teacher tried to arrange grade six students in equal rows and columns with 9/9 students, but the number of students exceeded by 3. Now find out thetotal number of students in the class. [2A](c) Anu paid a sum of Rs. 500 to a shopkeeper for buying five exercise books atthe rate of Rs 40 and two pens at the rate of Rs 25. How much will she receivein return? [2HA]3. Suman is enrolled in a private company as an accountant.(a) If she invests 25 of her income in food and 13 part of income in children'seducation, find out on which heading more money is invested? [2U](b) If her monthly income is Rs. 20,000, find the total money spent on herchildren's education. [1A](c) Write the monthly expenditure done on children's education in two places ofdecimal. [1U]4. Sushmita has bought 10 pens for her children from stationery costing Rs. 1200. (a) What was the cost of one pen? [1K](b) If a shopkeeper made a profit of Rs100 by selling 10 pens, how much had theshopkeeper paid for buying one pen? [1U](c) If Sushmita gave 6 pens out of 10 pens to her daughter, what would be thepercentage allocated to her son and daughter? [2A](d) If 50% of the total pen had been given to a daughter, how many more penwould she get? [1HA]Model QuestionClass - 6 F.M. 50Subject - Mathematics Time – 2 hrsAcme Mathematics 6 323
5. Ramila has a square land, and Shyam has rectangular land, but the area of bothlands is equal(a) Which formula to be use for finding area of Ramila's land? [1K](b) The length of Ramila's land is 50 m, then what is the area of her land? [1U](c) The length of Shyam's land is four times of its breadth then find the length ofShyam's land? [2A](d) Who needs to spend more on fencing if both of them have to fence a wire fora round the land once. [1HA]6. The enrolled studentsfrom classes 6 to 10 in Janta Secondary School in the academicyear 2078 is given below:Grade 6 7 8 9 10No. of students 80 60 100 90 70(a) Draw a bar diagram on a graph paper based on above table. [2A](b) What is the total number of students enrolled in the academic year 2078 inJanta Secondary School from classes 6 to 10? [1U]7. (a) State whether the given mathematical statement is true or false: 4x2y and 7x2yz are like terms. [1K](b) Fill in the blanks. The value of x is less than 5 is to represent as....... [1K](c) The first box contains 6 packets of chocolate; the second box contains 8packets of chocolate. If each packet contains x number of chocolate, find thetotal number of chocolate in both boxes. [2U]8. (a) A rectangular handkerchief has an area of 12x2y2 square centimeter and breadth is 3xy centimeter then what is its length? Find it. [2A](b) If x = 2 and y = 3, what is the length and area of the handkerchief? Find it. [2A]9. Bikash has Rs. 8 less than Bidur. If both of them have altogether Rs. 32. How manyrupees each of them has? Find it. [2HA]324 Acme Mathematics 6 Model Question
10. (a) The vertices of a cube or cuboid is supposed to be V, side is E and surface isF, then write the relation between them. [1K](b) Fill in the blanks. The line joining the two points on the circumference of the circle iscalled...... [1K](c) By using ruler, draw a line segment XY = 8 cm. By using compass construct∠PXY = 90° at X. [3A](d) What type of triangle is formed by joining the points P, X and Y? Givereason. [1HA]11. (a) In the given figure, write the relationbetween AB and CD as well as AB and AE. [2U](b) By using a protractor, measure theangles of the given triangle. On the basis of angles what type oftriangles is this? Write it. [2U]12. (a) Plot the coordinates of the given points A(0,3), B(3,0), C(0, –3) and D (–3,0)in a graph paper. Join the points in order and write the name of figure soformed. Also find its area. [3A](b) By using same measures of square shapes prepare tessellation and fill up thecolour. [2HA]ACEBDAB CAcme Mathematics 6 325
Exercise: 1.1 Show to your teacher. Exercise: 1.2 Show to your teacher.Exercise: 1.3 Show to your teacher.Exercise: 2.1 Show to your teacher.1. Show to your teacher2. Greatest → 97652, smallest → 25679, sum = 1233313. (a) 49995 (b) 49999500 (c) 4999950000 (d) 4999995004. (a) 9 (b) 90 (c) 90005. 1099999999 6. Show to your teacher7. (a) False (b) False (c) True (d) False (e) False(f) False (g) False8 Show to your teacher.Exercise: 2.21 to 3. Show to your teacher.4. (a) 7 (b) 209 (c) 1 (d) 4 (e) 8(f) 10 (g) 49 (h) 95. (a) 9 (b) 30 (c) – 9 (d) 98 (e) 26(f) 23 (g) 13 (h) 28 (i) 7226. (a) 16 (b) 21 (c) 1 (d) 21 (e) 48(f) 54 (g) 2Exercise: 2.3 Show to your teacher. Exercise: 2.41. (a) 2, 3, 5, 7 (b) 2 (c) 1 (d) 12, 14, 15, 16, 18(e) 1, 2, 3, 6 (f) 1, 3, 5, 15 (g) 2, 3, 5 (h) 2, 3, 7(i) 2, 4, 6 (j) 5, 10, 15, 202 to 4. Show to your teacher.5. (a) 1, 2, 5, 10 (b) 1, 3, 5, 15 (c) 1, 2, 4, 8, 16 (d) 6, 12, 18 (e) 7, 14, 21, 28 (f) 10, 20, 30 (g) 2, 3, 5, 7, 11, 13 (h) 97(i) 16, 18, 20, 21, 22, 24 (j) 91, 92, 93, 94, 95, 96, 98, 996 to 8. Show to your teacher.9. (a) 1, 3, 5, 15 (b) 1, 5, 25 (c) 1, 2, 3, 5, 6, 10, 15, 30 (d) 1, 2, 3, 6, 7, 14, 21, 42 (e) 1, 2, 4, 11, 22, 4410. (a) 2 × 3 × 3 (b) 2 × 2 × 2 × 3 (c) 5 × 5 × 3 (d) 2 × 3 × 3 × 5(e) 2 × 3 × 5 × 7 (f) 5 × 5 × 11 (g) 5 × 5 × 5 × 5 (h) 2 × 3 × 5 × 5Answer326 Acme Mathematics 6
(i) 2 × 2 × 3 × 3 × 3 × 5 (j) 3 × 3 × 3 × 5 × 711. (a) 6 (b) 4 (c) 24 (d) 9 (e) 12 (f) 3012. (a) 6 (b) 12 (c) 15 (d) 24 (e) 24 (f) 45Exercise: 2.51. (a) 2 (b) 2 (c) 2 (d) 2 (e) 2(f) 2 (g) 3 (h) 5 (i) 7 (j) 24(k) 121 (l) 322. (a) 9 (b) 12 (c) 18 (d) 7 (e) 24(f) 11 (g) 4 (h) 7 (i) 2 (j) 32(k) 38 (l) 293. (a) 5 (b) 704. (a) 8 litre (b) 10 (c) 2 m 5. (a) 4, 3 mangoes and 5 apples (b) 20 (c) 15Exercise: 2.61 to 3. Show to your teacher4. (a) 504 (b) 144 (c) 840 (d) 780 (e) 1680 (f) 29905. (a) 840 (b) 180 (c) 7315 (d) 280 (e) 3600(f) 2100 (g) 420 (h) 3168 (i) 6006. (a) 1980 (b) 90 (c) 168 (d) 630 cm7. (a) 1:00 pm (b) 10:30 a.m 8. (a) 500 (b) 5 (c) 100 (d) 500 (e) Same (f) STYTExercise: 2.71 to 3. Show to your teacher.4. (a) 2 (b) 3 (c) 5 (d) 105. (a) 9 (b) 10 (c) 8 (d) 7 m (e) (i) 87 (ii) 13 (6) 11 (7) 8 (8) 551. (a) STYT (b) 208 (c) 2972. (a) STYT (b) 0 (c) STYT3. (a) {1, 2, 4, 5, 10, 20) (b) 10 (c) {42, 56, 54, 60, 66, 72, 78}4. (a) 1 (b) 10 (c) 1005. (a) LCM (b) 35 (c) Rs. 3256. (a) 510 (b) 105 (c) 4057. (a) (25 – 9) ÷ 8 × 4 (b) 4(c) Replac ‘x’ by ‘–’8. (a) (400 – 180) + 200 (b) Rs. 420 (c) Yes9. (a) 139 (b) 931 (c) 1070, 79210. (a) HCF (b) 93 (c) Rs. 425Acme Mathematics 6 327
11. (a) (i) Thirty lakh thousand (ii) 10 (b) 2, 3, 4 (c) 3, 512. (a) STYT (b) Rs. 180 (c) 1024Exercise: 2.8 Show to your teacher. Mixed Exercise : Show to your teacher.Exercise: 2.9 Show to your teacher.Exercise: 2.101. (a) 15 (b) 14 (c) 56 (d) 78 (e) 47 (f) 3091(g) 35 (h) 23 2. Show to your teacher.3. (a) 25 (b) 34 (c) 12 (d) 520 (e) 514 (f) 154. (a) 47 (b) 1012 (c) 1021 (d) 25 (e) 34 (f) 4155 – 7 Show to your teacher.8. (a) (i) 25, 1120,34 (ii) 34, , 1120,25 (b) (i) 14, ,13,12 (ii) 12, ,13,14(c) (i) 16,29, 518 (ii) 518, ,29,16 (d) (i) 514, ,47,2028 (ii) 2028, ,47, 514(e) (i) 49, 714 ,23 (ii) 23, , 714 ,49 (f) (i) 58, ,23,34 (ii) 34,23,589. Black 10. Expense on foodExercise: 2.111. (a) 118 (b) 59 (c) 1121 (d) 1310 (e) 1924 (f) 1318(g) 4 718 (h) 32584 (i) 1856 (j) 3 730 (k) 31920 (l) 319352. (a) 89 (b) 56 (c) 1115 (d) 11320 (e) 114 (f) 11114(g) 67199 (h) 4 712 (i) 14 112 3. 1320 4. 1735Exercise: 2.121. (a) 25 (b) 113 (c) 114 (d) 718 (e) 215 (f) 148(g) 34 (h) 2 (i) 215 (j) 11324 (k) 234 (l) 12 9352. (a) 13 (b) 2425 (c) 317 (d) 334 (e) 345 (f) 323(g) 21213 (h) 0 (i) 349503. (a) 21136 (b) 32330 (c) 214 (d) 2 112 (e) 7 86315 (f) 319304. 18 5. Rina, 76 m 6. 2 112 m 7. 16 work 8. 534 m 9. 3510. 0 11. Silver, 1112 m 12. 12, KiranExercise: 2.131. (a) 245 (b) 723 (c) 910 (d) 11125 (e) 16 (f) 5452. (a) 25 (b) 30 (c) 25 (d) 15 (e) Rs. 8 (f) Rs. 30(g) 14 m (h) 360 liter (i) 40 m (j) 84 km (k) 350 kg (l) 100 kg328 Acme Mathematics 6
(m) 10 (n) 52 (o) 88 (p) 1593. (a) 335 (b) 213 (c) 12 (d) 175 (e) 821 (f) 512(g) 12 (h) 167 (i) 12 112 (4) Show to your teacher.Exercise: 2.141. Show to your teacher.2. (a) 12 (b) 34 (c) 32 (d) 1 (e) 8 (f) 1 211003. (a) 2 (b) 1 (c) 28 (d) 10 (e) 1 (f) 1(g) 1 (h) 212 (i) 3 (j) 911 (k) 6 (l) 3294. (a) 12527 (b) 113 (c) 214 (d) 312 (e) 23 (f) 25. (a) 17 (b) 14 (c) 7176 (d) 1 117 (e) 5 (f) 917(g) 58 (h) 24 (i) 34Exercise: 2.151. 12 2. – 415 3. 7 4. 2215. (a) 1 130 (b) – 13 (c) 1330 (d) 21415 (e) 425 (f) 3146. (a) 9 (b) 49 (c) 59 (d) 1 (e) The total number of studentsExercise: 2.161. (a) 0.2 (b) 0.13 (c) 0.123 (d) 0.05 (e) 0.02 (f) 0.12 (g) 1.4 (h) 0.4 (i) 0.9 (j) 0.75 (k) 0.5 (l) 0.375 (m) 0.025 (n) 0.5625 (o) 2.5 (P) 2.75 2. (a) 1.75 (b) 3.625 (c) 3.16 (d) 6.8 (e) 2.25(f) 1.6 (g) 2.5 (h) 12.75 3. Show to your teacher.4. (a) 35 (b) 45 (c) 950 (d) 1310 (e) 103100 (f) 11150(g) 2412 (h) 20 1120 (i) 50281500 5. (a) 35 (b) 112 (c) 22750 (d) 1200 (e) 1212 (f) 1214(g) 1218 (h) 940Exercise: 2.171. Show to your teacher. 2. Show to your teacher. 3. Show to your teacher.4. (a) 12.403 (b) 5.092 (c) 403.816 (d) 52.843 (e) 21.5075. 61.78 litre 6. 6.55 7. 23.17 8. 10.65 litreExercise: 2.181. Show to your teacher.2. (a) 14.4 (b) 7.2 (c) 30 (d) 0.84 (e) 1.71(f) 22.4 (g) 21.19 (h) 79.184 (i) 84.15 (j) 115.488(k) 21.872 (l) 35.014Acme Mathematics 6 329
3. (a) 1.632 (b) 3.645 (c) 16.4934 (d) 10.489 (e) 1.4112(f) 16.7761 4. Rs. 10137.50 5. Rs. 1167936. (a) 675.92 cm2 (b) 3.411 cm2 (c) 11.022 cm2Exercise: 2.191. Show to your teacher.2. (a) 5.2 (b) 4.1 (c) 6.1 (d) 4.1 (e) 4.1(f) 6.1 (g) 9.1 (h) 0.51 (i) 0.54 (j) 1.54(k) 1.28 (l) 0.97 (m) 12.78 (n) 7.47 (o) 16.933. (a) 0.48 (b) 68.57 (c) 0.72 (d) 0.83 (e) 2.21(f) 3.58 (g) 0.245 (h) 1.23 (i) 4.25 (j) 6.184. (a) 10.667 (b) 1.373 (c) 0.365 (d) 2.615 (e) 2.064(f) 17.6 (g) 23.53 (h) 13.55. Rs. 425.60 6. 55.807 km 7. (a) 32.5 m, 16.25 m (b) 528.125 cm28. (a) Rs. 35 (b) 3.7 kg9. (a) 12.7 ft (b) 58.4 ft (c) increased by 62.7 sq.ftExercise: 2.201. (a) 3.6 (b) 4.5 (c) 12.3 (d) 50.62. (a) 6.25 (b) 4.10 (c) 1.63 (d) 7.013. (a) 0.429 (b) 0.125 (c) 0.667 (d) 0.231 (e) 4.826 (f) 2.632 (g) 1.048 (h) 3.308 4. (a) 6 (b) 6.5 (c) 6.47 (d) 6.55. (a) 2 cm (b) 1 m (c) 2 km (d) Rs. 3 (e) Rs. 10(f) Rs. 10 (g) 3 litre (h) 5 l (j) 6 kg1. (a) Education (b) Rs. 20,000 (c) Rs. 20,0002. (a) 112 (b) 224 (c) 4 (d) 483. (a) House rent (b) Rs. 12,000 (c) Rs. 10,0004. (a) STYT (b) 1 (c) 215. (a) 28,38 (b) STYT (c) 58 (d) Proper, Since 5 < 86. (a) STYT (b) 58 (c) 115 (d) 24 kgExercise: 2.211. Show to your teacher. 2. Show to your teacher.3. Show to your teacher. 4. Show to your teacher.5. (a) 40% (b) 15% (c) 36% (d) 25% (e) 10%(f) 16% (g) 80% (h) 75%6. (a) 11% (b) 70% (c) 2% (d) 36% (e) 62%330 Acme Mathematics 6
(f) 91% (g) 1% (h) 90%7. (a) 15 (b) 150 (c) 35 (d) 2950 (e) 1625(f) 350 (g) 910 (h) 18. (a) 0.11 (b) 0.33 (c) 0.37 (d) 0.01 (e) 0.03(f) 0.99 (g) 0.65 (h) 1Exercise: 2.221. (a) 20% (b) 22.22% (c) 25% (d) 25% (e) 6.25%(f) 50% (g) 100% (h) 150% (i) 1.88% (j) 25% (k) 2%2. (a) 2.5 (b) 9 (c) 4.9 (d) 18 (e) 100(f) 133.1 (g) 192 (h) 700 (i) 0.52 kg (j) 1.6 hours(k) Rs. 80.16 (l) 26 kg (m) 12 liter (n) 900 ml3. (a) Rs. 250 (b) 1000 kg (c) 700 m (d) 2400 gram (e) 1000(f) Rs. 10000 (g) 4000 hours (h) 4004. (a) 250 ml (b) 1.25 cm (c) 1.5 kg (d) 25 (e) Rs. 37.50 (f) Rs. 400005. (a) Rs, 665 (b) Rs. 111.60 (c) Rs. 1620 (d) Rs. 49 (e) Rs. 6800 (f) Rs. 72806. 75% 7. 66.67% 8. Maths = 95%, Eng. = 74%, Nepali = 80% 9. 16 litre10. (a) 9 (b) 27 11. Krishna 12. Rs. 162013. (a) 30 (b) 33 13 % (c) 66 23 %14. 2000 15. 90 23% 16. 4800 17. 95% 18. Rs. 13800 19. (a) Rs. 595 (b) Rs. 340 (c) Rs. 170 (d) Rs. 850 (e) Rs. 42520. Rs. 40,000, Rs. 20,000, Rs. 30,000, Rs. 10,000Exercise: 2.231. Show to your teacher. 2. Show to your teacher.3. Rs. 300 4. Rs. 10 5. Rs. 60 6. Rs. 30 7. Rs. 6008. Rs. 13100 9. Rs. 700 10. Rs. 1865 11. Rs. 1043 12. Rs. 1026Exercise: 2.241. Show to your teacher.2. (a) 140 (b) Rs. 1800 (c) 200 (d) 18 (e) Rs. 560Exercise: 2.251 to 3 Show to your teacher.4. Rs. 936 5. 1720 6. Rs. 450 7. 480 km 8. Rs. 16009. Rs. 1765.20 10. Rs. 16 11. Rs. 139.30 12. & 13. Show to your teacher.Exercise: 2.261. Rs. 600 2. Rs. 48 3. 15 cups 4. 120 km 5. Rs. 12000 6. 1207. 181.25 km 8. Rs. 324000, Rs. 540000 9. (a) Rs. 4150 (b) Rs. 996 10. 17.78 kg 11. 11.25 'Bigaha'Acme Mathematics 6 331
1. (a) Rs. 100 (b) Rs. 92 (c) 50%, 50% (d) Neither more nor less2. (a) Rs. 50 (b) Rs. 45.83 (c) 33. (a) 1.5 km (b) 75% (c) 1000 (d) 1504. (a) Rs. 40 (b) Rs. 180 (c) Rs. 75 (d) Rs. 205. (a) 40% (b) 300 (c) 200 (d) 1 kg6. (a) Rs. 4900 (b) Rs. 4900 (c) Rs. 53,900 (d) Rs. 98,0007. (a) 15% (b) 20 Paisa (c) Rs. 100, Rs. 150, Rs. 250 (d) Rs. 1008. (a) 60% (b) 40% (c) Rs. 4, loss (d) Rs. 29. (a) Rs. 3 (b) 5 liter (c) 25 cups10. (a) Rs. 280 (b) Rs. 50 (c) Rs. 330 (d) Rs. 500Exercise: 3.1 Show to your teacher.Exercise: 3.21 to 3 Show to your teacher.4. (a) 26 cm (b) 20 inch (c) 44 ft5. (a) 8 cm (b) 14 cm (c) 32 cm6. (a) 28 cm (b) 42 cm (c) 73 cm (d) 190 cm7. (a) 18 cm (b) 24 cm (c) 60 cm (d) 100 cm (e) 66 cm (f) 90 cm8 to 9 Show to your teacher.10. (a) 5 times (b) 700 m 11. (a) 192 m (b) 320 m (c) 600 m12. (a) 1 cm (b) 4.5 cm (c) 5 cm 13. (a) 18 cm (b) 45 cm (c) 25 cm14. (a) 90 cm (b) 30 cm (c) 68 cm (d) 80 cm (e) 60 cm (f) 86 cm15. (a) 12 cm (b) 15 cm (c) 20 cm (d) 25 cm 16. Show to your teacher.Exercise: 3.31 to 3 Show to your teacher.4. (a) 7.5 cm2 (b) 55.25 cm2 (c) 12600 cm2 (d) 472.5 cm2 (e) 144 cm2 (f) 1050 m25. (a) 81 cm2 (b) 169 m2 (c) 16 cm2 (d) 225 cm26. (a) 3 m2 (b) 5400 m27. (a) 225 cm2 (b) 25 cm2 (c) 420.25 cm28. (a) 10 cm2 (b) 16 cm2 (c) 96 cm29. (a) 717.5 cm2 (b) 10.5 m2 10. (a) 3 m (b) 14 m11. (a) 10 m (b) 100 m2 12. Show to your teacher.13. (a) 6.48 m, 3.24 m (b) 6 m (c) 8 cm, 5.33 cm and 34.66 cm (d) 10 cm, 2.5 cm and 25 cm14. (a) 20 cm2 (b) 36 cm2 (c) 76 cm2 (d) 44 cm215. (a) 24 m2 (b) 12 m2 (c) Bathroom (d) 6.5 m2 16. Show to your teacher.17. (a) l × b (b) 24 m2 (c) 24 m2 (d) Rs. 3600332 Acme Mathematics 6
Exercise: 3.41. & 2. Show to your teacher.3. (a) 1600 cm3 (b) 56.25 cm3 (c) 1139.25 cm34. (a) 125 cm3 (b) 274.63 cm3 (c) 79.51 cm35. (a) 5 cm (b) 4 cm (c) 2 cm (d) 6 cm6. (a) 2 cm (b) 4 cm (c) 10 cm (d) 2 cm (e) 2 cm (f) 2 cm7. 6 m 8. 4 cm 9. 45 cm 10. 12 m 11. 20 cm, 10 cm12. & 13. Show to your teacher.1. (a) STYT 2. STYY3. (a) 60 cm3 (b) 60 cm2 (c) 20 cm2 (d) Bigger by 20 cm24. (a) 10 ft. (b) 9 ft2 (c) 141 ft2 (d) 12 ft5. (a) 20 cm and 10 cm (b) Yes (c) Length is double.6. (a) 80 m (b) 160 m (c) 40 m (d) Dinesh7. (a) 8 m (b) 4 m (c) 40 m8. (a) 81 cm2 (b) 135 m39. (a) 2 (l + b) unit (b) 60 m (c) 40 m10. (a) 52 inch (b) 5040 cm2, 288 m, 864 m (c) 12 cm11. (a) STYT (b) 2 (l + b) unit (c) lbh cubic units, 400 cm312. (a) 8 m (b) 256 m (c) 6 m313. (a) 30 ft (b) 900 ft2 (c) STYT14. (a) 80 m, 160 m (b) 106 cm (c) 20 sq. unitExercise: 4.11-2 Show to your teacher. 3. (a) 48 (b) 3375 (c) 3600 (d) 8100(e) 4320 (f) 6914. Show to your teacher. 5. (a) 739 (b) 1 (c) 3 (d) – 54 (e) 634(f) 55 (g) 48 (h) 12 (i) 5x56. (a) xy sq. unit (b) x2 sq. unit (c) 81 cm27. (a) xyz cu. unit (b) x3 cu. unit (c) 1728 cm3Exercise: 4.21 to 5 Show to your teacher.6. (a) (x – 5) years (b) (x + 10) years (c) (x – 30) years7. (a) 2x – 10 (b) 7x 8. (a) 8x units (b) 8x units (c) 4x2 square units (d) 4x2 square unitsAcme Mathematics 6 333
Exercise: 4.31 (a) 7 (b) 13 (c) 16 (d) 4 (e) 8 (f) 0(g) 7 (h) 2 (i) 102. (a) 1 (b) 4 (c) 9 (d) 4 (e) 9 (f) – 13. (a) 90 (b) 160 (c) 30 (d) 150 (e) 210 (f) 5204. (a) 20 (b) 8 (c) 120 (d) – 24 (e) 20 (f) 12(g) 10 (h) 5 (i) 2 (j) 25. (a) – 3 (b) 8 (c) 0 (d) 2 (e) 14 (f) 0(g) 198 (h) 1 (i) 49166. (x + 2y + 23) cm and 737. (a) 36 cm (b) 72 cm (c) 99 cm (d) 117 cm (e) 31 cm (f) 35 cm8. (a) 120 cm2 (b) 60 cm2 (c) 100 cm2 (d) 84 cm (e) 6300 cm2 (f) 280 cm29. (a) 20 and 60 (b) 30 and 45 (c) 16, 20 and 5 (d) 400, 117 and 1210. (a) 7.5 cm (b) 10 cm (c) 15 cm11. (a) 9 cm or 10 cm or 11 cm (b) 7 cm, 10 cm or 13 cm(c) 9 cm or 12 cm or 15 cm (d) 13 cm or 19 cm or 25 cmExercise: 4.41. Show to your teacher.2. (a) 11x (b) 18y (c) 11z (d) 35a2 (e) 15xy (f) 11ab (g) 28 abc (h) 21a2bc (i) 11ax33. (a) 7x (b) 4d (c) 4c (d) 4y2 (e) 7h (f) 3c(g) 6z2 (h) s (i) 13x (j) 16y (k) 7z (l) x34. (a) 5x (b) x + y (c) 6a (d) x2 + 2x 5. 33x6. (a) 10d (b) 12 mn (c) 16wt (d) 30z2 (e) 12a (f) 17b(g) 16x (h) 41y (i) 26p (j) 15r7. (a) 9x + 5 (b) 5x + 4 (c) 7x + 4 (d) 7x + 7 (e) 2x + 3 (f) 2x – 5(g) x – 5 (h) 13a + 3b + 3 (i) 10m + 3n + 1 (j) 3p – 2q – 18 (k) 2a + 1 (l) 5x – 4y + 4z (m) 4a + 5b – 9 (n) x + y + 7z8. (a) 6x cm (b) 6z ft. (c) (y + 5) inchExercise: 4.51. Show to your teacher.2. (a) 7x + 10y (b) 8p + 8q (c) 6xy + 4yz (d) 36ab+ 19bc(e) 13a + 7b + 9 (f) 24a + 18b +12 (g) 10x + 6y (h) 2x + 40y(i) 10x2 + 11xy (j) 31ac + 30a2 (k) 7xy2 + 11x2y (l) 15x2y2 + 19xy3. (a) 14a2 + 10a + 9 (b) 2x2 + 9 (c) 8x2 + 6y2 + 5xy (d) 3x2 – 8y2 – 3xy(e) 13p2 + 7q2 + 31 (f) 6x3 + 2x2 + 4x + 10 (g) 5a3 – 3a2 + 11a + 134. (a) 2x + 4y (b) 6x + 6y (c) 3x + 29y (d) 19x – 9y(e) 18x + 25y (f) – x – 6y 5. (a) 4x – 5 (b) a – 13 (c) 4a2 + 2a (d) 8a3 + 11a334 Acme Mathematics 6
(e) – 3ab + 13bc (f) – 4mn – 5ny (g) x + y + z (h) 3x – 3y(i) – 12x2 – 4x + 5 (j) – x2 – 12y – z (k) 7xy + 14yz + 10xz (l) x2 – x + 9y6. (a) 3x + 4y + 5z (b) 2a + 3b – 6c (c) 2x – 21y + 4z (d) – 6x + 3y + 4z(e) 10xy + 8yz – zx (f) – 12mn + 14mp + 6pn7. (a) 7x2 + 2x (b) 17x2 + 2xy (c) – 3ab2 + 6xy (d) 15x2 – 5x – 4(e) 4y2 + xy + 3 (f) – xy2 + 12xz – 9 (g) 2ax2 – 4bx – 2c (h) 3x2 z + 12px – 18q8. (a) 22y + 30k (b) 36k + w (c) 19w + 2y (d) – 4n – 148(e) 2x2 + 7x + 9 (f) 8x2 – x – 4 (g) 3x2 – 4x – 8 (h) 3x2 – 2x – 29. (a) x + 2y (b) 4a – 8c (c) a2 – 4b2 (d) – ab + 7ac(e) 8x + 3y (f) – 6ab – 2bc10. (a) 11y – 7 (b) – 14x + 36y – 34 (c) – 11x +35y – 20 (d) 51x – 9y + 62(e) – 15x + 7y – 20 (f) 43x – 65y + 6211. (a) 6x + 20y + 7 (b) 5x + 10y +14 (c) 10x + 6y + 5 (d) 8a + 14b + 44(e) 17xy + 8x + 2 (f) 7a + 15b + 3112. (a) 99 cm (b) 64 cm (c) 49 cm (d) 106 cm(e) 154 cm (f) 88 cmExercise: 4.61 – 3 show to your teacher.4. (a) x3y3 (b) 3a3b3 (c) 20m3n3 (d) 3a6b3(e) 24x6y3 (f) 120x6y6 (g) 120a2b2c2 (h) 2x3y4z25. (a) 7x2 (b) 25x2 (c) 18x2 (d) – 21xy (e) x2y (f) 0(g) 19x2y (h) 17a2x2 (i) 35pq2 (j) x2 + xy – 6x (k) 7x2 + 28xy – 70x(l) 35p2 – 15pq + 5p (m) 2x3 + 2ax2 + 14x2 (n) 7x3 + 63x2 +56x6. (a) x2 + 2xy + y2 (b) x2 – y2 (c) x2 – 2xy + y2 (d) 2x2 + 6x + 4(e) 4x2 + 14xy + 6y2 (f) 51x2 – 11xy (g) 7x2 – 20xy – 3y2 (h) 6x2 + 16xy + 8y27. (a) 15x2cm2 (b) (x2 + 5x)cm2 (c) (10xy + 10y2) cm2(d) (10xy– x2y) cm2 (e) (35xy + 7xy2) m2 (f) 6x2y2 + 34xy + 20(g) (i) 60 cm2 (ii) 14 cm2 (iii) 150 cm2 (iv) 48 cm2(v) 336 cm2 (vi) 440 m28. (a) 4x2 + 28xy (b) – 40x2 – 280xy (c) – 18x2 – 126xy (d) – 510x2 – 210xy (e) – 30x2 – 210xy (f) 1440x3 + 10080x2y9. (a) 4a23 (b) STYT (c) xy > z10. (a) 6 (b) 24 x3 cubic unit (c) 8 cmExercise: 4.71. to 3. Show to your teacher.4. (a) x + 5 (b) 6y – x (c) 4x + 3 (d) x + 3 (e) 3a – 5b (f) a + b(g) x – y (h) 3a – 2b (i) 2a + 3b (j) 2a2 + 3b (k) a + 2b (l) 2a2 + 15. (a) 3 + 2b2 (b) 4 – 5y (c) 4ab + 2 (d) 1 – 2x2y2(e) – 2ax3y3 + 4x2y2 (f) 2a – 10 (g) z + 9Acme Mathematics 6 335
6. (a) 2ab (b) 3a2b2 (c) 3ab2 (d) 3a2b2 7. 6a2b2 8. – 40ab9. (a) 4ab (b) 4ab, 12a2b2 (c) 5x2y52 , 2x, 5x3y5, (5x3y5 + 2x) and (2x – 5x3y5)10. Show to your teacher.11. (a) 4 cm (b) 5a cm (c) 25 x2yz2 cm (d) (4xy + 2) cm12. (a) 2 cm (b) 4 ft (c) 10 m (d) 2 ft (e) 2 m (f) 2 cm13. STYT1. STYT2. (a) False (b) 6xy cm (c) 36 cm and 864 cm23. (a) STYT (b) 7y (c) (y – 3) pens4. (a) 8x2 + 10x + 12 (b) 4x + 4y + 4z (c) 4x + 4 5. STYT6. (a) STYT (b) – 5 and q2 (c) STYT7. (a) 110 m (b) 49 m (c) (4x – 82) m8. (a) 1 (b) 38 (c) 7299. (a) lbh cu.unit (b) b3 cu. unit (c) 5410. (a) binomial (b) 3 (c) 1811. (a) 10 (b) STYT (c) 13x + 112. (a) 75a4 (b) 2x + 12y (c) 4x + 313. (a) 4x2 – xy (b) 6 (c) 4a2 + 2ab + 114. (a) (2x + y + 3) units (b) 12(c) 4x2 + 11xy – 3y2 (d) 2x2 – 2xy – 6x + 14y – 6y215. (a) 6x2y2 cm (b) 6x2y216. (a) 7 (b) seven square (c) 3417. (a) (5x)6 (b) 3x3 – x18. (a) STYT (b) 7 + y (c) 019. (a) 23 × 32 (b) 9xy (c) 5y – 720. (a) (18x + 6) m (b) (20x2 + 12x) m2 (c) (10x2 + 6x) m2 (d) (x + 3) m (e) 16x2 m2Exercise: 4.8 Show to your teacher.Exercise: 4.91. Show to your teacher.2. (a) 5 (b) 4 (c) 5 (d) 9 (e) 53. (a) 5 (b) 13 (c) 8 (d) 10 (e) 7(f) 5 (g) 6 (h) 154. (a) 3 (b) 2 (c) 12 (d) 10 (e) 3(f) 3 (g) 3 (h) 20 (i) 3Exercise: 4.101 – 4 Show to your teacher.5. (a) 8 (b) 5 (c) 4 (d) 4 (e) 6 (f) 6336 Acme Mathematics 6
(g) 2 (h) 2 (i) 3 (j) 5 (k) 65 (l) 1(m) 2 (n) 36. (a) 1 (b) 10 (c) 3 (d) 2 (e) 1 (f) 5(g) 1 (h) 5 (i) 4 (j) 8 (k) 9 (l) 16(m) 30 (n) 167. (a) 3 (b) 7 (c) 7 (d) 5 (e) 7 (f) – 1(g) – 6 (h) 10 (i) 2 (j) 1 (k) 0 (l) – 17(m) – 343 (n) – 24 (o) –1 (p) 4Exercise: 4.111. (a) 8 cm (b) 4 cm (c) 1 cm (d) 18 cm2. (a) x + 3 = 12 (b) 2x + 7 = 22 (c) x – 6 = 14 (d) x – 8 = 16 (e) 5x = 15(f) 3x7 = 10 (g) x9 = 9 (h) m3 = 20 3. (a) 18 (b) 23 (c) 12 (d) 28 (e) 6 (f) 34. (a) Rs. 5000 (b) 200 (c) 500 (d) Rs. 1000 (e) Rs. 2005. (a) 17 (b) 11 years (c) 46 years (d) 46. (a) 10 m, 17 m (b) 9 cm, 6 cm, 12 cm (c) 9 cm (d) 19 cm7. Show to your teacherExercise: 4.121 to 2. Show to your teacher.3. (a) 9 > 1 (b) 8 < 11 (c) 10 11 (d) 2 0 (e) x > 7 (f) x 6(g) x < – 3 (h) x – 3 (i) x = 21 (j) x ≠ 21Exercise: 4.131. (a) x > 2 (b) x < 0 (c) x ≤ 4 (d) x ≥ 4 (e) – 2 < x < 2(f) 2 ≤ x < 5 (g) 0 < x ≤ 4 (h) 2 ≤ x ≤ 82. Show to your teacher.3. (a) x > 7 (b) x < 0 (c) x ≥ 10 (d) x ≤ 10 (e) 2x + 1 > 0(f) 2x – 7 < – 8 (g) 1 < x < 6 (h) 5 < x < 10 (i) – 8 ≤ 2x ≤ 101. (a) 2x + 7 < 10 (b) 6 (c) x < 02. (a) 4 (b) 3 (c) STYT3. (a) 5 (b) 10 (c) – 54. (a) STYT (b) 189 (c) 125. (a) Samin = Rs. 35, Rajan = Rs. 17 (b) a > 8 (c) 126. (a) y – 5 > 10 (b) 8 (c) Nandani = Rs. 54, Samjhana = Rs. 427. (a) (x – 2) years (b) (x + 2) years (c) 4x years8. (a) STYT (b) True (c) x – 5 = 109. (a) Open (b) True (c) STYT10. (a) 4 (b) 6 + 3x = 24, x = 6cm (c) FalseAcme Mathematics 6 337
11. (a) True (b) True (c) True (d) FalseExercise: 5.1 Show to your teacherExercise: 5.21 to 9 show to your teacher10. (a) 46° (b) 55° (c) 10° (d) 80° (e) 65°(f) 27° (g) 20° (h) 1° 11. (a) 137° (b) 143° (c) 98° (d) 70° (e) 55°(f) 17° (g) 10° (h) 90°12. (a) 60° (b) 20° (c) 47° (d) 13.14° (e) 18.8°(f) 5.33° 13. (a) 100° (b) 75° (c) 60° (d) 54.5° (e) 62°(f) 14° 14. (a) 80°,100° (b) 160°, 160°, 20° (c) 89°, 91°, 91°(d) 75°, 75°, 35° (e) 121°, 50°, 130° (f) 90°, 45°, 90°Exercise: 5.3 Show to your teacherExercise: 5.41 to 6 Show to your teacher.7. (a) 70° (b) 60° (c) 140° (d) 50° (e) 70° (f) 50°(g) 60° (h) 40° (i) 30°8. (a) 120° (b) 80° (c) 90°, 60° (d) 50° (e) 30°, 45° (f) 45°, 105°(g) 20° (h) 45° (i) 120°, 80°9. (a) 44° (b) 45° (c) 70°, 90° (d) 70°, 70° (e) 30°, 60°, 90°(f) 105°, 45° (g) 18°, 60°, 102° (h) 70°, 55°, 55° (i) 30°10. Show to your teacher.11. (a) 135° (b) 75° 12 & 13. Show to your teacher.Exercise: 5.51 to 3 Show to your teacherExercise: 5.6 : Show to your teacherExercise: 5.7 : Show to your teacher.3. (c) x=78°, y°=z°= 102°5. (d) 20°6. (b) 30°7. (c) 91°11. (a) 50°, 130°14. (b) 100°16. (a) 45° (b) 17°Exercise: 5.8 to 5.10 : Show to your teacher.Exercise: 6.1 to 6.2 : Show to your teacher.338 Acme Mathematics 6