Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 301 Vedanta Excel in Mathematics - Book 8 Cotton 90° Nylon 54° 72° Others 144° Polyester d) The given pie chart shows the composition of different materials in a type of cloth in percent. i) Calculate the percentage of each material found in the cloth. ii) Calculate the weight of each material contained by a bundle of 50 kg of cloth. It’s your time - Project Work and Activity Section 4. a) Make a group of your friend. Take the number of students from classes 1 to 5 separately and present the data you obtained in pie-chart. b) Collect the number of students of your class who secured A+, A, B+, B, etc. grades in Mathematics exam and show the data in pie-chart. 20.7 Measures of central tendency The measure of central tendency gives a single central value that represents the characteristics of entire data. A single central value is the best representative of the given data towards which the values of all other data are approaching. Average of the given data is the measure of central tendency. There are three types of averages which are commonly used as the measure of central tendency. They are: mean, median, and mode. 20.8 Arithmetic mean Arithmetic mean is the most common type of average. It is the number obtained by dividing the sum of all the items by the number of items. i.e. mean = sum of all the items the number of items (i) Mean of non–repeated data If x represents all the items and n be the number of items, then mean (x) = å x n (ii) Computation of combined mean We can compute a single mean from the means of different sets of data. Such mean is called a combined mean. Let, n1 be the number of items in the first set of data and x1 be its mean. Also, n2 be the number of items in the second set of data and x2 be its mean. If the combined mean be x , then, x = n1 x1 + n2 x2 n1 + n2 Worked-out Examples Example 1: Calculate the average of the following marks obtained by 10 students of a class in mathematics. 25, 18, 35, 24, 15, 20, 33, 28, 22, 30 Statistics
Vedanta Excel in Mathematics - Book 8 302 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Solution: Here, Σx = 25 + 18 + 35 + 24 + 15 + 20 + 33 + 28 + 22 + 30 = 250 n = 10 Now, mean (x) = åx n = 250 10 = 25 Example 2: The average weight of 90 students from class I to V of a school is 20 kg and the average weight of 60 students from class VI to X is 35 kg. Find average weight of the students of the school. Solution: Here, n1 = 90 and x1= 20 kg , n2 = 60 and x2 = 35 kg ∴ Combined mean x n1 x1 + n2 x2 n1 + n2 = 90 × 20 + 60 × 35 90 + 60 = 1800 + 2100 150 = = 26 kg Hence, the average weight of the students of the school is 26 kg. Example 3: If the average of the following wages received by 5 workers is Rs 35, find the value of p. 30, 36, p, 40, 44. Solution: Here, Σx = 30 + 36 + p + 40 + 44 = 150 + p n = 5 Now, average = åx n or, 35 = 150 + p 5 or, 150 + p = 175 or, p = 25 So, the required value of p is Rs 25. (ii) Mean of individual repeated data (Mean of a frequency distribution) In the case of repeated data, follow the steps given below to calculate the mean. – Draw a table with 3 columns – Write down the items (x) in ascending or descending order in the first column and the corresponding frequencies in the second column. – Find the product of each item and its frequency (fx) and write in the third column. – Find the total of f column and fx column. – Divide the sum of fx by the sum of f (total number of items), the quotient is the required mean. Example 4: From the table given below, calculate the mean mark. Age (in years) 6 7 8 9 10 11 No. of students 3 5 4 9 7 2 Statistics
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 303 Vedanta Excel in Mathematics - Book 8 Solution: Calculation of average age: Marks (x) No. of students (f) fx 6 7 8 9 10 11 3 5 4 9 7 2 18 35 32 81 70 22 Total N = 30 Σfx =258 Now, mean mark (x) = åfx N = 258 30 = 8.6 years So, the required average age is 8.6 years. Example 5: If the mean of the data given below be 17, find the value of m. x 5 10 15 20 25 30 f 2 5 10 m 4 2 Solution: x f fx 5 10 15 20 25 30 2 5 10 m 4 2 10 50 150 20m 100 60 Total N = 23 + m Σfx = 370 + 20m Now, mean (x) = åfx N or, 17 = 370 + 20 m 23 + m or, 391 + 17m = 370 + 20 m or, 3m = 21 or, m = 7 So, the required value of m is 7. (iii) Mean of grouped and continuous data In the case of grouped and continuous data, we should find the mid–values (m) of each class interval and it is written in the second column. The mid–value of each class interval is obtained as: Mid–value = lower limit + upper limit 2 Then, each mid–value is multiplied by the corresponding frequency and the product fm is written in the fourth column. The process of calculation of mean is similar to the above mentioned process. Statistics
Vedanta Excel in Mathematics - Book 8 304 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Example 6: Calculate the mean from the table given below. Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 No. of students 3 8 12 7 2 Solution: Calculation of mean Marks (x) mid–value (m) No. of students (f) fm 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 5 15 25 35 45 3 8 12 7 2 15 120 300 245 90 Total N = 32 Σfm = 770 Now, mean marks (x) = å fx N 770 32 = = 24.06 EXERCISE 20.3 General Section – Classwork 1. Let’s say and write the answers as quickly as possible. a) Average of 4 and 6 is ........................ b) Average of 2, 5 and 9 is ....................... c) Average of 4, 6, 8, 10 is ........................ d) Average of 3 and x is 5, x = .................. e) Average of p and 4 is 3, p = ............................... 2. a) Σfx = 50 , n = 5, x = .............. b) Σfx = 60, n = 10, x = .............. c) Σfx = 80, n = 8, x = .............. d) Σfx = 150, n = 25, x = .............. e) Σfx = 40, x = 5, n = ............... f) Σfx = 70, x = 14, n = .............. Creative Section A 3. a) The ages of Ram, Hari, Shyam, Krishna, and Gopal are 12, 18, 13, 16, and 6 years respectively. Find their average age. b) Find the mean value of the following: 5, 11, 14, 10, 8, 6 c) Find the mean from the data given below. 57, 74, 83, 76, 60 4. a) If mean (x) = 9, Σx = 80 + p and N = 10, find the value of p. b) In an individual series, if Σx = 60 + a, N = a – 4 and mean (x) = 5, find the value of a. c) If Σx = 400 – m, N = 18 + m and x = 10, find the value of m. 5. a) The average age of 5 students is 9 years. Out of them the ages of 4 students are 5, 7, 8 and 15 years. What is the age of the remaining student? b) If 7 is the mean of 3, 6, a, 9, and 10, find the value of a. c) Find x if the mean of 2, 3, 4, 6, x, and 8 is 5. Statistics
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 305 Vedanta Excel in Mathematics - Book 8 6. a) The average rainfall in Kathmandu valley in the first 6 months of the year 2077 was 75 mm and the average rain fall of the last 6 months was 15 mm. Find the average rainfall in Kathmandu in the whole year. b) The average weight of 30 girls in class 8 is 42 kg and that of 20 boys is 45 kg. Find the average weight of the students of the class. c) The average height of x number of girls and 15 boys is 123 cm. If the average height of boys is 125 cm and that of girls is 120 cm, find the number of girls. 7. a) If Σfx = 40 + a, N = 4 + a and x = 5, find the value of a. b) If the mean of a series having Σfx = 100 – k and N = k – 4 is 15, find the value of k. Creative Section - B 8. a) Find the mean from the given table Marks obtained 15 25 35 45 55 No. of students 7 8 12 7 6 b) The ages of the students of a school are given below. Find the average age. Age (in years) 5 8 10 12 14 16 No. of students 20 16 24 18 25 15 c) Compute the arithmetic mean from the following frequency distribution table. Height (in cm) 58 60 62 64 66 68 No. of plants 12 14 20 13 8 5 9. a) Find the mean of the following frequency distribution. Class interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Frequency 7 5 6 12 8 2 b) Find mean. Wages (Rs.) 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 90 – 100 No. of workers 3 6 12 7 8 4 c) Find the mean from the following data. Marks obtained 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 No. of students 4 5 2 4 3 2 d) Compute the mean from the table given below. Age (years) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 No. of people 2 5 7 6 3 2 e) The table below gives the daily earnings of 110 workers in a textile mill. Daily earning 200 – 300 300 – 400 400 – 500 500 – 600 600 – 700 No. of workers 40 20 15 25 10 Find the average weekly earning. Statistics
Vedanta Excel in Mathematics - Book 8 306 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur f) The ages of workers in a factory are as follows Age in years 18 – 24 24 – 30 30 – 36 36 – 42 42 – 48 48 – 54 No. of workers 6 8 12 8 4 2 Calculate the average age of the groups. 10. a) Find the mean by constructing a frequency table of class interval of 10 from the data given below. 7, 47, 36, 39, 31, 19, 41, 49, 9, 51, 29, 22, 59, 17, 49, 21, 24, 12, 31, 8, 36, 18, 32, 16, 23 b) Construct a frequency table of class interval of 10 from the given data and find the mean. 23, 5, 17, 28, 39, 52, 16, 22, 69, 75 41, 33, 9, 49, 34, 59, 72, 46, 65, 58 60, 48, 64, 32, 50, 73, 57, 51, 63, 36 It’s your time - Project Work and Activity Section 11. a) Let’s ask your parents and write the ages of your family members. Then, calculate the average age of your family members. b) Let’s collect the marks obtained by your any 10 friends in the recently conducted mathematics exam and calculate the mean mark. c) Let’s collect and write the number of students in each class from class 1 to 8 in your school. Then find the average number of students in each class in your school. 20.9 Median Look at the following series. In the above series, the numbers are arranged in ascending order. Here, the fourth item 17 has three items before it and three items after it. So, 17 is the middle item in the series. 17 is called the median of the series. Thus, median is the value of the middle–most observation, when the data are arranged in ascending or descending order of magnitude. (i) Median of ungroupped data To find the median of an ungroupped data, arrange them in ascending or descending order. Let the total number of observation be n. – If n is odd, the median is the value of the n + 1 2 th observation. – If n is even, the median is the average of the and n 2 n 2 th th +1 observation. 5, 3 items Middle item 3 items 9, 13, 17 21, 25, 29 Statistics
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 307 Vedanta Excel in Mathematics - Book 8 Worked-out Examples Example 1: The weights in kg of 7 students are given below. Find the median weight. 35, 45, 43, 30, 52, 40, 37 Solution: Arranging the weights in ascending order, we have, 30, 35, 37, 40, 43, 45, 52 Here, n = 7 Now, the position of median = n + 1 2 th item = 7 + 1 2 th item = 4th item i.e., 4th item is the median. ∴ Median = 40 kg. Example 2: The marks obtained by 6 students are given below. Calculate the median mark. 15, 25, 10, 30, 20, 35 Solution: Arranging the marks in ascending order, we have, 10, 15, 20, 25, 30, 35 Here, n = 6 Now, the position of median = n + 1 2 th item = 6 + 1 2 th item = 3.5th item 3.5th item is the average of 3rd and 4th items. ∴ Median = 20 + 25 2 24 2 = = 22.5 (ii) Median of Discrete series To compute the median of a discrete series of frequency distribution, we should display the data in ascending or descending order in a cumulative frequency table. Then, the median is obtained by using the formula: Median = value of N + 1 2 th item Example 3: Compute the median from the table given below. x 4 8 12 16 20 24 f 3 5 4 7 6 2 Statistics
Vedanta Excel in Mathematics - Book 8 308 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Solution: Cumulative frequency table x f c.f. 4 6 12 16 20 24 3 5 4 7 6 2 3 8 12 19 25 27 Total N = 27 Now, position of median = N + 1 2 th item = 27 + 1 2 th item = 14th item In c.f. column, the c.f. just greater than 14 is 19 and its corresponding values is 16. ∴ Median = 16. 20.10 Quartiles Quartiles are the values that divide the data arranged in ascending or descending order into four equal parts. A distribution is divided into four equal parts by three quartiles. – the first or lower quartile (Q1 ) is the point below which 25 % of the items lie and above which 75 % of the items lie. – The second quartile (Q2 ) is the point below which 50 % of the items lie and above which 50 % of the items lie. Of course, the second quartile is the median. – The third or upper quartile (Q3 ) is the point below which 75 % of the items lie and above which 25 % of the items lie. If N be the number of items in ascending (or descending) order of a distribution, then in the case of discrete data the position of the first quartile (Q1 ) = N + 1 4 th item the position of the second quartile (Q2 ) = N + 1 2 th item 2(N + 1) 4 th = the position of the third quartile (Q3 ) = item 3(N + 1) 4 th Similarly, in the case of grouped data, the positions of quartiles are obtained in the following ways. The first quartile (Q1 ) = value of N 4 th item The second quartile (Q2 ) = 2(N) 4 th item = value of N 2 th item The third quartile (Q3 ) = value of 3(N) 4 th item After finding the positions, the process of computing the quartiles is as similar as the process of computing median. Statistics
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 309 Vedanta Excel in Mathematics - Book 8 Example 4: Find the first quartile (Q1 ) and the third quartile (Q3 ) from the data given below. 7, 17, 10, 20, 13, 28, 24 Solution: Arranging the data in ascending order, 7, 10, 13, 17, 20, 24, 28 Here, n = 7 The position of the first quartile (Q1 ) = n + 1 4 th item = 7 + 1 4 th item = 2nd item The value of 2nd item is 10. ∴ The first quartile (Q1 ) = 10. Again, the position of the third quartile (Q3 ) = 3 n + 1 4 th item = 6th item The value of 6th item is 24. ∴ The third quartile (Q3 ) = 24. Example 5: The marks obtained by 10 students of class 8 in Mathematics are given below. Compute Q1 and Q3 . 18, 14, 16, 10, 15, 12, 8, 5, 11, 20 Solution: Arranging the marks in ascending order, 5, 8, 10, 11, 12, 14, 15 16, 18, 20 The position of the Q1 = n + 1 4 th item = 10 + 1 4 th item = 2.75th item Here, the 2nd item is 14 and 3rd item is 16. ∴ Q1 = 14 + (16 – 14) × 75% = 14 + 2 × 75 100 = 15.5 Again, the position of Q3 = 3 n + 1 4 th item = 3 × 2.75th item = 8.25th item Here, 8th item is 16 and 9th item is 18. ∴ Q3 = 16 + (18 – 16) × 25% = 16 + 2 × 25 100 = 16.5 Example 6: Compute the first and the third quartiles from the table given below. Marks 30 40 50 60 70 80 No. of students 4 6 10 12 5 2 Solution: Cumulative frequency distribution table Marks (x) No. of students (f) c.f. 30 40 50 60 70 80 4 6 10 12 5 2 4 10 20 32 37 39 Total N = 39 Statistics
Vedanta Excel in Mathematics - Book 8 310 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Now, the position of the first quartile (Q1 ) = N + 1 4 th item = 39 + 1 4 th item = 10th item In c.f. column, the corresponding value of the c.f. 10 is 40. ∴ The first quartile (Q1 ) = 40 Again, the position of the third quartile (Q3 ) = 3 N + 1 4 th item = 30th item In c.f. column, the c.f. just greater than 30 is 32 and its corresponding value is 60. ∴ The third quartile (Q3 ) = 60 20.11 Mode The mode of a set of data is the value with the highest frequency. A distribution that has two modes is called bimodal. The mode of a set of data is denoted by Mo. (i) Mode of discrete data In the case of discrete data, mode can be found just by inspection, i.e. just by taking an item with highest frequency. Example 7: Find the mode for the following distribution. 25, 18, 20, 18, 22, 18, 20, 18, 20 Solution: Arranging the data in ascending order. 18, 18, 18, 18, 20, 20, 20, 22, 25 Here, 18 has the highest frequency. ∴ Mode = 18. 20.12 Range The difference between the largest and the smallest score is called range. ∴ Range = Largest score – Smallest score Example 8: The marks obtained by 10 students of class 8 in Mathematics are given below. Find the range. 78 36 27 95 43 15 69 84 72 51 Here, the highest marks = 95 The lowest marks = 15 ∴ Range = highest score – lowest score = 95 – 15 = 80 Statistics
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 311 Vedanta Excel in Mathematics - Book 8 EXERCISE 20.4 General Section – Classwork 1. Let’s say and write the correct answers as quickly as possible. a) Median of 4, 6, 9 is ..................... b) Median of 5, 8, 10, is ..................... c) Median of 6, 2, 5, 4, 8 is ..................... d) The first quartile of 2, 5, 6, 8, 10, 13, 15, is ..................... e) The third quartile of 3, 4, 7, 10, 12, 15, 17, is ..................... f) The observation which occurs maximum number of times in a data is called ..................... g) The mode of 4, 5, 7, 5, 5, 4, 9, 7, 4, 5 is ..................... h) The difference between the largest and score the smallest score is called ............ g) The range of 10, 30, 20, 80, 40, 60, 50, 70 is ..................... Creative Section - A 2. a) Find the medians of the following sets of data. i) 21, 18, 35, 46, 40 ii) 15, 30, 35, 25, 20, 45, 40 iii) 22, 16, 14, 26, 32, 30 b) The weights of five students are as follows. Find their median weight. 48 kg, 59 kg, 43 kg, 63 kg, 52 kg c) Find the median age of a group of 8 people whose ages in years are as follows: 47, 61, 13, 34, 56, 22, 30, 20 3. a) If the following numbers are in ascending order and median is 4, find the value of x. x, x + 1, x + 2, x + 3, x + 4 b) The numbers x – 2, x – 1, x + 2, x + 3, x + 5 are in ascending order. If the median is 10, find the value of x. 4. a) Find the first quartiles (Q1 ) of the following sets of data. (i) 14, 12, 17, 23, 20, 16, 10 (ii) 16, 25, 10, 30, 35, 8, 12 (iii) 40, 20, 30, 10, 16, 12, 18, 24, 28 Statistics
Vedanta Excel in Mathematics - Book 8 312 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur d) Find the modal size of the shoes from the data given below: Size of shoe 5 6 7 8 9 10 No. of men 10 15 30 25 18 12 e) Find the mode from the following data. Daily wages (in Rs) 70 90 110 130 150 170 No. of workers 4 12 15 18 20 12 Creative Section -B 6. Find the median marks from the data given below: a) Marks 24 36 50 65 78 No. of students 2 4 12 11 6 b) Marks 10 15 20 25 30 35 No. of students 3 7 15 12 7 3 c) Wage in Rs 45 55 65 75 85 95 No. of workers 20 25 24 18 15 7 b) Find the third quartiles (Q3 ) of the following sets of data. (i) 15, 9, 21, 33, 27, 39, 45 (ii) 18, 26, 14, 22, 30, 38, 34 (iii) 30, 20, 50, 80, 40, 60, 70, 90 5. a) Find the modes of the following distributions: (i) 7, 9, 5, 7, 10, 9, 7, 12 (ii) 15 kg, 21 kg, 17 kg, 21 kg, 28 kg, 21 kg, 15 kg, 21 kg b) In a class, there are 15 students of 16 years, 14 students of 17 years, and 16 students of 18 years. What will be the modal age of the class? c) In a factory, number of labourers and their remuneration are as follows. Find the modal class. Remuneration (in Rs) 1500 – 2000 2000 – 2500 2500 – 3000 No. of labourers 220 215 120 Statistics
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 313 Vedanta Excel in Mathematics - Book 8 b) Find the range of the following data. 25, 20, 38, 50, 45, 27, 36, 18 c) The marks obtained by 20 students in Mathematics are given below. Find the range. Marks 4 6 8 10 12 14 No. of students 2 3 5 7 2 1 7. a) Calculate the first quartile (Q1 ) from the data given below. Marks obtained 32 36 40 44 48 52 No. of students 2 5 9 6 3 2 b) Compute the third quartile (Q3 ) from the following table. Wages in Rs 50 60 70 80 90 100 No. of workers 6 10 15 13 8 3 c) Find the first quartile (Q1 ) and the third quartile (Q3 ) from the following distribution Ages in years 22 27 32 37 42 No. of people 35 42 40 30 24 8. a) The heights of 10 students of class 8 are given below. 95 cm, 110 cm, 120 cm 90 cm, 100 cm, 105 cm, 98 cm, 115 cm, 112 cm, 116 cm (i) What is the height of the tallest student? (ii) What is the height of the shortest student? (iii) Find the range of the height. It’s your time - Project Work and Activity Section 9. a) Let’s collect the marks obtained by any of your 9 friends and find: (i) the median marks (ii) the first and third quartiles marks. b) Let’s conduct a survey to find the number of students from class 4 to class 8 in your school. Show the number of students of different ages in a frequency distribution table and compute the following: (i) median age (ii) the first quartile age (iii) the third quartile age Statistics
Vedanta Excel in Mathematics - Book 8 314 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Assessment - V 1. The table given below shows the number of students of a school from class IV to VIII. Answer the following questions. Class IV V VI VII VIII No. of students 40 45 35 28 32 (a) Represent the data in a pie chart. (b) Find the average number of students. (c) Find the percentage of students of each class out of the total number of students from class IV to VIII. 2. Mrs. Magar’s monthly expenditure is Rs 27,000. The diagram on the right is a pie chart showing her expenditure on different headings. (a) On which heading did she spend most? (b) Calculate the expenditures of each heading. (c) Find the heading-wise average expenditure. 3. The marks obtained by 7 students of a group of class 8 in a terminal examination are given below. 40, 15, 25, 20, 30, 20, 45 (a) Find the mode. (b) Find the average mark (c) Find the median mark. (d) If the marks obtained by two more students of the same class in the same exam are also included so that the median mark of the data remains same, what would be the possible marks obtained by two more students? (i) 10 and 18 (ii) 25 and 40 (iii) 16 and 35 (iv) 32 and 36 4. The heights of a group of people are given below. 120 cm, 140 cm, 125 cm, 165 cm, 150 cm, 130 cm, 110 cm, 138 cm, 142 cm, 155 cm, 132 cm (a) Find the mode (b) Find the mean height. (c) Find the median height. 5. The average age of 5 students is 9 years. Out of them the ages of 4 students are 5, 7, 8 and 15 years. (a) What is the age of the remaining student? (b) Find the median. Food 150° 60° Study Rent 70° 50° 30° Transportation Miscellaneous
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 315 Vedanta Excel in Mathematics - Book 8 Answers 1. Sets Exercise : 1.1 Creative Section 4 and 5. Show to your teacher. 6. a) F12 = {1, 2, 3, 4, 6, 12} b) F18 = {x : x is a factor of 18} c) P = {1, 2, 3, 6}, n(P) = 4 7. a) M4 = {4, 8, 12, 16, 20}, M7 = {7, 14, 21, 28, 35} b) M4 = {x : x is a multiple of 4, x ≤ 20} M7 = {y : y is a multiple of 7, y ≤ 35} c) A = { } or f d) A is a null set 8. a) P = {2, 3, 5, 7}, Q = {2, 4, 6, 8} b) C = {2} c) C is a unit set 9. a) A = {4, 6, 8, 9, 10}, A = {x : x is a composite number, x < 12} b) B = {2, 4, 6, 8, 10}, B = {y : y is a multiple of 2, y ≤ 10} c) Z = {–1, 0, 1}, Z = {integers between –2 and 2} d) P = {prime numbers less than 10}, P= {x : x is a prime number, x < 10} e) A = {s, c, h, o, l}, (A) = 5 f) B = {1, 2, 3, 4, 6, 12}, n(B) = 6 10. Please complete your project work and discuss in the class. Then, show to your teacher. Exercise : 1. 2 Creative Section 4. Show to your teacher. 5. a) A = {3, 5, 15}, B = {2, 4, 8, 16} b) disjoint sets c) 6. a) P = {2, 4, 6, 8}, Q = {3, 6, 9} b) overlapping sets c) 7. a) A = {Dinesh, Pinky, Ram}, B = {Rosy, Gopal, Arjun, Ram} b) P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, Q = {1, 2, 3, 4, 5} c) X = {1, 2, 3, 4, 6, 8, 12 ,24}, Y = {1, 2, 4, 8, 16} 8. a) A = {Sanju, Binita, Harka, Kishan} B = {Binita, Rekha, Kishan, Gopal, Tashi} c = {Hari, Shaswat, Anamol, Rekha, Tashi} b) Equivalent c) disjoint d) overlapping e) D = {Binita, Rekha, Kishan, Gopal, Tashi, Hari, Shaswat, Anamol} 9. a) E and P b) E and O c) E and P, O and P d) A = {2, 3, 4, 5, 6, 7, 8} e) B = {1, 2, 3, 5, 7, 9} 10. a) C = {Bimala, Manoj, Raju, Gopal, Lakhan} V = {Gopal, Lakhan, Prem, Hari, Shiva, Kamala} A = {Raju, Harka, Rahim, Tshiring, Prem} b) n(C) = 5, n(V) = 6, n(A) = 5, C ~ A c) (i) {Gopal, Lakhan} (ii) {Raju} (iii) {Prem} 3 5 15 2 4 8 16 2 4 8 3 6 9 Kishan Hari Shaswat Gopal Anamol Rekha Tashi Binita B C 4 6 8 3 2 7 5 E P 1 3 9 5 2 7 O P
Vedanta Excel in Mathematics - Book 8 316 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 11. a) P = {2, 4, 6, 8, 10}, Q = {4, 8, 12, 16, 20} b) n(P) = 5, n(Q) = 5 c) {4, 8} d) {2, 6, 10} e) {12, 16, 20} 12. Please complete your project work individually or in groups and discuss the result in your class. Then, show to your teacher. Exercise : 1. 3 Creative Section 5. Show to your teacher. 6. a) No b) Yes c) improper subset 7. a) (i) 4 (ii) {mango}, {apple}, {mango, apple}, f (iii) {mango, apple} b) (i) 8 (ii) {b}, {a}, {l}, {b, a}, {b, l}, {a, l}, {b, a, l}, f (iii) {b, a, l} is improper subset c) (i) P = {2, 3, 5, 7} (ii) 16 (iii) {2}, {3}, {5}, {7} (iv) {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7} (v) {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7} (vi) {2, 3, 5, 7} 8. a) set A b) set B c) 9. a) P = {1, 2, 3, 4, 5, 6, ... 20}, Q = {1, 3, 5, 7, 9}, R = {3, 6, 9, 12, 15, 18} P is universal set, Q and R are subsets b) proper subsets c) {1, 3, 5, 6, 7, 9, 12, 15, 18} 10. a) U = {1, 2, 3, ..., 17}, U = {natural numbers less than 18}, U = {x : x is a natural number, x < 18} A = {1, 2, 3, 4, 6, 12}, A = {factors of 12}, A = {y : y is a factor of 12} B = {1, 2, 3, 6, 9, 18}, B = {factor of 18}, B = {p : p is a factor of 18} b) U = {1, 2, 3, ..., 15}, U = {natural numbers less than 16}, U = {q : q is a natural number, q < 16} C = {2, 4, 6, 8, 10, 12}, C = {even numbers less than 13}, C = {z : z is an even number, z < 13} D = {3, 6, 9, 12, 15}, D = {the first five multiples of 3}, D = {x : x is a multiple of 3, x ≤ 15} c) U = {1, 2, 3, ..., 15}, U = {natural numbers upto 15}, U = {y : y is a natural number, y ≤ 15} E = {2, 4, 6, 8, 10}, E = {even numbers less than 11}, E = {p : p is an even number, p < 11} F = {1, 3, 5, 7, 9}, F = {odd numbers less than 10}, F = {q : q is an odd number, q < 10} d) P = {1, 2, 3, 6} e) Q = {6, 12} f) disjoint 11. a) n(U) = 15 b) A = {Hem, Sundar, Maya, Dipak, Sita, Mahesh } V = {Dipak, Sita, Mahesh, Shiva, Goma, Bikram, Keshav, Mina} c) {Dipak, Sita, Mahesh} d) {Hem, Sundar, Maya} e) {Shiva, Goma, Bikram, Keshav, Mina} f) {Kedar, Laxmi, Gopal, Mohan} 12. a) n(U) = 36, n(S) = 18, n(M) = 14 b) 7 c) d) (i) 11 (ii) 7 (iii) 11 13. and 14. Please complete your project work individually or in groups and discuss the result in your class. Then, show to your teacher. 1 2 4 86 3 9 10 5 7 A B 1 Q R 3 9 6 12 15 18 5 7 11 7 7 11 S M U
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 317 Vedanta Excel in Mathematics - Book 8 Answers 2. Number system in different bases Exercise : 2.1 Creative Section 4. a) 243 b) 111100112 5. a) 11112 b) 15 6. a) 2 × 102 + 7 × 101 + 6 × 100 b) 3 × 103 + 8 × 102 + 1 × 101 + 6 × 100 c) 5 × 104 + 4 × 103 + 2 × 101 + 7 × 100 d) 8 × 105 + 9 × 103 + 5 × 100 e) 7 × 106 + 4 × 102 + 9 × 100 7. a) 10012 b) 10102 c) 10112 d) 11002 e) 100102 f) 1101112 g) 11111002 h) 110110002 i) 1011010012 j) 1111010102 8. a) 9 b) 10 c) 23 d) 42 e) 61 f) 87 g) 103 h) 203 i) 238 j) 443 9. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 2.2 Creative Section 4. a) 135 b) 205 c) 1025 d) 2425 e) 10215 f) 20125 g) 32345 h) 40315 i) 112325 j) 221245 5. a) 9 b) 13 c) 23 d) 59 e) 116 f) 238 g) 290 h) 586 i) 898 j) 1947 6. a) 101012 b) 21 c) 415 7. a) 32415b) 446 c) 1101111102 8. a) 245 b) 525 c) 2215 d) 10002 e) 10001112 f) 1100001012 9. a) 123105 , 11101110112 b) 11110112 > 1435 ; 75 c) 110112 < 3225 ; 60 10. Shashwat 11 and 12. Please complete your project work and compare with your friends. Then show to your teacher. 3. Real Numbers Exercise : 3.1 Creative Section 3. a) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 b) 12° C 4. a) -14 -13-12-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1011 12 13 14 b) 16° C 5. a) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 b) 20 feet c) 15 feet 6. a) Let's complete your project work and discuss in the class. Then, show to your teacher. Exercise : 3.2 Creative Section 4. a) 3 5 , 5 3 (i) 3 5 (ii) 5 3 b) 6 c) Real numbers 5. Show to your teacher. 6. No 7. No 8. a) 9 b) 10 9. a) 22 7 b) p 10. a) 4 is rational, 15 is irrational b) 4 > 15 11. Both are rational numbers, 27 3 = 3 12.a) irrational b) irrational 13. a) irrational b) rational c) rational 14.a) 2 2 b) 5 2 c) 6 3 d) 6 6 e) 2 2 f) 4 3 g) – 10 h) –3 7 15.a) 2 b) 6 3 c) 3 5 d) –3 10 16.a) 6 b) 2 15 c) 6 14 d) 20 30 e) 3 f) 5 g) 4 2 h) 2 2 17.a) 8 2 m b) irrational c) 8 sq. m d) rational 18.and 19. Please complete your project work and discuss in the class. Then, show to your teacher.
Vedanta Excel in Mathematics - Book 8 318 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Exercise : 3.3 Creative Section 3. a) 3.24 × 108 b) 6.12 × 1011 c) 7.48 × 1010 d) 3 × 10–6 e) 5.4 × 10–8 f) 9.36 × 10–10 4. a) 1010 sq.cm b) 2 × 106 c.c c) 10–4 sq.m d) 10–10 sq.km e) 10–6 cu.m f) 2.592 × 106 seconds 5. a) 2,100 kg b) 2.1 × 103 kg c) 2.1 × 106 g 6. a) 19,90,00,000 grams b) 1.99 × 108 grams 7. a) 0.000005 metre b) 0.0005 cm, 0.005 mm 8. a) 6,371 km b) 6.371 × 106 m, 63,71,000 m 9. a) 1.48 × 108 km b) 1.48 × 1011 m 10. a) 9.46 × 1012 km c) 9.46 × 1015 m 11.a) 2700 b) 45000 c) 756000 d) 8450000000 e) 0.025 f) 0.0056 g) 0.0000495 h) 0.0000000783 12.a) 4.4 × 103 b) 9.2 × 104 c) 1.1 × 106 d) 1.61 × 1010 e) 2.94 × 103 f) 2.4 × 103 g) 6.3 × 105 h) 1.405 × 107 i) 8.1 × 104 j) 2.78 × 10–4 k) 4.45 × 10–5 l) 5.314 × 10–3 13.a) 5.44 × 105 b) 1.053 × 108 c) 3.015 × 103 d) 1.944 × 10–12 14.a) 2.7 × 105 b) 8 × 10–3 c) 5.37 × 1012 d) 1.1 × 105 e) 3.2 × 102 f) 3.7 × 103 15.a) 1.86 × 104 litres b) 1.62 × 104 litres c) 1.2348 × 106 m d) 40 tanks e) 1.076 × 109 km 16.and 17. Please complete your project work and discuss in the class. Then, show to your teacher. 4. Ratio and Proportion Exercise : 4.1 Creative Section 3. a) (i) Show to your teacher (ii) antecedent is 1, consequent is 2 (iii) Rs 18,000 b) (i) 45 : 15 (ii) 3 : 1 (iii) three times c) (i) 2 : 5 (ii) 70 g 4. a) 4 : 3 b) 2 : 1 c) 4 : 5 d) 1 : 2 5. a) (i) 2 : 1 (ii) 1 : 3 b) (i) 3 : 2 (ii) 2 and 3 (iii) 3 : 4 6. a) (i) 90° (ii) 40° (iii) 5 : 4 b) (i) 180° (ii) 75° (iii) 5 : 7 7. a) 2 : 3 b) 3 : 10 c) 14 : 15 d) 5 : 2 8. a) (i) 2 : 3 (ii) 2 : 4 : 3 b) (i) 4 : 5 (ii) 4 : 6 : 5 9. a) 2 b) 3 c) 15 d) 14 10. a) 12 b) 100 m c) 12 boys d) (i) Rs 12,000 (ii) Rs 9,000 11. a) Rs 40, Rs 60 b) Rs 80,000 ; Rs 1,00,000 c) 600 g, 360 g 12. a) 4.5 km b) 3 cm 13. a) 30°, 60°, 90° b) 48°, 72°, 96°, 144° c) 36°, 54° d) 60°, 120° e) 40°, 50° 14. a) (i) Rs 2x (ii) Rs 4x (iii) 1 : 2 : 4 (iv) Rs 200, Rs 100, Rs 50 b) Rs 48,000 ; Rs 24,000 ; 8,000 c) (i) 18, 30 (ii) 9 : 15 : 4 : 2 15. a) Rs 40,000; Rs 60,000, Rs 80,000 b) (i) Rs 45,000; Rs 90,000; Rs 1,35,000, Rs 1,80,000 (ii) Rs 18,000 ; Rs 36,000 ; Rs 54,000, Rs 72,000 16. a) (i) 9 (ii) 3 b) (i) 5x (ii) 4x + 6 and 5x + 6 (iii) 24, 30 c) 70, 50 17. a) (i) 3x years (ii) (x + 5) years and (3x + 5) years (iii) 3x + 5 x + 5 = 5 2 (iv) 45 years, 15 years b) 12 years, 21 years c) 24 years , 18 years d) 30 years, 8 years 18. a) 7 cm b) (i) 24 m (ii) 80 m (iii) 384 m2 c) (i) 2(l + b) (ii) 36 m, 27 m (iii) 972 m2 d) (i) l×b (ii) 15 cm, 12 cm (iii) 54 cm 19.Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 4.2 Creative section 4. a) and c) are in proportion. 5. a) 6 b) 12 c) 6 d) 9 6. a) (i) 8 (ii) 12 (iii) 18 (iv) 21 b) (i) 4 (ii) 15 (iii) 16 (iv) 36 c) (i) 7 (ii) 8 (iii) 5 (iv) 9 d) (i) 5 (ii) 20 (iii) 6 (iv) 8 7. a) (i) 9 (ii) 8 (iii) 7 b) (i) 24 (ii) 48 (iii) 15 8. a) (i) 15 kg (ii) direct proportion (iii) Rs 1,800 b) (i) direct proportion (ii) 18 c) (i) direct proportion (ii) 7 hours 9. a) (i) direct proportion (ii) direct proportion (iii) inverse proportion (iv) 12 passengers b) 15 passengers 10. a) 12 workers b) 30 days c) 10 hours d) 3 more e) 40 days f) 120 days g) 15 days 11. a) (i) inverse proportion (ii) 45 days (iii) 27 (iv) 12 hours b) 6 days 12.Please complete your project work and compare with your friends. Then show to your teacher.
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 319 Vedanta Excel in Mathematics - Book 8 5. Unitary Method Exercise : 5.1 Creative section 4. a) (i) Rs 80, Rs 960 (ii) 3 kg b) (i) 8 hours (ii) 30 km/hr c) (i) 40 km/l (ii) 8l 5. a) (i) 1 14 (ii) 1 2 (iii) 6 7 parts of work b) (i) 3 4 parts of work (ii) 4 days c) (i) 2 hours (ii) 1 120 part (iii) 1 4 part d) (i) 1 3 (ii) 500l 6. a) (i) 48 km (ii) 32 km b) Rs 22,500 (ii) Rs 2,700 7. a) (i) Rs 160 (ii) Rs 550 (iii) Rs 880 b) Rs 720 8. a) (i) 4 h 30 min (ii) 54 minutes b) 8 days c) 10 days d) 4 workers e) 30 days f) 36 days g) 25 days 9. a) (i) 2400 MB (ii) 3 minutes b) (i) 2 minutes (ii) 15 MB per second 10.a) (i) 240 days (ii) 16 days (iii) 24 days b) 36 days c) 24 11. a) (i) direct proportion (ii) 12 days (iii) inverse proportion (iv) 15 days b) (i) 54,000 (ii) 10 h 12. a) 5 day b) 28,000 l c) 5 h 13, 14, 15. Please complete your project work and compare with your friends. Then show to your teacher. 6. Simple Interest Exercise : 6.1 Creative section 4. a) Rs 80 b) Rs 2,500 c) 4 years d) 12% e) Rs 1,500, Rs 300 f) Rs 3,000, Rs 2,250 5. a) 18% b) Rs 900 c) 34,000 6. a) Rs 9 b) Rs 8,100 7. a) (ii) PTR 100 (iii) Rs 1,584 (iv) Rs 11,484 b) Rs 20,250 c) Rs 11,853 8. a) (i) R = I × 100 P × T (ii) 11 % p.a. (iii) Rs 891 (iv) Rs 3,591 b) 10% c) 12% 9. a) Rs 3,500 b) Rs 6,400 c) 3 years 10. a) Rs 8,000 b) 7 years c) 6 months 11. a) Rs. 3,000 b) Rs 4,545 c) Rs 5,000 12. a) Rs 7,700 b) Rs 15,000 13. a) 3 years b) 2 years 14. a) 5% b) 4 years, 4% p.a. 15. Please complete your project work and compare with your friends. Then show to your teacher. 7. Profit and Loss Exercise : 7.1 Creative section 3. Rs 48, 10% b) Rs 32, 5% c) Rs 690 d) Rs 1,872 e) Rs 1,750 f) Rs 2,100 4. a) (i) Rs 720 (ii) 10% b) (i) Rs 60 (ii) 4% c) profit : 10% d) gain : 12.5% e) loss : 5% f) profit : 11.43% g) gain : 17.5% 5. a) (i) Rs 23 (ii) Rs 483 b) (i) Rs 152 (ii) Rs. 1,368 c) Rs 7,245 d) Rs 1,42,048 e) Rs 38 each f) Rs 108 each 6. a) Rs 400 b) Rs 700 c) Rs 75 each 7. a) (i) Rs 4,800 (ii) Rs 5,280 b) Rs 63,000 8. a) (i) Rs 9,200 (ii) Rs 10,000 b) (i) Rs 5,500 (ii) Rs 5,000 c) (i) Rs 2,160 (ii) Rs 1,800 9. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 7.2 Creative Section 4. a) 5% b) Rs 153, 10% c) Rs 47, Rs 893 d) 10% e) Rs 96, Rs 896 5. a) (i) Rs 96 (ii) Rs 864 b) Rs 2,125 c) Rs 2,720 6. a) Rs 200 b) Rs 600 7. a) (i) Rs 160 (ii) Rs 1,440 (iii) Rs 1,300 b) (i) Rs 900 (ii) Rs 5,100 (iii) Rs 4,600 c) Rs 350 8. a) (i) Rs 300 (ii) Rs 1,200 (iii) Rs 156 (iv) Rs 1,356 b) Rs 1,695 c) Rs 4,400 9. a) (i) Rs 1,000 (ii) Rs 100 (iii) Rs 900 (iv) Rs 1,017 b) Rs 2,346 c) Rs 9,492 10. a) (i) Rs 1,600 (ii) Rs 2,000 b) Rs 5,000 11. Please complete your project work and compare with your friends. Then discuss in the class.
Vedanta Excel in Mathematics - Book 8 320 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 8. Laws of Indices Exercise : 8.1 Creative Section 5. a) 26 b) 39 c) (5x) –5 d) (xy) –4 e) 3 (ax) 7 f) x3 g) 35 h) 55 i) 1 24 j) 1 y14 k) x l) 1 p2(a+b) 6. a) x6 b) p4 q6 c) 1 x4 y8 d) a3 b3 e) x4 y4 f) x g) y h) xy i) ( x y )3 j) x 7. a) 64 b) 27 c) 5 d) 1 7 e) 3 2 f) 2 g) 3 h) 4 i) 2 j) 1 2 k) 1 27 l) 4 5 m) 3 2 n) 9 25 o) 4 9 8. a) 2 b) 1 4 c) 5 d) 4 e) 8 f) 2 g) 2 h) 1 3 i) 1 3 j) 1 4 k) 4 5 l) 2 m) 2 n) 2 o) 3 9. a) 8 b) 27 c) 4 d) 1 5 e) 5 f) 48 g) 4 9 h) 3 10. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) 1 i) 1 j) 1 k) 1 l) 1 11. a) 1 b) 2 c) 4 d) 5 e) 3 f) 5 g) 10 h) 6 12. a) 16 b) 108 c) 3 d) 16 e) – 3 8 f) –27 4 g) –1 48 13. a) 8 9 b) 1024 14. a) (i) 2 (ii) 4 (iii) 8 (iv) 32 (v) 256 (vi) 1024 b) (i) 3 (ii) 9 (iii) 27 (iv) 81 (v) 243 15. Please complete your project work and compare with your friends. Then discuss in the class and show to your teacher. 9. Algebraic Expressions Exercise : 9.1 Creative Section 4. Answer the questions yourself and show to your teacher. 5. a) 3 b) 4 c) 2 d) 5 e) 3 f) 6 6. a) (i) 15 (ii) 16 b) (i) 400 (ii) 180 (iii) 340 c) (i) 154 (ii) 44 d) (i) 25, 25 (ii) 1, 1 (iii) 125, 125 (iv) 1, 1 v) 5, 5 (vi) 13 7. a) 20 b) 121 c) (i) 220 (ii) 528 (iii) 770 Exercise : 9.2 Creative Section 3. a) (x + 2)2 = x2 + 4x + 4 b) (x + 3)2 = x2 + 6x + 9 c) (x + y)2 = x2 + 2xy + y2 d) (x – 1)2 = x2 – 2x + 1 e) (x – 2)2 = x2 – 4x + 4 f) (x – y)2 = x2 – 2xy + y2 4. a) (x + 1) (x – 1) = x2 – 1 b) (x + 2) (x – 2) = x2 – 4 c) (x + y) (x – y) = x2 – y2 5. a) (i) 4a2 + 4a + 1 (ii) x2 – 6xy + 9y2 (iii) a2 – 2 + 1 a2 (iv) x2 + 2 + 1 x2 b) (i) 9x2 – 6x + 1 (ii) 4y2 + 2 + 1 4y2 6. a) (x + 1)2 b) (a – 2b)2 c) (3p + 2q)2 7. a) 8xy b) 4xy c) 6xy d) 20xy e) 42ab 8. a) a2 – 9 b) 4x2 – 1 c) 16 – 9p2 d) 4x2 – 9y2 e) x4 – y4 f) 4x4 – 25y4 g) a2 + 2ab + b2 – c2 h) x2 + 2xz + z2 – y2 i) p2 – 2pr + r2 – q2 j) x4 – y4 k) x4 – 16 l) 16a4 – y4 9. a) 399 b) 2499 c) 6396 d) 9996 10. a) 19 b) 20 c) 7 d) 51 11. a) (i) 7 (ii) 5 b) (i) 23 (ii) 21 c) (i) 18 (ii) 20 d) (i) 38 (ii) 40 12. a) 2(a2 + b2 ) b) 4xy c) 8p2 + 18 d) 12xy e) 2(x2 + 1 x2 ) f) – 8 a 13. a) 3 b) 2.2 c) 3.9 d) 1.8 14. a) (i) 2 (ii) 4 (iii) 8 (iv) 256 (vi) 1024 b) (i) 3 (ii) 9 (iii) 27 (iv) 8 (v) 243 15. Please complete your project work and compare with your friends. Then discuss in the class and show to your teacher. Exercise : 9.3 Creative Section 3. a) 2a (x + 2y) b) 3x (2x – 3) c) 4px2 (2x + 3) d) 2mx (2x + m – 3) e) 3b2 y2 (3y – 2b + 5)
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 321 Vedanta Excel in Mathematics - Book 8 f) –3a2 (3a3 + 2ax2 + 5 ) g) (2x + 3) (x + 4) h) (y – 4) (2y – 3) i) (x + 2y) (7x + y) 4. a) 150 b) 800 c) 0.058 5. a) (x + y) (a + b) b) (p + q) (x – y) c) (x + 2) (x + 3) d) (x – 4) (x – 3) e) (3x + 2y) (2x – y) f) (x2 + y2 ) (a + b) g) (x + y) (x2 + x + 1) h) (x – z) (x – y) i) (x + y) (a – 2x) j) (x + 3) (x – y) k) (a – x ) (ax + b2 ) l) (ac – b) (bc – a) 6. a) 3ab and a + 2 b) x + 2 and x + y c) x + 3 and x + 4a 7. a) 2a and 2x + 3y b) (x + y), (2x + y), (6x + 4y) c) 4x + 10y Exercise : 9.4 Creative Section 3. a) (x + 6) (x – 6) b) (a + 7) (a – 7) c) (5 + y) (5 – y) d) ( 4 + 9p ) (4 – 9p) e) x(x + 4) (x – 4) f) 2 (a + 6) (a – 6) g) 5p (p + 4) (p – 4) h) 3y (y + 3) (y – 3) i) 5a (a + 2b) (a – 2b) j) 2x3 y (2x + 3y) (2x – 3y) k) (5x + 1 7 ) (5x – 1 7 ) l) ( 1 2x + 1 9 ) ( 1 2x – 1 9 ) 4. a) (x2 + 4) (x + 2) (x – 2) b) (a2 + 9) (a + 3) (a – 3) c) (x2 + y2 ) (x + y) (x – y) d) (4p2 + q2 ) (2p + q) (2p – q) e) (9x2 + 25) (3x + 5) (3x – 5) f) 2 (4y2 + 9) (2y + 3) (2y – 3) g) (a4 + b4 ) (a2 + b2 ) (a + b) (a – b) h) (16x4 + y4 ) (4x2 + y2 ) (2x + y) (2x – y) 5. a) (a – b + 3) (a – b – 3) b) (x + y + 5) (x + y – 5) c) (a2 + b2 + 2) ( a2 + b2 – 2) d) (a2 + ab – b2 ) (a2 – ab – b2 ) e) (4 + x + y) (4 – x – y) f) (7 + a – b) (7 – a + b) g) (x + y + 5) (x – y + 1) h) (a + b – 1) (a + b – 9) 6. a) (x2 + xy + y2 ) (x2 – xy + y2 ) b) (x2 + x + 1) (x2 – x + 1) c) (x2 + xy + 4y2 ) (x2 – xy + 4y2 ) d) (a2 + 3ab + b2 ) (a2 – 3ab + b2 ) e) (x2 + 3xy + 3y2 ) (x2 – 3xy + 3y2 ) f) (a2 + 2ab + 5b2 ) (a2 – 2ab + 5b2 ) g) (2x2 + 3xy + 3y2 ) (2x2 – 3xy + 3y2 ) h) (5x2 + 4xy + 2y2 ) (5x2 – 4xy + 2y2 ) i) (2a2 + 5ab + 3b2 ) (2a2 – 5ab + 3b2 ) 7. a) 400 b) 2160 c) 1820 d) 201 e) 2499 f) 6396 g) 9999 h) 9991 8. a) 135 cm2 b) 299 cm2 c) 189 m2 d) 476 m2 e) 756 sq. ft. f) 1375 m2 Exercise : 9.5 Creative Section 4. b) (x + 2) (x + 2) = x2 + 4x + 4 c) (x + 3) (x + 1)=x2 + 4x + 3 d) (x + 3) (x + 2)=x2 +5x + 6 5. a) 2, 5 b) – 3, – 6 c) 8, – 4 d) – 6, 5 6. a) (x + 1) (x + 2) b) (x + 2) (x + 5) c) (x + 3) (x + 4) d) (x + 3) (x + 5) e) (x + 2) (x + 4) f) (x + 4) (x + 5) g) (x + 3) (x + 6) h) (x + 5) (x + 6) 7. a) (x – 1) (x – 2) b) (x – 2) (x – 3) c) (x – 1) (x – 5) d) (x – 4) (x – 6) e) (x – 3) (x – 7) f) (x – 2) (x – 6) g) (x – 4) (x – 9) h) (x – 3) (x – 10) 8. a) (x – 1) (x + 2) b) (x – 1) (x + 3) c) (x – 2) (x + 4) d) (x – 3) (x + 6) e) (x – 2) (x + 7) f) (x – 5) (x + 8) g) (x – 7) (x + 12) h) (x – 5) (x + 9) 9. a) (x + 1) (x – 2) b) (x + 2) (x – 3) c) (x + 3) (x – 5) d) (x + 4) (x – 7) e) (x + 2) (x – 6) f) (x + 5) (x – 8) g) (x + 4) (x – 11) h) (x + 5) (x – 13) 10. a) x (x + 7) (x + 8) b) x(x + 3) (x + 14) c) x2 (x + 3) (x – 7) d) x2 (x – 5) (x – 9) e) x (x – 2) (x + 15) f) x2 (x – 2) (x + 4) g) x3 (x – 6) (x – 12) h) x3 (x – 6) (x + 17) 11. a) (x + y + 2) (x + y + 3) b) (a + b + 11) (a + b + 3)
Vedanta Excel in Mathematics - Book 8 322 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur c) (p – q – 6) (p – q – 5) d) (x – y + 2) (x – y – 11) 12. a)(a + 4) unit, (a + 2) unit, (4a + 12) unit b) (x2 + x – 42) sq. units 13. and 14. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 9.6 Creative Section 3. a) (x + 3)2 b) (x + 4)2 c) (x + 5)2 d) (a + 6)2 e) (a + 7)2 f) (a + 8)2 g) (x – 2)2 h) (x – 1)2 i) (p – 9)2 j) (p – 10)2 k) (p – 12)2 l) (x – 15)2 4. a) (2a + 1)2 b) (2a + 5)2 c) (3a + 1)2 d) (3x + 2)2 e) (3a + 4)2 f) (4x + 3)2 g) (3x – 4)2 h) (5x – 8)2 i) (4a – 5)2 j) (7p – 1)2 k) (6 – 5p)2 l) (12 – 5x)2 5. a) (x + 1) (2x + 3) b) (x + 1) (2x + 5) c) (x + 2) (3x + 2) d) (x + 1) (3x + 1) e) (x + 1) (3x + 2) f) (x+ 3) (3x + 1) g) (2x + 1) (2x + 5) h) (x + 1) (4x + 7) i) (x – 1) (2x – 1) j) (x – 2) (3x – 4) k) 4 (x – 1) (x – 1) i) (2 – x) (4 – 9x) m) (1 – x) (13 – 4x) n) (x – 2) (6x – 7) o) (a – 1) (3a – 17) 6. a) (x – 1) (2x + 3) b) (x – 2) (3x + 7) c) (x + 2) (4x – 3) d) (x + 3) (5x – 2) e) (x + 2) (6x – 1) f) (x + 4) (7x – 3) g) (2x + 3) (2x – 1) h) (2x + 5) (3x – 2) i) (a – 4) (2a + 3) j) (a + 1) (3a – 8) k) (2a + 1) (2a – 9) l) (2a + 3) (a – 5) m) (4x + 3) (2x – 7) n) (2x + 1) (3x – 7) o) (x – 3) (5x + 2) 7. a) (x + 2y ) (2x + y) b) (x + y) (3x + 2y) c) (x + y) (2x – 3y) d) (2x + 3y) (4x – 5y) e) (3x – 4y) (5x + y) f) (4a – 3b) ( 6a – 5b) g) (3a – 2b) (5a – 6b) h) 2(a – 2b) (7a – 5b) i) (a – 6b) (8a + 3b) 8. a) (5x + y 5 ) 2 b) (7a – b 7 ) 2 c) (2x + 1 2x) 2 d) (3p – 1 6p) 2 9. a) (a + b + c + d) (a + b – c – d) b) (p – q + r + s) (p – q – r – s) c) (a + b + c) (a – b – c) d) (x + y – z) (x – y + z) 10. a) (x + y – 2) (2x + 2y – 5) b) (a + b – 2) (3a + 3b – 4) c) (p – q – 3) (2p – 2q + 3) d) (2m – 2n + 1) (3m – 3n – 7) 11. a) (i) (x + 4) unit (ii) (4x + 16) unit (iii) 2,500 sq unit b) (i) (2x + 1) ft. (ii) (2x2 +8x+6) sq. ft 12. and 13. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 9.7 Creative Section 3. a) 2xy b) 3a2 b2 c) pxy d) 4x2 e) 3x2 y2 f) 5abc 4. a) a + 7 b) a(a + b) c) x + 3 d) 2(x + 2) e) x(x + 2y) f) 2x – 3 g) a + 2 h) x + 1 i) (a + 3) j) 2x + 3 k) x – 5 l) 2x – 3 m) a + 2 n) a – 3 o) 2x – 3 p) 3x – 5 q) (x – 1) r) x (x – 5) 5. a) x + 2 b) x – 3 c) x – 2 d) x – 1 e) 1 f) 2x – 1 6. a) 2x3 b) x + 3 7. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 9.8 Creative Section 3. a) 4x2 y2 b) 6a3 b3 c) 12x3 y3 d) 6x4 y4 e) 24x5 y5 f) 84x3 y3 z3 4. a) a2 x (x + 1) b) 2x2 (x +2) c) 6a2 b (a + 2b) d) abx2 (a + b) e) 6x2 (x + 2) f) 2 (a2 – 4) g) 6a (a2 – 1) h) xy (x2 – 25) i) 7a2 x2 (a2 – x2 ) j) xy (x2 – y2 ) k) 2x (4x2 – 1) l) (x2 – 4) (x + 3) m) (x – 2) (x2 – 9) n) 2x (2x – 3) (x2 – 25) o) a (a + 3) (4a2 – 9) p) (x + 3) (x + 4) (x + 5) q) (a + 3) (a – 4) (a – 5) r) (a – 2) (a – 6) (a + 7) s) (2a + 1) (a2 – 4) t) (x2 – 16) (3x – 4) u) (x – 1) (3x + 1) (4x + 3) v) (x + 3) (4x2 – 12x + 9)
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 323 Vedanta Excel in Mathematics - Book 8 5. a) m(m2 – 4) (m + 1) b) 4(x2 – 25) (x + 2) c) (a2 – b2 ) (a + b) (2a – b) d) (x + 2) (x2 – 4) (x + 6) e) (x – 3) (x2 – 9) (x – 7) f) (x + 2) (x + 4) (x2 – 9) g) (a + 5) (a2 – 1) (a2 – 36) h) (2a + 1) (a2 – 4) (9a2 – 1) 6. and 7. Please complete your project work and compare with your friends. Then show to your teacher. 10. Rational Expressions Exercise : 10.1 Creative Section 3. a) x 2 b) 3 4x c) x 2y d) 2a2 3b2 e) 3 2ab2 f) p 4q g) 4q3 3p h) – 2x2 3z i) –bc 3a j) 3p2 4q2 r2 4. a) 1 2x b) 1 2y c) x x – 4 d) 1 x – y e) 3 x – 3 f) a + b g) x 2x – 5 h) 5a 3b i) 1 x + 2y j) 1 a2 + b2 k) 1 x+3 l) x x – 4 m) a+2 a– 7 n) a (a – 6) a – 3 o) 2(a + 5) a + 9 p) x – 7 x + 7 q) x + 6 x – 1 r) x – 4 x + 2 s) x + 5 x – 3 t) x + 2 x(2x + 1) u) x – 3 x – 1 Exercise : 10.2 Creative Section 2. a) 3x3 2y2 b) 2xy 5ab c) 12xp 5aby d) a 4b e) 20ab 9xy f) 4x2 y2 z2 3pqr 3. a) x2 b2 ayz2 b) 3xz ac c) 2x4 y4 3a6 b5 d) 3a7 4xc 4. a) 2 b) 4 3 (x + 3) c) 1 d) 1 e) xy(2a + 3b) 2 (x – y) f) 5x + 4y x + 2 g) a (2x + 9y) 1 + 2a h) a + 2 a – 1 i) (x + 2) (a – 4) (x – 3) (a – 1) j) 4xy – z2 k) – x (x + 2y) y (x + y) l) a(a + 4) (a – 2) (a – 4) (a + 2) m) a – 5 a – 1 Exercise : 10.3 Creative Section 2. a) 1 b) 3 c) 1 b d) p + q e) 1 x + y f) 1 a+b g) x – 2 x+2 h) 1 a+5 i) x x +2 j) a – 1 a – 2 3. a) 2x x2 – 1 b) 1 (p – 2) (p – 1) c) 4a 4a2 – 1 d) ab (a2 + b2 ) a2 – b2 e) x + y x2 y2 f) 1 x + 2 g) –x x2 – 1 h) – 10x x2 – 25 i) 2 x2 – a2 j) 2 x + 2 k) x2 + y2 (x + y) (x2 – y2 ) l) 6xy 9x2 – y2 m) –1 2a + 3b n) – 1 (a – b) (b – c) o) x + 4 x2 – 1 p) 2 – 7a (a + 2) (a2 – 4) q) 1 – 5a (a – 1) (a2 – 1) r) x + 4 x (x + 1) (x + 2) 4. a) 2 x (x + 1) (x + 2) b) 1 x2 – 1 c) 2x x + 2 d) x+5 x+1 e) 8a + 1 a2 – 1 f) 1 g) 1 h) 1 i) 6xy x2 – y2 j) 8xy3 x4 – y4
Vedanta Excel in Mathematics - Book 8 324 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 5. a) 3 (x – 3) (x – 5) b) 9 (x + 2) (x – 3) (x – 4) c) 1 (x – 2) (x – 3) d) 0 e) 1 (x – 2) (x – 3) f) 3x – 7 (x – 2) (x – 3) g) – 1 y – 3 11. Equation and Graph Exercise : 11.1 Creative Section 4. a) 5 b) 2 c) 3 d) 1 e) 4 f) 2 g) 12 h) 5 i) –2 j) – 7 k) –1 l) 2 m) – 1 3 n) 5 0) 0 5. a) 18 b) 21 c) 22 6. a) 15, 17, 19 b) 24, 26, 28 7. a) 16, 21 b) 32, 24 c) 19, 25 d) Rs 55, Rs 80 e) Rs 60, Rs 130 f) Rs 40, Rs 100 g) Rs 45, Rs 60 8. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 11.2 Creative Section 3. a) (4, 3) b) (3, 5) c) (4, –2) d) (7, 3) 4. Solve the given equations graphically and show to your teacher. a) (3, 1) b) (2, 5) c) (4, 5) d) (7, 3) e) (– 3, – 4) f) (2, 5) g) (5, 9) h) (1, – 2) (i) (3, 2) j) (5, 3) k) (4, 3) l) (2, 1) m) (– 2, – 4) n) (6, – 3) 5. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 11.3 Creative Section 4. a) 2, 1 b) 3, 2 c) 6, – 1 d) 5, 1 e) 9, – 1 f) 6, 3 g) 3, 4 h) 2, 5 i) 8, 5 j) 4, 1 5. a) 3, 1 b) 4, 2 c) 3, 5 d) 4, 10 e) 8, 3 f) 4, 5 g) 7, 6 h) 5, 8 i) – 3, 7 j) 2, 5 6. a) 11, 7 b) 22, 17 c) 30, 24 d) 18, 12 7. a) 15, 21 b) Rs 75, Rs 25 c) 18 chairs, 15 people 8. a) 34 years, 6 years b) 12 years, 8 years c) 36 years, 12 years d) 40 years, 8 years e) 39 years, 9 years f) 40 years, 15 years 9. a) 24 m, 12 m b) 35 m, 25 m 10. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 11.4 Creative Section 3. a) 2, 3 b) 1, 2 c) –3, 4 d) 4, –5 e) 9, 3 f) – 2, –11 g) 0, – 3 h) 0, 8 i) 0, 7 4. a) ±1 b) ± 2 c) ± 3 d) ± 4 e) ± 5 f) ± 6 g) ± 7 h) ± 8 i) ± 9 j) ± 10 k) ± 3 2 l) ± 5 4 m) ± 7 6 n) ± 10 9 o) ± 8 3 p) ± 11 8 5. a) 1, 2 b) 2, 3 c) 1, 4 d) 3, 4 e) ± 6 f) ± 2 g) 3, 6 h) – 2, – 3 i) – 4, – 3 j) – 2, – 7 k) – 6, – 7 l) – 9, – 5 m) 14, – 5 n) – 3, 13 o) 5, – 2 p) – 10, 4 q) – 15, 5 r) – 7, 4 6. a) 0, 1 2 b) 0, 1 3 c) 0, 1 4 d) 0, 3 2 e) 0. 4 3 f) 0, 5 4 g) – 1, – 1 2 h) 1, 1 2 i) – 3, 7 2 j) 2, – 3 2 k) 2, – 4 3 l) 2, 4 3 m) 2, – 1 3 n) – 3, – 1 3 o) ± 3 2 p) 6, 2 5 q) – 4 3 , – 3 2 r) 2 3 , –1 2 7. a) 4, 8 b) 6, 9 c) 10, 6 d) 12, 7 e) 3, 6 f) 3, 4 g) 8, 5 h) 5, 7 i) 3 j) 4 8. a) 9 years, 5 years b) 4 years, 9 years 9. a) 12 m, 8 m b) 10 m, 7 m 10. Please complete your project work and compare with your friends. Then show to your teacher.
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 325 Vedanta Excel in Mathematics - Book 8 Answers 12. Transformation Exercise : 12.1 Creative Section 3. a) A' (– 6, – 3) b) P' (– 5, – 1) c) E' (– 6, 1 ) B' (– 2, – 1) Q' (– 3, – 6) F' (– 2, 1) C' (– 1, – 6) R' (– 2, 0) G' (– 1, 4) D' (1, – 4) K' (2, 1) H' (– 5, 5) E' (5, – 2) L' (0, 4) P' (3, 6) F' (7, – 6) M' (6, 3) Q' (1, 1) R' (5, 2) S' (7, 4) 4. a) A' (– 4, 6), B' (– 1, 4), C' (– 5, 2) O' (0, 0) Q' (– 2, – 4), R' (– 6, – 3) b) E' (6, 3), F' (2, 6) G' (3, 1) K' (2, 0), L' (4, – 5), M' (1, – 3) c) A' (5, 4) , B' (3, 1), C' (1, 3), D' (0, 6) P' (– 1, – 6), Q' (5, –9), R' (– 6, – 1) S' (– 2, – 2) 5. a) P' (3, – 6), Q' (5, – 9) , R' (4, – 2) b) A' (– 2, – 4) B' (3, – 3), C' (– 5, – 7) c) K' (– 1, 4), L' (– 6, 3), M' (– 2, – 4) d) D' (3, 5), E' (2, – 6) , F' (4, 1) 6. a) A' (– 1, 4), B' (– 4, 7), C' (– 6, 3) b)P' (2, 3), Q' (4, – 6), R' (5, 5) c) E' (– 3, – 7), F' (– 5, – 2), G' (0, – 3) d) X' (– 1, 4), Y' (– 4, – 5), Z' (– 2, 6) 7. a) A' (0, 4), B' (– 3, 0), C' (2, – 5) b) P' (– 7, – 8), Q' (– 4, 6), R' (6, 2) 8. a) W' (4, – 2), X' (– 3, – 6), Y' (– 1, 4), W" (– 4, – 2), X" (3, – 6), Y" (1, 4) b) R' (– 7, – 2), S' (4, – 5), T' (6, 3) R" (– 7, 2), S" (4, 5), T" (6, – 3) 8. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 12.2 Creative Section 2. Rotate the given figures through the given angles about the given centre of ration and show to your teacher. 3. (i) Anti clock direction a) A' (– 6, 1) B' (– 8, 4), C' (– 2, 2) P' (11 – 1), Q' (3, – 4), R' (6, – 2) b) D' (0, – 3), E' (– 4, – 1), F' (– 5, – 5) K' (2, 2), L' (2, 5), M' (6, 3) c) A' (2, – 3), B' (5, – 5), C' (4, – 1) E' (– 6, 4), F' (– 3, 0), G' (– 1, 3) (ii) Clockwise direction a) A' (6, – 1), B' (8, – 4), C' (2, – 2) P' (– 1, 1), Q' (– 3, 4) R' (– 6, 2) b) D' (0, 3), E' (4, 1), F' (5.5) K' (– 2, – 2), L' (– 2, – 5), M' (–6, 2) c) A' (– 2, 3), B' (– 5, 5), C' (– 4, 1) E' (6, – 4), F' (3, 0), G' (1, – 3) 4. a) A' (– 5, – 3), B' (– 1, – 5) , C' (– 2, – 1) P' (1, – 6), Q' (5, – 3), R' (2, – 2) b) D' (4, – 4), E' (0, – 4), F' (2, – 1) K' (3, 0), L' (5, 4), M' (1, 3) c) A' (– 1, 1), B' (– 2, 5), C' (– 5, 1) E' (– 5, – 5), F' (– 1, – 5), G' (– 3, –1) 5. a) (i) P' (– 2, – 4), Q' (– 7, 3), R' (6, – 1) (ii) P' (2, 4), Q' (7, – 3), R' (– 6, 1) b) A' (5, 8), B' (– 2, 3), C' (2, – 9) 6. a) K' (4, – 1), L' (– 5, 3), M' (–2, –5) K" (– 4, 1), L" (5, – 3), M" (2, 5) b) D' (1, – 4), E' (6, 0), F' (0, 5) D" (1, 4), E" (6, 0), F" (0, – 5) 7. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 12.3 2. Displace the given figures and show to your teacher
Vedanta Excel in Mathematics - Book 8 326 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers 3. a) A' (3, 7) b) B' (2, –1) c) C' (3, 2) d) D' (–7, –4) 4. a) P' (10, 11), Q' (13, 7), R' (12, 13) b) A' (–2, 11), B' (–6, 6), C' (–12, 10), D' (–9, 13) 5. a) 3 units right and 5 units up b) 5 units left and 3 units down 6. a) M' (–1, 2), M" (–7, 11) b) A' (3, 0), B' (5, –6), C' (–2, –9), A" (–2, 1), B" (0, –5), C" (–7, –8) 7. Please complete your project work and compare with your friends. Then show to your teacher. 13. Geometry- Lines and Angles Exercise : 13.1 Creative Section 2. a) 130° b) 72°, 108° c) 42° d) 40°, 50° e) 36°, 144° f) 24°, 66° g) 75°, 105° 3. a) 122° b) 55° c) 20° d) 36° e) 20° f) 120° g) 144° h) 26° 4. a) 40°, 60°, 80° b) 30°, 60°, 90° c) 18°, 36°, 54°, 72° d) 88°, 88°, 92° e) 45°, 45°, 135°, 135° f) 90°, 120°, 150° g) 103°, 115°, 142° h) 35°, 105°, 40°, 40°, 65°, 75° 5. a) 60°, 120° b) 45°, 135° 6. a) and b) Show to your teacher 7. Show to your teacher Exercise : 13.2 Creative Section 3. a) 75°, 75°, 75° b) 100°, 100°, 80° c) 130°, 50° d) 100°, 80°, 80°, 100° e) 85°, 95°, 95° f) 115°, 65°, 115°, 65°, 115° g) 112°, 112°, 78° 102° h) 75°, 60°, 120°, 105°, 105°, 120° 4. a) 20° b) 25° c) 45° d) 50° e) 36° f) 60° g) 30° h) 35° 5. a) 88°, 92° b) 130°, 50°, 50° c) 70°, 70°, 70° d) 96°, 84°, 84°, 84° e) 60°, 60°, 120° f) 90°, 90° g) 60°, 70°, 50°, 120°, 50° h) 40°, 80°, 60° i) 50°, 70°, 60° j) 30°, 28° k) 64° l) 280° m) 70°, 290° n) 75° o) 52° p) 291° 6. a) 80°, 100°, 80° b) 110°, 70°, 70°, 70° c) 110°, 110°, 40°, 30° d) 75°, 55°, 50°, 50° 7. a) 70° b) x = 40° , y = 140°, z = 40° 8., 9. and 10. Show to your teacher 11. Please complete your project work and discuss in the class. Then show to your teacher. 14. Geometry- Triangle Exercise : 14.1 Creative Section 2. a) 100° b) 50°, 100° c) 45°, 60°, 75° d) 36°, 54°, 90° e) 30°, 60° f) 120° 3. a) 90° b) 35°, 105° c) 56°, 61°, 63° d) x = y = 64° e) a = b = 45° f) x = 50°, y = z = 65° g) x = 72°, y = 108° h) x = 86°, y = 38° 4. a) a = 70°, b = 65°, c = 70° b) x = 58°, y = 52°, z = 70° c) x = 85°, y = 55°, z = 95° d) x = 29°, y = 58° , 2x = 58° e) x = 65°, y = 55°, z = 60° f) x = 65°, y = z = 57.5° g) x = 72°, y = 66°, z = 42° h) x = 105°, y = 45° i) x = 54°, y = 29° j) p = q = r = 40° k) a = 50°, b = 40°, c = 90°, d = 30°, e = 150° l) x = 90°, y = 80°, z = 43° 5. and 6. Show to your teacher Exercise : 14.2 Creative Section 4. and 5. Show to your teacher 6. a) S.A.S. axiom, 5 cm b) A.S.A. axiom, 6.5 cm c) S.S.S. axiom, 50° d) R.H.S. axiom, 45° 7. a) x = 3.2 cm, ∠A = ∠ P = 85°, ∠ B = ∠ Q = 35°, AB = PQ = 4.5 cm, AC = PR = 3.2 cm , BC = QR = 5.5 cm b) x = 2.5 cm, ∠ W = ∠ D = 20°, ∠ Y = ∠ F = 45° , ∠ X = ∠ E = 115°
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 327 Vedanta Excel in Mathematics - Book 8 Answers XY = EF = 2.5 cm, XW = DE = 3.5 cm, WY = DF = 6 cm. c) x = 2 cm, ∠ Q = ∠ K = 90°, ∠ R = ∠ L = 52°, ∠ P = ∠ M = 38°, QR = LK = 2.8 cm, RP = LM = 5.2 cm QP = MK = 4.3 cm. d) x = 4.5 cm, ∠ A = ∠ D = 64°, ∠ B= ∠ F = 86°, ∠ C = ∠ E = 30°, AB = DF = 3.1 cm, BC = EF = 6.5 cm, AC = DE = 7 cm. 8. Show to your teacher. 9. Please complete your project work and discuss in the class. Exercise : 14.3 Creative Section 2. a) PQ = 6 cm, ∠ A = 75°, ∠ Q = 55° b) x = 16 cm, y = 20 cm 3. a) AB = 6 cm b) x = 5.6 cm c) AB = 37.5 cm, AE = 8 cm d) BD = 2 cm e) ∠QXY = 80° , QX = 9 cm f) 3.2 cm. Exercise : 14.4 Creative Section 2. Show to your teacher 3. a) (ii) x = 6 cm b) (ii) AC = 6 cm c) (ii) 16 m 15. Geometry - Quadrilateral and Regular Polygon Exercise : 15.1 Show to your teacher. Exercise : 15.2 Creative Section 3. a) 55°, 125°, 125° b) 120°, 60°, 60° c) 105°, 105°, 75°, 75° d) 70°, 110°, 110°, 70° e) 55°, 125°, 125° f) 80° 100°, 100°, 80°, 80° g) 105°, 75°, 75° 75° h) 115°, 115°, 30°, 35° i) 80°, 80°, 100° j) 45°, 105°, 105° k) 40°, l) 70°, 70°, 70°, 70°, 110° m) 75°, 75°, 105° n) 110°, 70° o) 56°, 124°, 84°, 84° p) 45°, 135°, 30°, 15° 4. a) 10 cm, 17 cm, 17 cm b) 3 cm, 7 cm, 7 cm c) 2 cm, 7 cm, 7 cm d) 5 cm, 10 cm, 10 cm. 5. and 6. Show to your teacher 7. and 8. Please complete your project work and discuss in the class. Exercise : 15.3 Creative Section 2. a) 360° b) 540° c) 720° d) 900° e) 1080° f) 1260° g) 1440° h) 1800° 3. a) 90° b) 108° c) 120° d) 128.57° e) 135° f) 140° g) 144° h) 150° 4. a) 90° b) 72° c) 60° d) 51.42° e) 45° f) 40° g) 36° h) 30° 5. a) 5 b) 6 c) 7 d) 8 e) 10 6. a) 4 b) 5 c) 6 d) 8 e) 9 7. a) 5 b) 6 c) 8 d) 9 e) 10 8. a) 115° b) 70° c) 107° d) 115° e) 235° f) 79° g) 97° h) 60° i) 111.67° 9. a) 150° b) 102° c) 36° d) 90° 10. Please complete your project work and discuss in the class. 16. Coordinates Exercise : 16. 1 Creative Section 3. a) 5 cm b) 8 cm c) 5 cm d) 15 cm 4. a) yes b) yes c) no d) no e) yes f) no 5. a) yes b) no c) yes 6. a) 24 cm b) 20 cm c) 13 cm 7. a) x = 5 cm, y = 12 cm b) x = 5 cm, y = 10 cm 8. a) 8 m b) 12 m c) Shyam, by 20 m d) (i) 12 m (ii) 28 m e) (i) 6 cm (ii) 5 cm, 4 cm, 3 cm
Vedanta Excel in Mathematics - Book 8 328 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers Exercise : 16. 2 Creative Section 2. a ) 2 2 units b) 5 units c) 2 10 d) 5 2 e) 10 units f) 4 units 3. a) 10 units b) 15 units c) 5 2 units 4. a) 2 units, 200 km b) 45 km c) 4 5 units, 360 km d) 348.5 km 5. a) (i) 15 units (ii) 30 units (iii) Show to your teacher b) 20 units, Show to your teacher 6. Show to your teacher 7. Show to your teacher 8. a) a = 1 b) a = 12 9. and 10. Please complete your project work and discuss in the class. Then show to your teacher. 17. Area and Volume Exercise : 17.1 Creative Section 2. a) 35 cm2 b) 24 cm2 c) 63 cm2 d) 116 cm2 e) 81 cm2 f) 9 cm2 g) 9 3 cm2 h) 8 3 cm2 i) 192 cm2 j) 36 cm2 k) 100 cm2 l) 60 cm2 m) 24 cm2 n) 26 cm2 o) 45 cm2 p) 102 cm2 q) 66 cm2 r) 55 cm2 3. a) 100 cm2 b) 247.5 cm2 c) 540 cm2 d) 375 cm2 e) 357 cm2 f) 122.5 cm2 4. a) 40 cm2 b) 135 cm2 c) 96 cm2 d) 119 cm2 e) 360 cm2 f) 240 cm2 g) 108 cm2 h) 43 cm2 i) 88 cm2 j) 140 cm2 k) 84 cm2 l) 100 cm2 5. a) (i) 10 m (ii) 100 m2 (iii) Rs 7,000 b) Rs 50,000 6. a) (i) 1120 m2 (ii) Rs 1,00,800 b) (i) 25 m (ii) 800 m2 (iii) Rs 60,000 c) Rs 9000 d) Rs 16,000 e) Rs 28080 7. a) 2820 m2 , Rs 3,10,200 b) 2184 ft2 , Rs 24,024 8. Please complete your project work and discuss in the class. Then show to your teacher. Exercise : 17.2 Creative Section 3. a) 44 cm, 154 cm2 b) 88 cm, 616 cm2 4. a) 22 cm b) 616 cm2 c) 44 m, 154 m2 5. a) (i) 440 m (ii) 15400 m2 b) (i) 110 m (ii) 962.5 m2 6. a) 2640 m b) 2420 m c) 3 rounds 7. a) 3.5 km b) 280 ft c) 70 cm 8. a) (i) 21 cm (ii) 1386 cm2 b) 61600 m2 c) 22 m d) 132 m 9. a) 7 cm b) 42 cm 10. a) 42 cm2 b) 1039.5 cm2 c) 286 cm2 d) 82 cm2 e) 42 cm2 f) 38.5 cm2 g) 87.43 cm2 h) 168 cm2 i) 462 cm2 11. Please complete your project work and discuss in the class. Then show to your teacher. Exercise : 17.3 Show to your teacher. 5. Please complete your project work and discuss in the class. Then show to your teacher. Exercise : 17.4 Creative Section 4. a) 54 cm2 b) 288 cm2 c) 179 cm2 5. a) 100 cm2 b) 2350 cm2 , 1350 cm2 6. a) 64 cm3 b) 300 cm3 c) 868 cm3 7. a) (i) 125 cm3 (ii) 91.125 cm3 (iii) 512 cm3 (iv) 15.625 m3 b) (i) 60 cm3 (ii) 150000 cm3 (or 0.15 m3 ) (iii) 315000 cm3 (or 0.315 m3 ) (iv) 960000 cm3 (or 0.96 m3 ) 8. a) (i) l 2 , (ii) 10 cm, (iii) 1000 cm3 b) 15 cm, 225 cm2 c) 1728 l 9. a) (i) l × b × h (ii) 60,000 cm3 (iii) 60 l b) 4,200 l 10. a) (i) 15 cm (ii) 900 cm2 (iii) Rs 450 b) 50 cm c) 1.5 m d) (i) 40,000 cm3 (ii) 20 cm 11. a) (i) 1, 20, 000 cm3 (ii) 8,000 cm3 (iii) 15 b) 225 c) 30,300 d) 10,000 12. a) 136 cm3 b) 510 cm3 c) 81 cm3 d) 345 cm3 e) 90 cm3 f) 756 cm3 13. a) 24 cm3 b) 48 m2 c) 12 m, 8m, 4 m d) 30 cm, 15 cm, 10 cm 14. Please complete your project work and compare with your friends. Then show to your teacher. 18. Symmetry, Design and Tessellation Show to your teacher.
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 329 Vedanta Excel in Mathematics - Book 8 Answers 19. Bearing and scale drawing Exercise : 19.1 Creative Section 4. a) 045° b) 135° c) 180° d) 225° e) 270° f) 315° 5. a) 060° b) 090° c) 125° d) 160° e) 210° f) 230° g) 270° h) 318° 6. A : 040° , B : 100°, C : 200° , D 230° , E: 325° 7. a) 220° b) 258° c) 295° d) 330° e) 020° f) 090° g) 105° h) 150° 8. a) 235° b) 350° c) 275° d) 262° e) 235° 9. Please complete your project work and discuss in the class. Exercise : 19.2 3. a) 100 m b) 300 m c) 4.2 km d) 110 km 4. a) 12 cm b) 65 cm c) 8 cm d) 8 cm 5. a) 22.5 m b) 32 km c) 470 km 6. Show to your teacher 7. Please complete your project work and compare with your friends. Then show to your teacher. 20. Statistics Exercise : 20.1 3. and 4. Show to your teacher 5. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 20.2 Creative Section 2. Show to your teacher 3. a) Items Food Rent Study Transportation Miscellaneous Rs 4,500 2,100 1,800 1,500 900 b) Items Wages Fuel Raw materials Rent Rs 60,000 16,000 48,000 20,000 c) (i) 6720 (ii) B secured the least votes of 4,800. d) Items Cotton Nylon Polyster Other (i) (%) 25 15 40 20 (ii) (Kg) 12.5 7.5 20 10 4. Please complete your project work and discuss in the class. Then show to your teacher. Exercise : 20.3 Creative Section 3. a) 13 years b) 9 c) 70 4. a) 10 b) 20 c) 20 5. a) 10 years b) 7 c) 7 6. a) 45 mm b) 43.2 kg c) 10 7. a) 5 b) 10 8. a) 34.25 b) 10.8 years c) 62.17 cm 9. a) 28.5 b) 70.75 c) 46.5 d) 38.6 e) Rs 400 f) 33.3 years 10. a) 28.6 b) 45 11. Please complete your project work and compare with your friends. Then show to your teacher. Exercise : 20.4 Creative Section 2. a) (i) 35 (ii) 30 (iii) 24 b) 52 kg c) 32 3. a) 2 b) 8 4. a) (i) 12 (ii) 10 (iii) 14 b) (i) 39 (ii) 34 (iii) 77.5 5. a) (i) 7 (ii) 21 b) 18 years c) Rs 1,500 to Rs 2,000 d) 7 e) Rs 150 6. a) 50 b) 20 c) Rs 65 7. a) 36 b) 80 c) 27, 37 8. a) (i) 120 cm (ii) 90 cm (iii) 30 cm b) 32 c) 10 9. Please complete your project work and compare with your friends. Then show to your teacher.
Vedanta Excel in Mathematics - Book 8 330 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur MODEL QUESTION SET Mathematics Class: 8 F.M.: 50 Time: 2 hours Attempt all the questions. 1. Given that a set A = {1, 2, 3}. The sets B and C are defined as B = {y: y = 2x, x ∈ A} C = {z: z = x + 3, x ∈ A} Answer the following questions. (1 + 1 + 1) (a) Write any one proper subset of set A that consists of only two elements. (b) Show the sets A and B in a Venn-diagram. (c) State whether the sets A and C are overlapping or disjoint sets. Give reason. 2. Suresh is a student of class VIII. He writes his monthly fee in the expanded form as: 4 × 54 +3 × 53 + 1 × 52 + 0 × 51 + 0 × 50 . Answer the following questions. (1 + 2 + 2) (a) Write the short form of his fee in quinary number. (b) Convert his monthly fee in to binary number. (c) Find his yearly fee in scientific notation. 3. In a shop, the marked price of a computer and a mobile are in the ratio of 3: 2. The marked price of a computer is Rs 60,000. Ramesh buys a computer from the shop after allowing 10% discount. But, due to financial crisis, he sells the computer to Pemba for Rs 48,600. (1 + 1 + 1 + 2) (a) What is the marked price of the mobile in the shop? (b) Find the discount amount. (c) At what price does Ramesh buy the computer? (d) What percent of loss did he bear in the computer? 4. Mr. Lama is a farmer. He borrows a loan of Rs 2,40,000 for upgrading his poultry farm from Agricultural Development Bank at the rate of 10% p.a. for 2 years 6 months. Answer the following questions. (1 + 2 + 1) (a) Write the formula to find the simple interest. (b) How much simple interest does he pay after 2 years 6 months? (c) How much amount will he have to pay to clear the debt?
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 331 Vedanta Excel in Mathematics - Book 8 5. Rohit draws the outline of the compound of his house. The compound is in the shape of a parallelogram. There is a circular swimming pool and a house. Study the given map and answer the following questions. (1 +1 + 2 + 1) (a) Find the area of the land occupied by the house. (b) Find the area of the swimming pool. (c) Which one is more spacious, the land occupied by house or by the swimming pool? Find by how many square meters is the area more? (d) What is the total area of his land within the compound? 6. Answer the following questions. (1 + 2) (a) Which of the laws is called product law of indices? (i) am × an = am + n (ii) am ÷ an = am – n (iii) (am) n = amn (iv) ao = 1 (b) Simplify: (xa+ b) a – b × (x b + c) b – c ×(x c + a) c – a 7. Two given algebraic expressions are x2 + 6x + 8 and x2 – 4. Answer the following questions. (2 + 2) (a) Find the highest common factors of these expressions. (b) Prove that: 1 x2 + 6x + 8 + 2 x2 – 4 = 3 x2 + 2x – 8 8. Swornim was ready for school and waiting for his school bus. During his waiting period, he saw some cars and motorcycles running in the road. The total number of people driving the cars and motorcycles are 7 and total number of wheels is 20. Answer the following questions. (1 + 2) (a) If the number of cars is x and the number of motorcycle is y, make the pair of simultaneous equations according to the given information. (b) Find the number of cars and motorcycles by solving the equations by graphical method. 9. In the given figure, AB // CD and CG = GH. If ∠AGC = 50o , ∠GCH = (x + 10)o and ∠GHD = y, study the figure and answer the following questions. (a) Which is the corresponding angle of ∠BGH? (b) Find the value of x and y. (c) If the triangle GCH were a regular triangle, what would be the measurement of its each exterior angle? A D C G 25 m 50 m 14 m 30 m 20 m Swimming Pool House F E H B A B G F E D y H 50° (x + 10)° C (1 + 2 + 1) Model Questions
Vedanta Excel in Mathematics - Book 8 332 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 10. A rectangle ABCD with length BC = 8 cm and width CD = 6 cm are given alongside. Answer the following questions. (2 + 3 + 1) (a) Find the length of its diagonal BD. (b) Construct the rectangle ABCD with the given measurements. (c) Are the triangles ABD and BCD congruent? Give reason with appropriate axiom. 11. The vertices of a triangle ABC are A (1, 1), B (0, 4) and C (-3, 4). Answer the following questions. (3 + 2) (a) Reflect the triangle ABC about x-axis and preset both the triangles on the same graph paper. (b) Find the length of side BC by using distance formula. 12. The table given below shows the number of students of a school from class 6 to 10. Class VI VII VIII IX X No. of students 45 35 40 34 26 Answer the following questions. (2 + 1) (a) Represent the data in a pie chart. (b) Find the classes which have the students more than the class-wise average number of students. A B C D6 cm 8 cm Model Questions Students' Evaluation System (Class 6 to class 8) (a) Internal (Formative) Evaluation Students’ individual portfolio should be managed with the marks under the following headings. S.N. Measures of evaluation Weightage 1. Participation in classroom activities 4 2. Project work 36 3. Terminal examinations 10 Total 50 (b) External (Summative) Evaluation Summative evaluation covers 50% of the entire weightage of the course intended by the curriculum. The items should be chosen from all the chapters of the course of a session for the test paper prepared to the external evaluation. The test should contain knowledge, skill, application and higher ability based items by following specification grid. Specification Grid for External Evaluation F.M.: 50 Time: 2 hours S.N. Area Working hours Knowledge Understanding Application Higher ability Total no. of items Total no. of questions Total Marks No. of items Marks No. of items Marks No. of items Marks No. of items Marks 1. Set 10 1 1 1 1 2 3 1 1 5 2 3 2. Statistics 10 3 3. Arithmetic 45 2 2 3 4 3 5 2 3 10 3 14 4. Mensuration 15 1 1 1 1 1 2 1 1 4 1 5 5. Algebra 30 2 2 1 2 2 4 1 2 6 3 10 6. Geometry 50 2 2 2 4 2 6 2 3 8 3 15 Total 160 8 8 8 12 10 20 7 10 33 12 50