Page 1 GYAN SAGAR PUBLI SCHOOL SUMMATIVE ASSESSMENTI, 201516 CLASSX, MATHERMATYICS V9Y3QA1 Time allowed: 3 hours Maximum Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. SectionA comprises of 4 question of 1 mark each; SectionB comprises of 6 question of 2 marks each; Section C comprises of 3 marks each and Section D comprises of 11 question of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. Section A Question number 1 to 4 carry one mark each Q.1 In D E W , ? ABEW. If AD=4 cm, DE=12 cm and DW=24 cm, then find the value of DB. Q.2 In a A B C , ? write tan A B 2 ? in terms of angle C. Q.3 If 3 sin =cos , ? ? find the value of 2 3 cos 2 cos 3 c os 2 ? ? ? ? ? Q.4 If the mode of the data: 3, 5, 8, 9, 8, 12, 7, 12 and x is 8, find the value of x. Section B Question number 5 to 10 carry two mark each Q.5 Prove that 5 2 ? is an irrational number Q.6 Use Euclid division algorithm to find if the following pair of numbers is coprime : 121, 573 Q.7 On dividing 2 2 x 3x x 3 , ? ? ? by a polynomial g(x), the quotient and the remainder were 2 x x 1 ? ? and 2 x 5 ? ? respectively. Find g(x). Q.8 R and S are points on the sides DE and EF respectively of a DE F ? such that ER=5 cm, RD=2.5 cm, SD=1.5 cm and FS=3.5 cm. Find whether RSDF or not. Q.9 Express sinA and cosA in terms of cotA Q.10 Given below is a frequency distribution table showing daily income of 50 workers of a factory: Page 2 GYAN SAGAR PUBLI SCHOOL SUMMATIVE ASSESSMENTI, 201516 CLASSX, MATHERMATYICS V9Y3QA1 Time allowed: 3 hours Maximum Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. SectionA comprises of 4 question of 1 mark each; SectionB comprises of 6 question of 2 marks each; Section C comprises of 3 marks each and Section D comprises of 11 question of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. Section A Question number 1 to 4 carry one mark each Q.1 In D E W , ? ABEW. If AD=4 cm, DE=12 cm and DW=24 cm, then find the value of DB. Q.2 In a A B C , ? write tan A B 2 ? in terms of angle C. Q.3 If 3 sin =cos , ? ? find the value of 2 3 cos 2 cos 3 c os 2 ? ? ? ? ? Q.4 If the mode of the data: 3, 5, 8, 9, 8, 12, 7, 12 and x is 8, find the value of x. Section B Question number 5 to 10 carry two mark each Q.5 Prove that 5 2 ? is an irrational number Q.6 Use Euclid division algorithm to find if the following pair of numbers is coprime : 121, 573 Q.7 On dividing 2 2 x 3x x 3 , ? ? ? by a polynomial g(x), the quotient and the remainder were 2 x x 1 ? ? and 2 x 5 ? ? respectively. Find g(x). Q.8 R and S are points on the sides DE and EF respectively of a DE F ? such that ER=5 cm, RD=2.5 cm, SD=1.5 cm and FS=3.5 cm. Find whether RSDF or not. Q.9 Express sinA and cosA in terms of cotA Q.10 Given below is a frequency distribution table showing daily income of 50 workers of a factory: Daily income of Workers (in rs) 200205 250300 300350 350400 400450 Number of workers 60 10 12 08 14 Change this tabel to a ‘less than type’ cumulative frequency table. Section C Question number 11 to 20 carry three mark each Q.11 During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both both and the same number of pencils and crayons, how many of each would you need to buy? Q.12 Solve the following pair of linear equations by the cross multiplication method: x 2 y 2 ? ? x 3y 7 ? ? Q.13 Find the zeros of the polynomial 3 x 7 x 6 ? ? . Q.14 Check graphically whether the following pair of linear equations is consistent. If yes, solve it graphically: 2 x 5 y 0 ? ? , x y 0 ? ? Q.15 Prove that area of the equilateral triangle described on the side of a square is half of the area of the equilateral triangle described on its diagonal. Q.16 In the figure of A B C , ? D divides CA in the ration 4 : 3 If DEBC, then find ar (BCDE) : ar ( A B C ? ) Q.17 If b c o s a ? ? , then prove that b a c os e c c ot b a ? ? ? ? ? ? Q.18 Prove the identity: 2 2 2 2 c os ta n 1 ta n s i n ? ? ? ? ? ? ? Q.19 In a study on asthmatic patients, the following frequency distribution was obtained. Find the average (mean) age at the detection. Age at detection (in years) 09 1019 2029 3039 4049 Number of patients 12 25 13 10 5 Page 3 GYAN SAGAR PUBLI SCHOOL SUMMATIVE ASSESSMENTI, 201516 CLASSX, MATHERMATYICS V9Y3QA1 Time allowed: 3 hours Maximum Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. SectionA comprises of 4 question of 1 mark each; SectionB comprises of 6 question of 2 marks each; Section C comprises of 3 marks each and Section D comprises of 11 question of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. Section A Question number 1 to 4 carry one mark each Q.1 In D E W , ? ABEW. If AD=4 cm, DE=12 cm and DW=24 cm, then find the value of DB. Q.2 In a A B C , ? write tan A B 2 ? in terms of angle C. Q.3 If 3 sin =cos , ? ? find the value of 2 3 cos 2 cos 3 c os 2 ? ? ? ? ? Q.4 If the mode of the data: 3, 5, 8, 9, 8, 12, 7, 12 and x is 8, find the value of x. Section B Question number 5 to 10 carry two mark each Q.5 Prove that 5 2 ? is an irrational number Q.6 Use Euclid division algorithm to find if the following pair of numbers is coprime : 121, 573 Q.7 On dividing 2 2 x 3x x 3 , ? ? ? by a polynomial g(x), the quotient and the remainder were 2 x x 1 ? ? and 2 x 5 ? ? respectively. Find g(x). Q.8 R and S are points on the sides DE and EF respectively of a DE F ? such that ER=5 cm, RD=2.5 cm, SD=1.5 cm and FS=3.5 cm. Find whether RSDF or not. Q.9 Express sinA and cosA in terms of cotA Q.10 Given below is a frequency distribution table showing daily income of 50 workers of a factory: Daily income of Workers (in rs) 200205 250300 300350 350400 400450 Number of workers 60 10 12 08 14 Change this tabel to a ‘less than type’ cumulative frequency table. Section C Question number 11 to 20 carry three mark each Q.11 During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both both and the same number of pencils and crayons, how many of each would you need to buy? Q.12 Solve the following pair of linear equations by the cross multiplication method: x 2 y 2 ? ? x 3y 7 ? ? Q.13 Find the zeros of the polynomial 3 x 7 x 6 ? ? . Q.14 Check graphically whether the following pair of linear equations is consistent. If yes, solve it graphically: 2 x 5 y 0 ? ? , x y 0 ? ? Q.15 Prove that area of the equilateral triangle described on the side of a square is half of the area of the equilateral triangle described on its diagonal. Q.16 In the figure of A B C , ? D divides CA in the ration 4 : 3 If DEBC, then find ar (BCDE) : ar ( A B C ? ) Q.17 If b c o s a ? ? , then prove that b a c os e c c ot b a ? ? ? ? ? ? Q.18 Prove the identity: 2 2 2 2 c os ta n 1 ta n s i n ? ? ? ? ? ? ? Q.19 In a study on asthmatic patients, the following frequency distribution was obtained. Find the average (mean) age at the detection. Age at detection (in years) 09 1019 2029 3039 4049 Number of patients 12 25 13 10 5 Q.20 Find the mean and median for the following data: Class 04 48 812 1216 1620 Frequency 3 5 9 5 3 Section D Question number 21 to 31 carry four mark each Q.21 Show that 2 n 1 ? is divisible by 8, if n is an odd positive integer. Q.22 A boat goes 30 km upstream and 20km downstream in 7 hours. In 6 hours, it can go 18 km upstream and 30 km downstream. Determine the speed of the stream and that of the boat in still water. Q.23 Find the values of a and b so that 4 3 2 x x 8 x ax b ? ? ? ? is divisible by 2 x 1 ? . Q.24 The ratio of income of two persons A and B are in the ration 3:4 and the ratio of their expenditures is 5:7 If their saving are Rs.15000 annually, find their annual incomes. What value will be promoted if expenditure is under control? Q.25 In ABC, ? from A and B altitudes AD and BE are drawn. Prove that A D C BEC . ? ? ? Is and A D B AD C ? ? ? ? Q.26 The sides of triangle are 30 cm, 70 cm and 80 cm. If an altitude is dropped upon the side of length 80 cm, then find the length of larger segment cut off on this side. Q.27 If cos(A+B)=0 and cot(AB)= 3 , then evaluate : (i) cosA. cosB – sinA. sinB (ii) c os t B cot A cot A cotB+1 ? Q.28 If m = cosA – sinA and n = cosA + sinA, show that 2 2 2 2 m 1 2 m n  n ? ? ? secA. cosecA = ( co s t A t a n A ) 2 ? ? Q.29 If se c a m s ec ? ? and s ec a n cosec ? ? , show that 2 2 2 2 m n n cos ec . ? ? ? Q.30 Find the median and mode of the following data and then find the mean from the empirical relationship between them : Class interval Frequency Page 4 GYAN SAGAR PUBLI SCHOOL SUMMATIVE ASSESSMENTI, 201516 CLASSX, MATHERMATYICS V9Y3QA1 Time allowed: 3 hours Maximum Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D. SectionA comprises of 4 question of 1 mark each; SectionB comprises of 6 question of 2 marks each; Section C comprises of 3 marks each and Section D comprises of 11 question of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. Section A Question number 1 to 4 carry one mark each Q.1 In D E W , ? ABEW. If AD=4 cm, DE=12 cm and DW=24 cm, then find the value of DB. Q.2 In a A B C , ? write tan A B 2 ? in terms of angle C. Q.3 If 3 sin =cos , ? ? find the value of 2 3 cos 2 cos 3 c os 2 ? ? ? ? ? Q.4 If the mode of the data: 3, 5, 8, 9, 8, 12, 7, 12 and x is 8, find the value of x. Section B Question number 5 to 10 carry two mark each Q.5 Prove that 5 2 ? is an irrational number Q.6 Use Euclid division algorithm to find if the following pair of numbers is coprime : 121, 573 Q.7 On dividing 2 2 x 3x x 3 , ? ? ? by a polynomial g(x), the quotient and the remainder were 2 x x 1 ? ? and 2 x 5 ? ? respectively. Find g(x). Q.8 R and S are points on the sides DE and EF respectively of a DE F ? such that ER=5 cm, RD=2.5 cm, SD=1.5 cm and FS=3.5 cm. Find whether RSDF or not. Q.9 Express sinA and cosA in terms of cotA Q.10 Given below is a frequency distribution table showing daily income of 50 workers of a factory: Daily income of Workers (in rs) 200205 250300 300350 350400 400450 Number of workers 60 10 12 08 14 Change this tabel to a ‘less than type’ cumulative frequency table. Section C Question number 11 to 20 carry three mark each Q.11 During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both both and the same number of pencils and crayons, how many of each would you need to buy? Q.12 Solve the following pair of linear equations by the cross multiplication method: x 2 y 2 ? ? x 3y 7 ? ? Q.13 Find the zeros of the polynomial 3 x 7 x 6 ? ? . Q.14 Check graphically whether the following pair of linear equations is consistent. If yes, solve it graphically: 2 x 5 y 0 ? ? , x y 0 ? ? Q.15 Prove that area of the equilateral triangle described on the side of a square is half of the area of the equilateral triangle described on its diagonal. Q.16 In the figure of A B C , ? D divides CA in the ration 4 : 3 If DEBC, then find ar (BCDE) : ar ( A B C ? ) Q.17 If b c o s a ? ? , then prove that b a c os e c c ot b a ? ? ? ? ? ? Q.18 Prove the identity: 2 2 2 2 c os ta n 1 ta n s i n ? ? ? ? ? ? ? Q.19 In a study on asthmatic patients, the following frequency distribution was obtained. Find the average (mean) age at the detection. Age at detection (in years) 09 1019 2029 3039 4049 Number of patients 12 25 13 10 5 Q.20 Find the mean and median for the following data: Class 04 48 812 1216 1620 Frequency 3 5 9 5 3 Section D Question number 21 to 31 carry four mark each Q.21 Show that 2 n 1 ? is divisible by 8, if n is an odd positive integer. Q.22 A boat goes 30 km upstream and 20km downstream in 7 hours. In 6 hours, it can go 18 km upstream and 30 km downstream. Determine the speed of the stream and that of the boat in still water. Q.23 Find the values of a and b so that 4 3 2 x x 8 x ax b ? ? ? ? is divisible by 2 x 1 ? . Q.24 The ratio of income of two persons A and B are in the ration 3:4 and the ratio of their expenditures is 5:7 If their saving are Rs.15000 annually, find their annual incomes. What value will be promoted if expenditure is under control? Q.25 In ABC, ? from A and B altitudes AD and BE are drawn. Prove that A D C BEC . ? ? ? Is and A D B AD C ? ? ? ? Q.26 The sides of triangle are 30 cm, 70 cm and 80 cm. If an altitude is dropped upon the side of length 80 cm, then find the length of larger segment cut off on this side. Q.27 If cos(A+B)=0 and cot(AB)= 3 , then evaluate : (i) cosA. cosB – sinA. sinB (ii) c os t B cot A cot A cotB+1 ? Q.28 If m = cosA – sinA and n = cosA + sinA, show that 2 2 2 2 m 1 2 m n  n ? ? ? secA. cosecA = ( co s t A t a n A ) 2 ? ? Q.29 If se c a m s ec ? ? and s ec a n cosec ? ? , show that 2 2 2 2 m n n cos ec . ? ? ? Q.30 Find the median and mode of the following data and then find the mean from the empirical relationship between them : Class interval Frequency 020 2040 4060 6080 80100 100120 120140 6 8 10 12 6 5 3 Q.31 Following distribution give the marks obtained, out of 200, by the students of Class IX in their class test: Find the mean and mode of the data. marks 025 2550 5075 75100 100125 125150 150175 175200 Number of students 10 15 22 30 28 27 12 6Read More
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