CBSE Math Past Year Paper SA-1: Set 3 (2015) | Past Year Papers for Class 10 PDF Download

 Page 1


 
 
 
  
 
GYAN SAGAR PUBLI SCHOOL 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, 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. Section-A 
comprises of 4 question of 1 mark each; Section-B 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 , ? AB||EW. 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 co-prime : 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 RS||DF 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 ASSESSMENT-I, 2015-16 
 CLASS-X, 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. Section-A 
comprises of 4 question of 1 mark each; Section-B 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 , ? AB||EW. 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 co-prime : 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 RS||DF 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) 
200-205 250-300 300-350 350-400 400-450 
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 DE||BC, 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) 
0-9 10-19 20-29 30-39 40-49 
Number of patients 12 25 13 10 5 
Page 3


 
 
 
  
 
GYAN SAGAR PUBLI SCHOOL 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, 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. Section-A 
comprises of 4 question of 1 mark each; Section-B 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 , ? AB||EW. 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 co-prime : 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 RS||DF 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) 
200-205 250-300 300-350 350-400 400-450 
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 DE||BC, 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) 
0-9 10-19 20-29 30-39 40-49 
Number of patients 12 25 13 10 5 
 
 
 
  
 
Q.20 Find the mean and median for the following data: 
Class 0-4 4-8 8-12 12-16 16-20 
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(A-B)= 
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 ASSESSMENT-I, 2015-16 
 CLASS-X, 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. Section-A 
comprises of 4 question of 1 mark each; Section-B 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 , ? AB||EW. 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 co-prime : 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 RS||DF 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) 
200-205 250-300 300-350 350-400 400-450 
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 DE||BC, 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) 
0-9 10-19 20-29 30-39 40-49 
Number of patients 12 25 13 10 5 
 
 
 
  
 
Q.20 Find the mean and median for the following data: 
Class 0-4 4-8 8-12 12-16 16-20 
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(A-B)= 
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 
 
 
 
  
 
0-20 
20-40 
40-60 
60-80 
80-100 
100-120 
120-140 
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 0-25 25-50 50-75 75-100 100-125 125-150 150-175 175-200 
Number of 
students 
10 15 22 30 28 27 12 6