CBSE Math Past Year Paper SA-1: Set 4 (2015) | Past Year Papers for Class 10 PDF Download

 Page 1


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS LYSVYI3 
 
 Time allowed: 3 hours                                Maximum Marks: 90 
 
General Instructions: 
1. This question are compulsory. 
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6 
question (2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. There is no overall choice in this question paper. 
4. Use of calculators is not permitted. 
Section A 
Question number 1 to 4 carry one mark each 
Q. 1  If the corresponding medians of two similar triangles are in the ratio 5:7, then find the ratio 
of their corresponding sides. 
Q. 2 If 24 c o tA – 7 , Find the value of sinA 
Q.3 Simplify : 
2
2
c os e c A
1 c ot A ?
 
Q.4 If the point of intersection of two gives is (18, 54), then find the value of median. 
Section B 
Question number 5 to 10 carry two mark each 
Q.5 Show that 5 6 is an irrational number 
Q.6 Express 5050 as product of its prime factors. Is it unique? 
Q.7 The taxi charges in a city consists of a fixed change together with the charge for the distance 
covered. For a distance of 6 km, the charges paid are Rs 58 while for a journey of 10 km, the 
charges paid are Rs. 90. Find the charge per km and the fixed charge. 
Q.8 State which of the two triangles given in the figure are similar. Also state the similarity 
criterion used. 
 
Q.9 Prove that: 
? ? ? ?
2 2
s ec 1 1 c os ec 1 ? ? ? ? ? ? 
Page 2


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS LYSVYI3 
 
 Time allowed: 3 hours                                Maximum Marks: 90 
 
General Instructions: 
1. This question are compulsory. 
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6 
question (2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. There is no overall choice in this question paper. 
4. Use of calculators is not permitted. 
Section A 
Question number 1 to 4 carry one mark each 
Q. 1  If the corresponding medians of two similar triangles are in the ratio 5:7, then find the ratio 
of their corresponding sides. 
Q. 2 If 24 c o tA – 7 , Find the value of sinA 
Q.3 Simplify : 
2
2
c os e c A
1 c ot A ?
 
Q.4 If the point of intersection of two gives is (18, 54), then find the value of median. 
Section B 
Question number 5 to 10 carry two mark each 
Q.5 Show that 5 6 is an irrational number 
Q.6 Express 5050 as product of its prime factors. Is it unique? 
Q.7 The taxi charges in a city consists of a fixed change together with the charge for the distance 
covered. For a distance of 6 km, the charges paid are Rs 58 while for a journey of 10 km, the 
charges paid are Rs. 90. Find the charge per km and the fixed charge. 
Q.8 State which of the two triangles given in the figure are similar. Also state the similarity 
criterion used. 
 
Q.9 Prove that: 
? ? ? ?
2 2
s ec 1 1 c os ec 1 ? ? ? ? ? ? 
 
 
 
  
 
Q.10 Show that the mode of the series obtained by combining the two series 
1
S and 
2
S give below 
is different from that of 
1
S and 
2
S taken separately: 
1
S : 3,5,8,8,9,12,13,9,9 
2
S : 7,4,7,8,7,8,13 
Section C 
Question number 11 to 20 carry three mark each 
Q.11 Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack 
of each type that one should buy so that there are equal number of pen and notepads.  
Q.12 Solve using cross multiplication method : 
2 u 7 v 1 ? ? ? 
4 u 3 v 1 5 ? ? 
Q.13 If ? ?
2
p x x 5x 2 ? ? ? , what is the value of ? ? ? ? p 3 q 2 ? ? 
Q.14 For what value of K, will the following system of equations have no solution? 
? ? ? ? ? ?
2
3 k 1 x 3 y 2 ; k 1 x k 2 y 5 ? ? ? ? ? ? ? 
Q.15 In A BC , X ? is middle point of AC. If XY||AB then prove that Y is middle point of AB 
Q.16 In the figure, ABCD is a rectangle. If in AD E ? and A B E ? , E F ? ? ? , then prove that 
A D A B
AE A F
? . 
 
Q.17 If 
2 2
7 sin A _ 3 c os A 4 ? , show that 
1
t a n A
3
? . 
Q.18 Prove that: 
3
3
si n 2 sin
t a n
2 c os c os
? ? ?
? ?
? ? ?
 
Q.19 In a class test, marks scored by students are given in the following frequency distribution : 
Page 3


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS LYSVYI3 
 
 Time allowed: 3 hours                                Maximum Marks: 90 
 
General Instructions: 
1. This question are compulsory. 
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6 
question (2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. There is no overall choice in this question paper. 
4. Use of calculators is not permitted. 
Section A 
Question number 1 to 4 carry one mark each 
Q. 1  If the corresponding medians of two similar triangles are in the ratio 5:7, then find the ratio 
of their corresponding sides. 
Q. 2 If 24 c o tA – 7 , Find the value of sinA 
Q.3 Simplify : 
2
2
c os e c A
1 c ot A ?
 
Q.4 If the point of intersection of two gives is (18, 54), then find the value of median. 
Section B 
Question number 5 to 10 carry two mark each 
Q.5 Show that 5 6 is an irrational number 
Q.6 Express 5050 as product of its prime factors. Is it unique? 
Q.7 The taxi charges in a city consists of a fixed change together with the charge for the distance 
covered. For a distance of 6 km, the charges paid are Rs 58 while for a journey of 10 km, the 
charges paid are Rs. 90. Find the charge per km and the fixed charge. 
Q.8 State which of the two triangles given in the figure are similar. Also state the similarity 
criterion used. 
 
Q.9 Prove that: 
? ? ? ?
2 2
s ec 1 1 c os ec 1 ? ? ? ? ? ? 
 
 
 
  
 
Q.10 Show that the mode of the series obtained by combining the two series 
1
S and 
2
S give below 
is different from that of 
1
S and 
2
S taken separately: 
1
S : 3,5,8,8,9,12,13,9,9 
2
S : 7,4,7,8,7,8,13 
Section C 
Question number 11 to 20 carry three mark each 
Q.11 Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack 
of each type that one should buy so that there are equal number of pen and notepads.  
Q.12 Solve using cross multiplication method : 
2 u 7 v 1 ? ? ? 
4 u 3 v 1 5 ? ? 
Q.13 If ? ?
2
p x x 5x 2 ? ? ? , what is the value of ? ? ? ? p 3 q 2 ? ? 
Q.14 For what value of K, will the following system of equations have no solution? 
? ? ? ? ? ?
2
3 k 1 x 3 y 2 ; k 1 x k 2 y 5 ? ? ? ? ? ? ? 
Q.15 In A BC , X ? is middle point of AC. If XY||AB then prove that Y is middle point of AB 
Q.16 In the figure, ABCD is a rectangle. If in AD E ? and A B E ? , E F ? ? ? , then prove that 
A D A B
AE A F
? . 
 
Q.17 If 
2 2
7 sin A _ 3 c os A 4 ? , show that 
1
t a n A
3
? . 
Q.18 Prove that: 
3
3
si n 2 sin
t a n
2 c os c os
? ? ?
? ?
? ? ?
 
Q.19 In a class test, marks scored by students are given in the following frequency distribution : 
 
 
 
  
 
Marks 0-6 6-12 12-18 18-24 24-30 
Number of students 1  4 9 3 3 
Find the mean and median of the data. 
Q.20 Some surnames were picked up from a local telephone directory and the frequentation 
distribution of the number of letters of the English alphabets was obtained as follows: 
Number of letters 1-4 4-7 7-10 10-13 13-16 16-19 
Number of surnames 10  25 35 x 12 8 
If it is given that mode of the distribution is 8, then find the missing frequency (x). 
Section D 
Question number 21 to 31 carry four mark each 
Q.21 What is the HCF and LCM of two prime numbers a and b? 
Three alarm clocks ring at intervals of 6, 9 and 15 minutes respectively. If they start ringing 
together, after what time will they next ring together. 
Q.22 Draw the graph of the following pair of linear equation: x 3 y 6 ? ? and 2 x 3 y 1 2 ? ? 
Find the ratio of the areas of the two triangles formed by first line, x 0, y 0 ? ? and second line 
x 0, y 0 ? ? 
Q.23 If the polynomial 
? ?
4 3 2
x 2 x 8 12 x 18 ? ? ? ? is divided by another polynomial 
? ?
2
x 5 ? , the 
remainder comes out to be ? ? p x q ? , find the values of p and q. 
Q.24 Ram’s mother has given him money to buy some boxes from the market at the rate of 
2
4 x 3 x 2 ? ? . The total amount of money is represented by
4 3 2
8 x 1 4 x 2 x 7 x 8 ? ? ? ? . Out of this 
money he donated some amount to a child who was studying in the light of street Iamp. Find 
how much amount of money he donated and purchased how many boxes from the market? 
Why Ram did so?  
Q.25 In a right angled triangle ABC, 
o
A 9 0 ? ? and A D B C ? . Prove that: 
(i) 
2
A B B D BC ? ? 
(ii) 
2
AD BD D C ? ? 
Page 4


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS LYSVYI3 
 
 Time allowed: 3 hours                                Maximum Marks: 90 
 
General Instructions: 
1. This question are compulsory. 
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6 
question (2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. There is no overall choice in this question paper. 
4. Use of calculators is not permitted. 
Section A 
Question number 1 to 4 carry one mark each 
Q. 1  If the corresponding medians of two similar triangles are in the ratio 5:7, then find the ratio 
of their corresponding sides. 
Q. 2 If 24 c o tA – 7 , Find the value of sinA 
Q.3 Simplify : 
2
2
c os e c A
1 c ot A ?
 
Q.4 If the point of intersection of two gives is (18, 54), then find the value of median. 
Section B 
Question number 5 to 10 carry two mark each 
Q.5 Show that 5 6 is an irrational number 
Q.6 Express 5050 as product of its prime factors. Is it unique? 
Q.7 The taxi charges in a city consists of a fixed change together with the charge for the distance 
covered. For a distance of 6 km, the charges paid are Rs 58 while for a journey of 10 km, the 
charges paid are Rs. 90. Find the charge per km and the fixed charge. 
Q.8 State which of the two triangles given in the figure are similar. Also state the similarity 
criterion used. 
 
Q.9 Prove that: 
? ? ? ?
2 2
s ec 1 1 c os ec 1 ? ? ? ? ? ? 
 
 
 
  
 
Q.10 Show that the mode of the series obtained by combining the two series 
1
S and 
2
S give below 
is different from that of 
1
S and 
2
S taken separately: 
1
S : 3,5,8,8,9,12,13,9,9 
2
S : 7,4,7,8,7,8,13 
Section C 
Question number 11 to 20 carry three mark each 
Q.11 Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack 
of each type that one should buy so that there are equal number of pen and notepads.  
Q.12 Solve using cross multiplication method : 
2 u 7 v 1 ? ? ? 
4 u 3 v 1 5 ? ? 
Q.13 If ? ?
2
p x x 5x 2 ? ? ? , what is the value of ? ? ? ? p 3 q 2 ? ? 
Q.14 For what value of K, will the following system of equations have no solution? 
? ? ? ? ? ?
2
3 k 1 x 3 y 2 ; k 1 x k 2 y 5 ? ? ? ? ? ? ? 
Q.15 In A BC , X ? is middle point of AC. If XY||AB then prove that Y is middle point of AB 
Q.16 In the figure, ABCD is a rectangle. If in AD E ? and A B E ? , E F ? ? ? , then prove that 
A D A B
AE A F
? . 
 
Q.17 If 
2 2
7 sin A _ 3 c os A 4 ? , show that 
1
t a n A
3
? . 
Q.18 Prove that: 
3
3
si n 2 sin
t a n
2 c os c os
? ? ?
? ?
? ? ?
 
Q.19 In a class test, marks scored by students are given in the following frequency distribution : 
 
 
 
  
 
Marks 0-6 6-12 12-18 18-24 24-30 
Number of students 1  4 9 3 3 
Find the mean and median of the data. 
Q.20 Some surnames were picked up from a local telephone directory and the frequentation 
distribution of the number of letters of the English alphabets was obtained as follows: 
Number of letters 1-4 4-7 7-10 10-13 13-16 16-19 
Number of surnames 10  25 35 x 12 8 
If it is given that mode of the distribution is 8, then find the missing frequency (x). 
Section D 
Question number 21 to 31 carry four mark each 
Q.21 What is the HCF and LCM of two prime numbers a and b? 
Three alarm clocks ring at intervals of 6, 9 and 15 minutes respectively. If they start ringing 
together, after what time will they next ring together. 
Q.22 Draw the graph of the following pair of linear equation: x 3 y 6 ? ? and 2 x 3 y 1 2 ? ? 
Find the ratio of the areas of the two triangles formed by first line, x 0, y 0 ? ? and second line 
x 0, y 0 ? ? 
Q.23 If the polynomial 
? ?
4 3 2
x 2 x 8 12 x 18 ? ? ? ? is divided by another polynomial 
? ?
2
x 5 ? , the 
remainder comes out to be ? ? p x q ? , find the values of p and q. 
Q.24 Ram’s mother has given him money to buy some boxes from the market at the rate of 
2
4 x 3 x 2 ? ? . The total amount of money is represented by
4 3 2
8 x 1 4 x 2 x 7 x 8 ? ? ? ? . Out of this 
money he donated some amount to a child who was studying in the light of street Iamp. Find 
how much amount of money he donated and purchased how many boxes from the market? 
Why Ram did so?  
Q.25 In a right angled triangle ABC, 
o
A 9 0 ? ? and A D B C ? . Prove that: 
(i) 
2
A B B D BC ? ? 
(ii) 
2
AD BD D C ? ? 
 
 
 
  
 
(iii) 
2
A C B C C D ? ? 
Q.26 Find the length of the diagonal of the rectangle BCDE, If B C E D CF ? ? ? , AC=6 m and 
CF=12m. 
 
Q.27 Evaluate 
o o o o
t an 1 ta n 2 t an 3 .. .. .. t an 8 9 
Q.28 Prove that 
2 2 2 2 2 2
b x a y a b ? ? , if : 
(i) x a s ec , y b t an ? ? ? ? 
(ii) x a co ec , y b c o t ? ? ? ? 
Q.29 Prove that: ? ? ? ? c o t c o s e c 1 . c o t c o s e c 1 . t a n 2 ? ? ? ? ? ? ? ? ? ? 
Q.30 Cost of Living Index fox some period is given in the following frequency distribution : 
Index 1500-
1600 
1600-
1700 
1700-
1800 
1800-
1900 
1900-
2000 
2000-
2100 
2100-
2200 
Number 
of weeks 
3 11 12 7 9 8 2 
Q.31 Following is the ages of asthmatic patients admitted during a year in a hospital. Find the 
mean age of the patients. 
Age (in 
years) 
0-8 8-16 16-24 24-32 32-40 40-48 48-56 56-64 
Number of 
weeks 
6 25 12 13 11 14 11 8