CBSE Math Past Year Paper SA-1: Set 5 (2015) | Past Year Papers for Class 10 PDF Download

 Page 1


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS GG-RO-103 
 
Time allowed: 3 hours                                Maximum Marks: 80 
 
General Instructions: 
1. All questions are compulsory. 
2. Question paper contains 31 questions divided into 4 section A, B, C & D. 
3. Section-A comprises of 4 questions carrying 1 mark each, 
Section-B comprises of 6 questions carrying 2 marks each, 
Section-C comprises of 10 questions carrying 3 marks each, 
Section-D comprises of 11 questions carrying 4 marks each, 
4. Al questions in section-A are very short answer questions. 
5. There are no overall choices in the question paper. 
6. Use of calculator is not permitted. 
7. If required Graph papers will be provided. 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
Q. 1  Find the value of  
o
o
ta n 30
c o t 60
 
Q. 2 What is the altitude of an equilateral triangle of each side 6 cm. 
Q. 3 If the sum of zeroes of quadratic polynomial 
2
3 x k x 6 ? ? is 3, then fine the value of k. 
Q. 4 Find the class marks of class 35-55. 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
Q. 5 In a right isosceles triangle A BC ? right angled at C prove that 
2 2
A B 2A C ? 
Q. 6 Use Euclid’s division algorithm to find the HCF of 870 and 255. 
Q. 7 Find the mode of the following distribution of marks obtained by 80 students: 
Marks obtained No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
06 
10 
12 
32 
20 
Page 2


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS GG-RO-103 
 
Time allowed: 3 hours                                Maximum Marks: 80 
 
General Instructions: 
1. All questions are compulsory. 
2. Question paper contains 31 questions divided into 4 section A, B, C & D. 
3. Section-A comprises of 4 questions carrying 1 mark each, 
Section-B comprises of 6 questions carrying 2 marks each, 
Section-C comprises of 10 questions carrying 3 marks each, 
Section-D comprises of 11 questions carrying 4 marks each, 
4. Al questions in section-A are very short answer questions. 
5. There are no overall choices in the question paper. 
6. Use of calculator is not permitted. 
7. If required Graph papers will be provided. 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
Q. 1  Find the value of  
o
o
ta n 30
c o t 60
 
Q. 2 What is the altitude of an equilateral triangle of each side 6 cm. 
Q. 3 If the sum of zeroes of quadratic polynomial 
2
3 x k x 6 ? ? is 3, then fine the value of k. 
Q. 4 Find the class marks of class 35-55. 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
Q. 5 In a right isosceles triangle A BC ? right angled at C prove that 
2 2
A B 2A C ? 
Q. 6 Use Euclid’s division algorithm to find the HCF of 870 and 255. 
Q. 7 Find the mode of the following distribution of marks obtained by 80 students: 
Marks obtained No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
06 
10 
12 
32 
20 
 
 
 
  
 
Q. 8 Find the value of k. If the pair of linear equation : 
3 x 4 y k ? ? 
9 x 1 2 y 6 ? ? 
 Has infinitely many solutions. 
Q. 9 If the LCM of ‘a’ and 18 is 36 and the HCF of ‘a’ and 18 is 2, then find the value of ‘a’. 
Q. 10 Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively. 
Section C 
Question numbers 11 to 20 carry 3 marks each. 
Q. 11 Use Euclid’s division Lemma, to show that the square of any positive integer is either of the 
form 3m or 3m+1 for some integer m. 
Q. 12 Solve the following pairs of linear equations by Cross-multiplication method : 
4 x y 1 4 ? ? 
5x 6 y 2 7 ? ? 
Q. 13 If the areas of two similar triangles are equal, then prove that they are congruent. 
Q. 14 ? ?
1 sin A
se c A tan A
1 sin A
?
? ?
?
 
Q. 15 Find the mean of the following distribution, using step deviation method : 
Class Frequency 
0-10 
10-20 
20-30 
30-40 
40-50 
07 
12 
13 
10 
08 
Q. 16 Find the zeroes of the quadratic polynomial 
2
6 x 3 7 x ? ? and verify the relationship between 
the zeroes and the coefficients. 
Q. 17 In triangle PQR right angled at Q, PR+QR=25cm and PQ=5cm determine the value of sin P, cos 
P and tan P. 
Q. 18 In figure PQ||CD and PR||CB, 
Prove that 
A Q A R
Q D RB
? 
Page 3


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS GG-RO-103 
 
Time allowed: 3 hours                                Maximum Marks: 80 
 
General Instructions: 
1. All questions are compulsory. 
2. Question paper contains 31 questions divided into 4 section A, B, C & D. 
3. Section-A comprises of 4 questions carrying 1 mark each, 
Section-B comprises of 6 questions carrying 2 marks each, 
Section-C comprises of 10 questions carrying 3 marks each, 
Section-D comprises of 11 questions carrying 4 marks each, 
4. Al questions in section-A are very short answer questions. 
5. There are no overall choices in the question paper. 
6. Use of calculator is not permitted. 
7. If required Graph papers will be provided. 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
Q. 1  Find the value of  
o
o
ta n 30
c o t 60
 
Q. 2 What is the altitude of an equilateral triangle of each side 6 cm. 
Q. 3 If the sum of zeroes of quadratic polynomial 
2
3 x k x 6 ? ? is 3, then fine the value of k. 
Q. 4 Find the class marks of class 35-55. 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
Q. 5 In a right isosceles triangle A BC ? right angled at C prove that 
2 2
A B 2A C ? 
Q. 6 Use Euclid’s division algorithm to find the HCF of 870 and 255. 
Q. 7 Find the mode of the following distribution of marks obtained by 80 students: 
Marks obtained No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
06 
10 
12 
32 
20 
 
 
 
  
 
Q. 8 Find the value of k. If the pair of linear equation : 
3 x 4 y k ? ? 
9 x 1 2 y 6 ? ? 
 Has infinitely many solutions. 
Q. 9 If the LCM of ‘a’ and 18 is 36 and the HCF of ‘a’ and 18 is 2, then find the value of ‘a’. 
Q. 10 Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively. 
Section C 
Question numbers 11 to 20 carry 3 marks each. 
Q. 11 Use Euclid’s division Lemma, to show that the square of any positive integer is either of the 
form 3m or 3m+1 for some integer m. 
Q. 12 Solve the following pairs of linear equations by Cross-multiplication method : 
4 x y 1 4 ? ? 
5x 6 y 2 7 ? ? 
Q. 13 If the areas of two similar triangles are equal, then prove that they are congruent. 
Q. 14 ? ?
1 sin A
se c A tan A
1 sin A
?
? ?
?
 
Q. 15 Find the mean of the following distribution, using step deviation method : 
Class Frequency 
0-10 
10-20 
20-30 
30-40 
40-50 
07 
12 
13 
10 
08 
Q. 16 Find the zeroes of the quadratic polynomial 
2
6 x 3 7 x ? ? and verify the relationship between 
the zeroes and the coefficients. 
Q. 17 In triangle PQR right angled at Q, PR+QR=25cm and PQ=5cm determine the value of sin P, cos 
P and tan P. 
Q. 18 In figure PQ||CD and PR||CB, 
Prove that 
A Q A R
Q D RB
? 
 
 
 
  
 
 
Q. 19 Find the median of the following frequency distribution table: 
marks No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
50-60 
05 
08 
06 
10 
06 
05 
Q. 20 If  ? ? ? ?
1 1
si n A B co s A B
2 2
? ? ? ? , 
0 0
0 A B 90 , A B , ? ? ? ? Find A and B. 
Section D 
Question numbers 21 to 31 carry 4 marks each. 
Q. 21 Show that: 
2
5 3 ? is an irrational number 
Q. 22 Find all the zeroes of the polynomials
4 3 2
x x 9 x 3 x 1 8 ? ? ? ? . If it is given that two of its zeroes 
are 3 and 3 ? 
OR 
Divide 
2 3
3 x x 3 x 5 ? ? ? by 
2
x 1 x ? ? and verify the division algorithm. 
Q. 23 Prove that in a Right Angled Triangle, the square of the Hypotenuse is equal to the sum of the 
square of the others two sides’ 
OR 
Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their 
corresponding medians. 
Q. 24 Prove that:
t a n c o t
1 _ s e c c o s e c
1 c o t 1 ta n
? ?
? ? ? ?
? ? ? ?
 
OR 
Page 4


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS GG-RO-103 
 
Time allowed: 3 hours                                Maximum Marks: 80 
 
General Instructions: 
1. All questions are compulsory. 
2. Question paper contains 31 questions divided into 4 section A, B, C & D. 
3. Section-A comprises of 4 questions carrying 1 mark each, 
Section-B comprises of 6 questions carrying 2 marks each, 
Section-C comprises of 10 questions carrying 3 marks each, 
Section-D comprises of 11 questions carrying 4 marks each, 
4. Al questions in section-A are very short answer questions. 
5. There are no overall choices in the question paper. 
6. Use of calculator is not permitted. 
7. If required Graph papers will be provided. 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
Q. 1  Find the value of  
o
o
ta n 30
c o t 60
 
Q. 2 What is the altitude of an equilateral triangle of each side 6 cm. 
Q. 3 If the sum of zeroes of quadratic polynomial 
2
3 x k x 6 ? ? is 3, then fine the value of k. 
Q. 4 Find the class marks of class 35-55. 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
Q. 5 In a right isosceles triangle A BC ? right angled at C prove that 
2 2
A B 2A C ? 
Q. 6 Use Euclid’s division algorithm to find the HCF of 870 and 255. 
Q. 7 Find the mode of the following distribution of marks obtained by 80 students: 
Marks obtained No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
06 
10 
12 
32 
20 
 
 
 
  
 
Q. 8 Find the value of k. If the pair of linear equation : 
3 x 4 y k ? ? 
9 x 1 2 y 6 ? ? 
 Has infinitely many solutions. 
Q. 9 If the LCM of ‘a’ and 18 is 36 and the HCF of ‘a’ and 18 is 2, then find the value of ‘a’. 
Q. 10 Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively. 
Section C 
Question numbers 11 to 20 carry 3 marks each. 
Q. 11 Use Euclid’s division Lemma, to show that the square of any positive integer is either of the 
form 3m or 3m+1 for some integer m. 
Q. 12 Solve the following pairs of linear equations by Cross-multiplication method : 
4 x y 1 4 ? ? 
5x 6 y 2 7 ? ? 
Q. 13 If the areas of two similar triangles are equal, then prove that they are congruent. 
Q. 14 ? ?
1 sin A
se c A tan A
1 sin A
?
? ?
?
 
Q. 15 Find the mean of the following distribution, using step deviation method : 
Class Frequency 
0-10 
10-20 
20-30 
30-40 
40-50 
07 
12 
13 
10 
08 
Q. 16 Find the zeroes of the quadratic polynomial 
2
6 x 3 7 x ? ? and verify the relationship between 
the zeroes and the coefficients. 
Q. 17 In triangle PQR right angled at Q, PR+QR=25cm and PQ=5cm determine the value of sin P, cos 
P and tan P. 
Q. 18 In figure PQ||CD and PR||CB, 
Prove that 
A Q A R
Q D RB
? 
 
 
 
  
 
 
Q. 19 Find the median of the following frequency distribution table: 
marks No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
50-60 
05 
08 
06 
10 
06 
05 
Q. 20 If  ? ? ? ?
1 1
si n A B co s A B
2 2
? ? ? ? , 
0 0
0 A B 90 , A B , ? ? ? ? Find A and B. 
Section D 
Question numbers 21 to 31 carry 4 marks each. 
Q. 21 Show that: 
2
5 3 ? is an irrational number 
Q. 22 Find all the zeroes of the polynomials
4 3 2
x x 9 x 3 x 1 8 ? ? ? ? . If it is given that two of its zeroes 
are 3 and 3 ? 
OR 
Divide 
2 3
3 x x 3 x 5 ? ? ? by 
2
x 1 x ? ? and verify the division algorithm. 
Q. 23 Prove that in a Right Angled Triangle, the square of the Hypotenuse is equal to the sum of the 
square of the others two sides’ 
OR 
Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their 
corresponding medians. 
Q. 24 Prove that:
t a n c o t
1 _ s e c c o s e c
1 c o t 1 ta n
? ?
? ? ? ?
? ? ? ?
 
OR 
 
 
 
  
 
3
3
sin 2 sin
t a n
2 c os co s
? ? ?
? ?
? ? ?
 
Q. 25 Solve the following system of Linear Equation Graphically: 
X – Y = 1, 2 X + Y = 8. 
Shade the area bounded by these two lines and Y-axis. 
Q. 26 The median of the following data is 50. Find the values of p and q if the sum of all the 
frequencies is 90. 
marks No. of students 
20-30 
30-40 
40-50 
50-60 
60-70 
70-80 
80-90 
P 
15 
25 
20 
Q 
08 
10 
Q. 27 If  
1
si n
2
? Show that 3 
3
co s B 4 Co s B 0 ? ? 
Q. 28 During the medical check-up of the 35 students of a class their weights were recorded as 
follows: 
Weight in KG No. of students 
38-40 
40-42 
42-44 
44-46 
46-48 
48-50 
50-52 
03 
02 
04 
05 
14 
04 
03 
Draw a less than type give for the above data. 
Q. 29 Solve the pair of linear equation:
1 1 3
3x y 3x y 4
? ?
? ?
, 
? ? ? ?
1 1 1
2 3x y 2 3x y 8
? ?
? ?
 
Page 5


 
 
 
  
 
SUMMATIVE ASSESSMENT-I, 2015-16 
 CLASS-X, MATHEMATICS GG-RO-103 
 
Time allowed: 3 hours                                Maximum Marks: 80 
 
General Instructions: 
1. All questions are compulsory. 
2. Question paper contains 31 questions divided into 4 section A, B, C & D. 
3. Section-A comprises of 4 questions carrying 1 mark each, 
Section-B comprises of 6 questions carrying 2 marks each, 
Section-C comprises of 10 questions carrying 3 marks each, 
Section-D comprises of 11 questions carrying 4 marks each, 
4. Al questions in section-A are very short answer questions. 
5. There are no overall choices in the question paper. 
6. Use of calculator is not permitted. 
7. If required Graph papers will be provided. 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
Q. 1  Find the value of  
o
o
ta n 30
c o t 60
 
Q. 2 What is the altitude of an equilateral triangle of each side 6 cm. 
Q. 3 If the sum of zeroes of quadratic polynomial 
2
3 x k x 6 ? ? is 3, then fine the value of k. 
Q. 4 Find the class marks of class 35-55. 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
Q. 5 In a right isosceles triangle A BC ? right angled at C prove that 
2 2
A B 2A C ? 
Q. 6 Use Euclid’s division algorithm to find the HCF of 870 and 255. 
Q. 7 Find the mode of the following distribution of marks obtained by 80 students: 
Marks obtained No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
06 
10 
12 
32 
20 
 
 
 
  
 
Q. 8 Find the value of k. If the pair of linear equation : 
3 x 4 y k ? ? 
9 x 1 2 y 6 ? ? 
 Has infinitely many solutions. 
Q. 9 If the LCM of ‘a’ and 18 is 36 and the HCF of ‘a’ and 18 is 2, then find the value of ‘a’. 
Q. 10 Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively. 
Section C 
Question numbers 11 to 20 carry 3 marks each. 
Q. 11 Use Euclid’s division Lemma, to show that the square of any positive integer is either of the 
form 3m or 3m+1 for some integer m. 
Q. 12 Solve the following pairs of linear equations by Cross-multiplication method : 
4 x y 1 4 ? ? 
5x 6 y 2 7 ? ? 
Q. 13 If the areas of two similar triangles are equal, then prove that they are congruent. 
Q. 14 ? ?
1 sin A
se c A tan A
1 sin A
?
? ?
?
 
Q. 15 Find the mean of the following distribution, using step deviation method : 
Class Frequency 
0-10 
10-20 
20-30 
30-40 
40-50 
07 
12 
13 
10 
08 
Q. 16 Find the zeroes of the quadratic polynomial 
2
6 x 3 7 x ? ? and verify the relationship between 
the zeroes and the coefficients. 
Q. 17 In triangle PQR right angled at Q, PR+QR=25cm and PQ=5cm determine the value of sin P, cos 
P and tan P. 
Q. 18 In figure PQ||CD and PR||CB, 
Prove that 
A Q A R
Q D RB
? 
 
 
 
  
 
 
Q. 19 Find the median of the following frequency distribution table: 
marks No. of students 
0-10 
10-20 
20-30 
30-40 
40-50 
50-60 
05 
08 
06 
10 
06 
05 
Q. 20 If  ? ? ? ?
1 1
si n A B co s A B
2 2
? ? ? ? , 
0 0
0 A B 90 , A B , ? ? ? ? Find A and B. 
Section D 
Question numbers 21 to 31 carry 4 marks each. 
Q. 21 Show that: 
2
5 3 ? is an irrational number 
Q. 22 Find all the zeroes of the polynomials
4 3 2
x x 9 x 3 x 1 8 ? ? ? ? . If it is given that two of its zeroes 
are 3 and 3 ? 
OR 
Divide 
2 3
3 x x 3 x 5 ? ? ? by 
2
x 1 x ? ? and verify the division algorithm. 
Q. 23 Prove that in a Right Angled Triangle, the square of the Hypotenuse is equal to the sum of the 
square of the others two sides’ 
OR 
Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their 
corresponding medians. 
Q. 24 Prove that:
t a n c o t
1 _ s e c c o s e c
1 c o t 1 ta n
? ?
? ? ? ?
? ? ? ?
 
OR 
 
 
 
  
 
3
3
sin 2 sin
t a n
2 c os co s
? ? ?
? ?
? ? ?
 
Q. 25 Solve the following system of Linear Equation Graphically: 
X – Y = 1, 2 X + Y = 8. 
Shade the area bounded by these two lines and Y-axis. 
Q. 26 The median of the following data is 50. Find the values of p and q if the sum of all the 
frequencies is 90. 
marks No. of students 
20-30 
30-40 
40-50 
50-60 
60-70 
70-80 
80-90 
P 
15 
25 
20 
Q 
08 
10 
Q. 27 If  
1
si n
2
? Show that 3 
3
co s B 4 Co s B 0 ? ? 
Q. 28 During the medical check-up of the 35 students of a class their weights were recorded as 
follows: 
Weight in KG No. of students 
38-40 
40-42 
42-44 
44-46 
46-48 
48-50 
50-52 
03 
02 
04 
05 
14 
04 
03 
Draw a less than type give for the above data. 
Q. 29 Solve the pair of linear equation:
1 1 3
3x y 3x y 4
? ?
? ?
, 
? ? ? ?
1 1 1
2 3x y 2 3x y 8
? ?
? ?
 
 
 
 
  
 
OR 
The Sum of the digits of a two digit number is 9, Also nine times this number is twice the –
number obtain by reversing the order the digits. Find the number. 
Q. 30 Evaluate:
o o o
o o o o o o
7 c os 70 3 co s 55 c os e c 35
2 s i n 20 2 ta n 5 t a n 45 t a n 85 t a n 65 ta n 25
? 
Q. 31 Mr. Balwant Singh has a triangular field ABC. He has three sons. He wants to divide the field 
into four equal and identical parts, so that he may give three parts to his three sons and 
retain the fourth part with him. 
i) Is it possible to divide the field into four parts which are equal and identical? 
ii) If yes, explain the method of division. 
iii) By doing so, which values is depicted by Mr. Balwant Singh.