CBSE Math Past Year Paper SA-1: Set 5 (2016) | Past Year Papers for Class 10 PDF Download

 Page 1


 
 
 
 
M0AVBUN 
GYAN SAGAR PUBLIC SCHOOL 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
MATHEMATICS 
Class: X 
Time: 3Hrs.                  M.M: 90 
 
General Instruction: 
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 questions of 1 mark each; Section B comprises of 6 questions of 
2 marks each; Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 11 questions 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. 
1. M and N are points in the sides PQ and PR respectively of a PQR. ? If PN = 4.8 cm, NR = 
1.6 cm, PM = 4.5 cm and MQ = 1.5 cm, then find whether MN||QR or not. 
 
2. In a ABC, ? write tan
2
A B +
 in terms of angles C. 
 
3. Find the value of 
0 0 0
cot10 .cot 30 .cot80 . 
 
4. If mode = 10.6 and median = 11.5, then find mean, using an empirical relation. 
 
SECTION B 
 Question numbers 5 to 10 carry two marks each. 
5. Explain why (17 5 11 3 2 2 11) × × × × + × is a composite number? 
 
6. The decimal expansion of 
3 2
51
2 5 ×
 will terminate after how many decimal places? 
 
7. Given the linear equation 3 4 9 x y + = write another linear equation in these two variables 
such that the geometrical representation of the pair so formed is: 
 (i) intersecting lines 
 (ii) coincident lines 
 
 
 
Page 2


 
 
 
 
M0AVBUN 
GYAN SAGAR PUBLIC SCHOOL 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
MATHEMATICS 
Class: X 
Time: 3Hrs.                  M.M: 90 
 
General Instruction: 
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 questions of 1 mark each; Section B comprises of 6 questions of 
2 marks each; Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 11 questions 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. 
1. M and N are points in the sides PQ and PR respectively of a PQR. ? If PN = 4.8 cm, NR = 
1.6 cm, PM = 4.5 cm and MQ = 1.5 cm, then find whether MN||QR or not. 
 
2. In a ABC, ? write tan
2
A B +
 in terms of angles C. 
 
3. Find the value of 
0 0 0
cot10 .cot 30 .cot80 . 
 
4. If mode = 10.6 and median = 11.5, then find mean, using an empirical relation. 
 
SECTION B 
 Question numbers 5 to 10 carry two marks each. 
5. Explain why (17 5 11 3 2 2 11) × × × × + × is a composite number? 
 
6. The decimal expansion of 
3 2
51
2 5 ×
 will terminate after how many decimal places? 
 
7. Given the linear equation 3 4 9 x y + = write another linear equation in these two variables 
such that the geometrical representation of the pair so formed is: 
 (i) intersecting lines 
 (ii) coincident lines 
 
 
 
 
 
 
 
8. In the given figure, OA = 3cm, OB = 4 cm, 
0
AOB=90 , ? AC = 12cm and BC = 13 cm. Prove 
that 
0
CAB=90 . ? 
  
 
9. If 
1
tan(A-B)=
3
 and tan(A+B)= 3, Find A and B. 
 
10. The width of 50 leaves of a plant were measured in mm and their cumulative frequency 
distribution is shown in the following table. Make an ordinary frequency distribution 
table for this. 
  
Width (in 
mm) 
> 20 > 30 > 40 > 50 > 60 > 70 > 80 
Cumulative 
frequency 
50 44 28 20 15 7 0 
 
SECTION C 
 Question numbers 11 to 20 carry three marks each. 
11. Find the smallest number of 5 digits which is exactly divisible by 12, 16 and 20. 
 
12. What should be added in the polynomial 
3 2
2 3 4 x x x - - - so that it is completely divisible 
by 
2
. x x - 
 
13. Find a quadratic polynomial, the sum and product of whose zeroes are – 10 and 25 
respectively. Hence find the zeroes. 
 
14. Solve the following pairs of linear equation by the substitution method: 
 0.4x + 0.5y = 2.3 
 0.3x + 0.2y = 1.2 
 
15. ABCD is a square. If points E and F are such that BE is one – third of AB and BF is one-
third of BC and area ( area)=128sq. cm, ? then find diagonal BD of the square. 
  
  
Page 3


 
 
 
 
M0AVBUN 
GYAN SAGAR PUBLIC SCHOOL 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
MATHEMATICS 
Class: X 
Time: 3Hrs.                  M.M: 90 
 
General Instruction: 
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 questions of 1 mark each; Section B comprises of 6 questions of 
2 marks each; Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 11 questions 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. 
1. M and N are points in the sides PQ and PR respectively of a PQR. ? If PN = 4.8 cm, NR = 
1.6 cm, PM = 4.5 cm and MQ = 1.5 cm, then find whether MN||QR or not. 
 
2. In a ABC, ? write tan
2
A B +
 in terms of angles C. 
 
3. Find the value of 
0 0 0
cot10 .cot 30 .cot80 . 
 
4. If mode = 10.6 and median = 11.5, then find mean, using an empirical relation. 
 
SECTION B 
 Question numbers 5 to 10 carry two marks each. 
5. Explain why (17 5 11 3 2 2 11) × × × × + × is a composite number? 
 
6. The decimal expansion of 
3 2
51
2 5 ×
 will terminate after how many decimal places? 
 
7. Given the linear equation 3 4 9 x y + = write another linear equation in these two variables 
such that the geometrical representation of the pair so formed is: 
 (i) intersecting lines 
 (ii) coincident lines 
 
 
 
 
 
 
 
8. In the given figure, OA = 3cm, OB = 4 cm, 
0
AOB=90 , ? AC = 12cm and BC = 13 cm. Prove 
that 
0
CAB=90 . ? 
  
 
9. If 
1
tan(A-B)=
3
 and tan(A+B)= 3, Find A and B. 
 
10. The width of 50 leaves of a plant were measured in mm and their cumulative frequency 
distribution is shown in the following table. Make an ordinary frequency distribution 
table for this. 
  
Width (in 
mm) 
> 20 > 30 > 40 > 50 > 60 > 70 > 80 
Cumulative 
frequency 
50 44 28 20 15 7 0 
 
SECTION C 
 Question numbers 11 to 20 carry three marks each. 
11. Find the smallest number of 5 digits which is exactly divisible by 12, 16 and 20. 
 
12. What should be added in the polynomial 
3 2
2 3 4 x x x - - - so that it is completely divisible 
by 
2
. x x - 
 
13. Find a quadratic polynomial, the sum and product of whose zeroes are – 10 and 25 
respectively. Hence find the zeroes. 
 
14. Solve the following pairs of linear equation by the substitution method: 
 0.4x + 0.5y = 2.3 
 0.3x + 0.2y = 1.2 
 
15. ABCD is a square. If points E and F are such that BE is one – third of AB and BF is one-
third of BC and area ( area)=128sq. cm, ? then find diagonal BD of the square. 
  
  
 
 
 
 
16. ABC ? and EBC ? are on the same base BC. If AE produced intersects BC at D then, prove 
that 
ar( ABC) AD
ar( EBC) ED
?
=
?
 
  
 
17. Evaluate 
2 0 2 0 2 0 2 0 2 0 2 0
cos 0 cos 1 cos 2 cos 3 ... cos 88 cos 89 + + + + + + 
 
18. Prove that:  
 
2 2 2 2
(sin? cosec?) (cos? sec?) 7 tan ? cot ? + + + = + + 
 
 
19. Calculate the mean for the following frequency distribution: 
  
Class 10-30 30-50 50-70 70-90 90-110 
Frequency 15 18 25 10 2 
 
20. Find the missing frequency (x) of the following distribution, if mode is 34.5: 
  
Marks 
obtained 
0-10 10-20 20-30 30-40 40-50 
No. of 
students 
4 8 10 x 8 
 
SECTION D 
 Question numbers 21 to 31 carry for marks each. 
21. If HCF of 480 and 685 is expressed in the form 480x – 475, find the value of x. 
 
22. Find all the zeroes of the polynomial 
4 3
3 6 4, x x x - + - if two of its zeroes are 2 and 
2. - 
 
23. Solve graphically the pair of linear equations: 
 3x – 2y + 7 = 0 
 2x + 3y – 4 = 0 
 Also shade the region enclosed by these lines and x-axis. 
 
24. Rani decided to distribute some amount to poor students for their books. If there are 8 
students less, everyone will get Rs10 more. If there are 16 students more every one will 
get Rs10 less. What is the number of students and how much does each gets? What is the 
total amount distributed? 
Page 4


 
 
 
 
M0AVBUN 
GYAN SAGAR PUBLIC SCHOOL 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
MATHEMATICS 
Class: X 
Time: 3Hrs.                  M.M: 90 
 
General Instruction: 
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 questions of 1 mark each; Section B comprises of 6 questions of 
2 marks each; Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 11 questions 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. 
1. M and N are points in the sides PQ and PR respectively of a PQR. ? If PN = 4.8 cm, NR = 
1.6 cm, PM = 4.5 cm and MQ = 1.5 cm, then find whether MN||QR or not. 
 
2. In a ABC, ? write tan
2
A B +
 in terms of angles C. 
 
3. Find the value of 
0 0 0
cot10 .cot 30 .cot80 . 
 
4. If mode = 10.6 and median = 11.5, then find mean, using an empirical relation. 
 
SECTION B 
 Question numbers 5 to 10 carry two marks each. 
5. Explain why (17 5 11 3 2 2 11) × × × × + × is a composite number? 
 
6. The decimal expansion of 
3 2
51
2 5 ×
 will terminate after how many decimal places? 
 
7. Given the linear equation 3 4 9 x y + = write another linear equation in these two variables 
such that the geometrical representation of the pair so formed is: 
 (i) intersecting lines 
 (ii) coincident lines 
 
 
 
 
 
 
 
8. In the given figure, OA = 3cm, OB = 4 cm, 
0
AOB=90 , ? AC = 12cm and BC = 13 cm. Prove 
that 
0
CAB=90 . ? 
  
 
9. If 
1
tan(A-B)=
3
 and tan(A+B)= 3, Find A and B. 
 
10. The width of 50 leaves of a plant were measured in mm and their cumulative frequency 
distribution is shown in the following table. Make an ordinary frequency distribution 
table for this. 
  
Width (in 
mm) 
> 20 > 30 > 40 > 50 > 60 > 70 > 80 
Cumulative 
frequency 
50 44 28 20 15 7 0 
 
SECTION C 
 Question numbers 11 to 20 carry three marks each. 
11. Find the smallest number of 5 digits which is exactly divisible by 12, 16 and 20. 
 
12. What should be added in the polynomial 
3 2
2 3 4 x x x - - - so that it is completely divisible 
by 
2
. x x - 
 
13. Find a quadratic polynomial, the sum and product of whose zeroes are – 10 and 25 
respectively. Hence find the zeroes. 
 
14. Solve the following pairs of linear equation by the substitution method: 
 0.4x + 0.5y = 2.3 
 0.3x + 0.2y = 1.2 
 
15. ABCD is a square. If points E and F are such that BE is one – third of AB and BF is one-
third of BC and area ( area)=128sq. cm, ? then find diagonal BD of the square. 
  
  
 
 
 
 
16. ABC ? and EBC ? are on the same base BC. If AE produced intersects BC at D then, prove 
that 
ar( ABC) AD
ar( EBC) ED
?
=
?
 
  
 
17. Evaluate 
2 0 2 0 2 0 2 0 2 0 2 0
cos 0 cos 1 cos 2 cos 3 ... cos 88 cos 89 + + + + + + 
 
18. Prove that:  
 
2 2 2 2
(sin? cosec?) (cos? sec?) 7 tan ? cot ? + + + = + + 
 
 
19. Calculate the mean for the following frequency distribution: 
  
Class 10-30 30-50 50-70 70-90 90-110 
Frequency 15 18 25 10 2 
 
20. Find the missing frequency (x) of the following distribution, if mode is 34.5: 
  
Marks 
obtained 
0-10 10-20 20-30 30-40 40-50 
No. of 
students 
4 8 10 x 8 
 
SECTION D 
 Question numbers 21 to 31 carry for marks each. 
21. If HCF of 480 and 685 is expressed in the form 480x – 475, find the value of x. 
 
22. Find all the zeroes of the polynomial 
4 3
3 6 4, x x x - + - if two of its zeroes are 2 and 
2. - 
 
23. Solve graphically the pair of linear equations: 
 3x – 2y + 7 = 0 
 2x + 3y – 4 = 0 
 Also shade the region enclosed by these lines and x-axis. 
 
24. Rani decided to distribute some amount to poor students for their books. If there are 8 
students less, everyone will get Rs10 more. If there are 16 students more every one will 
get Rs10 less. What is the number of students and how much does each gets? What is the 
total amount distributed? 
 
 
 
 
 What is the reason that motivated Rani to distribute money for books? 
 
25. If in ABC, ? AD is median and AM BC, ? then prove that 
2 2 2 2
1
AB +AC =2AD + BC .
2
 
 
26. In a ABC, ? the middle points of sides BC, CA and AB are D, E and F respectively. Find 
ratio of ar( DEF) ? to ar( ABC). ? 
 
27. If 
0
(cos? + sin?)= 2 sin(90 ?), - show that (sin? cos?)= 2 cos? - 
 
28. If tanA=n tanB and sin A = m sin B, then prove thet 
2
2
2
1
cos A
1
m
n
- =
+
 
 
 
29. If sec tan , x ? ? - = show that: 
 
1 1
sec
2
x
x
?
? ?
= +
? ?
? ?
 and 
1 1
tan
2
x
x
?
? ?
= - ? ?
? ?
 
 
30. An NGO organized a marathon to promote healthy habits. Age – wise participation is 
shown in the following data: 
  
Age (in 
years) 
0-15 15-30 30-45 45-60 60-75 75-80 
No. of 
participate  
37 45 27 9 7 3 
 Draw a ‘less than and more than type’ ogives and from the curves, find the median. 
 
31. In the following data, median of the runs scored by 60 top batsmen of the world in one-
day international cricket matches is 5000. Find the missing frequencies x and y. 
 
  
Runs 
scored  
2500-3500 3500-4500 4500-5500 5500-6500 6500-7500 7500-8500 
No. of 
batsmen 
5 x y 12 6 2