CBSE Math Past Year Paper SA-1: Set 12 (2014) Notes | Study Past Year Papers for Class 10 - Class 10

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Summative Assessment-1 2014-2015 
 Mathematics 
Class – X 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. In XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ 
 . If AY=2.2 
cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. Find the value of
2 2
4cos 60 16 tan 30 ec + ° - ° . 
3. If tan(3 30 ) 1 x + ° = , then find the value of x. 
4. Find the mean of first five prime numbers. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Prove that 2 2 is an irrational number. 
6. Find the HCF of the numbers 520 and 468 by prime factorization method. 
7. Find the zeroes of the quadratic polynomial
2
5 6 x x + + and verify the relationship between 
the zeroes and their coefficients. 
8. In the figure, , 120 OAC OBD AOD ? ? ? = ° ~ and 80 ODB ? = ° . Find OAC ? and BOD ? 
 
9. If sec tan x p q ? ? = + and tan sec y p q ? ? = + , then prove that 
2 2 2 2
x y p q - = - 
10. Draw a cumulative frequency curve for the following cumulative frequency distribution. 
Class 
interval 
0-10 10-20 20-30 30-40 40-50 50-60 
Cumulative 50 48 45 32 15 5 
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Summative Assessment-1 2014-2015 
 Mathematics 
Class – X 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. In XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ 
 . If AY=2.2 
cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. Find the value of
2 2
4cos 60 16 tan 30 ec + ° - ° . 
3. If tan(3 30 ) 1 x + ° = , then find the value of x. 
4. Find the mean of first five prime numbers. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Prove that 2 2 is an irrational number. 
6. Find the HCF of the numbers 520 and 468 by prime factorization method. 
7. Find the zeroes of the quadratic polynomial
2
5 6 x x + + and verify the relationship between 
the zeroes and their coefficients. 
8. In the figure, , 120 OAC OBD AOD ? ? ? = ° ~ and 80 ODB ? = ° . Find OAC ? and BOD ? 
 
9. If sec tan x p q ? ? = + and tan sec y p q ? ? = + , then prove that 
2 2 2 2
x y p q - = - 
10. Draw a cumulative frequency curve for the following cumulative frequency distribution. 
Class 
interval 
0-10 10-20 20-30 30-40 40-50 50-60 
Cumulative 50 48 45 32 15 5 
 
 
 
 
frequency 
 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Show that square of any positive odd integer is of the form 8m+1 for some integer m. 
12. Solve by elimination: 
5 2 11
3 4 4
x y
x y
- =
+ =
 
13. Solve for x and y: 
1 1
10
1 1
1 1
4
1 1
x y
x y
+ =
+ +
- =
+ +
 
14. Solve the following pair of equations graphically: 
4 4
3 2 14
x y
x y
- =
+ =
 
15. In equilateral triangle ABC, point E lies on CA such that BE CA ? . Find
2 2 2
AB BC CA + + in 
terms of
2
BE . 
16. In an isosceles triangle AB=AC. If BD AC ? , then show that
2 2
2 . BD CD CD AD - = . 
17. If 4sec 5 ? = , then evaluate:
2cos
tan cot
sin? ?
? ?
- - 
18. Prove that:
tan tan
2cos
sec 1 sec 1
ec
? ?
?
? ?
+ =
- +
 
19. The following table gives the literacy rate of 40 cities: 
Literacy 
rate (in %) 
30-40 40-50 50-60 60-70 70-80 80-90 
Number of 
cities 
6 7 10 6 8 3 
Find the modal literacy rate. 
20. In the following distribution, if mean is 78, find the missing frequency (x): 
Class 50-60 60-70 70-80 80-90 90-100 
Frequency 8 6 12 11 x 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. If two positive integers x and y are expressible in terms of primes as
2 3
x p q = and
3
y p q = . 
What can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain. 
22. Sita devi wants to make a rectangular pond on the road side for the purpose of providing 
drinking water for street animals. The area of the pond will be decrease by 3 square feets if 
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Summative Assessment-1 2014-2015 
 Mathematics 
Class – X 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. In XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ 
 . If AY=2.2 
cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. Find the value of
2 2
4cos 60 16 tan 30 ec + ° - ° . 
3. If tan(3 30 ) 1 x + ° = , then find the value of x. 
4. Find the mean of first five prime numbers. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Prove that 2 2 is an irrational number. 
6. Find the HCF of the numbers 520 and 468 by prime factorization method. 
7. Find the zeroes of the quadratic polynomial
2
5 6 x x + + and verify the relationship between 
the zeroes and their coefficients. 
8. In the figure, , 120 OAC OBD AOD ? ? ? = ° ~ and 80 ODB ? = ° . Find OAC ? and BOD ? 
 
9. If sec tan x p q ? ? = + and tan sec y p q ? ? = + , then prove that 
2 2 2 2
x y p q - = - 
10. Draw a cumulative frequency curve for the following cumulative frequency distribution. 
Class 
interval 
0-10 10-20 20-30 30-40 40-50 50-60 
Cumulative 50 48 45 32 15 5 
 
 
 
 
frequency 
 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Show that square of any positive odd integer is of the form 8m+1 for some integer m. 
12. Solve by elimination: 
5 2 11
3 4 4
x y
x y
- =
+ =
 
13. Solve for x and y: 
1 1
10
1 1
1 1
4
1 1
x y
x y
+ =
+ +
- =
+ +
 
14. Solve the following pair of equations graphically: 
4 4
3 2 14
x y
x y
- =
+ =
 
15. In equilateral triangle ABC, point E lies on CA such that BE CA ? . Find
2 2 2
AB BC CA + + in 
terms of
2
BE . 
16. In an isosceles triangle AB=AC. If BD AC ? , then show that
2 2
2 . BD CD CD AD - = . 
17. If 4sec 5 ? = , then evaluate:
2cos
tan cot
sin? ?
? ?
- - 
18. Prove that:
tan tan
2cos
sec 1 sec 1
ec
? ?
?
? ?
+ =
- +
 
19. The following table gives the literacy rate of 40 cities: 
Literacy 
rate (in %) 
30-40 40-50 50-60 60-70 70-80 80-90 
Number of 
cities 
6 7 10 6 8 3 
Find the modal literacy rate. 
20. In the following distribution, if mean is 78, find the missing frequency (x): 
Class 50-60 60-70 70-80 80-90 90-100 
Frequency 8 6 12 11 x 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. If two positive integers x and y are expressible in terms of primes as
2 3
x p q = and
3
y p q = . 
What can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain. 
22. Sita devi wants to make a rectangular pond on the road side for the purpose of providing 
drinking water for street animals. The area of the pond will be decrease by 3 square feets if 
 
 
 
 
its length is decreased by 2ft. and breadth is increased by 1 ft. Its area will be increased by 4 
square feets if the length is increase by 1 ft. and breadth remains same. Find the dimension of 
the pond. What motivated Sita Devi to provide water pond for street animals? 
23. Pocket money of Zahira and Zohra are in the ratio 6:5 and the ratio of their expenditure are 
in the ratio 4:3. If each of them saves Rs. 50 at the end of the month, find their pocket money. 
24. Obtain all other zeroes of the polynomial
4 3 2
3 3 15 10 x x x + - - - , if two of its zeroes are 5 and
5 - . 
25. In right angle , 90 ABC C ? ? = ° and D, E, F are three points on BC such that they divide it in 
equal parts. Then prove that
2 2 2 2
8( ) 11 5 AF AD AC AB + = + 
 
26. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of 
their corresponding altitudes. 
27. If cos(A+B)=0 and cot( ) 3 A B - = , then evaluate: 
a) cos .cos sin .sin A B A B - 
b) 
cot cot
cot .cot 1
B A
A B
- +
 
28. Prove that:
2
cos 1
(sec tan )
cos 1
ec
ec
?
? ?
+
+ =
- 
29. Evaluate:
2 2
2 2 2 2 2 2 2
cos 61 tan 29 2sin 30 3cot11 .cot 21 .cot 31 .cot 59 .cot 69 .cot 79
cos tan (90 ) tan 45 2(sin 21 sin 69 ) (cos 41 cos 49 )
ec
ec A A
° - ° + ° ° ° ° ° ° °
+
- ° - + ° ° + ° - ° + °
 
30. From a local telephone directory, some surnames were randomly picked up and the 
frequency distribution of the number of letters of the English alphabets in the surnames was 
obtained as follows: 
Number of 
letters 
1-3 3-6 6-9 9-12 12-15 15-18 18-21 
Number of 
surnames 
6 50 40 18 5 3 1 
Draw a ‘less than type’ ogive and a ‘more than type’ ogive for the above data. 
31. If median salary of 100 employees of a factory is Rs.24800, then find the missing frequencies 
1
f and
2
f in the given distribution table: 
Salary (in 
Rs.) 
10000-
15000 
15000-
20000 
20000-
25000 
25000-
30000 
30000-
35000 
35000-
40000 
Number of 
employees 
18 
1
f 
2
f 15 12 22