Page 1
Summative Assessment1 20142015
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
010 1020 2030 3040 4050 5060
Cumulative 50 48 45 32 15 5
Page 2
Summative Assessment1 20142015
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
010 1020 2030 3040 4050 5060
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 %)
3040 4050 5060 6070 7080 8090
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 5060 6070 7080 8090 90100
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
Page 3
Summative Assessment1 20142015
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
010 1020 2030 3040 4050 5060
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 %)
3040 4050 5060 6070 7080 8090
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 5060 6070 7080 8090 90100
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
13 36 69 912 1215 1518 1821
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
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