CBSE Math Past Year Paper SA-1: Set 5 (2014) Notes | Study Past Year Papers for Class 10 - Class 10

 Page 1


 
 
 
 
Summative Assessment-1 2014-15 
 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. If ABC RPQ ? ? ~ , AB=3cm, BC=5cm, AC=6cm, RP=6cm and PQ=10cm, then find QR. 
2. Express cos 48 tan88 ec ° + ° in term of t – ratios of angles between 0° and 45°. 
3. In PQR ? , if 90 Q ? = ° and 
3
sin
5
R = , then find the value of cos P. 
4. In the frequency distribution, if 50 fi =
?
 and 2550 fi =
?
, then what is the mean of the 
distribution? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Find HCF of the number 31, 310 and 3100. 
6. Find the least positive integer which on adding 1 is exactly divisible by 126 and 600. 
7. Find solution of the following pair of linear equations: 
3x – 7y=5 
x + y=15 
8. In the figure,  l m  and OAC OBD ? ? ~ . If AC=5cm, OA=3cm and BD=2cm, find OB. 
 
9. Solve the equation for ? : 
2
2 2
cos
3
cot cos
?
? ?
=
- 
Page 2


 
 
 
 
Summative Assessment-1 2014-15 
 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. If ABC RPQ ? ? ~ , AB=3cm, BC=5cm, AC=6cm, RP=6cm and PQ=10cm, then find QR. 
2. Express cos 48 tan88 ec ° + ° in term of t – ratios of angles between 0° and 45°. 
3. In PQR ? , if 90 Q ? = ° and 
3
sin
5
R = , then find the value of cos P. 
4. In the frequency distribution, if 50 fi =
?
 and 2550 fi =
?
, then what is the mean of the 
distribution? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Find HCF of the number 31, 310 and 3100. 
6. Find the least positive integer which on adding 1 is exactly divisible by 126 and 600. 
7. Find solution of the following pair of linear equations: 
3x – 7y=5 
x + y=15 
8. In the figure,  l m  and OAC OBD ? ? ~ . If AC=5cm, OA=3cm and BD=2cm, find OB. 
 
9. Solve the equation for ? : 
2
2 2
cos
3
cot cos
?
? ?
=
- 
 
 
 
 
10. Find the median of the data using an empirical formula, when it is given that mode=35.3 and 
mean=30.5 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Write 32875 as product of prime factors. Is this factorization unique? 
12. Divide the polynomial 
2 2
4 6 10 3 x x x - - - by the polynomial 
2
x x + and verify the division 
algorithm. 
13. Find the zeroes of the quadratic polynomial 
2
2 5 3 x x + - and verify the relationship between 
the zeroes and the coefficients. 
14. Solve using cross multiplication method. 
4c – v =4 
3u + 2v =14 
15. If in ABC ? , AD is median and AM BC ? , then that 
2 2 2
1
4
AC AD BC DM BC = + × + 
16. ABC is an isosceles triangle. If 90 B ? = ° , then prove that 
2 2
2 AC BC = . 
17. If cos(40 ) sin 30 x ° + = ° , find the value of x. 
18. Prove the identify: 
(1 tan sec )(1 cot cos ) 2 ec ? ? ? ? + + + - = 
19. The given distribution shows the number of runs scored by the batsmen in inter-school 
cricket matches: 
Runs scored 0-50 50-100 100-150 150-200 200-250 
Number of 
batsmen 
4 6 9 7 5 
20. In a health check-up, the number of heart beats of 40 women were recorded in the following 
table: 
Number of heart 
beats/minute 
65-69 70-74 75-79 80-84 
Number of 
women 
2 18 16 4 
 
 
Section D 
Questions 21 to 31 carry 4 marks each. 
21. Express the HCF of number 72 and 124 as a linear combination of 72 and 124. 
22. Ridhi decided to use public transport to cover a distance of 300 km. She travels this distance 
partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and 
remaining by bus. If she travels 100km by train and the remaining by bus, she takes 10 
minutes more. Find the speed of train and bus separately. Why does Ridhi decide to opt for 
public transport? 
Page 3


 
 
 
 
Summative Assessment-1 2014-15 
 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. If ABC RPQ ? ? ~ , AB=3cm, BC=5cm, AC=6cm, RP=6cm and PQ=10cm, then find QR. 
2. Express cos 48 tan88 ec ° + ° in term of t – ratios of angles between 0° and 45°. 
3. In PQR ? , if 90 Q ? = ° and 
3
sin
5
R = , then find the value of cos P. 
4. In the frequency distribution, if 50 fi =
?
 and 2550 fi =
?
, then what is the mean of the 
distribution? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Find HCF of the number 31, 310 and 3100. 
6. Find the least positive integer which on adding 1 is exactly divisible by 126 and 600. 
7. Find solution of the following pair of linear equations: 
3x – 7y=5 
x + y=15 
8. In the figure,  l m  and OAC OBD ? ? ~ . If AC=5cm, OA=3cm and BD=2cm, find OB. 
 
9. Solve the equation for ? : 
2
2 2
cos
3
cot cos
?
? ?
=
- 
 
 
 
 
10. Find the median of the data using an empirical formula, when it is given that mode=35.3 and 
mean=30.5 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Write 32875 as product of prime factors. Is this factorization unique? 
12. Divide the polynomial 
2 2
4 6 10 3 x x x - - - by the polynomial 
2
x x + and verify the division 
algorithm. 
13. Find the zeroes of the quadratic polynomial 
2
2 5 3 x x + - and verify the relationship between 
the zeroes and the coefficients. 
14. Solve using cross multiplication method. 
4c – v =4 
3u + 2v =14 
15. If in ABC ? , AD is median and AM BC ? , then that 
2 2 2
1
4
AC AD BC DM BC = + × + 
16. ABC is an isosceles triangle. If 90 B ? = ° , then prove that 
2 2
2 AC BC = . 
17. If cos(40 ) sin 30 x ° + = ° , find the value of x. 
18. Prove the identify: 
(1 tan sec )(1 cot cos ) 2 ec ? ? ? ? + + + - = 
19. The given distribution shows the number of runs scored by the batsmen in inter-school 
cricket matches: 
Runs scored 0-50 50-100 100-150 150-200 200-250 
Number of 
batsmen 
4 6 9 7 5 
20. In a health check-up, the number of heart beats of 40 women were recorded in the following 
table: 
Number of heart 
beats/minute 
65-69 70-74 75-79 80-84 
Number of 
women 
2 18 16 4 
 
 
Section D 
Questions 21 to 31 carry 4 marks each. 
21. Express the HCF of number 72 and 124 as a linear combination of 72 and 124. 
22. Ridhi decided to use public transport to cover a distance of 300 km. She travels this distance 
partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and 
remaining by bus. If she travels 100km by train and the remaining by bus, she takes 10 
minutes more. Find the speed of train and bus separately. Why does Ridhi decide to opt for 
public transport? 
 
 
 
 
23. 5 years ago, age of one sister was twice the other sister. 5 years hence ages will be in the ratio 
2:3. Find their present ages. 
24. Obtain all other zeroes of the polynomial 
4 3 2
2 3 15 24 8 x x x x + - - - , if two of its zeroes are 
2 2 and 2 2 - . 
25. In figure of ABC ? , P is the middle point of BC and Q is middle point of AP. If extended BQ 
meets AC in R, then prove that 
1
3
RA CA = 
 
26. In a parallelogram ABCD, E is any point on side BC. Diagonal BD and AE intersect at P. prove 
that DP EP PB PA × = × . 
27. If cos (A + B)=0 and cot( ) 3 A B - = , find the value of  
a) secA. tanB – cotA. sinB 
b) cosecA. cotB + sinA. tanB 
28. If tanA + sin A = m and tanA – sinA = n, then prove that 
( )
2
2 2
16 m n mn - = . 
29. In the adjoining figure, ABCD is a rectangle with breadth BC=7cm and 30 CAB ? = ° . Find the 
length of side AB of the rectangle and length of diagonal AC. If the 60 CAB ? = ° , then what is 
the size of the side AB of the rectangle [ 3 1.73 2 1.41 use and = = if required] 
 
30. During an examination, percentage of marks scored by the students are recorded and are 
shown in the following table: 
Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 
Number 
of 
students 
1 3 2 8 20 15 13 25 18 10 
Find the mode and median for the above data. 
31. In a class, heights of students are recorded as follows: 
Height 
(in cm) 
Less 
than 
142 
Less 
than 
146 
Less 
than 
150 
Less 
than 
154 
Less 
than 
158 
Less 
than 
162 
Less 
than 
166 
Less 
than 
170 
Number 
of 
students 
2 5 20 40 57 75 79 80 
For above data, draw a ‘less than type’ ogive and from the curve, find median. Also, verify 
median by actual calculations.