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Page 1
PRE – SA 1 (2016)
Class – X
SUB : MATHEMATICS
Time Allowed : 3 Hrs. Maximum Marks : 90
Section – A (1 Marks)
Q.1 If 9
2 2
sin 5cos 6. ? ? + = Find tan ?
Q.2 In ABC ?
|| DF BC
Find the value of x
Q.3 If mean of 1,2, 3 ……. n is
16
,
11
n then find the value of n.
Q.4 State whether the following statement is true or false. Justify your answer.
( ) Sin Sin Sin A B A B + = +
Section – B ( 2 Marks Each)
Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your
answer.
Q.6 In the given fig || DE AC and || . DF AE Prove that
EF EC
BF BE
-
Page 2
PRE – SA 1 (2016)
Class – X
SUB : MATHEMATICS
Time Allowed : 3 Hrs. Maximum Marks : 90
Section – A (1 Marks)
Q.1 If 9
2 2
sin 5cos 6. ? ? + = Find tan ?
Q.2 In ABC ?
|| DF BC
Find the value of x
Q.3 If mean of 1,2, 3 ……. n is
16
,
11
n then find the value of n.
Q.4 State whether the following statement is true or false. Justify your answer.
( ) Sin Sin Sin A B A B + = +
Section – B ( 2 Marks Each)
Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your
answer.
Q.6 In the given fig || DE AC and || . DF AE Prove that
EF EC
BF BE
-
Q.7 The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg. and that of B
and C be 43 kg. Find the weight of B.
Q. 8 Find the value of tan 60 geometrically.
Q. 9 Find HCF of 3.5 , and 6.5 and 8.5
Q.10 If 2 23 4 19 x y and x y + = - =
Find the value of 2
y
x
-
Section-C (Three Marks Each)
Q.11 Check whether 4
n
can end with the digit 0 for any natural number n.
Q.12 Draw the graph of the equation 5 7 50 7 5 46 x y and x y + = + = and shade the triangular region
formed by the lines and x-axis also find the area of triangle.
Q.13 Two candles of equal height but different thickness are lighted. The first burns off in 6 hours
and the second in 8 hours. How long, after lighting both, will be first candle be half the height
of the second?
Q.14 If and a ß are the zeroes of the polynomial
2
2 15 x x - - then form a quadratic polynomial
whose zeroes are ( ) ( ) 2 2 and a ß
Q.15 If Cos sin 2cos ? ? ? + = Show that os sin 2sin C ? ? ? - =
Q.16 Evaluate
2 2 2 2
2
tan 60 4sin 45 3Sec 30 5Cos 90
Cos 30 Sec60 30 ec Cot
+ + +
+ -
Q.17 ABC ? and DBC ? are on the same box BC and on opposite sides of BC. O is the point of
intersection of AD and BC. Prove that:
area ABC AO
areaof DBC DO
?
=
?
Q.18 In ABC ? , A is obtuse angle PB AC ? and QC AB ? . Prove that AB AQ AC AP × = ×
Page 3
PRE – SA 1 (2016)
Class – X
SUB : MATHEMATICS
Time Allowed : 3 Hrs. Maximum Marks : 90
Section – A (1 Marks)
Q.1 If 9
2 2
sin 5cos 6. ? ? + = Find tan ?
Q.2 In ABC ?
|| DF BC
Find the value of x
Q.3 If mean of 1,2, 3 ……. n is
16
,
11
n then find the value of n.
Q.4 State whether the following statement is true or false. Justify your answer.
( ) Sin Sin Sin A B A B + = +
Section – B ( 2 Marks Each)
Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your
answer.
Q.6 In the given fig || DE AC and || . DF AE Prove that
EF EC
BF BE
-
Q.7 The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg. and that of B
and C be 43 kg. Find the weight of B.
Q. 8 Find the value of tan 60 geometrically.
Q. 9 Find HCF of 3.5 , and 6.5 and 8.5
Q.10 If 2 23 4 19 x y and x y + = - =
Find the value of 2
y
x
-
Section-C (Three Marks Each)
Q.11 Check whether 4
n
can end with the digit 0 for any natural number n.
Q.12 Draw the graph of the equation 5 7 50 7 5 46 x y and x y + = + = and shade the triangular region
formed by the lines and x-axis also find the area of triangle.
Q.13 Two candles of equal height but different thickness are lighted. The first burns off in 6 hours
and the second in 8 hours. How long, after lighting both, will be first candle be half the height
of the second?
Q.14 If and a ß are the zeroes of the polynomial
2
2 15 x x - - then form a quadratic polynomial
whose zeroes are ( ) ( ) 2 2 and a ß
Q.15 If Cos sin 2cos ? ? ? + = Show that os sin 2sin C ? ? ? - =
Q.16 Evaluate
2 2 2 2
2
tan 60 4sin 45 3Sec 30 5Cos 90
Cos 30 Sec60 30 ec Cot
+ + +
+ -
Q.17 ABC ? and DBC ? are on the same box BC and on opposite sides of BC. O is the point of
intersection of AD and BC. Prove that:
area ABC AO
areaof DBC DO
?
=
?
Q.18 In ABC ? , A is obtuse angle PB AC ? and QC AB ? . Prove that AB AQ AC AP × = ×
Q. 19 Find mean :
CLASS 0-10 10-20 20-30 30-40 40-50
FREQUENCY 7 12 13 10 8
Q.20 Find the median of the data:
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
No. of
students
5 3 4 3 3 4 7 9 7 8
Section – D (Four Marks Each)
Q. 21 Find other zeroes of the polynomial ( )
4 3 2
2 7 19 14 30 p x x x x x = + - - + if two of its zeroes are
2 2 and - .
Q.22 In a triangle, if the square of one side is equal to the sum of the squares of the other two sides
then the angle opposite to the first side is a right angle.
Q.23 Evaluate:
( ) ( )
2 2
Sec Cos 90 tan cot 90 Sin 55 Sin 35
tan10tan20tan60tan70tan80
ec ? ? ? ? - - - + +
Q.24 If
1
tan , tan
1 2 1
m
A B
m m
= =
+ +
Using the formula ( )
tan tan
tan
1 tan tan
A B
A B
A B
+
+ =
-
Find A and B where A+B is an acute angle and 3A+B= 105.
Q.25 p(x) is a polynomial of degree more than 2, when p(x) is divided by 2 x + it leaves a remainder
2 and when it is divided by ( ) 3 x - it leaves a remainder 3. If p(x) when divided by
2
6 x x - -
leaves a remainder ax+b. Find the value of a-b.
Q.26 The following table gives the production yield per hectare of wheat of 100 farms of a village:
Production yield in kg/Hectare 50-55 55-60 60-65 65-70 70-75 75-80
No. of Farms 2 8 12 24 38 16
Change the above distribution to more than type distribution and draw its again.
Page 4
PRE – SA 1 (2016)
Class – X
SUB : MATHEMATICS
Time Allowed : 3 Hrs. Maximum Marks : 90
Section – A (1 Marks)
Q.1 If 9
2 2
sin 5cos 6. ? ? + = Find tan ?
Q.2 In ABC ?
|| DF BC
Find the value of x
Q.3 If mean of 1,2, 3 ……. n is
16
,
11
n then find the value of n.
Q.4 State whether the following statement is true or false. Justify your answer.
( ) Sin Sin Sin A B A B + = +
Section – B ( 2 Marks Each)
Q.5 25 and 147 are HCF and LCM of two natural numbers respectively. Is it true? Justify your
answer.
Q.6 In the given fig || DE AC and || . DF AE Prove that
EF EC
BF BE
-
Q.7 The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg. and that of B
and C be 43 kg. Find the weight of B.
Q. 8 Find the value of tan 60 geometrically.
Q. 9 Find HCF of 3.5 , and 6.5 and 8.5
Q.10 If 2 23 4 19 x y and x y + = - =
Find the value of 2
y
x
-
Section-C (Three Marks Each)
Q.11 Check whether 4
n
can end with the digit 0 for any natural number n.
Q.12 Draw the graph of the equation 5 7 50 7 5 46 x y and x y + = + = and shade the triangular region
formed by the lines and x-axis also find the area of triangle.
Q.13 Two candles of equal height but different thickness are lighted. The first burns off in 6 hours
and the second in 8 hours. How long, after lighting both, will be first candle be half the height
of the second?
Q.14 If and a ß are the zeroes of the polynomial
2
2 15 x x - - then form a quadratic polynomial
whose zeroes are ( ) ( ) 2 2 and a ß
Q.15 If Cos sin 2cos ? ? ? + = Show that os sin 2sin C ? ? ? - =
Q.16 Evaluate
2 2 2 2
2
tan 60 4sin 45 3Sec 30 5Cos 90
Cos 30 Sec60 30 ec Cot
+ + +
+ -
Q.17 ABC ? and DBC ? are on the same box BC and on opposite sides of BC. O is the point of
intersection of AD and BC. Prove that:
area ABC AO
areaof DBC DO
?
=
?
Q.18 In ABC ? , A is obtuse angle PB AC ? and QC AB ? . Prove that AB AQ AC AP × = ×
Q. 19 Find mean :
CLASS 0-10 10-20 20-30 30-40 40-50
FREQUENCY 7 12 13 10 8
Q.20 Find the median of the data:
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
No. of
students
5 3 4 3 3 4 7 9 7 8
Section – D (Four Marks Each)
Q. 21 Find other zeroes of the polynomial ( )
4 3 2
2 7 19 14 30 p x x x x x = + - - + if two of its zeroes are
2 2 and - .
Q.22 In a triangle, if the square of one side is equal to the sum of the squares of the other two sides
then the angle opposite to the first side is a right angle.
Q.23 Evaluate:
( ) ( )
2 2
Sec Cos 90 tan cot 90 Sin 55 Sin 35
tan10tan20tan60tan70tan80
ec ? ? ? ? - - - + +
Q.24 If
1
tan , tan
1 2 1
m
A B
m m
= =
+ +
Using the formula ( )
tan tan
tan
1 tan tan
A B
A B
A B
+
+ =
-
Find A and B where A+B is an acute angle and 3A+B= 105.
Q.25 p(x) is a polynomial of degree more than 2, when p(x) is divided by 2 x + it leaves a remainder
2 and when it is divided by ( ) 3 x - it leaves a remainder 3. If p(x) when divided by
2
6 x x - -
leaves a remainder ax+b. Find the value of a-b.
Q.26 The following table gives the production yield per hectare of wheat of 100 farms of a village:
Production yield in kg/Hectare 50-55 55-60 60-65 65-70 70-75 75-80
No. of Farms 2 8 12 24 38 16
Change the above distribution to more than type distribution and draw its again.
Q.27 Prove that:
in os
1
ec tan 1 os cot 1
s A c A
s A A c ecA A
+ =
+ - + -
Q.28 If the mean of the following frequency distribution is 65.6. Find the missing frequencies x & y.
Class 10-30 30-50 50-70 70-90 90-110 110-130
Frequency 5 8 x 20 y 2 =50
Q.29 A railway half ticket costs half the full fare and the reservation charge is the same on half ticket
as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs. 216 and
full and one half reserved first class tickets costs Rs. 327. What is the basic first class full fare
and what is the reservation charge?
Q.30 In ABC ? is triangle. PQ is a line segment intersecting AB in P and AC in Q. Such that PQ/BC
and divides ABC ? into two parts equal in area. Find BP/AB.
Q.31 Show that
2
p will leave a remainder 1 when divided by 8 if p is an odd positive integer.
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FAQs on CBSE Math Past Year Paper SA-1: Set 4 (2016) - Past Year Papers for Class 10
| 1. What is the CBSE Math Past Year Paper SA-1? |  |
Ans. The CBSE Math Past Year Paper SA-1 refers to the first summative assessment conducted by the Central Board of Secondary Education (CBSE) for the subject of Mathematics. It is an examination that assesses the knowledge and understanding of students in Class 10 based on the syllabus and topics covered during the first half of the academic year.
| 2. How can I access the CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016)? | |
Ans. The CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016) can be accessed through various sources. One way is to visit the official website of CBSE (cbse.nic.in) and look for the previous years' question papers section. Another way is to search for reliable educational websites or forums that provide access to past year papers. Additionally, some books or study materials may also include these question papers.
| 3. What topics are covered in the CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016)? | |
Ans. The CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016) covers a range of topics from the Mathematics syllabus for Class 10. Some of the common topics that may be included are algebra, geometry, trigonometry, statistics, and probability. It is important for students to thoroughly revise and practice these topics to perform well in the examination.
| 4. How can solving the CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016) help in exam preparation? | |
Ans. Solving the CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016) can be beneficial in exam preparation in several ways. Firstly, it provides students with an understanding of the exam pattern, marking scheme, and types of questions that can be expected in the actual examination. Secondly, it allows students to assess their level of preparedness and identify areas where they need to focus more. Lastly, it helps in improving time management skills and builds confidence by familiarizing students with the format of the exam.
| 5. Are there any additional resources available to support the preparation for the CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016)? | |
Ans. Yes, there are several additional resources available to support the preparation for the CBSE Math Past Year Paper SA-1 for Class 10 Set 4 (2016). Students can refer to textbooks prescribed by CBSE, solve sample question papers, enroll in online or offline coaching classes, and seek guidance from teachers or subject matter experts. Additionally, there are various educational websites and mobile applications that offer study materials, video lessons, and practice quizzes to enhance exam preparation.
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