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SUMMATIVE
ग�णत/
�नधा��रत समय: 3 घंटे
Time Allowed : 3 hours
समा$य �नद&श:
1. सभी ��न अ�नवाय� ह� |
2. इस ��न प� म� 31 ��न ह�, िज�ह�
��येक 1 अंक का है; ख-ड-ब म� 6 12न
3 अंक ह� ; तथा ख-ड-द म� 11 12न ह� िजनम� ��येक के
3. इस ��न प� म� कोई #वक%प नह&ं है
4. कैलकुलेटर का �योग विज.त है |
General Instructions:
1. All questions are compulsory.
2. The question paper consists of
Section-A comprises of 4 questions
marks each; section-C comprises of
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
ख�ड
��न सं�या 1 से 4 तक ��येक ��न
Question numbers 1 to 4 carry 1 mark each.
Q1. y = 3 का �ाफ �कस अ के समांतर रेखा
The graph of y = 3 will be parallel to which axis?
Q2. 2.739 को �
� के �प म� �य�त क�िजए
Express 2.739 in the form of
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ATP Model Sample Paper
संक�लत पर�ा – I, 2016
SUMMATIVE ASSESSMENT – I, 2016-17
/ MATHEMATICS (code-15-00152)
क�ा – IX / CLASS – IX
घंटे अ�धकतम अंक
hours Maximum Marks
िज�ह� चार ख,ड. अ, ब, स तथा द म� बांटा गया है | खंड-अ
12न ह� िजनम� ��येक के 2 अंक ह�; ख,ड-स म� 10 12न ह� िजनम� ��येक के
ह� िजनम� ��येक के 4 अंक ह� |
इस ��न प� म� कोई वक"प नह#ं है |
.
2. The question paper consists of 31 questions divided into four sections A, B, C
4 questions of 1 mark each; section-B comprises of 6 questions
comprises of 10 questions of 3 marks each; section-D
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
ख�ड-अ / SECTION-A
तक ��येक ��न 1 अंक का है |
Question numbers 1 to 4 carry 1 mark each.
�ाफ �कस अ के समांतर रेखा है ?
3 will be parallel to which axis?
के �प म� �य�त क�िजए |
in the form of �
�.
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अ�धकतम अंक : 90
Maximum Marks : 90
म� 4 ��न ह� िजनम�
ह� िजनम� ��येक के
sections A, B, C and D.
6 questions of 2
D comprises of 11
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Q3. बहुपद 2x - 3 का श#ुयक $ात क�िजए
Find the zero of polynomial 2
Q4. द% गयी आकृ*त PQR म�,
In the given fig. PQR,
��न स�ंया 5 से 10 तक �येक ��न
Question numbers 5 to 10 carry 2 marks each.
Q5. उपयु�त सव1स2मका के 3योग से
Simplify using suitable identity.
997 × 995
Q6. एक समबाहु 45भुज का प7रमाप
का े5फल $ात क�िजए |
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 c
Find the area of the triangle.
Q7. द% गई आकृ*त म�, AC = XD, AB
अ2भगहृ%त के 3योग से ;दखाइए �क
In the given figure, AC = XD, C is the midpoint of AB and D is the midpoint of
XY. Using Euclid’s axiom show that AB = XY.
B
C ·
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का श ुयक !ात क�िजए |
Find the zero of polynomial 2x – 3.
, QPR = 47o तथा PQR = 63o है तो x मान !ात क�िजए
, QPR = 47o and PQR = 63o, Then find the value of x.
खड-ब / SECTION-B
तक ��येक ��न 2 अंक का है |
Question numbers 5 to 10 carry 2 marks each.
उपयु�त सव)स*मका के +योग से सरल क�िजए |
using suitable identity.
एक समबाहु /0भुज का प2रमाप 30 cm है और इसक� +9येक समान भुजा 12 cm
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 c
the area of the triangle.
AC = XD, AB का मा
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Q8. आकृ*त म�, PQR = PRQ
In figure, PQR = PRQ, then prove that
Q9. =व>ता7रत �प म� 2ल?खए |
Write in expanded form.
(3x – 2y + 5z)2
Q10. √3 को सं@या रेखा पर दशा1इए
Show √3 on the number line.
��न स�ंया 11 से 20 तक �येक ��न
Question numbers 11 to 20 carry 3 marks each.
Q11. दशा1इए �क;
Show that;
�
�� √��
�
√� � √�
�
√�
Q12. 1.32� + 0. 35���� को सरलतम 2भ#न के �प म� 2लखये
Express 1.32� + 0. 35���� as a fraction in simplest form.
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PRQ है, तो *सEध क�िजए �क PQS = PRT है |
PRQ, then prove that PQS = PRT.
को सGंया रेखा पर दशा)इए |
on the number line.
खड-स / SECTION-C
तक ��येक ��न 3 अंक का है |
Question numbers 11 to 20 carry 3 marks each.
√��
�
√�� √��
�
√� � � 5
को सरलतम *भ न के �प म� *लखये |
� as a fraction in simplest form.
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PRT.
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Q13. द% गई आकृ*त म�, रेखा XY
POY = 90° और a : b = 2 : 3
In the given figure, lines XY and MN intersect at O.
If POY = 90° and a :
Q14. सLया=पत क�िजए �क:
Verify that:
x3 + y3 + z3 – 3xyz = �
�
Q15. 2सNध क�िजए �क समबाहु 45भुज के बराबर भुजाओ ंके सQमुख कोण बराबर होते है
Prove that the opposite angles of equal side of an isosceles triangle are equal.
Q16. गुणनखंड क�िजए ;
Factorise;
a3 – b3 + 1 + 3ab
Q17. एक पाक1 चतुभु1ज ABCD के आकार का है
CD = 5 m और AD = 8 m
A park, in the shape of a quadrilateral ABCD, has
BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
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XY तथा MN एक दसुरे को /बदं ुO पर +KतLछेद करते हN
= 2 : 3 है तो c का मान !ात क�िजए |
given figure, lines XY and MN intersect at O.
: b = 2 : 3, find c.
�
��� � � � ����� ��� � �� ��� � �� ���
*सEध क�िजए �क समबाहु /0भुज के बराबर भुजाओ ंके सPमुख कोण बराबर होते है
Prove that the opposite angles of equal side of an isosceles triangle are equal.
के आकार का है, िजसम� C = 90º, AB = 9 m, BC = 12 m,
AD = 8 m है | इस पाक) का �कतना े0फल है ? देSखए आकृKत
A park, in the shape of a quadrilateral ABCD, has C = 90º, AB = 9 m,
CD = 5 m and AD = 8 m. How much area does it occupy?
A
B
C D
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पर ��त छेद करते ह# | य$द
�
%स'ध क�िजए )क समबाहु ��भुज के बराबर भजुाओ ंके स-मुख कोण बराबर होते है |
Prove that the opposite angles of equal side of an isosceles triangle are equal.
= 90º, AB = 9 m, BC = 12 m,
दे0खए आकृ�त,
= 90º, AB = 9 m,
CD = 5 m and AD = 8 m. How much area does it occupy?
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See figure,
Q18. आकृ*त म�, ;दया है �क AB = CF, EF = BD
AFE CBD.
In given figure, given that
that AFE CBD.
Q19. P का मान $ात क�िजए य;द
है |
Find the value of p, if (x + 2) is the one of factor of
Q20. द% गई आकृ*त म�, DAC का समN=वभाजक
AE || BC है |
In given figure, AE bisects
��न स�ंया 21 से 31 तक �येक ��न
Question numbers 21 to 31 carry 4 marks each.
Q21. य;द � � √�√�
√��√� और � �
If � � √�√�
√��√� and �
Q22. य;द �� � �
� = 47 हो, तो
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AB = CF, EF = BD तथा AFE = CBD, तो *सEध क�िजए �क
In given figure, given that AB = CF, EF = BD and AFE = CBD, then prove
का मान !ात क�िजए यDद (x + 2), P(x) = 3x3 – 4x2 + 5x + p बहुपद का एक गुणनखंड
Find the value of p, if (x + 2) is the one of factor of P(x) = 3x3 –
का समEYवभाजक AE है तथा B = C है तो *सEध क�िजए �क
AE bisects DAC and B = C, prove that AE || BC.
खड-द / SECTION-D
तक ��येक ��न 4 अंक का है |
Question numbers 21 to 31 carry 4 marks each.
� √�√
√�√ है तो a2 + b2 - 5ab का मान !ात क�िजए
� � √�√
√�√ , find the value of a2 + b2 - 5ab
तो � � �
�� का मान !ात क�िजए |
A
E
D
B
C
A
B
D
E
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तो %स'ध क�िजए )क
CBD, then prove
बहुपद का एक गुणनखंड
4x2 + 5x + p.
है तो %स'ध क�िजए )क
, prove that AE || BC.
का मान �ात क�िजए |
5ab.
C
F
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If �� � �
� = 47 then find the value of
Q23. द% गई आकृ*त म�, AB = AD,
|
In the given figure, AB = AD,
Q24. य;द (x + 2) बहुपद x3 + 13x
If (x + 2) is the one of the factor of polynomial x
its other factors.
Q25. बहुपदf x3 + 2x2 – 5ax – 7
=वभािजत करने पर शषेफल R
$ात क�िजए |
On dividing polynomials
and (x – 2) respectively gives remainder R
value of a.
Q26. एक खेत समलबं के आकार का है िजसक� समांतर भुजाएँ
असमांतर भुजाएँ 14 m और 13
A field is in the shape of a trapezium whose parallel
The non-parallel sides are 14 m and 13 m. Find the area of the field.
Q27. गुणनखंड क�िजए;
Factorise;
8(a + 1)2 + 2(a + 1)(b + 2)
A
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= 47 then find the value of � � �
��.
AB = AD, 1 = 2 और 3 = 4 है | *सEध क�िजए �क
In the given figure, AB = AD, 1 = 2 and 3 = 4. Prove that AP =
+ 13x2 + 32x + 20 का एक गुणनखडं है तो इसके शषे !ात क�िजए
is the one of the factor of polynomial x3 + 13x2 + 32x + 20, then find
7 तथा x3 + ax2 – 12x + 6 ^मश: (x + 1) तथा
R1 तथा R2 +ाdत होते हN | यDद 2R1 + R2 = 6 हो तो
polynomials x3 + 2x2 – 5ax – 7 and x3 + ax2 – 12x + 6 by (x + 1)
2) respectively gives remainder R1 and R2. If 2R1 + R2 = 6 then find the
एक खेत समलबं के आकार का है िजसक� समांतर भुजाएँ 25 m और 10 m हN
13 m हN | इस खेत का े0फल !ात क�िजए |
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m.
are 14 m and 13 m. Find the area of the field.
+ 2(a + 1)(b + 2) – 15(b + 2)2
P
B
C
Q
D
1 3 4
2
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%स'ध क�िजए )क AP = AQ है
= AQ
का एक गुणनखडं है तो इसके शषे �ात क�िजए|
+ 32x + 20, then find
तथा (x - 2) से
हो तो a का मान
12x + 6 by (x + 1)
= 6 then find the
ह# | इसक�
sides are 25 m and 10 m.
are 14 m and 13 m. Find the area of the field.
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Q28. द% गई आकृ*त म�, POQ एक रेखा है
है जो �करण OP तथा OR के बीच ि>थत है
POS)
In given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another
ray lying between rays OP and OR. Prove that
Q29. आकृ*त म�, रेखा l कोण A को समN=वभािजत करती
BP और BQ कोण A क� भुजाओ ंपर
(i) APB AQB
(ii) BP = BQ
In figure, line l is the bisector of an angle
BQ are perpendiculars from B
(i) APB AQB
(ii) BP = BQ
Q30. आकृ*त म�, AB और CD चतुभु1ज
दशा1इए �क A > C और B
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एक रेखा है | �करण OR रेखा PQ पर लबं है | OS
के बीच िjथत है | *सEध क�िजए �क ROS = �� (
In given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another
ray lying between rays OP and OR. Prove that ROS = �
� (QOS -
को समEYवभािजत करती है और B रेखा l पर िjथत कोई /बदं ुहै
क� भुजाओ ंपर B से डाले गए लंब हN | दशा)इए �क
is the bisector of an angle A and B is any point on
BQ are perpendiculars from B to the arms of A. Show that:
चतुभु)ज ABCD के ^मश: सबसे छोटC और बड़ी भुजाएँ हN
B > D.
A P
B
Q
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OS एक अEय )करण
(QOS -
In given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another
- POS).
पर िFथत कोई �बदं ुहै |
point on l. BP and
सबसे छोटI और बड़ी भजुाएँ ह# |
l
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In figure, AB and CD are respectively the smallest and
quadrilateral ABCD. Show that
Q31. 2सNध क�िजए �क समबाहु 45भुज के 3Lयेक कोण
Prove that the each angle of a equilateral triangle is 60
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and CD are respectively the smallest and longest sides of a
quadrilateral ABCD. Show that A > C and B > D.
*सEध क�िजए �क समबाहु /0भुज के +9येक कोण 60o होता है |
Prove that the each angle of a equilateral triangle is 60o.
***(---***----)***
The Best of Luck
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longest sides of a