Cbse class 9 maths sample paper model 1 - http://cbse.edurite.com/cbse-maths/maths-cbse-class-9.html

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MATHEMATICS
SAMPLE TEST PAPER
CLASS IX
Class:9 Max Mks:90
Time 3hrs No of pages: 4
General Instructions:
Ò All questions are compulsory.
Ò The question paper consists of 37questions divided into four sections - A, B, C and D.
Ò Section - A contains 10 questions of 1 mark each,
Ò Section B is of 9 questions of 2 marks each, Section C is of 10 questions of 3 marks each and
Ò section D is of 8 questions of 4 marks each.
Ò The drawing should be maintained as per the given measurements.
SECTION A
1. The (√a+√b) (√a-√b) identity hold _____
a) a+b b) a-b c) a*b d) a÷b
2. The highest power of the variable x5
+4x4
+6 is ___
a) 5 b) 4 c) 2 d) 5
3. The linear equation as 5x+8y =10
a) unique solution b)Two solutions c) Infinitely many solutions d) No solution
4. curved surface area of cone with h= 10 cm and r = 7 cm
a) 210 cm2
b) 220 cm2
c) 240 cm2
d) 250 cm2
5. Simplify (5+√5) (5-√5)
a) 20 b) 10 c) 01 d) 25
6. The value of the polynomial 5x2
+2x-4 at x = 2 is
a) 20 b) 40 c) 21 d) 25
7. If a+b+c= 0then a3+b3+c3 is
a) (a+b+c) b) 3ab c) 3abc d) 3bc
8. In a cylinder the radius is doubled and height is halved , curved surface are will be
a) halved b) doubled c) same d) four times
9. The number of zeros in quadrilateral polynomial are
a) 4 b) 3 c) 2 d) 1
10. Three coins are tossed simultaneously 200 times with the following frequencies of different
outcomes:
a)3 heads b)2heads c)1 heads d)no head
SECTION B

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11. Find the differential ration number between
5
7 and
9
13
12. Represent 4.765 on the number line, using successive magnification
13. Explain Euclid's postulates for an circle.
14. The weight of 8 students are given below find the median of the data
54,58,62,60,54,52,60,66
15. Find the lateral or curved surface area of a closed cylinder tank of 5.2m in diameter and 6.2m
high.
16. The sides of triangle are in the ratio of 7:9:11 and the perimeter is 500m . find its area
17. construct a angle and verify by measuring them using protractor.
1350
18. In the given parallelogram the value of x will be
19. If the volume of a right circular cone of height 9 cm,is 52πcm3
,find the diameter of the base.
SECTION C
20. Rationalize the denominator
1
(√ 7+ √ 2)
21.
Write in expanded form (3a+5b)2
22. PQ is parallel to ST, angle PQR = 1100
and RST = 1500
, find QRS
23. Angle B > Angle A and Angle C > Angle D Show that AD>BC
24. ABCD is a rectangle, PQ,R,S are mid points of side AB,BC,CD and DA Respectively . Show
that the quadrilateral PQRS is a rectangle.

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25. A coin is tossed 1000 times, with the following frequencies Head : 600 tail : 400
26.
Find the cost of digging a cuboidal pit 9m long, 5 m board and 4 m deep at the rate of 50 per
m3
27. Show that a median of a triangle divides it into two triangles of equal areas.
28. In the given figure, E is the mid-point of side AD of a trapezium ABCD with AB||CD. A line
through E parallel to AB meets BC in F show that F is the mid-point of BC.
29. Draw on graph paper x+2y = 6
SECTION D
30. Find the remainder when x4
+3x2
+5x+1 is divided by x+3
31. If two lines intersect each other ; then the vertically opposite angel are equal
32. Construct a triangle XYZ in which angle Y = 400
, Z = 900
and XY+YZ+ZX = 14cm.
33. XYZ is a n isosceles triangle in which altitude YL and ZM are drawn to equal sides XY and XZ
respectively . Show that the altitudes are equal.
34. Show that the bisectors of angles of a parallelogram form a rectangle.

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35. The relative humidity of a certain city for a month of 30 days was as follows:
98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1
89.2 92.3 37.1 93.5 92.7 97.2 93.3. 95.2 97.3 96..5
96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89
a) construct a grouped frequency distribution with class 84-86,86-88,
b) which month or season do you think this data is about?
c) What is the range of this data
36. one angle of triangle is 760 and the other two angles are in the ration 5:8 . find the measure of
other angles.
37. An insurance company selected 2000 drivers at random in a particular city to find a relationship
between age and accidents. The data obtained are given in the following table.
find the probability of the following events for a drivers chosen at random from the city:
a) being 18-29 years of age and having exactly 3 accidents in one year.
b) Being 30-50 years of age and having one or more accidents in ayear
c) having no accident in one year.