This document is a sample test paper for Class 9 mathematics. It consists of 37 total questions divided into 4 sections - Section A has 10 single mark questions, Section B has 9 two mark questions, Section C has 10 three mark questions, and Section D has 8 four mark questions. The test covers a range of mathematics topics and concepts, including geometry, algebra, trigonometry, and statistics. Students are instructed to answer all questions within the allotted time of 3 hours.

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MATHEMATICS
SAMPLE TEST PAPER (SEMSTER )
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. ABCD is a parallelogram and X and Y are the mid – points of sides AB and CD respectively.
Then the quadrilateral AXCY is
a) parallelogram b) a rectangle c)a rhombus d) a square
2. The remainder when 2x3-5x2-7 is divisible by x-2
a) 12 b) 16 c)9 d) 2
3. The point (-3, 2) lies in which quadrant.
a) I b) II c)III d) IV
4. volume of sphere of radius 11.2 cm
a) 588cm3
b) 588.56cm3
c)560.86cm3
9d) 5887.32cm3
5. The condition that the equation ax+by+c= 0 represents a linear equation is two variables is
a) a#0,b=0 b) b#0,a=0 c) a=0,b=0 d) a#0,b#0
6.
If two sides of a triangle are 18cm, 10cm and the perimeter is 42 cm, then its area in cm2
a) 8√30 b) 21√11 c) 24√6 d) 9√2
7. The class marks of a frequency distribution are 15,20,25. the call corresponding to the class
marks 20 is
a) 17.5,22.5 b) 12.5,17.5 c) 18.5 ,21.5 d) 19.5,20.5
8. The factorization of -x2+5x-6 yields
a) (x-2) (x-3) b) (2+x) (3-x) c) -(x-2) (3-x) d) -(2-x)(3-x)
9. The mean of seven observation is 20. if one number is added , the mean become 21. the added
number is
a) 28 b)18 c)7 d) 38
10. In ∆ABC, BC = AB and B = 80°. Then angle A is equal to
a) 800 b) 400c) 500 d)1000
SECTION B

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11. Rationalize the denominator
1
(7+ 5√ 2)
12.
Expand (5x+1)2
13.
expand (x+2y+4z)2
14. A Right circular cone of base radius 7 cm and height 24 cm. Find the area of sheet required to
make 20 such cone.
15. Find the volume of the right circular cone with radius 5cm and height 15cm.
16. State Euclid postulates
17. A right triangle ABC with sides 5 cm, 12cm and 15 cm is revolved about the side 12cm, find the
volume of the solid obtained.
18. How many liters of milk can a hemispherical bowl of diameter 15cm hold.
19. Side of a triangle are in the ratio of 12:17:25 and its perimeter is 240cm. Find the area
SECTION C
20. In which quadrant does the point lie (-3,4) ,(5,-6) (-1,0) (-3,8)
21. In the figure ABC is an equatorial triangle . The coordinates of vertices B and C are (2,0) and
(-2, 0)
22. PQ is perpendicular to PS, PQ is parallel to SR, SRQ = 280,QRT = 650, then find the value of
x.
23. Plot the following on the graph . Join the points and name the figure so formed.
A(-3,1) B(1,1) C(-3,-3) and D (2,-3)
24. Find surface area of sphere of diameter 24 cm.
25. Construct an equilateral triangle, given its side and justify the construction.
26. Find the value of k if x – 1 is a factor of x2
- 3x + 2k
27. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y .
Prove that ar (ADX)=ar(ACY).
28.

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29. A random survey of the number of children of various age groups playing in a park was found
as follows, draw a histogram to represent the data above.
SECTION D
30. Factories 8x3
+y3
+27z3
-18xyz
31. Write four solution for the equation π x+y = 5
32. If land m are two parallel lines intersected by another pair of parallel lines pa nd q show that
triangle ABC is equal to triangle CDA.
33. A shot put is a metallic sphere of radius 5cm, if the density of the metal is 10 per cm3, find the
mass of the shot put.
34. In an isosceles triangle ABC with AB =AC , D and E are points on BC such that BE=CD. Show
that AD=AE.

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35. Construct a triangle ABC in which BC = 8 cm, angle B = 800
and AB+AC = 12 cm.
36. An umbrella is made by stitching 1 triangles pieces of cloth of two different colors, each piece
measuring 20cm,50 cm and 50 cm. How much h cloth of each co lour is required for the
umbrella
37. Three coins are tossed simultaneously 300 times with the following frequencies of different
outcomes:
If three coins are tossed simultaneously tossed again, compute the probability of 3 heads coming up.
Outcomes 3 heads 2 heads 1 heads No
heads
Frequency 43 85 92 80