9th class sample paper2015

Mock Test Papersth
(For Class 9 CBSE Summative Assessment-2 )
Apex Institute for IIT-JEE / PMT
Head Office : 62 Nitikhand -3 Indirapuram Cont. +91-9990495952, +91-9910817866, www.apexiit.co.in
Mathematics & Science

Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad: 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180, 9990495952 | www.apexiit.co.in/
Apex Institute Science & Mathematics Sample Paper: Class (IX)
MATHEMATICS-IX (Term-II)
Time : 3 hours M.M. : 90
SECTION A
(Question numbers 1 to 8 carry 1 mark each. For each
question, four alternative choices
have been provided of which only one is correct. You have
to select the correct choice.)
1. In the given figure, PQRS is a
rectangle. If ∠RPQ = 30°, then the
value of (x + y) is :
(a) 90° (b) 120°
(c) 150° (d) 180°
2. In the figure, if area of
parallelogram ABCD is 30 cm2, then
ar (ADE) + ar (BCE) is equal to :
(a) 20 cm2 (b) 30 cm2
(c) 15 cm2 (d) 25 cm2
3. In the figure, chord AB is greater
than chord CD. OL and OM are the
perpendiculars from the centre O on
these two chords as shown in the
figure. The correct relation between
OL and OM is :
(a) OL = OM (b) OL < OM
(c) OL > OM (d) none of these
4. Ratio of the volume of a cone and a cylinder of same
radius of base and same height is :
(a) 1 : 1 (b) 1 : 2 (c) 1 : 3 (d) 1 : 4
5. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are written in
ascending order. If median of data is 63, then x is :
(a) 62 (b) 63 (c) 124 (d) 126
6. In the given figure, ABCD is a
rhombus. If ∠OAB = 35°, then the
value of x is :
(a) 25° (b) 35°
(c) 55° (d) 70°
7. If the slant height of a cone is 13 cm and the base radius
is 5 cm, then the height of cone is :
(a) 12 cm (b) 8 cm (c) 10 cm (d) 18 cm
8. If P(E) denotes the probability of an event E, then :
(a) P(E) < 0 (b) P(E) >1
(c) 0 < P(E) < 1 (d) –1 < P(E) < 1
SECTION B
(Question numbers 9 to 14 carry 2 marks each.)
9. The cost of 6 eggs is the same as the cost of one bread.
Express this statement as a linear equation in two
variables. (Take the cost of one egg to be Rs x and that of a
bread to be Rs y).
10. In the figure, ABCD is a
quadrilateral and BD is one of its
diagonals. Show that ABCD is a
parallelogram and find its area.
11. In the figure, ABCD is a rectangle.
P and Q are the mid-points of AD
and DC respectively. Find the
length of PQ.
12. AOB is a diameter of a circle and C is a point on the
circle. Check whether
AC
2
+ BC
2
= AB
2
is true or not.
OR
For what value of x in the figure,
points A, B, C and D are concyclic?
13. If the edge of a cube is doubled,
what is the ratio of the volume of the
first cube to that of the second cube?
14. A die is thrown 225 times and the results were as
follows :
Outcome 1 2 3 4 5 6
Frequencies 34 50 16 71 24 30
Find the probability of getting a prime number.
SECTION C
15. Draw the graph of the equation 2y – x = 7 and
determine from the graph whether x = 3, y = 2 is its
solution or not.
16. Determine the point on the graph of the linear
equation 2x + 5y = 19 whose ordinate is
3
2
times its
abscissa.
17. The angles between two altitudes of a parallelogram
through the vertex of an obtuse angle of the parallelogram
is 60°. Find the angles of the parallelogram.
OR
ABCD is a trapezium with parallel sides AB = a cm and DC =
b cm. E and F are the mid-points of the non-parallel sides.
Show that the ratio of ar(ABFE) and ar(EFCD)
is (3a + b) : (a + 3b).
18. Construct a triangle whose sides are 4.2 cm, 3.9 cm and
6.1 cm. Bisect its greatest angle and measure each part.
19. If the perpendicular bisector of a chord AB of a circle
PXAQBY intersects the circle at P and Q, prove that
arcPXA arcPYB .
20. The total surface area of a solid cylinder is 462 cm2 and
its curved surface area is one third of its total surface area.
Find the radius of the cylinder.
21. A hemispherical vessel full of water is emptied in a
cone. The radii of the vessel and the cone are 12 cm and 8
cm respectively. Find the height of the water in the cone.
OR
A shopkeeper has one spherical ladoo of the radius 5 cm.
With the same amount of material, how many ladoos of
radius 2.5 cm can be made?
22. Prepare a continuous grouped frequency distribution
from the following data
Mid Point Frequencies
5
15
25
35
45
4
8
13
12
6
Also find the size of class intervals.

23. Show that if diagonals of a quadrilateral bisect each
other at right angles, then it is a
rhombus.
24. Find the mean of the following data
f 4 6 8 10 12
x 4 8 14 11 3
OR
A class consists of 50 students out of which 30 are girls.
The mean of marks scored by girls in a test is 73 and that
of boys is 71. Find the mean score of the whole class.
SECTION D
25. Draw the graph of the linear equation 2x + 3y = 12. At
what points, the graph of the equation cuts the x-axis and
the y-axis?
26. E and F are points on diagonal AC of a parallelogram
ABCD such that AE = CF. Show that BFDE is a
parallelogram.
27. Diagonals AC and BD of a quadrilateral ABCD intersect
at O in such a way that ar(AOD) = ar(BOC). Prove that
ABCD is a trapezium.
28. Prove that the angle subtended by an arc at the centre
is double the angle subtended by it at any point on the
remaining part of the circle.
29. A cloth having an area of 165 m2 is shaped into the
form of a conical tent of radius 5 cm.
(i) How many students can sit in the tent if a student on an
average, occupies5/7 m
2
on the ground?
(ii) Find the volume of the cone.
OR
The surface area of a sphere of radius 5 cm is five times the
area of the curved surface of a cone of radius 4 cm. Find
the height and volume of the cone.
30. Draw a histogram for the following data :
C.I. 25-29 30-34 35-39 40-44 45-49 50-54
Frequency 8 15 23 20 10 9
31. Show that the diagonals of a rhombus are
perpendicular to each other.
OR
Show that a diagonal of a parallelogram divides it into two
congruent triangles and hence prove that the opposite
sides of a parallelogram are equal.
32. The parking charges of a car in a parking lot is Rs 30 for
the first two hours and Rs 10
for subsequent hours. Taking total parking time to be x
hours and total charges as Rs y, write a linear equation in
two variables to express the above statement. Draw a
graph for the linear equation and read the charges for five
hours.
33. Draw a frequency polygon for the following
distribution
Class Interval Frequencies
10 - 19 20
20 - 29 15
30 - 39 45
40 - 49 60
50 – 59 12
60 - 69 6
70 - 79 15
34. Metal spheres, each of radius 2 cm are packed into a
rectangular box of dimensions 16 cm × 8 cm × 8 cm. When
16 spheres are packed in the box, it is filled with
preservative liquid. Find the volume of this liquid to the
nearest integer.

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SCIENCE-IX (Term-II)
Maximum Marks : 90 Maximum Time : 3 hours
SECTION A
1. In the figure given below, if
the bob of the pendulum
swings from P to Q, what is the
kinetic energy at Q? [1]
2. What is ammonification? [1]
3. Name one control measure
for overcoming the problem of ozone depletion. [1]
4. Draw a sketch of Bohr’s model of an atom with three
shells. [2]
5. Name the group of plants with the following characters:
[2]
(a) Plants with seeds
(b) Plants without roots, stem, leaves or flowers
(c) Plants having seeds with two cotyledons
(d) Plants visible with naked eye but having no chlorophyll.
6. Name and define the force experienced by a body when
immersed in a fluid. What is the direction of this force? [2]
7. Why does the percentage of gases like oxygen, nitrogen
and carbon dioxide remain almost the same in the
atmosphere? [2]
8. What is the qualitative meaning of the symbol of
chlorine (Cl) of atomic mass 35.5 u? [3]
9. (a) Mention the postulate of Dalton's Atomic Theory
that explain the Law of Constant Proportion. [3]
(b) Mention any two rules to write a chemical formula.
(c) Write the chemical formulae of the following
compounds :
(i) Calcium hydroxide (ii) Ammonium sulphate
10. In the following table the mass number and the atomic
number of certain elements are given.
Element A B C D E
Mass No 1 7 14 40 40
At. NO. 1 3 7 18 20
(a) Select a pair of isobars from the above table.
(b) What would be the valency of element C listed in the
above table?
(c) Which two subatomic particles are equal in number in a
neutral atom?
11. Which do you think is a more basic characteristic for
classifying organisms—the place where they live or the
kind of cells they are made of ? Why? [3]
12. (i) What do you mean by disease symptoms? [3]
(ii) Suggest two lines of treatment given to patients
suffering from infectious diseases.
13. What precautions will you take to justify “prevention is
better than cure"? [3]
14. (a) Name any two air-borne diseases. How does the
disease causing microbes spread through air? [3]
(b) How does the immune system of our body function?
15. What happens when:
(a) Buoyant Force exerted by the fluid is less than the
weight of the body? [3]
(b) Buoyant Force exerted by the fluid is equal to the
weight of the body?
16. (a) The potential energy of a freely falling object
decreases progressively. What happens to its (i) kinetic
energy (ii) total mechanical energy? State the law on
which your answer is based. [3]
(b) A household consumes 1 kWh of energy per day.
How much energy is this in joule?
17. 50 sound waves pass through a point in 0.1 s. If the
distance between one compression and the subsequent
rarefaction is 0.34 m, calculate (a) frequency (b)
wavelength
(c) wave velocity of the longitudinal wave in air. [3]
18. Represent graphically by two separate diagrams in
each case. [3]
(i) Two sound waves having the same amplitude but
different frequencies.
(iii) Two sound waves having different amplitudes and also
different wavelengths.
19. Explain with the help of a labelled diagram carbon
cycle in nature. [3]
20. Give reasons for the following : [5]
(a) 4040
18 20
&CaAr are called isobars. (b) 'He' and 'Ne' have
zero valency.
(c) An atom is neutral. (d) Nucleus is positively charged.
(e) Isotopes have similar chemical properties.
OR
(a) What are isobars? Give one example. (b) Write any two
uses of isotopes. [5]
(c) Write two differences between isobars and isotopes.
21. (a) Draw a well labelled diagram of Euglena.
(b) Name the kingdom to which it belongs. [5]
OR
Pick the odd one out and justify your choice by giving
reasons.
(a) Moss, Fern, Pinus, Spirogyra. [5]
(b) Sea cucumber, Octopus, Feather star, Star fish.
22. (a) Derive the formula of kinetic energy of an object of
mass ‘m’ moving with a uniform velocity ‘v’. [5]
(b) A force acting on a 20 kg mass changes its velocity from
5 m/s to 3m/s. Calculate the work done by the force.
OR
(a) Define power.
(b) State and define the S.I. unit of power.
(c) A force applied on a body of mass 4 kg for 5 seconds
changes its velocity from 10 m/s to 20 m/s. Find the power
required.
23. (i) How the bats make use of ultrasonic waves to catch
their prey? Explain. [5]
(ii) A radar signal is reflected by an aeroplane and is
received 2 × 10
–5
s after it was sent. If the speed of these
waves is 3 × 10
8
m/s, how far is the aeroplane?
OR
(i) What causes reverberation of thunder sound?
(ii) A SONAR device on a submarine sends a signal and
receives an echo 5 s later.

Calculate the speed of sound in water if the distance of the
object from the submarine is 3625 m.
24. (a) How can we prevent the loss of top soil? Discuss. [5]
(b) Why are root nodules useful for plants?
OR
(a) What is biogeochemical cycle? Describe the oxygen-
cycle with the help of a labelled diagram.
SECTION B
25. Which of the following information is not conveyed by
a chemical equation? [1]
(a) The reactants taking part in the reaction
(b) The products formed in the reaction
(c) The speed of the reaction
(d) The ratio of the weights of reactants and products
taking part in the reaction
26. Observe the following pictures. The common feature
that assigns them to the same
phylum is : [1]
(a) wings
(b) three pairs of legs
(c) jointed appendages
(d) antennae
27. Which one of the following characteristics can be used
to distinguish gymnosperms from angiosperms? [1]
(a) Presence of pollen chamber in gymnosperms
(b) Presence of naked ovules in gymnosperms
(c) Presence of stomata in angiosperms
(d) Absence of naked ovules in gymnosperms
28. Parallel venation is the characteristic feature of [1]
(a) monocots (b) dicots (c) both (a) and (b) (d) none of
these
29. In Pinus, the fertilisation takes place in the : [1]
(a) 1st year cone (b) 2nd year cone
(c) 3rd year cone (d) microsporangia
30. Scales are present in : [1]
(a) fish (b) reptiles (c) both (a) and (b) (d) none of these
31. A female Anopheles lays the eggs about : [1]
(a) one at a time (b) 5 at a time
(c) 50 to 200 at a time (d) None of the above
32. The readings of the spring balance will be : [1]
(a) equal to each other in all cases A, B and C
(b) equal to each other in cases B and C only
(c) equal to each other in cases A and C only
(d) different in every case
33. The density of which of the following cannot be
measured accurately using a spring
balance and a measuring cylinder? [1]
(a) A ball filled with a liquid having a leakage (b) A block of
ice at 0°C
(c) A small porous solid (d) All of these
34. The principle of a spring balance is : [1]
(a) the extension produced in spring is directly
proportional to the square of the stretching force
(b) the extension produced in spring is directly
proportional to the stretching force
(c) the extension produced in spring is inversely
proportional to the stretching force
(d) the extension produced in spring is inversely
proportional to the square of the stretching force.
35. If the reflecting body is covered with a loose woollen
cloth, the reflected sound : [1]
(a) heard will be more louder (b) heard will be less louder
(c) heard will be of the same loudness (d) will not be heard.
36. The figure given below shows a line diagram [1]
for the verification of laws of reflection of a sound wave.
The vibrating tuning fork should be held at :
(a) A (b) B (c) D (d) C
37. It is easier to lift a heavy stone in water because : [1]
(a) the stone loses its mass in water (b) the stone loses its
weight in water
(c) the stone experiences an up thrust equal to the volume
of water displaced
(d) the stone experiences an up thrust equal to the weight
of water displaced.
38. During the formation of a pulse, most of the medium at
any time is : [1]
(a) in the state of rest (b) in the state of motion
(c) some parts in the state of rest and some parts in the
state of motion
(d) none of the above.
39. A pulse travels through a slinky 10 m long from one
end to the other end and then
back to the point of origin in 3 s. The velocity of the pulse
in the slinky is : [1]
(a) 3.33 ms–1 (b) 4.5 ms–1 (c) 6.00 ms–1 (d) 6.66 ms–1.
40. In which case is the pressure exerted by the brick on
the ground maximum? [1]
(a) A
(b) B
(c) C
(d) none of these
41. During sharpening of a knife we : [1]
(a) decrease the surface area of the cutting edge
(b) increase the surface area of the cutting edge
(c) remove rust from the cutting edge (d) none of the
above
42. The tuning fork in the experiment to prove laws of
reflection of sound has to be placed with its prongs. [1]
(a) Vertical near the tube (b) Horizontal near the tube

(c) Vertically or horizontally near the tube makes on
difference
(d) Inclined near the tube.
ANSWERS
16. 3.6 × 10
6
J 17. 500 Hz, 0.68 m, 340 m/s 22. (b) 210 J OR
(c) 40 W 23. (ii) 3 km OR ((ii) 1450 m/s 25. (c) 26. (c) 27. (b)
28. (a) 29. (b) 30. (c) 31. (c) 32. (b) 33. (d) 34. (b) 35. (d) 36.
(a) 37. (d)
38. (a) 39. (d) 40. (a) 41. (a) 42. (b)

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