Download D.A.V. PUBLIC SCHOOL, NEW PANVEL

Page - 1
D.A.V. PUBLIC SCHOOL, NEW PANVEL
Plot No. 267, 268, Sector-10, New Panvel,
Navi Mumbai-410206 (Maharashtra).
Phone 022-27468211, 27451793, Tel-fax-27482276
E-mail – [email protected], www.davnewpanvel.com
SAMPLE PAPER FOR II PREPARATORY EXAMINATION
2015-2016
STD:- VIII
Sub: - Mathematics
Time:- 3 Hours
Date:Marks:- 90
…….…………………………………………………………………………………………………
General Instructions:1. All questions are compulsory.
2. The question paper consists of 34 questions divided into 4 sections–A, B, C and D.
i) Section A comprises 8 questions of 1 mark each.
ii) Section B comprises 6 questions of 2 marks each.
iii) Section C comprises 10 questions of 3 marks each.
iv) Section D comprises 10 questions of 4 marks each.
3. In questions on construction, the drawing should be neat and exactly as per the
given measurements. Use ruler and compass only.
4. Internal choice has been provided in some questions. You have to attempt only
one of the alternatives in all such questions.
………………………………………………………………………………………………………
SECTION – A
1.
3
7
⎛ 7 ⎞4 ⎛ 5 ⎞4
Simplify form of ⎜ ⎟ × ⎜ ⎟ is
⎝5⎠ ⎝7⎠
2
7
⎛7⎞
(a)
(b) ⎜ ⎟
5
⎝5⎠
2.
3.
4.
5.
5
7
(b) 150cm2
(c) 150cm3
(d) 150m2
(b) 5
(c) 6
(d) 3
(c) 900
(d) 1800
Angle of rotation of an equilateral triangle is
(a) 1200
8.
(d)
The number of faces of a rectangular pyramid are:
(a) 4
7.
2
The area of trapezium is 1586cm2 and sum of parallel sides is 122cm.What is
the distance between two sides?
(a) 26cm
(b) 36cm
(c) 13cm
(d) 671cm
Degree of (x2+3x+1) (x4+3x+1) is
(a) 4
(b) 6
(c) 8
(d) 10
Which of the following is a polynomial?
1
(a) 3z2 + 5 z +6
(b) 5x - +2
x
7
5
(c) 3x2+ 2 x + 3
(d) y3+4y+ +1
5
3y
Total Surface area of a cube whose side measures 5cm is
(a) 100cm2
6.
⎛5⎞
(c) ⎜ ⎟
⎝7⎠
(b) 600
The order of rotation of a regular hexagon is :
(a) 1
(b) 5
(c) 6
(d) 60
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SECTION – B
−1
⎡
−1 4 ⎤
⎧
⎫
⎢⎨(625) 2 ⎬ ⎥
⎢⎩
⎭ ⎥
⎣
⎦
2
9.
Evaluate:
10.
Simplify : 255 x 260 – 297 x 218
11.
2x −1
1
=−
5x
6
Solve the following equation:
OR
The sum of two positive integers is 105.The integers are in the ratio 2:3. Find
the integers.
12.
Rajeev bought a car at Rs 1,75,000. If its value depreciates at the rate of
20% p.a., what will be its value after 3 years?
13.
Two adjacent sides of a parallelogram are in the ratio 3:8 and its perimeter is
110cm.Find the sides of the parallelogram.
14.
Write the order and angle of rotational symmetry of square with the help of
rough sketch.
SECTION – C
−1
−1
(64) 6 × (216) 3 × (81)4
−1
−1
1
(512) 3 × (16)4 × (9) 2
1
15.
Simplify :
16.
At what rate percent will a sum of Rs 64,000 be compounded to Rs 68,921 in
3 years?
OR
Find the compound interest on Rs 24,000 for 6 months if the interest is payable
quarterly at the rate of 20% per annum.
17.
24000 blood donors were registered with a charitable hospital. The number of
donors increased at the rate of 5% per annum. Find the time period at the end
of which the total numbers of blood donors become 27783.Which value depicts
here?
18.
Find the difference between the compound interest and the simple interest on
Rs 30,000 at 7% per annum for 3 years.
19.
Divide the polynomial x3 + 4x2 – 3x + 5 by x – 3
OR
Divide x4 - 16 by x + 2
20.
21.
22.
23.
Using factor method divide y2 + 12y + 35 by y + 7
The sum of the digits of a 2-digit number is 11. The number obtained by
interchanging the digits exceeds the original number by 27. Find the numbers.
(1 − 2 x ) + (1 + 2 x ) = 1
Solve the following equation:
(4 x + 1) + (x − 3) 2
Construct a quadrilateral ABCD in which AB= 5cm, BC =4cm, CD=5cm and
diagonals AC = BD = 6.5 cm.
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24.
The dimensions of an oil tin are 26cm x 26cm x 45cm.Find the area of tin sheet
required to make 20 such tins.
OR
The outer diameter of a gas cylinder is 20cm.Find the cost of the painting its
outer curved surface at Rs 4 per square centimeter if the height of the cylinder is
7cm.
SECTION – D
25.
Find x ,if 5x + 5x-1 = 750
OR
1
2
⎡
−3 ⎤
2+ x
3
⎛ 7⎞
⎛ 7⎞ ⎛ 7⎞ ⎛ 7⎞
Find x : ⎜ − ⎟ ⎢⎜ − ⎟ ÷ ⎜ − ⎟ ⎥ = ⎜ − ⎟
⎝ 8 ⎠ ⎢⎝ 8 ⎠ ⎝ 8 ⎠ ⎥ ⎝ 8 ⎠
⎣⎢
⎦⎥
3
2
26.
A builder employed 4,000 workers to work on a residential project. At the end of
the first year, 10% workers were removed, at the end of second year, 5% of
those working at that time were retrenched. However, to complete the project in
time, the number of workers were increased by 15% at the end of third year.
How many workers were working during the fourth year?
27.
Find out whether or not the first polynomial is a factor of the second polynomial.
2x2 + 1, -6x4 + 5x2 + 11x + 1
A steamer, going down stream in a river, covers the distance between two
towns in 15 hours. Coming back upstream, it covers this distance in 20 hours.
The speed of water is 3 km/hr. Find the distance between two towns.
28.
OR
A purse has only one-rupee and two-rupees coins in it. The number of
two rupees coins is one third the number of one rupee coins. If purse has
Rs.115, find the number of two rupees coins.
29.
The diagonals of a rhombus are in the ratio 3:4. If its perimeter is 40cm, find the
length of the sides and diagonals of the rhombus.
30.
(i)
(ii)
ABCD is a parallelogram whose diagonals intersect each other at right
angles. If the length of the diagonals is 6cm and 8cm find the length of all
the sides of the parallelogram.
ABCD is a rhombus. If ∠ ADB = 50o, find the angles of the rhombus.
31.
ABCD is a parallelogram. AP bisects ∠A and CQ bisects ∠C .P lies on CD and
Q lies on AB. Show that : i) AP║ CQ ii) AQCP is a parallelogram.
32.
Construct a quadrilateral ABCD in which AB = 5 cm, BC= 6cm, CD=6.5cm
∠B = 1050, ∠C = 750.
33.
The length, breadth and height of a room are 5m, 4m and 3m respectively. Find
the cost of white washing the inner of the room and ceiling at the rate of
Rs 50 per square meter.
34.
The radius and height of a cylinder are in the ratio 5:7 and its volume is 550cm3.
Find its radius.
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