Answer key SESSION ENDING EXAMINATION Practice Exam -2
Grade: VIII Subject: Mathematics Max. Marks: 80 Duration: 180 +15 Minutes
SECTION-A (1 x 20 = 20)
1. Simplify the expression, (25x8 y9 z6) × (-2xyz)²
(a) 50x9 y10 z6 (b) 100x10 y11 z8 (c) -100x10 y11 z8 (d) -50x9 y10 z6
Answer = (b) 100x10 y11 z8
2. Value of 70 x 50
1 (b) 0 (c) 35 (d) (1/35)
Answer = a)
3. A rhombus is also a —
a) Square b) Rectangle c) Parallelogram d) Trapezium
ANSWER = (C)
4. The ratio of radii of two cylinders is 1: 2. If the ratio of their heights is 2: 1, then the ratio of their volumes will be __
a) 1: 2 (b) 1: 4 (c) 2: 1 (d) 4: 1
ANSWER = (A)
5. Two cubes each of edge 5 cm are joined end to end. The surface area of the resulting cuboid is
(a) 125 cm² (b) 240 cm² (c) 250 cm² (d) 500 cm²
ANSWER=(C )
6.The value of 25x³y²z for x=1, y=2 and z=3 is—--- .
600 (b) 500 (c) 900 (d) 300
Answer = (d) 300
7. If 256 x 4² = x, then the value of is ___
(a) 256 (b) 196 (c) 64 (d) 1224
ANSWER = (a)
8. The measure of each angle of a convex quadrilateral is ___
(a) less than 180° (b) more than 180° (c) equal to 180° (d) none of these
ANSWER= (a)
9.One sixth of a number when subtracted from the number itself gives 25. The number is __
(a) 30 (b) 32 (c) 35 (d) 28
ANSWER = (a)
10.If 5(x-3) - 4(x-2) = 0, then the value of x is ___
(a) x = 7 (b) x= 8 (c) x= - 8 (d) x= - 7
ANSWER = (a)
11. Two adjacent angles of a parallelogram are equal, the measure of each angle is __
ANSWER = 90 degree
12. Is (1,2,3) a pythagorean triplet?
ANSWER = no
13. Find the product of (-x+a) (-x+b).
ANSWER = x² - (a+b)x+ab
14.Find the value of (30 + 4-1) × 22
ANSWER =5
15. Find k if 0.7k – 1.9 = 0.3 ( k + 14 )
ANSWER = K =15.25
16. If 12 m uniform iron rod weighs 42 kg, then the weight of 5m rod of the same type will be __.
ANSWER =17.5 KG
17. Raja types 108 words in 6 minutes. How many words would he type in half an hour?
ANSWER = 540
18. Find the area of a square with side 5x²y .
Answer = 25x4y2.
19. Factorise x4 – 1
ANSWER (X² +1) (X+1) (X-1)
20. The quotient when 12xy(9x² - 16y²) is divided by 4xy (3x+ 4y is —--
ANSWER =3(3X - 4Y)
SECTION-B (2x8=16 marks)
21. Subtract 1+x2 +y2 from the sum of x2 - y2 and 1-x² + y²
ANSWER = - x^2 - y^ 2
22. Find the number of sides of a regular polygon, the sum of whose interior angle is 10 right angles.
ANSWER =
Sum of interior angles of polygon right angles = 10 × 90 o = 900 o (given)
But sum of interior angles of a polygon = ( 2 n − 4 ) right angles.
⇒ 180 n − 360 = 900.
⇒ 180 n = 900 + 360.
⇒ n = 1260 / 180.
⇒ n = 7.
23. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?
ANSWER
Let the digits of the number be a and b such that the number is (10a+b).
a−b=3 or b−a=3 ...... (1)
10a+b+10b+a=143
⇒11a+11b=143
⇒a+b=13 ...... (2)
By adding equations (i) and (ii) , we get
2a=16or2b=16
⇒a=8orb=8
b=5 or a=5
Therefore, the required number is 85 or 58.
24. Write a Pythagorean triplets using when the smallest member is12 .
ANSWER = Given, smallest number is 12,
2m=12
or m=6.
m²+1=6²+1=36+1=37
m²−1=6²−1=36−1=35
∴ The Pythagorean triplet is 12, 35, 37.
25. Two buildings are 20 m and 25 m high. If the buildings are 12 m apart, find the distance between their tops.
ANSWER B
C=√AC²+AB²
AC = 25 - 20 = 5
AB = 12
BC=√12²+5²=13
Distance = 13m
26.Evaluate
ANSWER =
= (3^4)^-¾ x (7³ )^ ⅔
=49/27
27. The scale of a map is given as 1:30000000. Two cities are 4 cm apart on the map. Find the actual distance between them.
ANSWER =
1:30000000=x:y.⇒13×107=xy
Since x=4,⇒13×107=4y
⇒y=4×3×107=12×107cm=1200km
28. Factorise: (25a2 + c² +10ac ) - 49b²
ANSWER = (5a +c+7b)(5a+c-7b)
SECTION-C (3x8=24 marks)
29. The diagonals of a rhombus are in the ratio 3:4 if its perimeter is 40cm, find the length of the diagonals of the rhombus.
ANSWER= d1= 12 d2 =16 =
30. Solve:
ANSWER 8x-6x=9-8
2x=-1
x=½
31. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
ANSWER =
Let the number of rows and columns be x
Total number of plant 1000
less than 31² <1000>32²
∴ Hence, 24 more plants
32. Simplify: 3x² +4x (3x-4y)-20xy
ANSWER = 15x^2 - 36 xy
33.The height and radius of a cylinder are in the ratio 7:5 and its volume is 550cm3.Find the radius of its base.
ANSWER
Volume = 550 cm3
22/7×(5x)(5x)×(7x)=550
22×25x3=550
x=1 cm
Hence, radius of the cylinder = 5x = 5 cm.=
34. Evaluate :
ANSWER
3−5×2−5×5−5×5³/(5−7×2−5×3−5)
=5−5+3+7=55
35. Simplify :x4 + 4+3x²
ANSWER=
Adding and subtracting , we get
= + 3
+ 4 +
-
= + 4
+ 4 -
= [ + 2(
)(2) +
] -
= -
= ( + 2 + x)(
+ 2 - x)
= ( + x + 2 )(
- x + 2)
$(x^2-x+2) (x^2+x+2)$
36. (a) A labourer is paid Rs 806 for 13 days of work. If he receives Rs. 1798, for how many days did he work?
ANSWER = 1798 x 13 / 806=29
A milk man mixes 2 litres of water in 11 litres of milk. What is the amount of milk required if he wants to add 13 litres of water to it?
ANSWER = 13 x 13 / 2= 71.5 litres
SECTION-D (5x4=20 marks)
37. (i) The area of a square field is 8464 sq.m. A man takes 3 rounds of this field. Find the distance covered by him (2 marks)
ANSWER Area of square = 8464
Side² = 8464
Side = √8464
Side = 92
Perimeter of square = 4×92 = 368 m
Distance covered by him = 3×368 = 1104 m
(ii)Simplify: 35 x²(5x³ - 4) + 5x5(3 marks)
ANSWER =
38. (i)Find the angle measure x in the following figure. x:(2 marks)
ANSWER
70 + a = 180° (Linear pair)
a = 110°
60° + b = 180° (Linear pair)
b = 120°
Sum of the measures of all interior angles of a pentagon is 540º.
120° + 110° + 30° + x + x = 540°
260° + 2x = 540°
2x = 280°
x = 140°
(ii) A cubical box with lid has a length 45cm find the cost of painting inside and outside of the box at Rs.150 per m2. (3 marks)
ANSWER = 2x 6 x 0.45 x 0.45 x 150=364.5
39. (i) (2 marks)
ANSWER
19x-21=-9x+5
28x=26
x=13/14
(ii) A 5m 60cm high pole casts a shadow of length 3m 20cm.
a) Find at the same time the length of a shadow cast by another pole 10m 50cm high.
ANSWER
= x1/y1=x2/y2
⇒5.6/3.2=10.5/y2
⇒y2=6 cm
b) Find the height of the pole if the length of the shadow is 6m 40cm. (3 marks)
ANSWER
(ii) x1/y1=x3/y3
⇒5.6/3.2=x3/5
⇒x3=8.75 m
40.(i) Factorise: 16a2 – 25b2 + 60 bc – 36c2 (3 marks)
ANSWER (4a+5b-6c)(4a-5b+6c)
(ii) Evaluate : ( 2 marks)
ANSWER = 10^13/3/ 5^4 x 3³
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