Answer Key SESSION ENDING EXAMINATION Model Exam -2
Grade: VIII Subject: Mathematics Max. Marks: 50 Duration: 120 +15 Minutes
Chapters : Understanding Quadrilaterals, Mensuration, Squares and Square roots & Linear Equations in One variable.
SECTION-A (1 x 10 = 10)
1. (b) -1
2. d) 54
3.d) 6
4. c) 2√26 cm
5. b) 280 cm³
6. 112.5 & 31.5
7. 60
8. Divide by 3
9. 8 cubes
10.11cm
SECTION-B (2x5=10 marks)
11. Find three consecutive odd numbers whose sum is 147.
x+x+2+x+4=147
3x+6=147
x=47
x+2=47+2=49
x+4=47+4=51
Numbers are 47,49,51
12. How many sides does a regular polygon have if each of its interior angles is 165°?
each exterior angle = 180-165 =15 (exterior angle = 180- interior angle)
no. of sides x measure of each exterior angle = 360
No. of sides x 15 = 360
No.of sides =360/15 = 24
Therefore, a polygon with interior angles 165 has 24 sides.
13. If the smallest side of a trapezium is 20 m and distance between the two parallel sides of the trapezium is 15 m and also its area is 480 m², then find the other side of the trapezium.
14. The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
15. The height and radius of a cylinder are in the ratio 7:5 and its volume is 550cm3.Find the radius of its base.
SECTION-C (3x5=15 marks)
16. Solve for x:
(6x+7)(2x+5) = (4x+13)(3x+2)
44x+35 = 47x+26
3x=9
x=3
17. Two adjacent angles of parallelogram are in the ratio 2:7, Find all the angles of parallelogram.
Or
Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
18.Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.
LCM of 6,9,15 = 2x3x3x5=90
90 = 3x3x2x5
To make it perfect square must be multiplied by 2x5=10
90x10=900 is the smallest square number which is divisible by 6,9,15
19. Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir. What are the advantages of reservoir for farmer?
20. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?
SECTION-D (5x3=15 marks)
21.The sum of digit of two digit number is 15,if the number formed by reversing the digits is less than the original number by 27,find the original number
Original number = 10(15-x)+x
= 150-10x+x
150-9x
REversing the digits new number = 10x+(15-x)=10x+15-x
=9x+15
Original number - New number= 27
150-9x-9x-15=27
-18x+135=27
-18x=-108
x=6
Original number = 96 (2 marks)
(ii) Solve: (3 marks)
22. (i)In the figure, BEST is a parallelogram. Find the values x, y and z.
(2 marks)
In parallelogram the adjacent angles are supplementary
∠TBE+z=180∘
100+z=180∘
z=80∘
Also, opposite angles of a parallelogram are equal.
x=∠TBE=100∘
y=x=100∘
(ii) Diagram of the given picture frame has outer dimensions as 24cm × 28cm and inner dimensions as 16cm × 20cm. Find the area of each section of the frame, if the width of each section is same. (3 marks)
the width of each Section is same.
Therefore, IB = BJ= CK =CL = DM = DN = AO =AP
IL= IB +BC + CL
28= IB + 20 +CL
IB+CL =28cm - 20 cm = 8cm
IB =CL = 4cm
Hence, IB =BJ=CK=CL=DM=DN=AO=AP=4cm
Area of Section BEFC =Area of section DGHA =1/2(20+28)(4)cm2=96cm2
Area of Section ABEH = Area of Section CDGF = Area of Section BEFC =Area of section DGHA =
96cm2
23. (i) Write a Pythagorean triplets using when the smallest member is 9.
Since 9 is an odd number, we can form a Pythagorean triplet which will have 9 as the smallest number of the triplet.
Take square of 9.
9²= 81.
Divide 81 into two parts. For this divide 81 by 2.
On dividing 81 by 2, the quotient is 40.
Thus the next number is 40 + 1 = 41.
Thus the Pythagorean triplet is 9, 40, 41. (2 marks)
(ii) The dimensions of a room are 16 × 14 × 10 meters. There are 4 windows of 1.3 m × 1.4 cm and 2 doors of 2m × 1m. What will be the cost of white washing the walls and painting the doors and windows, if the rate of white washing is Rs.5 per m2 and rate of painting is Rs.8 per m2.
Area of 4 rooms = 2h(l+b) = 2 x10(16+14) =600m²
Area of 4 windows 4 x 1.3 x 1.4 = 7.28
Area of 2 doors = 2 x 2 x 1 = 4
Area = 600- 7.28 - 4 = 581.72
Cost = 5x 581.72= Rs 2943.60
Painting = 8 x 11.28 = Rs 90.24
Total cost = 3033.84
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