Class 8 Maths SESSION ENDING EXAMINATION Practice Exam-1

 SESSION ENDING EXAMINATION   Practice Exam-1 

Grade: VIII                 Subject: Mathematics      Max. Marks: 80    Duration: 180 +15 Minutes

General Instructions

All questions are compulsory

The duration of the paper is: 3 hrs 15 min (Reading time 15 min)

Read all the questions carefully before attempting. 

The question paper consists of 40 questions divided into 4 Sections A, B, C, D

Section- A comprises 20 questions of I marks each. 

Section- B comprises 8 questions of 2 marks each.

Section-C comprises 8 questions of 3 marks each

Section-D comprises 4 questions of 5 marks each.

SECTION-A (1 x 20 = 20)

1. Simplify the expression, (a22 × a−12) × (b−10 × b20) 

   (a) (ab)10 (b)       a22 × b20 (c)         (ab)12(ab)12 (d)       a12 × b10 

2. Express 81−2in the powers of 3 

  (a)  38 (b)    (1/3)8 (c)   3−6 (d)     (1/3)6 

3. If sum of the length , breadth ,depth of the cuboid is 19 cm. and its diagonal is 5√5 cm and then  its surface area is  —

a) 216 cm2 b) 236 cm2 c) 256 cm2 d) 276 cm2 

4.  The volume of a cube is 64 cm3. Its surface area is

(a) 16 cm2            (b) 64 cm2           (c) 96 cm2           (d) 128 cm2

5.If the radius of a cylinder is tripled, but its curved surface area is unchanged, then its height will be

(a) tripled              (b) constant         (c) one-sixth       (d) one third

6.Find the volume of the rectangular box whose length (l) = mn, breadth (b) = m2p, depth (d)= pmn2. 

 (a) m4n2p (b) m4n3p2 (c)  m3n2p (d) m3n2p2 

7.  If n is odd, then (1+3+5+7+... to n terms) is equal to : 

      (a) n²+1 (b) n²-1 (c) n² (d) 2n²+1

8.  In a quadrilateral ‘Rock’ which of the following is a diagonal? 

      (a) RO (b) OK (c) OC (d) KR 

9.Which of the following shows three consecutive multiples of 8? 

      (a) 8x, (x +8), (x +16) (b) 8x, 8x +8, x +16  (c) 8x, 8(x +1), 8(x + 2) (d) x, (x + 8), (x +16) 

10.Solve: 8x+4 = 3(x-1)+7

 (a) x = 0 (b) x=  3/8 (c) x= 8/5 (d) x=1/5

11. Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm

12. Is 225 a perfect square? If so, find the number whose square is 225. Explain.  

13. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively: (3mn,4np)

14.Find the value of (2-1 -4-1)2

15. Find the value of the expression 3x (4x – 5) + 3 for x = 3 

16. The cost of 5 metres of a particular quality of cloth is Rs 210. Find the cost 2 metres of the same cloth. 

17.  If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2 ½ kilograms? 

18. 5pq (p2 – q2) 2p (p + q) 

19. Factorise x2 – 14x + 13 

20. Find the highest common factor of 16x 3, -4x2, 32x

SECTION-B (2x8=16 marks)

21.  Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q 

22.  Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.

23. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number? 

24.  Write a Pythagorean triplets using when the smallest member is18 . 

25.  The length of the fence of a trapezium shaped field ABCD  is 130 m and side AB is Perpendicular to each of the parallel sides AD and BC. If  BC = 54 m, CD =19 m and AD = 42 , find the area of the field. 

26. (a) Express Mass of Uranus = 86,800,000,000,000,000,000,000,000 kg in standard form. 

(b) Find the value of m for which 5m÷5– 3 = 125. 

27. 6 pipes are required to fill a tank in 1 hour 20 minutes. How long will it take if only 5 pipes of the same type are used? 

28. Factorise: x4 – (y + z)4 

SECTION-C (3x8=24 marks)

29. The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each  other at right angles, what is the length of each side of the quadrilateral?

30. Solve:

31. There are 2401 students in a school. P.T. teacher wants them to stand in rows & columns such that the   no. of rows to equal to the no. of columns. Find the number of rows. 

32. Simplify: (a) Add: p ( p – q), q ( q – r) and r ( r – p) 

                      (b) Subtract 5x2 – 4y2 + 6y – 3 from 7x2 – 4xy + 8y2 + 5x –3y.

33.In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m2. 

34. Evaluate :   (ii)

35. Factorise: (a) m4– 256      (b) x2+ xy + 8x + 8y 

36. An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions. 

SECTION-D  (5x4=20 marks)

37. (i)  Find the least number which must be subtracted from 18265 to make it a perfect square. Also,  find the square root of the resulting number.

OR

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.   (2 marks)

 (ii)Simplify: (i) (5x – 6) (2 x – 3) + (3 x + 5)2 

          (ii ) (2x + 5y) (2 x + 3y) (3 marks)

38. (i)Find area of the below figure:(2 marks)

(ii)  .A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form embankment. Find height embankment. (3 marks)

39. (i) Solve: (2 marks)

(ii)  (a) If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4? 

(b) A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle? (3 marks)

40.(i)  Factorise then divide (3 marks) 156(36y²-64)y³ / 104(6y+8)y²

(ii) Find the value of x : ( 2 marks)

Answer key Class 8 Maths SEE Model Exam -2

 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