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

Class 8 Maths SEE Model Exam -2 for Understanding Quadrilaterals, Mensuration, Squares and Square roots & Linear Equations in One variable

 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.

General Instructions

All questions are compulsory. Read all the questions carefully before attempting.(Reading time 15 mins) 

Subject Specific Instructions:

The question paper consists of 23 questions divided into 4 Sections A, B, C, D

Section- A comprises of 10 questions of I marks each.

 Section- B comprises of 5 questions of 2 marks each.

Section-C comprises of 5 questions of 3 marks each

Section-D comprises of 3 questions of 5 marks each.

SECTION-A (1 x 10 = 10)

1. If 5t -3 = 3t - 5 then t is

1. 1                (b) -1         (c) 2      (d) -2 

2. How many diagonals are there in a polygon having 12 sides?

1. 12 b) 24 c) 36 d) 54

3. If square root of 25x is 16 . what is the value of x? 

1. 4  b) 2 c) 5 d) 6

4. The maximum length of pencil that can be placed in a rectangular box of dimensions 8cm x 6cm x 2cm is 

        a) 2√13 cm b) 2√14 cm c) 2√26 cm d) 3√26 cm 

5. The area of the base of a circular cylinder is 35 cm² and its height is 8 cm. The volume of the cylinder is  

1. 140 cm³ b) 280  cm³ c) 420  cm³ d) 210  cm³

6. The sum of two numbers is 144. One of the numbers decreased the other by 81. Find the  numbers.

7. Find x in the adjoining figure:  

8. By which smallest number 48 must be divided so as to make it a perfect square ?

9. How many cubes of side length 6 cm can be obtained from a cube whose edge is 12 cm?

10.Find the height of a cuboid whose volume is 275cm and base area is 25 cm² 

SECTION-B (2x5=10 marks)

11.   Find three consecutive odd numbers whose sum is 147.

12. How many sides does a regular polygon have if each of its interior angles is 165°?

13. If the smallest side of a trapezium is 10 m and distance between the two parallel sides of the   trapezium is 20 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:

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.

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  (2 marks)

 (ii) Solve: (3 marks)

22. (i)In the figure, BEST is a parallelogram. Find the values x, y and z.  

(2 marks)

(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)

23. (i)  Write a Pythagorean triplets using when the smallest member is 9.                     (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. 

ANSWER KEY SESSION ENDING EXAMINATION Model Exam -1

 ANSWER KEY   SESSION ENDING EXAMINATION   Model Exam  -1

Grade: VIII                 Subject: Mathematics      Max.Marks: 50    Duration: 120 +15 Min

Chapters : Algebraic Expressions, Factorization, Exponents and Powers & Direct and Inverse proportions

SECTION-A (1 x 10 = 10)

1.(a) 12a3bc2              

2.c) Rs. 13.00

3.d) 2x(1-4)(1+4x)

4.d) 7(a-3b)(a+3b)

5. c) 34/24

6.0.000532

7. 6

8. 240 MIN

9.(pq-1)(q+1)

10. 2x (3x + 5xy) =6x²+10x²y

SECTION-B (2x5=10 marks)

11. Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y , –3xz + 5x – 2xy.

12. State whether or not 2x + 3 is a factor of 6x3 +19x2 +13x – 3 

2x+3=0

x=-3/2

Yes. 6(-3/2)³  -3 +19 (-3/2)² + 13(-3/2)

13. A train is moving at a uniform speed of 75 km/hour. (i) How far will it travel in 20 minutes? (ii) Find the time required to cover a distance of 250 km. 

14. Evaluate : (6-1 – 7-1 )-1 – (5-1 – 4-1 )-1.  ‘

= (⅙-1/7)^-1 x (⅕-¼)^-1= (1/42)x(1/-20) = (-840)

15. Find the factors of 16l2 + 24lm + 9m2.  = (4l+3m)²

SECTION-C (3x5=15 marks)

16.  Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c ) 

Or

 Simplify: 3y(2y – 7) – 3(y – 4) – 63 and evaluate for y = – 2. 

17. Factorize the following expressions: a)  x4 – (x – z)4  b) a4 – 2a²b² + b4 

18.The vertical pole 5 m 60 cm high  casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole which casts a shadow 5m long

19. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same? 

20.Express the number appearing in the following statements in standard form. 

  (i) Sun is located 300,000,000,000,000,000,000 m from the centre of our Milky Way.  

3x 10^20 m

 (ii) The distance between Sun and Saturn is 1,433,500,000,000 m = 1.4335 x 10^12

SECTION-D  (5x3=15 marks)

21. Simplify:

 (i) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd) (3 marks)

 (ii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y (2 marks)

22. (i) Factorise the expressions and divide them as directed.  (3 marks)

(a) (5p2 – 25p + 20) ÷ (p – 1)  

 

(b) 4yz(z2 + 6z – 16) ÷ 2y(z + 8) 

(ii) Find the value of x for which    

(2 marks)

23. (i) By what number should be divided that quotient is ? (2 marks)

(ii)  Ramesh is making a wheel using spokes. He wants to  x equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table:   (3 marks)

a) Are the number of spokes and the angles formed between the pair of consecutive spokes in inverse proportion? 

b) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. 

c) How many spokes would be needed if the angle between a pair of consecutive spokes is 40o?