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Mid term(Half yearly) Examination ModelPaper-1

SECTION-A (4 x 1 = 4)

1. Find x if . 34x = 8

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2. Find the sum of all exterior angles of a regular pentagon.

3. The edge of a cube is 24cm. How many smaller cubes each of side 8cm can be formed from this

larger cube?

4. Express in power notation: .343−27

SECTION-B (5 x 2 = 10)

5. A shopkeeper has just enough money to buy 52 cycles, worth Rs. 525 each. If each cycle were to

cost Rs. 21 more than the amount he has, how many cycles would he be able to buy?

6. Find the cube root of 46656.

7. Simplify ➗6 5 x 3( −1 −1)−1−1

8. Find the value of unknown angles in a parallelogram ABCD.

9. Solve the given equation 3y + 22y − 4 = 3

−2

SECTION-C (10 x 3 = 30)

10. The sum of the digits of a two digit number is 14. The number obtained by interchanging the digits

is 36 more than the given number. Find the number.

11. Charan has money for buying 6 shirts worth Rs 1250 each. How many shirts he will be able to buy

if he wants to buy shirts each costing Rs. 250 more?

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12. a) ABCD is a parallelogram. Find x, y, z.

b) Find the measure of each interior and exterior angle of a polygon with 12 sides.

13. a) Find all the angles of the given quadrilateral.

b)The exterior angle of a regular polygon is one-third of its interior angle. How many sides has the

polygon?

14. Construct a quadrilateral DPSE where DP=PS=4.2cm, SE=4.6cm, ED=3.2cm and PE=4.1cm.

15. The shape of a field is rectangular in the middle and semicircular at the two ends as shown in the

figure. Find the area of this field.

16. A rectangular paper of width 42cm is rolled along its width and a cylinder of radius 7cm is formed.

Find the volume of the cylinder.

17. a) Simplify and express with positive exponents.

X [( 911)−3 ( 9

11)−7]➗( 911)−3

b) Find the value of n: [( 52)2]n + 2

= [( 52)−2]− 3

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18. a)A cuboidal diesel tanker is 2m long, 2m wide and 40m deep. How many litres of diesel can it

hold?

b) By what number should be divided to get ( 83)−3 9

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19. The denominator of a rational number is greater than its numerator by 8. If the numerator is

increased by 17 and the denominator is decreased by 1, the number obtained is . Find the23

rational number.

SECTION-D (9 x 4 = 36) 20. a) Find the smallest number by which 9000 multiplied so that the product is a perfect cube. And

also find the cube root of the product.

b) Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

21. a)The diagonals of a rhombus are 5.5cm and 10cm find its area.

b) The sum of three consecutive multiples of 5 is 1110. Find these multiples.

22. Construct a quadrilateral LMNO where LM=6cm, MN=4.5cm,∠M=75o, ∠N=120o. NO=4cm (write

the steps of construction)

23. a) A swimming pool is 250 m long and 130m wide. 3250 cubic metres of water is pumped into it.

Find the rise in the level of water.

b) The inner diameter of a circular well is 3.5m. It is 10m deep. Find the cost of plastering its inner

curved surface at Rs 4 per square meter.

24. a) Rahul's father is 3 times as old as Rahul. Four years ago his father was 4 times as old as

Rahul. How old is Rahul?

b) The ages of Ashok and Naresh are in the ratio 5 : 8. If Ashok were 5 years older and Naresh 4

years younger, the age of Ashok would have been the same as the age of Naresh. Find their

present ages.

25. Roshni’s father gave her Rs. 245 for buying Diwali cards. She bought some 10 rupee cards, 5

rupee cards and 15 rupee cards. Number of 5 rupee cards and 15 rupee cards are rd and th of32

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the number of 10 rupee cards respectively. Find how many of each kind did she buy?

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26. In the given figure ABCD and PQRS are parallelograms. Find the value of x.

27. a)The volume of a rectangular tank is 182m3. If its length and breadth be 8m and 6.5m

respectively. Find its depth.

b) A rectangular piece of paper 22cm X 6cm is folded without overlapping to make a cylinder of

height 6 cm. Find the volume of the cylinder.

28. a) Evaluate {( 34)−1

− ( 41)−1}−1

b) Find the value of m if X ( 92)3 ( 9

2)−6= ( 9

2)2m−1

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Mid term(Half yearly) Examination Model Paper-2

SECTION-A (4 x 1 = 4)

1. The radius of a right circular cylinder is 5cm and its height 7cm. Find its lateral surface area.

2. If the length of the side of a cube is 24cm. Find its volume.

3. Find the value of −[{( 21)2}−2]−1

4. Find the number of sides of a regular polygon if each interior angle is 156o.

SECTION-B (5 x 2 = 10)

5. The sum of two numbers is 90 and the greater number exceeds thrice the smaller number by 14.

Find the numbers.

6. Solve ― 1 ― y 2y − 1 = 3

y−2 7. An exterior angle of a regular polygon is one-fifth of its interior angle. Find the number of sides in

the polygon.

8. The diagonals of a rectangle ABCD intersect at O. If ∠BOC = 68o. Find

a) ∠ODA

b) ∠AOB

9. Simplify X 2( −1 + 5−1)2( 8

−5)−1

SECTION-C (10 x 3 = 30) 10. Construct a parallelogram ABCD such that AB=5cm, BC=3.2 cm and ∠B=120o. (steps of

construction is not required)

11. Construct a square whose on side is 4.3cm. (steps of construction is not required)

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12. In the parallelogram ROPE given below, find angles x, y and z

13. The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.

Calculate the ratio of their curved surface areas.

14. Find x, y, z in the following figure.

15. A rectangular water reservoir contains 42,000 litres of water. Find the depth of the water in the

reservoir it its base measures 6m by 3.5m.

16. Simplify 8 x 10−2 −4

2 x 5 x 2−5 −4 −2

17. The length, breadth and height of a room are 8m, 7m and 6m respectively. Find the cost of

plastering the four walls and the ceiling of the room at the rate of ₹6 per sq m.

18. Solve: 4y+6 + 5

y−3 = 85y −4

19. Find the area of the shaded region:

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SECTION-D (9 x 4 = 36) 20. a) In the adjoining figure, ABCD is a parallelogram whose diagonals AC and BD intersect at O. If

∠OBC = 36o, ∠ODC=28o and ∠AOD=64o, find the measure of (i)∠OAD (ii)∠OCD

b) In the given figure, PQRS is a rectangle. Find the value of x, y, z.

21. a) Find the cost of painting the outer surface of a hollow cylindrical pipe of radius 2 m and height

21m at the rate of ₹ 5 per m2.

b) Find the area of the adjoining figure, it being given that AB||CD, AB = 12 cm, CD = 15 cm, BD =

4cm and one end of the figure is semi-circle with BD as diameter. (Take π = 3.14)

22. Construct a rhombus whose diagonals are 6.8 cm and 5.2 cm. Write the steps of construction.

23. a) Find the measure of angle x in the given diagram.

b) In the given figure, ABCD is a rhombus, where BO=12 cm and OC=5cm. Find the value of x, y,

and z.

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24. Simplify and express the result in exponential form with positive exponent

a) {[( 98 )−2] 3

1}6

b) 2−4

8 x 5−1 3

25. a) A father is 7 times as old as his son. Two years ago, the father was 13 times as old as his son.

How old are they now?

b) A steamer goes downstream and covers the distance between two ports in3h. It covers the

same distance in 5h, when it goes upstream. If the stream flows at 4km/h, then what is the speed

of steamer upstream?

26. a) A bag contains Rs 155 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio 3:5:7.

Find the number of coins of each type.

b) Find the value of q: 106(q+5) − 5

4q = 2

27. a) Find the value of x √3 968 √3 1375

b) Three numbers are in the ratio 2:3:4 and the sum of their cubes is 33957. Find the numbers.

28. a) A rectangular piece of paper with 22 cm long x 6 cm is folded without overlapping to make a

cylinder of height 6 cm. Find the volume of the cylinder.

b) Two cylinders of equal volume have heights in the ratio 1:9. What is the ratio of their radii?

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Mid term(Half yearly) Examination ModelPaper-3

SECTION-A (4 x 1 = 4)

1. Find the value of (1 )−100 2

2. The length of a rectangle is 15 cm and each of its diagonals measures 17 cm. Find its breadth.

3. Evaluate 2 x 3[ −2 −1] + ( 61)0

4. Total surface area of a cube is 294 sq cm. Find its volume.

SECTION-B (5 x 2 = 10)

5. A room contains 750.4 cu m of air and its height is 4m. Find the area of the floor.

6. Simplify the following: (2-4 + 2-3) x (2-4 - 2-3)

7. If , Find the value of x. 2x + 4 + 3

x − 3 = 4 x + 2 + 5

x + 3

8. The present age of a man is twice that of his son. Eight years hence their ages will be in the ratio

7:4. Find the son’s present age.

9. In the adjoining figure, EC丄OB and ED丄OA. If ∠AOB = 36o, Find the measure of ∠CED?

SECTION-C (10 x 3 = 30)

10. The angles of a quadrilateral are in the ratio 5:3:2. If the fourth angle is 130, find the other three

angles of the quadrilateral.

11. Find the value of ― 6 7( −1 − −1)−1 5 4( −1 − −1)−1

12. Two adjacent angles of a Rhombus are (4x-30)o and (x + 20)o. Find all the angles of the Rhombus.

13. The circumference of the base of a cylindrical vessel is 132cm and its height is 25cm. How many

litres of water can it hold?

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14. By what number should be multiplied so that the product becomes (− )6 −1 (9)−1

15. The sum of the digits of a 2 digit number is 9. If the digits are interchanged, it is found that the

resulting number is greater than the original number by 27. What is the original number?

16. If each side of a given triangle is increased by 4cm, the ratio of the perimeters of the new triangle

to the given triangle is 7:5. Find the perimeter of the given triangle.

17. In the adjoining figure, AB is parallel to DC, ∠A=74o and ∠B: ∠C = 4:5. Find ∠B, ∠C and ∠D

18. The denominator of a rational number is greater than its numerator by 5. If (-3) is added to the

numerator and (-2) is subtracted from the denominator, the new number becomes . Find the62

original number.

19. Construct a quadrilateral ABCD in which AB = 4.5cm, BC = 3.5cm, CD = 4.2cm, ∠B = 40o and

∠A= 135o.

SECTION-D (9 x 4 = 36)

20. a) A circle of circumference 88 cm is cut out of a square sheet of paper of side 30cm. What is the

area of the paper left?

b) The dimensions of a cuboid are equal to half the dimensions of another cuboid. Find the ratio of

the (i) volumes, (ii) surface areas of the two cuboids.

21. a) By what number should be multiplied to get ? ( 53)−3

( 65)2

b) The sum of two number is 90. One third of the larger number is 9 more than twice the smaller

one. What are the numbers?

22. a) A man’s age is seven times that of his son. In 5 years, he will be four times as old as his son.

What are the present ages of the man and his son?

b) 4 years ago, Lal was twice as old as he was 9 years ago. Find his present age.

23. a) The smallest number by which 686 should be divided to make it a perfect cube.

b) Multiply 210125 by the smallest number so that the product is a perfect cube. Also, find out the

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cube root of the product.

24. a)ABCD is a square. Find x.

b)In the given isosceles trapezium ABCD, AB||DC and AD=BC. If ∠D=60o, AB=18cm and

AD=12cm, find the length of DC.

25. Construct a quadrilateral MIST where MI = 3.5cm, IS = 6.5cm, ∠M=75o, ∠I=105o and ∠S=120o.

(write the steps of construction).

26. The exterior angles of a pentagon are in the ratio 3:5:2:1:4. Find all the interior angles of the

pentagon.

27. a) Find the height of the wall, whose length is 4m and which will be covered by 2400 tiles of size

25cm X 20cm.

b) Find the cost of polishing the outer surface of a cuboid wooden box at the rate of ₹4 per sq.m,

whose length, breadth and height respectively are 20m, 12m and 8m.

28. a) Write 0.00000602 in standard form.

b) Find x, if ➗ ( 94)4 ( 9

4)7 = ( 9

4)2x −1

Mid term(Half yearly) Examination ModelPaper-4 SECTION-A (4 x 1 = 4)

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1. If 3(2p ― 1) = 5 ― (3p ― 2), then p =____________

2. If , then x = _______________ x 4 4 24 3 = x

3. If two adjacent sides of a parallelogram are equal then it is called a _____________

4. Solve 3z + 2 = -6 - z

SECTION-B (5 x 2 = 10)

5. Find the value of y in the given figure

6. Find “x” if x ( 3−2)−13 ( 3

−2)8= ( 3

−2)−2x + 1

7. Solve: 3(5p -7) -2(9p-11) = (8p + 13) -10

8. Find the volume of a cube whose T.S.A is 1536 cm2.

9. Four less than three times a number is 8 more than twice the number. Find the number.

SECTION-C (10 x 3 = 30)

10. The sum of the digits of a 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?

11. Find the cost of erecting a fence around a square field whose area is 9 hectares if fencing costs ₹

35 per metre.

12. The difference between three - fourth and three - fifth of a number is 15. Determine the number.

13. Find the smallest number which when multiplied with 137592 will make the product a perfect cube.

Further find the cube root of the product.

14. The distance between sun and earth is m and the distance between earth and 1.496 x 10( 11)

moon is m. During solar eclipse moon comes in between earth and sun. At that time, 3.84 x 10( 8)

what is the distance a between moon and sun?

15. Two adjacent sides of a parallelogram are 4cm and 6cm respectively. The angle between them is

60o. Construct the parallelogram. Write the steps of construction.

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16. Construct a quadrilateral ABCD in which BC=4.5cm, CA=5.4cm, AD=4cm, CD=5cm and

BD=5.5cm

17. a) ABCD is a rhombus whose diagonals AC and BD intersect at point O. If side AB = 10 cm and

diagonal BD = 16 cm. Find the length of diagonal AC.

b) From the figure, calculate the remaining angles of the parallelogram ABCD.

18. The dimensions of a hall are 80m, 40m and 20m respectively. How many persons can sit in the

hall, if each person requires 160m3 of air.

19. a) (− ) [( ) ]( )31 0

+ 31 0

+ 31 0 2

b) √3( )8

272

SECTION-D (9 x 4 = 36)

20. a) Find the cost of digging a well of diameter 6m and having depth 21m at the rate of ₹2.50 per

m3.

b) The dimensions of a cuboid are in the ratio of 2:3:4 and its total surface area is 468 sq.m. Find

the dimensions.

21. a) Difference of two perfect cubes is 189. If cube root of the smaller of the two numbers is 3, find

the cube root of the larger number.

b) Find the smallest number by which 9000 divided so that the quotient is a perfect cube. Also find

the cube root of the quotient.

22. a) By what number should be divided to get ? ( 3−2)−3

( 32)2

b) Simplify X 3 4 4 2[ 0 + 2 − 3] −2

23. a) Find the ratio of the volumes of two cubes if the length of an edge of the bigger cube is thrice

the length of an edge of the smaller cube.

b) A wire is in the shape of a circle of area 3850 cm2. If the same wire is bent in the form of a

square, find the area of the square.

24. a) A plane takes 2 hours and 45 minutes to cover the distance between two airports. If it travels 20

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km/h slower, then it takes 3 hours. Find the speed of the plane. Also, find distance between the

two airports.

b) If a number is subtracted from the numerator of the fraction and thrice that number is added 53

to the denominator, the fraction becomes . Find the number.41

25. Construct a quadrilateral PQRS in which PQ = 3.5cm, QR = 6.5cm, ∠P=100o, ∠R=110o, and

∠S=75o. (write the steps of construction)

26. a) Simplify : [(82)-3]-2 ÷ [(4-3)-2]2 x (2-3)4

b) Find a number such that if 25, 7 and 1 are added to it, the product of the first and third results is

equal to the square of the second.

27. a) Find the value of x, y and z in the given diagram.

b) From the given diagram, find the value of x.

28. a) The sum of the two opposite angles of a quadrilateral is 172o and other two angles are equal,

find the measurement of equal angles.

b) The ratio between between an exterior angle and the interior angle of a regular polygon is 2:3.

Find:

i) The measure of each exterior angle.

ii) The measure of each interior angle.

iii) The number of sides in the polygon.

iv) The number of diagonals in the polygon.