Maths Olympiad Class 7

SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1. 2. 3. 4.

Topic : Integers

DPPS. NO. – 01

Closure property is observed with respect to .......... operation in integers. (A) +,X (B) +,X, / (C) +,X,–

(D) +,–,/

The sum of two integers is – 16. If one them is 20, then the other is : (A) 36 (B) 4 (C) – 36

(D) none of these

What must be subtracted from – 3 to get – 9 ? (A) – 6 (B) 12 (C) 6 (D) – 12 During a school tennis tournament each player is awarded 2 pt for winning a game , –1 for loosing a game and 1 for drawing a game. The detail of three players (A,B,C) is given below. Who had won the tournament. win lose draw A 4 3 1 B 3 4 3 C 1 2 5 (A) B

(B) A

(C) C

(D) Can’t be determined

5.

A frog is climbing on the water slide. In one jump he goes 50 cm up and the he comes back 20 cm. The total distance of slide is 260 cm. Assuming at the top of the water slide there is no sliding effect, in how many jumps will he reach top of the slide (A) 9 jumps (B) 8 jumps (C) 7 jumps (D) none of these

6.

Fill in the blanks. (i) 3 + 2 + (– 5) = ............ (ii) 5 – (– 7) + (– 2) = ....... (iii) – 3 + (– 2) – (5) = ....... (iv) 750 + ..... = 0 (v) 312 + ..... = 312 (vi) 7 × (– 3) × (– 2) = ..... (vii) (– 2) × (– 3) × (– 4) = ...... (viii) 5 × 6 × .... = – 30 (ix) 30  .... = – 6 (x) – 42  ....... = 21 (xi) 301 × 305 × 307 = 307 × ..... × 305 (xii) 7 × [60 + 75] = 7 × 60 + 7 × ..... (xiii) 3 × .... = 3 (xiv) 5  .... = 1 (xv) 0  700 = ....

7.

(a) Write a pair of negative integers whose difference is 7. (b) Write a pair of positive integers whose difference is – 5.

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8.

A man walks 22 m due east and then 17 m west then find the position of the man with respect to starting point.

9.

A certain freezing process requires that room temperature be lowered from 60ºC at the rate of 4ºC every hour. What will be the room temperature 8 hour after the process begins ?

10.

In a class test ( + 4) marks are given for every correct answer and (– 1) marks for every incorrect answer and no marks for not attempting any question. Ram scores 12 mark after giving 6 correct answer, how many question she attempted incorrectly ?

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

2.

Which of the following is a reducible fraction? 105 104 (A) (B) 112 121 2 1 By what number should 1 be divided to get 3 ? 2 (A) 2

3. 4. 5.

2 3

(D)

(C)

4 9

(D) 2

1 4

The place value of 3 in 9.453 is: (A) tenth (B) hundredth

(C) thousandth

(D) thousand

(C) a = b

(D) none of the above

If a = 2

1 1 1 1 × 3 and b = 3  2 then 2 2 2 2

(B) a < b

An ornament is made of gold and copper. Its total weight is 96 gm. If (B) 88 gm

1 th part of the ornament is copper, then the 12

(C) 12 gm

(D) 90 gm

Find the value of

(v) 3 (ix)

9.

77 72

(D) none of these

(i) 2 –

8.

2 3

46 63

(C)

(C) 0.007

weight of gold is: (A) 8 gm 7.

(B) 1

DPPS. NO. – 02

What should be subtracted from 0.1 to get 0.03 ? (A) 0.7 (B) 0.07

(A) a > b 6.

Topic : Fractions & Decimals

8 5

1 1 ×2 5 4

9 5 3 2 6

Find the value of (i) 0.3 × 0.3 × 0.3 = (iii) 39.13  1.3 = (v) 0.3  100 =

(ii) 8

5 1 –3 9 2

(vi)

2 1 ×3 9 4

(x)

7 3 8 + × 6 2 4 9

(iii)

3 ×15 5

(vii) 2

1 1 5 3 3

(iv)

20 × 18 3

(viii) 7  2

1 4

(ii) 0.3 + 0.03 + 0.003 = (iv) 2.73 × 1000 =

(a) Express in rupee (i) 335 paise (ii) 8 rupees and 5 paise (b) Arrange decimal in ascending order 2.3450, 2.34, 2.3415, 2.34005. (c) Express 45 mm in cm, m and km. (d) Write 2305.007 in expanded form.

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1 5 3 9 , , , . 8 2 16 24

10.

Arrange the following in descending order

11.

Ram having Rs. 100. He purchased 5 pencil, cost of each pencil is Rs. 2

3 2 and 7 copy, cost of each copy is 8 . Find 5 7

the money left with him. 12.

Each side of polygon is 3.5 cm is length, the perimeter of the polygon is 21 cm. Find the number of sides.

13.

A car cover 79.2 km in 3.3 h. Find the distance travelled in 4.2 hours.

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics

1.

3.

4 7

(B)

If 22

6 17

(D) none of these

(C) 21

(D) – 21

1 m rope is cut into 10 equal pieces, then the length of each piece will be: 2

(B) 2

1 m 2

(C) 2

1 m 3

(D) 2

1 m 4

2 6 , z  2, then (x÷y)÷z is equal to: If x  , y  3 5

If

4 18

(B)

18 5

(C)

5 18

(D)

5 18

3 6 of a number is 22. What is of that number? 11 11

(A) 6

6.

(C)

x 7 = , then the value of x is : 6 3 (A) – 14 (B) 14

(A) 5.

6 7

If

1 (A) 1 m 4

4.

DPPS. NO. – 03

102 in standard form is : 119

(A)

2.

Topic : Rational Numbers

(B) 11

(C) 12

(E) 44

Arrange the following in ascending order 3 4 2 1 7 , , , , 5 5 15 20 5

7.

Find the value of 5 3 × 6   15 

(ii)

5 7 2 +  6  – 9      3

  7   14  (iii)  12    24     

(iv)

3 3 3 3 × –  7 7 7 7

(iv)

2 11

(i)

8.

Draw a number line and represent (i) –

3 4

(ii)

9 7

(iii) –

8 3

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9.

In the given figure OP = PQ = QR = RS and AB = BC = CD = DE = EF. Find the distance CQ

10.

Misthee had birthday party. She had a sheet cake that she could cut in 12 equal sizes. She wanted to invite 20 friends for her birthday party . How many sheet of cake would she need if each of her friend received two pieces of cakes? If so what would be the fraction left?

11.

Find the multiplicative and additive inverse of

3 . 5

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

Topic : Lines and Angles

In the given figure, if AOB is a straight line, then the value of x is : D x + 15°

(A) 90°

4.

5.

45°

s

x + 30° B

(C) 22

(B) 45°

1 2

(D) 150°

In the given figure, the sum of 1, 2, and 3 is :

(A) 360º 3.

C O

A

2.

DPPS. NO. – 04

(B) 270º

(C) 120º

(D) 300º

Find the complement of each of the following angle : 360 40’ (A) 53º 20’ (B) 52º 20’ (C) 53º 40’

(D) 55º 20’

Write the supplementary angles of the following angles. 540 28’ (A) 105º 32´ (B) 125º 22´ (C) 125º 32´

(D) 122º 32´

In the given figure, for what value of x will line  be parallel to line m ? (3x-5)°

(2x+10)°

(A) 35º

(B) 40º

l

m

(C) 45º

(D) 50º

6.

The number of triangles with any three of the lengths 1, 4, 6 and 8 cms consider is : (A) 1 (B) 2 (C) 3 (D) 4

7.

In triangle ABC ,If A = (A) 30º

C B = , find A of a triangle. 3 2 (B) 60º (C) 90º

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(D) none of these

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8.

In given figure, AB divides DAC in the ratio of DAB : BAC = 1 : 3 and AB = DB. Find the value of x . A 108º

xº D

(A) 100º 9.

B

C

(B) 90º

(C) 125º

(D)110º

In figure, find value of x.

105º

Y

(A) 80º 10.

(B) 75º

(C) 90º

In the given figure, find the values of x and y.

0

B

60

C 45

0

y0 E

x0 A

(A) 75º,120º 11.

(D) 85º

D

(B) 80º, 115º

(C) 60º, 120º

(D) 75º, 115º

In the Figure, AB || CD,  ABO = 40º and  CDO = 30º. If  DOB = xº, then the value of x is :– A B 40º O C (A) 35º

(B) 110º

X 30º

D

(C) 70º

(D) 140º

20º q 88º p

12. 27º

Find measure of p and q . (A) p = 130º, q = 115º (C) p = 135º, q = 115º

(B) p = 115º, q = 135º (D) p = 135º, q = 110º

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13.

14.

Two complementary angles differ by 16º find the angles. (A) 53º , 37º (B) 56º , 40º (C) 62º , 28º

(D) 59º, 31º

Diagonal DB of a rhombus ABCD is equal to one of its sides.The value of A is : D

(A) 30º

C

(B) 60º A

B

(C) 120º (D) 90º 15.

In figure, if x + y = w + z then measure of AOB is C

A

(A) 180° 16.

(B) 150°

B

y x o w z

(C) 200°

(D) 190°

In the figure,  parallel to m and AX and AY are transversals. Then the value of the angle (x + y – z) is : (A) 110º (B) 80º (C) 40 (D) 30º

17.

How many degrees are there in an angle which equals one fifth of its supplement ? (A) 15° (B) 30° (C) 75° (D) 150°

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

Topic : Triangles C B = , find A of a triangle. 3 2 (B) 60º (C) 90º

In triangle ABC ,If A = (A) 30º

2. 3. 4.

DPPS. NO. – 05

(D) none of these

The perimeter of rectangle whose length is 40 cm and a diagonal 41 cm (A) 96 cm (B) 98 cm (C) 92 cm

(D) 90 cm

The largest side of a right triangle is : (A) median (B) altitude

(D) hypotenuse

(C) angle bisector

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find original height of the tree (A) 13 m (B) 18 m (C) 17 m (D) 19 m A

5.

In the given figure D is the mid point of BC then B

C

D

E

(i) AD is ____________ (ii) AE is ___________ (iii) It BE = EC 6.

Find the value of x in the given figure. A

80º

2x

(i)

(ii)

2x

50º

C

A

A

60º

x

(iii)

(iv) B B

(v) B

x

50º

2x

2x

x

70º

C

A

A

x

x

150º C

D

C

D

(vi) B

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30º

50º C

D

Page # 1

7.

Find the unknown length x. A

A

(i)

8 B

8.

x

10

(ii) x

C

5 B

C

12

C

In a quadrilateral ABCD . Prove that

D O

(i) AB + BC + CD + DA > AC + BD (ii) AB + BC + CD + DA < 2( AC + BD)

B

A

9.

Two poles are 6m apart of length 18m and 10m. Find the distance between their tops.

10.

From which of the option we can make the triangle. (a) with side 7, 8, 2 (c) with angle 30º, 60º, 90º (e) with two right angle

11.

(b) with side 8, 4, 4 (d) with two obtuse angle (f) with all angle less than 60º.

In the diagram if AB = AD = BD = DC, then find out the xº

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

Topic : Congruency of Triangles

DPPS. NO. – 06

In figure, BD and CE are altitudes. If BE = CD, prove that BD = CE. A

E

D

B

C

2.

If LMN IJK write all corresponding congruent part of the triangle

3.

In given figure DA  AB, CB  AB and AC = BD. State three pairs of equal parts in ABC and DAB. Which of the following statement is meaningfull C D (i) ABC BAD (ii) ABC ABD

4.

A

B

In the given figure ray AZ bisects DAB as well as DCB D

A

C

Z

B

(i) state the three pairs of equal parts in triangle BAC and DAC (ii) Is BAC DAC ?. Given reasan (iii) Is AB = AD ? (iv) Is CD = BC ? Given reasan 5.

Are the following pairs of triangle are congruent. If yes name the criteria A

P 5

5

3

(A) B

6

3

CQ P

A

1

1

(B) B

R

6

5

C

5

R

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P

A

40º

(C)

60º

B

40º 5

CQ

60º

R

5 P

A

70º 5

8

5

(D) 70º

B

C

8

Q

R

5 P

A 40º

(E)

6

3 B

8

6

C

Q

40º

R

3

6.

In figure, O is the mid-point of PQ and RS. Prove that PR = SQ and PR | | SQ.

7.

In figure, D and E are the mid-points of equal sides AB and AC of ABC respectively. Prove that BE = CD. A

D

E

B

8.

C

In figure, in ABC, AD is the bisector of A and AD  BC. Prove that ABC is an isosceles triangle. A

B

9.

D

C

In figure, ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that BCD is a right angle. D

A

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10.

In figure, line m is the bisector of an angle A and O is any point on m. OQ and OP are perpendiculars from O to the arms of A. Prove that P m

O

A Q

(i) AOQ AOP (ii) OQ = OP.

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics

1.

2.

2  2    1     2       1 (A) 16

5 If   3

(A) 3.

5.

1

=? (B) 16 11

5 ×  3

5 =  3

1 2

(C)

1 16

(D) – 16

8x

, then x = ? (B) – 2

4 5

(B)

(C) 2

5 4

3  1  3  1  3   1          = ?  2    4   3  19 64 (A) (B) 64 19 If 5 x + 3 = (25)3x – 4, then the value of x is :

(A)

5 11

(B) 5

6.

DPPS. NO. – 07

(D)

3 4

By what number should (– 8)–1 be multiplied to get 10–1 ? (A)

4.

5

Topic : Exponents

x

(C)

(C)

4 5

27 16

11 5

(D) none of these

(D) none of these

(C)

11 3

(D)

13 5

18

 125   125  5  ×  =   . Then x is equal to : If  8 8      2 (A) 5 (B) 3 (C) 1

(D) 2

7.

Write exponents form of 9 × 9 × 9 × 9 taking base as 3.

8.

Using law of exponent simplify and write the answer in exponential form (i) 23 × 25 × 24 (ii) x5 × x7 (iii) (310  38) × 35 (iv) 2º × 3º × 5º (v) (3º + 5º ) × 7º

9.

Express each of the following as product of power of their prime factors (i) 48 (ii) 500

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7. Exponents

10.

Compare the following numbers. (i) 3.5 × 1010 and 0.478 × 1012

(ii) 23 and 32

11.

Write the following number in the standard form (a) 0.0034378 (b) 340008923

12.

Find the value of (a) (– 1)100 + (– 1)102

(b) (– 1)100 + (– 1)101

(c)

15 2  303  3 3 ( 45 )3

13.

If 2a = 32 and 3b = 27 then find the value of (a + b)2

14.

Using law of exponent simplify and write the answer in exponential form (i)

( 2 3 )5  5 6 8 3  25 3

(ii)

t 3  t 2  53 t 5  125

(iii)

835 (iv) 910 × 275 × 816 235

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

Topic : Algebraic Expression

The degree of the polynomial 7x –5x3 + 2x2 + 7 is : (A) 2 (B) 3

(C) 7

DPPS. NO. – 08

(D) – 5

2.

What is the value of (2x + 3) (x + 6) –(2x –5) (x + 10)? (A) 5x (B)18 (C) 2x2

(D) 68

3.

What should be the value a if the value of 3x – 5x + a equals to 7, when x = – 1 (A) 1 (B) –1 (C) 2

(D) – 2

If a = 2, b = 3a + 4 and c = 3b , then b – c is (A) 30 (B) 20

(D) – 22

4. 5. 6.

2

If 2a – 3 = 5 and 3b +1 = 2, then 3b – 2a is : (A) – 3 (B) – 7 (C) 7 (D) – 9 Let ab = a + b + ab where a, b are rational numbers , neither of them equal to – 1. If a x = 0, then x is : (A)

7. 8.

9.

a a1

(B)

a a –1

(C)

–a a –1

What should be subtracted from (2 – x + x2) to obtain (x – 1) ? (A) 2x – 3 – x2 (B) 3 + 2x – x2 (C) 3 + 2x + x2 Which of the following is a trinomial (A) x2 + 2x + x (B) 3x3 + 2x2 – x2 y If x > 2y and z < then 3 (A) x > 6z

10.

(C) – 20

(B) x < 6z

Instead of multiplying a given number by answer. The given number was : (A) 8 (B) 19

(C) 22 – x2 – 3

(C) y <

6 x

(D)

–a a1

(D) 3 – 2x + x2 (D) x2 + x + 1

(D) z >

6 x

8 8 , a student divided it by . His answer was 297 more than the correct 19 19

(C) 152

(D) 64

11.

A man loses one third of his money ; then he gains Rs. 10 . Then he loses one-third of his possession and again gains Rs. 20. Now he finds that he has what exactly he had at the begining. What was the amount he had originally ? (A) 48 (B) 49 (C) 42 (D) 44

12.

If a – b > 0, then ..........Fill in the blank with proper option. (A) a < b (B) a = b (C) a > b

(D) a  b

If A = 2, B = –1, C = – 3, find the value of 2(A +B) + 3(B + C) – 4 (C + A). (A) – 6 (B) 6 (C)– 8

(D) 8

13.

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14.

If a = – 2, b = 3 and c = 4, then the value of a 3 + b3 + 3a2c – 4bc3 is : (A) 107 (B) – 107 (C) 701

15.

How much is 3p4 + p3 – 2p2 + p + 4 greater than 2p3 + 7p2 – 5p + 6 ? (A) 3p4 – p3 – 9p2 + 6p – 2. (B) 3p6 – 2p3 – p2 + 6p – 4. (C) p4 – 4p3 – 6p2 + 3p – 2. (D) 3p4 + p3 – 6p2 + 10p – 2.

16.

Simplify : – m – [m + {m + n – 2m – (m – 2n)} – n] (A)– 2n (B)– 2m (C)– 3n

(D) – 701

(D)– 6n

17.

The product of (a + b – c) and (a – b + c) is (A) a2 – b2 – c2 – 2bc (B) a2 – b2 – c2 + 2bc (C) a2 + b2 + c2 + 2bc (D) a2 + b2 + c2 – 2bc

18.

Find the sum of f(x) & g(x) where f(x) = 4x5 + 3x3 + 4x2 + x + 1 g(x) = 5x4 + x5 + x3 + 3 (A) 5x5 + 5x4 + 4x3 + 4x2 + x + 4 (B) 5x5 + 5x4 + 4x3 + 4x2 + x – 4 (C) 5x5 + 5x4 + 4x3 – 4x2 + x – 4 (C) 5x5 – 5x4 + 4x3 – 4x2 + x – 4

19.

Divide : –15x3y4z5 + 10x2y3z4 – 25x4y3z5 by – 5x2y3z3.

(A)3xyz2 – 2z + 5x2z2 (C)–4xyz2 – 2zx + 5x2z2 20.

(B)2yz2 – 2xz + 5xz2 (D)–3xyz2 – 2z – 5x2z2

Simplify : 7 – [ 3x + { – 2y + 3z – ( 3y + 5z) + 8 } – ( 3y2 + 7x) + 9] (A) – 10 + 4x + 5y + 2z + 3y2 (B) 10 + 5x + 5y + 10z + 3y2 (C)– 15 + 4x + 3y + 3z + 3y2 (D)– 10 + 10x + 5y + 2z + 6y2

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Page # 2

SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

Topic : Statistics

If the arithmetic mean of 7, 5, 13, x and 9 be 10, then the value of x is : (A) 10 (B) 12 (C)14

DPPS. NO. – 09

(D) 16

2.

If the mean of five obseration x, x + 2, x + 4, x + 6, x + 8 is 11, then the mean of first three observations is : (A) 9 (B) 11 (C) 13 (D) none

3.

The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 40, the resulting mean will be : (A) 50 (B) 49.90 (C) 70 (D) 40 A cricketer has a certain average run for 10 innings. In the 11 th inning, he scores 100 runs, and now his average run is .increased by 9 runs. Then average of 11 inning is : (A) 10 runs (B) 20 runs (C) 11 runs (D) 21 runs

4.

5.

If the mean of the following data is 18.75, find the value of p : x

10

15

p

25

30

f

5

10

7

8

2

(A) 20

(B) 21

(C) 22

6.

Find the median of 18, 35, 10, 42, 21.

7.

What is the mode of 5, 7, 9, 12, 10, 15, 7, 8, 7, 25 ?

8.

Read the following graph carefully and answer the following questions :

(D) 25

(i) What information does the bar graph give ? (ii) Which state has the largest production of wheat ? (iii) Which state has the largest production of rice ? (iv) Which state has total production of rice and wheat maximum ? (v) Which state has total production of rice and wheat minimum ? CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892

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9.

Find the value of p, if the median of following observations is 48. 14, 17, 33, 35, p – 5, p + 7, 57, 63, 69, 80. The above observation are in ascending order.

10.

The distance (in km) of 40 engineers from their residence to their place of work were found as follows : 5, 3, 10, 20, 25, 11, 13, 7, 12, 31, 19, 10, 12, 17, 18, 11, 32, 16, 17, 2, 7, 9, 7, 8, 3, 5, 12, 15, 18, 3, 12, 14, 2, 9, 6, 15, 15, 7, 6, 12. Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0 – 5.

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

2. 3.

DPPS. NO. – 10

Which of the following can not be the probability of any events. 2007 1001 (A) 1 (B) 0 (C) (D) 2008 1000 If probability of happening of any event A is 0.63 then what is the probability of not happening of A. (A) 0.37 (B) 1 (C) 0 (D) 0.47 Probability of getting a face card (A)

4.

Topic : Probability

12 13

(B)

3 13

(C)

1 13

(D)

1 4

5.

If the odds in favour of an event be 3 : 5 then the probability of non-happening of the event is 3 5 3 5 (A) (B) (C) (D) 5 3 8 8 All the red face cards are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probabilty of getting queen of black suit 1 1 1 1 (A) (B) (C) (D) 13 23 26 46

6.

1500 families with 2 children were selected randomly and the following data were recorded : Number of girls in a family 2 1 0 Number of families 475 814 211 Compute the probability of a family chosen at random, having (i) 2 girls (ii) 1 girl (iii) no girl. Also, check whether the sum of these probabilities is 1.

7.

Given an example of sure chance and impossible chance.

8.

In a circket match, a batsman hits a boundary 6 times out of 90 balls he plays. Find the probability that he : (i) hit a boundary (ii) did not hit a boundary.

9.

A number from 1 to 20 is choosen at random. What in the probability of getting (i) a prime number(ii) multiple of 3. (iii) multiple of 2 (iv) multiple of 2 and 3 (v) multiple of 2 or 3

10.

A bag contains 5 red, 2 black, and 3 green balls, find probability of getting (i) Red ball (ii) Black ball (iii) Green ball (iv) Red or green ball (v) Not black ball

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SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

Topic : Mensuration

DPPS. NO. – 11

Find the perimeter of triangle ABC. If A = 90º,AB = 8cm and AC = 6cm. (A) 24 cm (B) 22 cm

(C) 18 cm

(D) 20 cm

2.

The perimeter of a triangle is 36 cm and its sides are in the ratio 3 : 4 : 5. Find the area of the triangle. (A) 54 cm2 (B) 50 cm2 (C) 20 cm2 (D)24 cm2

3.

In figure, ABCD is a parallelogram, DL  AB and DM  BC. If AB = 18 cm, BC=12 cm and DM=9.3 cm, find D C M DL. A L (A) 6.2 m

4.

(D) 6.8 m

(B) 48 cm,16 cm

(C)15 cm,16 cm

(D)51 cm,16 cm

Side of rhombus is 13 cm and one of the diagonal is 24cm, find the other diagonal of the rhombus. (A) 10 cm

6.

(C) 6.6 m

The base of a parallelogram is thrice its height. If the area is 867cm 2, find the base and height of the parallelogram. (A) 51 cm,17 cm

5.

B (B) 6.4 m

(B) 120 2 cm

(C) 120 cm

(D) 140 2 cm

In figure, ABCD is a trapezium in which AB || DC; AB = 7 cm; AD = BC = 5 cm and the distance between AB and DC is 4 cm.

Find the length of DC and hence, find the area of trapezium ABCD. (A)13 cm, 40 cm2 (B)13 cm, 26 cm2 (C) 10 cm, 40cm2

(D) 10 cm, 26 cm2

7.

A lawn is in the shape of a rectangle of length 80 m and width 40 m. Out side the lawn there is a footpath of uniform width 3m. Find the area of the path (A) 775 m2 (B) 825 m2 (C) 756 m2 (D) 1100 m2

8.

The two parallel sides of a trapezium are 1.5 m and 2.5 m respectively, If perpendicular distance between them is 6.5 m, what is area of the trapezium ? (A) 26 m2 (B) 13 m2 (C) 20 m2 (D) 10 m2

9.

The area of a rhombus is 36 cm2. Once of its diagonals is of length 12 cm. The other is of length (A) 7 cm (B) 6 cm (C) 3 cm (D) 9 cm

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10.

Find the area of the given quadrilateral ABCD, whose diagonal AC = 19.5 cm and the offsets on it are 5.4 cm and 10.6 cm.

(A)156 sq cm

(B)312 sq cm

(C) 273 sq cm

(D) 137 sq cm

11.

If the area of an equilateral triangle is 4 3 square cm, then its perimeter, in cm, is : (A) 12 (B) 15 (C) 16 (D) 20

12.

Area of a rectangle is A. If its length is reduced by 10% and its breadth is increased by 10% then which of the following statements is true ? (A) A remains unchanged (B) A is decreased by 1% (C) A is decreased by 0.1% (D) A is increased by 0.1%

13.

Length of two sides of a parallelogram are in the ratio of 2 : 3. Find the sides of the parallelogram if its perimeter is 120 m. (A) 36,24

(B) 72,48

(C) 36,48

(D) 72,24

14.

Length of rectangle is 10 metres less than 3 times of its breadth. If its perimeter is 60 metres, length in meter is (A) 10 (B) 20 (C) 30 (D) 40

15.

In the given figure, the area of triangle LMN is : (A) 18 cm2 (B) 12 cm2 (C) 36 cm2 (D) 40 cm2

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Page # 2

SUMMER WORKSHOP (VII - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

DPPS. NO. – 12

The area of a square is 225 sqm. Then, the perimeter of the square is : (A) 50 m

2.

Topic : Mensuration

(B) 15 m

(C) 15 2 m

(D) 60 m

If the length of a diagonal of a square is a + b., then the area of the square is: (A) (a + b)2

(B)

1 (a  b ) 2 2

(C) a2 + b2

(D)

1 2 (a  b 2 ) 2

3.

The areas of two circles are in the ratio 16 : 25. Find the ratio of their circumferences. (A) 4 : 1 (B) 4 : 5 (C) 3 : 4 (D) 5 : 4

4.

A race track is in the form of a ring whose inner circumference is 352 m, and the outer circumference is 396 m. Find the width of the track. (A) 7 (B) 6 (C) 11 (D) 5

5.

The circumference of a circle exceeds the diameter by 16.8 cm. Then, the radius of the circle. (A) 3.10 cm (B) 3.25 cm (C) 3.92 cm (D) 3.5 cm

6.

The edge of cube is 20 cm. How many small cubes of 5 cm edge can be formed from this cube ? (A) 4 (B) 32 (C) 64 (D) 100

7.

A water tank whose dimensions are 1.5 m, 0.75 m and 0.48 m is full. Its contents are emptied into another empty tank whose area is 1 m2. How much the water level shall rise ? (A) 64 cm (B) 54 cm (C) 5.4 cm (D) 34 cm

8.

The area of a square and a rectangle is equal. If the side of a square is 40 cm and the breadth of the rectangle is 25 cm. Then the length of rectangle will be : (A) 128 cm (B) 64 cm (C) 32 cm (D) 16 cm

9.

The area of a quadrant of a circle is (A) 14 cm

10.

77 cm2. Its radius is 2 (B) 17 cm (C) 7 cm

(D) 12 cm

When two cube of side 12 cm are joined end to end to form a cuboid then the total surface area of cuboid is. (A) 1740 cm2 (B) 1640 cm2 (C) 1540 cm2 (D) 1440 cm2

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11.

If ratio between digonals of two squares is 2 : 1. Then the ratio between their areas will be – (A) 2 : 1 (B) 4 : 1 (C) 3 : 1 (D) 6 : 1

12.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to that of the sum of the surface areas of three cubes. (A) 7 : 19 (B) 7 : 9

(C) 8 : 9

(D) 7 : 8

13.

A thin wire is bent into the form of a circle of radius 7 cm. If a square is made out of this wire, the side of the square would be : (A) 7 cm (B) 14 cm (C) 11 cm (D) 22 cm

14.

A beam 10 m long, 50 cm wide, 2 m high is made up of iron which weighs 20 kg per cubic metre. The weight of the beam is : (A) 200 kg (B) 100 kg (C) 150 kg (D) 175 kg

15.

One room’s breadth is double its height and half its length. If volume of room is 512 cubic meter then length of the room will be – (A) 12 m (B) 16 m (C) 20 m (D) 32 m

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SUMMER WORKSHOP (VII Olympiad) Daily Practice Problem Sheet ANSWER KEY

Que s Ans.

1 C

DPPS - 1. Integers 2 3 4 C C B

5 B

6. (i) 0, (ii) 10, (iii) – 10, (iv) – 750, (v) 0, (vi) 42, (vii) – 24, (viii) – 1, (ix) – 5, (x) – 2, (xi) 301, (xii) 75, (xiii) 1, (xiv) 5, (xv) 0 7. (a) –2, – 9 (b) 2, 7 8. 5 metre towrads East 9. 28° 10. 12 DPPS - 2. Fraction & Decimals

Ques Ans.

7. (i)

1 A

2 D

3 B

4 C

5 A

2 91 36 13 7 28 27 65 , (ii) , (iii) 9, (iv) 120, (v) , (vi) , (vii) , (viii) , (ix) , (x) 5 18 5 18 16 9 23 18

8. (i) 0.027, (ii) 0.333, (iii) 30.1, (iv) 2730, (v) 0.003 9. (a) (i) Rs. 3.35 (ii) Rs. 8.05 (b) 2.34, 2.34005, 2.3415, 2.3450 (d) 2000 + 300 + 0 + 5 +

10.

6 B

(c) 4.5 cm, 0.045 m, 0.000045 km

  7 + + 10 100 1000

5 9 3 1 , , , 2 24 16 18

11. Rs. 29

12. 6

13. 24 km/hr

DPPS - 3. Rational Numbers

Ques Ans.

6.

7 4 1 2 3 , , , , 5 5 20 15 5

7. (i) –

1 B

2 A

3 A

4 C

1 11 40 , (ii) (iii) –1, (iv) 6 18 49

5 D

9.

29 10

10.

12 C

13 A

1 8

11.

3 5

DPPS - 4. Lines & Angles

Ques Ans.

1 B

2 D

3 A

4 C

5 A

6 A

7 A

8 B

9 A

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10 A

11 C

14 B

15 A

16 C

17 B

Page # 1

DPPS - 5. Triangles

Ques Ans. 5. (i) median, (ii) altitude, (iii) no 7. (i) 6, (ii) 13 9. 10 metre 11. 30° s

1 A

2 B

3 D

4 B

6. (i) 32.5° , (ii) 50°, (iii) 36°, (iv) 130°, (v) 120°, (vi) 70° 10. (a) yes, (b) no, (c) yes, (d) no, (e) no (f) no DPPS - 6. Congruency of Triangles

2.  L =  I,  M=  J,  N=  K ; LM= IJ, MN= JK, LN = IK 5. (A) yes, SSS (B) yes, RHS (c) no, (D) yes, SAS, (E) no

Que s Ans.

7. 38 9. (i) 24 × 3

1 A

DPPS - 7. Exponents 2 3 4 D C A

5 B

6 C

8. (i) 212, (ii) x12, (iii) 37, (iv) 1 , (v) 2 (ii) 22 × 53 10. (i) 0.47 × 1012 > 3.5 × 1010 , (ii) 32 > 23

12. (a) 2, (b) 0, (c) 1800

13. 64

11. (a) 3.4 × 10–6 (b) 3.4 × 10 –8

14. (i) 26 ,(ii) 1, (iii) 270 , (iv) 359 DPPS - 8. Algebraic Expression

Ques Ans. Ques Ans.

1 B 16 A

2 D 17 B

3 B 18 A

4 C 19 A

5 B 20 A

6 D

Que s Ans.

6. 21 9. 47

7. 7

19 407 211 , (ii) , (iii) 60 750 1500

9. (i) 0.4, (ii)

8 D

9 A

10 C

11 A

DPPS - 9. Statistics 1 2 3 4 D A B A

12 C

13 A

14 D

15 A

5 A

8. (i) rice and wheat production in different state (ii) U.P. (iii) W. B. (iv) U.P. (V) Maharashtra

Que s Ans.

6. (i)

7 D

DPPS - 10. Probability 1 2 3 4 D A B D

7. getting 7 when a dice is thrown

3 1 3 13 , (iii) , (iv) , (v ) 10 2 20 20

5 B

8. (i)

1 14 , (ii) 15 15

10. (i) 0.5, (ii) 0.2, (iii) 0.3, (iv) 0.8, (v) 0.8 DPPS - 11. Mensuration

Ques Ans.

Que s Ans.

1 A

1 D

2 A

2 B

3 A

3 B

4 A

4 A

5 A

5 C

6 A

7 C

8 B

9 B

DPPS - 12. Mensuration 6 7 8 9 C B B C

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10 A

11 A

12 B

13 A

14 B

15 A

10 D

11 B

12 B

13 C

14 A

15 B Page # 2