Maths Olympiad Class 6

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics

Topic : Knowing Our Numbers

DPPS. NO. – 01

Choose the correct option: 1. 2. 3.

4.

Write the corresponding Hindu-Arabic numerals for MMMDCXL (A) 3640 (B) 3660 (C) 3460

(D) 3530

Write the Roman numeral for 1008 (A) MV (B) MVIII

(C) MIX

(D) MX

MMM stands for ________ . (A) 3000 (B) 1000

(C) 300

(D) 1000

CM = __________ . (A) 100 – 1000

(C) 500 – 100

(D) 1000 – 10

(B) 1000 – 100

5.

Which of the following statement is false ? (A) Symbol V, L, D can be used more than once (B) Symbol I, X, C, M can be repeated 3 times (C) Symbol I can be subtracted only from V and X (D) None of these

6.

The smallest three digit number having three distinct digits is (A) 123 (B) 101 (C) 102

7.

(D) 201

Write the greatest 4-digit number using different digits with 6 in the ten’s place ? (A) 9865

(B) 9867

(C) 9687

(D) 6987

8.

The standard numeral of thirty-one crore, fifty-five lakh, thirty two thousand, eight hundred is (A) 31, 55, 32, 800 (B) 3, 01, 55, 32, 800 (C) 3, 15, 05, 32, 800 (D) 3, 15, 53, 02, 800

9.

Difference of the greatest 7 digit number and the smallest 5 digit number is (A) 998999 (B) 9989999 (C) 99899

(D) 998099

The largest and smallest number using the digits 4, 0, 3, 7 is (A) 4370, 4307 (B) 3740, 3047 (C) 7403, 3704

(D) 7430, 3047

10.

11.

The number 315233729 can be written in International system (A) Three hundred fifteen million, two hundred thirty three thousand seven hundred twenty nine (B) Thirty one crore fifty two lakh thirty three thousand seven hundred twenty nine (C) Three one five lakhs two three thousand seven hundred twenty nine (D) Three hundred fifteen million

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12.

How many numbers are there containing 3-digits? (A) 999 (B) 899

(C) 900

(D) 800

13.

Total number of numbers which when rounded off to nearest ten give us 200 is : (A) 9 (B) 10 (C) 8 (D) 7

14.

The greatest number which when rounded off to the nearest thousand as 7000, is (A) 6500 (B) 6549 (C) 7499 (D) 6499

15.

There are about 20 times as many species of ants as there are species of bats. Let b represents the number of species of bats. Which expression represents the number of species of ants? (A) b + 20 (B) b - 20 (C) 20 × b (D) 20 ÷b

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Page # 2

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics

Topic : Whole Number

DPPS. NO. – 02

Choose the correct option : 1.

Simon and Julie need 72 paper flowers to complete a bulletin board. They have 19 paper flowers so far. Which operation should be used in the box below to find how many more paper flowers they need? 72 ? 19 = (A) Addition (B) Division (C) Multiplication (D) Subtraction

2.

The whole number which does not have a predecessor (in whole numbers) is (A) 100 (B) 0 (C) 1

3.

4.

5.

Which is true ? (A) 2,934,106 < 2,873,014 (C) 2,874,365 < 2,897,056

(B) 2,163,489 < 2,089,634 (D) 2,457,831 < 2,359,678

42(4 + 2) = (42 x 2) + (42 x 2) is an example of (A) closure property (C) associative property

(B) commutative property (D) distributive property

The product of the place values of two threes in 53432 is (A) 9000 (B) 90000 (C) 10000

(D) 9

(D) 99000

6.

Which of the following properties are not applicable to the subtraction of whole numbers? (A) closure property (B) commutative property (C) associative property (D) all the above

7.

Anita and Chris are solving this problem.There are 4 bags of oranges. There are 6 oranges in each bag. How many oranges are there in all ? Anita wrote 6 + 6 +6 + 6 = Chris wrote 6 x 4 = Whose answer will be correct? (A) Only Anita (B) Only Chris (C) Both Anita and Chris (D) Neither Anita and nor Chris

8.

If a and b are two whole numbers, then commutative law is applicable to subtraction if and only if (A) a = b (B) a is not equal to b (C) a > b (D) a < b

9.

A gardener bought 450 apple trees. He wants to plant 15 trees in each row. How many rows can he plant? (A) 0 (B) 30 (C) 80 (D) 60

10.

The value of 555 x193 – 555 x 93 is (A) 555,931 (B) 1,210,321

(C) 53,912

(D) 55,500

11.

The property satisfied by the division of whole numbers is (A) closure property (B) commutative property (C) associative property (D) none of these

12.

What least number should be added to 1330 to get a number exactly divisible by 43? (A) 6 (B) 1 (C) 3 (D) 7

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13.

14.

15.

16.

The largest 3-digit number divisible by 19 is (A) 988 (B) 998

(C) 999

(D) 969

On dividing 55,390 by 299 the remainder is 75. The quotient is (A) 195 (B) 185 (C) 175

(D) 193

The difference between the place values of 6 and 3 in 256839 is (A) 3 (B) 9 (C) 6800

(D) 5970

What least number must be subtracted from 13,601 to get a number exactly divisible by 87? (A) 25 (B) 29 (C) 27 (D) 23

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SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

2. 3. 4. 5. 6. 7. 8. 9.

10.

Topic : Playing with Numbers

DPPS. NO. – 03

The numbers which are multiples of 2 are called (A) odd numbers. (B) even numbers. (C) integers. (D) prime numbers. The sum of the prime numbers between 90 and 100 is (A) 188. (B) 281. (C) 376.

(D) 97.

Least prime number is (A) 0.

(D) 3.

(B) 1.

(C) 2.

The two numbers which have only 1 as their common factor are called (A) co-primes. (B) twin primes. (C) composites.

(D) integers.

The twin prime numbers out of the following are: (A) 2,4 (B) 3,5

(C) 7,13

(D) 13,17

Co-prime pair of numbers among the following is (A) (2, 4). (B) (2, 3).

(C) (3, 9).

(D) (4, 16).

Among the following options, the numbers which is a multiple of 11, is (A) 142. (B) 132. (C) 122.

(D) 112.

What least value should be given to so that the number 84564107 is divisible by 3? (A) 0 (B) 1 (C) 2 (D) 3 The number divisible by 11 is (A) 1,116,365. (B) 1,802,701. (C) 8,790,322. (D) 901,351. The prime factors of 24 are (A) 2 × 3 × 4 (B) 2 × 2 × 2 × 3

(C) 6 × 4

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(D) 8 × 3

Page # 1

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics

Topic : Integers

DPPS. NO. – 04

Choose the correct option: 1.

Sum of two negative number is always (A) Positive

2.

4. 5.

6.

11.

12.

(D) –2

(D) 29.

(C) 28.

In addition and subtraction of two integers , sign of the answer depends upon (A) Smaller number

(B) Their difference

(C) Their sum

(D) Greater numerical value

What will be the additive inverse of –5 (B) –4

(C) 3

(D) 5

(B) 8

(C) –10

(D) 10

(C) -289

(D) -291

(C) +11.

(D) +315

Predecessor of –9 is

The successor of (-297 – (- 7)) is (B) 290

The sum of [(-101) - (29) + (-33) - (-84) + (68)] is (A) –315.

10.

(C) 2

The additive inverse of -29 is (A) 26. (B) 27.

(A) -290 9.

(B) 40

(D) 2 > –2 > –3

(A) –8 8.

(D) 1

The correct sequence in descending order is _______. (A) 0 > 1 > 2 (B) 0 > –1 > 1 (C) –1 > 1 > 2

(A) –6 7.

(C) 0

Sum of – 19 and –21 is (A) – 40

3.

(B) Negative

(B) -11.

Which of the following statement is false: (A) –7 + (–6 ) = –13 (C) 2 + (–1 ) = 1

(B) –5 + 1 = 4 (D) 8 + (–9 ) = –1

The pair of integers whose sum is –5 (A) 1, –4 (B) –1 , 6

(C) –3 , –2

(D) 5, 0

What integers or number should be added to –5 to get 4 (A) 1

(B) –1

(C) –9

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(D) 9 Page # 1

13.

14.

15.

The product of two negative integers is (A) always positive. (B) always negative.

(C) negative or positive.

(D) zero.

30  (– 23) + 30  14 = ? (A) – 270

(C) 1110

(D) – 1110

(B) 270

Which of the following divisions has the greatest quotient ? (A) 20  (– 4) (B) 20  4 (C) (– 20)  (– 5)

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(D) (– 30)  5

Page # 2

SUMMER WORKSHOP (VI - 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

2 3

46 63

(C)

77 72

(D)

(C)

4 9

(D) 2

1 4

(C) 0.007

(D) none of these

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 weight of gold is: (A) 8 gm

7.

(B) 1

DPPS. NO. – 05

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

(A) a > b 6.

Topic : Fraction and Decimals

(B) 88 gm

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

(C) 12 gm

(D) 90 gm

The value of 200 + 60 + 5 + (1/10) in the decimal form is (A) 2065.1 (B) 265.1. (C) 26.51.

(D) 2.651.

8.

Renu bought 3 m 20 cm cloth for shirt and 2 m 5 cm cloth for her trousers. Find the total length of the cloth bought by her? (A) 4 m 28 cm (B) 3 m 25 cm (C) 5 m 34 cm (D) 5 m 25 cm

9.

Ritu’s school is at a distance of 6 km 530 m from her home. She traveled 1 km 70 m by foot and rest by bus. How much distance did she covered by bus? (A) 8.460 km (B) 7.500 km (C) 6.490 km (D) 5.460 km

10.

2 of a number is 14. The number is : 3 (A) 10 (B) 15

(C) 17

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(D) 21

Page # 1

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics

1.

2.

The quotient of x by 3 is multiplied by y is written as

5.

x +5 2

(C)

xy 9

9 (D) x  y

(C) 2x – 5

(D) 5x + 2

(B)

2 +5 x

(C)

x2 5

(D)

x 25

(B) 2a3b5

(C) 2ab

(D) a3b5

(B) 60a6b5

(C) 60a6b6

(D) a6b6

If 2x2y and 3xy2 denote the length and breadth of a rectangle, then its area is (B) 6x2y2

(C) 6x3y3

(D) x3y3

In a room there are x2 rows of chairs and each row contains 2x2 chairs. The total number of chairs in the room is (A) 2x3

10.

(D)

4a2b3 x 3ab2 x 5a3b is equal to

(A) 6xy 9.

3y x

a2b3 x 2ab2 is equal to

(A) 60a3b5 8.

xy 3

(C)

The quotient of x by 2 is added to 5 is written as

(A) 2a3b4 7.

(B) 9 – (x + y)

5 more than twice a number ‘x’ is written as (A) 5 + x + 2 (B) 2x + 5

(A) 6.

3x (B) y

9 taken away from the sum of x and y is (A) x + y – 9

4.

DPPS. NO. – 06

Choose the correct option: State in words the meaning of the following algebraic expression: (2a – b) (A) b subtracted from twice of a. (B) a subtracted from twice of b. (C) b diminished by twice of a. (D) Twice of a subtracted from b.

x (A) 3 y

3.

Topic : Algebra

(B) 2x4

(C) x4

(D) x

(B) 23a6b6

(C) 6a6b6

(D) none of these

a3 x 2a2b x 3ab5 is equal to (A) a6b6

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11. 12. 13.

14.

The coefficient of ba2 in 16a2bc is : (A) 16a2 (B) 16b

(D) 16.

The number should be added to (a2 + c2) to get (a + b2 + c2) is (A) a +b2. (B) a2 +b2. (C) a + b2 +c2.

(D) a + b2 - a2.

If we subtract 6x + 10y from 8x + 13y, then we get (A) x + y. (B) 2x + y.

(D) 2x + 3y.

A matchstick pattern of letter F as (A) 4.

15.

(C) 16c

(B) 8.

(C) 2x - 3Y.

To make three F’s, number of matchsticks required (C) 12.

Anna is k years old now. How old was he 2 years before? (A) k+2 (B) 2k (C) k - 2

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(D) 16. (D) None of these

Page # 2

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1. 2.

Topic : Equations

DPPS. NO. – 07

Number of variables in a simple linear equation (A) two (B) one

(C) 0

(D) none

Power of variable in a simple equation (A) 0 (B) one

(C) two

(D) none

3.

The method of finding solution by trying out various values for the variable is called (A) error method (B) trial and error method (C) testing method (D) Checking

4.

If 6 times a number is 48 then the number is (A) -8 (B) 1

(C) 48

(D) 8

If a = b then ax = ______ (A) b+x (B) bx

(C) b-x

(D) b+x

If a = b then a + x =______ (A) b + x (B) bx

(C) b – x

(D) b  x

5. 6. 7.

Half of a number is added to 18 then the sum is 46. The number is (A) 92 (B) 56 (C) 65

(D) 0

8.

A number is multiplied by 6 and 12 is added to the product. The result is 84. Then the number is (A) -12 (B) 72 (C) +12 (D) -72

9.

6x – 1 = 2x + 9 value of x (A) 1

10.

11. 12. 13. 14. 15.

1 2

(B) –2

1 2

(C)

4 10

(D) 2

1 2

a a + = 6, the value of a is 8 4 (A) 122 (B) -16

(C) 16

(D) 0

If the value of t = 4, then the value of 5t + 4 is (A) 19. (B) 20.

(C) 24.

(D) 29.

Solve the equation : 28 = p + 4 for variable ‘p’. (A) p=32 (B) p=24

(C) p = 7

(D) p=4

In

If 5x + 2 = 3x + 14, then the value of x is equal to (A) 2. (B) 5. (C) 6. (D) 8. The sum of two numbers is 80 and one of them is 22 more than the other. The two numbers are (A) 20 and 60. (B) 29 and 51. (C) 30 and 50. (D) 36 and 44. If 3x + 4 = - x + 8, then the value of x is (A) 1. (B) 2.

(C) 3.

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(D) 4.

Page # 1

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

(B) 1

(C) 2

(D) 3

(C) Side

(D) Triangle

In a quadrilateral ABCD, the part AC is known as (A) Angle

3.

DPPS. NO. – 08

How many dimensions are there in a point ? (A) 0

2.

Topic : Basic Geometrical Idea

(B) Diagonal

Which of the following is not a pair of adjacent sides of a quadrilateral ABCD ? (A) AB , BC

(B) BC , CD

(D) AB CD

(C) CD , DA

4.

If one of the angles in a triangle is 90°, then the triangle is called (A) an acute-angled triangle. (B) an obtuse-angled triangle. (C) a right-angled triangle. (D) an equilateral triangle.

5.

Half of a semicircle has (A) four quadrants.

6.

(B) three quadrants.

Base of a cone is in the shape of a (A) rectangle. (B) triangle.

(C) two quadrants.

(D) one quadrant.

(C) circle.

(D) square.

7.

Two or more circles are said to be concentric if they have (A) same centre and same radius. (B) same centre and different radii. (C) different centre and same radius. (D) different centre and different radii.

8.

Match of the following from the code given below : Column A

Column B

(A) All the three sides of a triangle are of unequal length.

(i) Rectangle

(B) Parallelogram with all angles 90° is

(ii) Equilateral Triangle

(C) All the three sides of a triangle are equal.

(iii) Parallelogram

(D) A quadrilateral having two pairs of parallel sides.

(iv) Scalene Triangle

(A) A-(i); B-(ii); C-(iii); D-(iv) (C) A-(iii); B-(ii); C-(i); D-(iv)

(B) A-(iv); B-(i); C-(ii); D-(iii) (D) A-(ii); B-(iii); C-(i); D-(iv)

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9.

10.

A rectangle has 4 vertices and 4 sides. A triangle has 3 vertices and 3 sides. A circle has _____vertices and _____ sides (A) v = 2, s = 2 (B) v = 5, s = 5

(C) v = 1, s = 1

(D) v = 0, s = 0

How many corners does this shape below have?



(A) 6

(B) 10

(C) 12

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(D) 13

Page # 2

SUMMER WORKSHOP (VI - OLYMPIAD)

Daily Practice Problem Sheet Subject : Mathematics 1.

2. 3.

Topic : Mensuration

________m - 75 cm = 4.25 m The missing number is : (A) 0.5 (B) 5

(C) 50

DPPS. NO. – 09

(D) 500

The total boundary length of a closed figure is called (A) Area (B) volume (C) perimeter

(D) region

The amount of surface enclosed by a closed figure is called its (A) volume (B) area (C) space

(D) perimeter

4.

Samual wanted to implant some vertical stones along the boundary of his plot at a distance of 10 m each. If length of the plot is 30 m and the breadth is 15 m then the number of stones used is (A) 450 (B) 45 (C) 9 (D) 10

5.

The area of a rectangle is 28 sq. cm. If length of rectangle is 7 cm, then its breadth will be (A) 4 cm. (B) 6 cm. (C) 8 cm. (D) 10 cm.

6.

1 cm is equal to 10 mm. How many square mm are there in one square cm ? (A) 10 (B) 1000 (C) 100 (D) 5

7.

A plank is 5 m long. A carpenter saws it into 10 equal pieces. Find the length of each piece in cm. (A) 2 (B) 5 (C) 20 (D) 50

8.

Stick P is 40 cm shorter than stick Q. Stick R is 60 cm longer than stick Q. Find the difference in length between stick P and stick R. (A) 20 cm (B) 100 cm (C) 80 cm (D) 160 cm

9.

This figure has an area of _____________ triangles

(A) 5 10.

(C) 9

(D) 10

(C) 8 cm2

(D) 10 cm2

(C) 480 cm = 4.80 m

(D) 810 cm = 8 m 10 mm

What is the area of the shaded figure ?

(A) 4 cm\2 11.

(B) 7

(B) 6 cm2

Which of the following is not true ? (A) 200 cm = 2 m (B) 350 cm = 3m 50 cm

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12.

The diagram shows the road map of four places, K, L, M and N. The distance from K to L is the same as the distance from L to M. The distance from M to N is

1 of the distance from K to M. 3

What is the distance from K to N ? L

45

00

cm

N

K

(A) 10.2 Km 13.

14.

(C) 1,20,000 cm

Find the perimeter of the hexagon figure each side measures 100 m. (A) 800 m (B) 600 m (C) 1200 m

(D)

8  4500 m 3

(D) none

6 th of its breadth. If its perimeter is 132 m, its area will be _______. 5 (B) 640 sq m (C) 1,620 sq m (D) 2,160 sq m

The length of a rectangle is (A)1,080 sq m

15.

(B) 12000 m

M

Area of a rectangle is 120 sq m and the breadth is 5 m. Then its length is (A) 204 m (B) 24 m (C) 28 m (D) 26 m

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Page # 2

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

Que s Ans.

1 A

2 B

3 A

4 B

DPPS - 1. Knowing our Numbers 6 7 8 9 10 11 C B A B D A

5 A

12 C

13 B

14 C

15 C

DPPS - 2.Whole Numbers

Ques Ans.

1 D

2 B

3 C

4 D

5 B

6 D

7 C

8 A

9 B

10 D

11 D

12 C

13 A

14 B

15 D

16 B

DPPS - 3. Playing with Numbers

Ques Ans.

1

2

3

4

5

6

7

8

9

10

B

D

C

A

B

B

B

B

D

B

10 B

11 C

12 D

13 A

7 B

8 D

9 D

10 D

10 C

11 C

12 D

10 C

11 C

7 B

10 C

DPPS - 4. Integers Que s Ans.

1 B

2 A

3 D

4 D

5 D

6 D

7 C

8 C

9 B

14 A

15 B

13 D

14 C

15 C

12 B

13 B

14 B

15 A

8 B

9 D

10 B

11 D

12 C

13 B

14 A

15 B

DPPS - 5. Fraction and Decimals Que s Ans.

1 A

2 D

3 B

4 C

5 A

6 B

DPPS - 6. Algebra Que s Ans.

1 A

2 D

3 A

4 B

5 A

6 B

7 C

8 C

9 B

DPPS - 7. Equations Que s Ans.

1 B

2 B

3 B

4 D

5 B

6 A

7 B

8 C

9 D

DPPS - 8. Basic Geometrical Idea

Ques Ans.

1 A

2 B

3 D

4 C

5 C

6 C

DPPS - 9. Mensuration Que s Ans.

1 B

2 C

3 B

4 C

5 B

6 C

7 D

8 B

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9 D

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