Embed Size (px)
Citation preview
TCV - MATHEMATICS
1
2
Practice work book
Class - VI
This book is based on TCV MATHS CURRICULUM.
EXERCISES are in TEST FORMAT ( giving you plenty of practice for test taking)
Each step is designed for SPEED in learning.
Work from easy problems to more difficult ones to make learning EASY.
1. Number System ----------------------------------------------------------------------------- 3
2. Playing with numbers ------------------------------------------------------------------------ 6
3. Fractions ---------------------------------------------------------------------------------------- 15
4. Decimals --------------------------------------------------------------------------------------- 25
5. Integers ---------------------------------------------------------------------------------------- 31
6. Ratio and Proportion ------------------------------------------------------------------------ 37
7. Unitary Method ----------------------------------------------------------------------------- 39
3
contents
EDRC
8. Area and Perimeter ------------------------------------------------------------------------- 40
8. Algebraic Expressions --------------------------------------------------------------------- 44
9. Basic Geometrical Ideas ------------------------------------------------------------------- 47
10. Understanding Elementary Shapes -------------------------------------------------- 49
11. Data Handling ---------------------------------------------------------------------------- 55
Number system
1. Write in words
i) 3456 ______________________________________________________________________________
ii) 2045 ______________________________________________________________________________
iii) 7255 ______________________________________________________________________________
iv) 88599 _____________________________________________________________________________
v) 93011 _____________________________________________________________________________
vi) 56321 _____________________________________________________________________________
2. Insert commas accordingly with Indian system of numeration
i) 232345 = __________________ ii) 800908 = _______________________
iii) 3500670 = ________________ iv) 3476001 = ______________________
v) 10090065 = ________________ vi) 707070707 = ____________________
3. Write the number name (Indian System of numeration)
i) 777777
______________________________________________________________________
ii) 4005006
4
_________________________________________________________________________________________________________________________________________________________________
iii) 5654555
_______________________________________________________________________
iv) 72346346
______________________________________________________________________
v) 605589000
___________________________________________________________________
4. Insert commas accordingly with International system of numeration
i) 680109 = ___________ ii) 20304020 = ___________
iii) 109467980 = ______________ iv) 708900005 = _________
5. Write in the standard form
i) one million, two hundred forty thousand, seven hundred fifty two = ___________________ .
ii) Twenty five million two hundred thousand five = ___________________
iii) sixty one million three thousand forty nine = _____________________
iv) eight million five hundred ninety seven = ____________________
6. Write each number in word form
i) 45,679,000 =
_______________________________________________________________________
_____________________________________________________________________________________
ii) 702, 090, 123 = _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
iii) 888,999,777 = _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
5
iv) 70,000,609 = _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
v) 200, 050, 720 = _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
7. Express in the international system of numeration.
i) Three crore forty seven lakh seven thousand two hundred twelve.__________________________________________________________________________________________________________________________________________________________________________ii) Forty seven crore seventeen lakh twenty thousand eight hundred eleven __________________________________________________________________________________________________________________________________________________________________________iii) Sixty eight crore nine thousand thirty seven__________________________________________________________________________________________________________________________________________________________________________iv) Nine crore forty nine thousand five hundred__________________________________________________________________________________________________________________________________________________________________________8. Write in the Indian system of numeration
i) Three million four hundred seventy five thousand twenty eight__________________________________________________________________________________________________________________________________________________________________________ii) Six hundred million twelve thousand two hundred eleven __________________________________________________________________________________________________________________________________________________________________________
iii) Tthree hundred twenty six million five hundred and three thousand nine hundred one.__________________________________________________________________________________________________________________________________________________________________________
iv) Nnine hundred thirty million six hundred thirty four thousand forty four .__________________________________________________________________________________________________________________________________________________________________________
v) A school’s library has 1350705 books. Write this number in word form Indian system _______________________________________________________________________
6
___________________________________________________________________________________
International system ________________________________________________________________
___________________________________________________________________________________
9. How many thousands are there in a lakh? ________________________________________
10. ______ lakhs make one million
11. _______ thousands make a million
12. ______ thousands make a crore.
13. ______ millions make 10 crore.
14. How many 500 notes are required to make ten thousand?
15. How many Rs 2000 notes will make one lakh?
16. How many Rs 50 notes are needed to make Rs ten thousand .
Playing with Numbers
Divisibility test
1. Which of the following numbers are divisible by 2
234 215 777 104 168 899 22345 4030
____ ___ ___ ___ ___ ___ ____ ____
2. A number is divisible by 3 if the sum of _____ is divisible by ____.
3. Without actual dividing the numbers, check whether the given numbers are divisible by 3.
615 234 1002 90901 123476 345690 222222141
___ ___ ___ ___ ____ ____ ____
4. If the unit digit of a number is of ___ or ___ ,then the number is divisible by 5.
5. Which of the following numbers are divisible by 5.
1345 2344 5006 1280 367905 38760
___ ____ ____ ____ ____ ____
6. Determine whether the given numbers are divisible by 10.
1290 3465 123400 10009 12340
____ ____ ____ ____ ____
7. A number is divisible by 11, if _______________________________________________________
7
___________________________________________________________________________________ .
8. Check whether the following numbers are divisible by 11.
1234 615 1331 9090301 234749
_____ ____ _____ ______ ______
Complete the table. Place a check mark to show divisibility.
45 2300 738 1000 7590
Divisible by 2
Divisible by 3
Divisible by 5
Divisible by 11
Factors
9. Write all the factors of the following numbers.
i) 18 ii) 20____________________________ _______________________________
iii) 24 iv) 32
____________________________________ ______________________________________
v) 27 vi) 28
_____________________________________ _______________________________________
vii) 39 vii) 42____________________________ _______________________________
ix) 45 x) 63
____________________________________ ______________________________________
xi) 54 xii) 60
_____________________________________ _______________________________________
xiii) 66 xiv) 72
___________________________________ _______________________________________
xv) 81 xvi) 88
8
____________________________________ ______________________________________
10. Which of the above numbers are divisible by 2? ___________________________________________________
11. Numbers which are divisible by 2 are called ____________
12. IF the unit’s digit of a number is of ___________________, the number is even number
13. Numbers which are not divisible by 2 are called _________ and their unit’s digit can be of _____________.
14. Pick out all the odd numbers 405, 703, 706, 1008, 345, 543, 354, 657, 756, 778, 900, 109, 802
__________________________
Common factors and H.C.F
7. Find all the common factors of each pair of numbers by listing the factors of each.
i) 60, 80 ii) 55 , 33
Factors of 60 are ________________ Factors of 55 are ________________
Factors of 80 are ________________ Factors of 33 are ________________
Common factors are ____________ Common factors are_____________
iii) 49, 35 iv) 69, 44
Factors of 49 are ________________ Factors of 68 are ________________
Factors of 35 are ________________ Factors of 34 are ________________
Common factors are ____________ Common factors are______________
8. Find the H.C.F. of each of pair of numbers.
i) 14, 21 ii) 15, 33
Factors of 14 _____________________ Factors of 15 ____________________
Factors of 21 _____________________ Factors of 33 ____________________
H.C.F = _______ H.C.F =________
iii) 40,48 iv) 30,75
Factors of 40 _____________________ Factors of 30 ____________________
9
Factors of 48 _____________________ Factors of 75 ____________________
H.C.F = _______ H.C.F =________
v)54, 72 vi) 27,63
Factors of 54 _____________________ Factors of 27 ____________________
Factors of 72 _____________________ Factors of 63____________________
H.C.F = _______ H.C.F =________
vii) 16,28,36 viii) 20, 60,100
Factors of 16 _____________________ Factors of 20 ____________________
Factors of 28 _____________________ Factors of 60 ____________________
Factors of 36_______________________ Factors of 100 _____________________
H.C.F = _______ H.C.F =________
Prime and composite numbers
9. Prime numbers have only ____ factors , they are ____ and ______.
10. List all the prime numbers under 20.
11. Composite numbers have more than ___ factors.
12. List first 10 composite numbers.
_______________________________________________________________________
13. ________ is prime and also even number.
14. _____ is the smallest composite number.
15. _____ is neither prime nor composite number.
16. The smallest prime number is ______ .
17. List all factor pairs for each numbers. Then identify each numbers as prime or composite.
i) 87 ii) 94 iii) 51
10
______________________ _________________________ ____________________
Prime , composite Prime , composite Prime , composite
iv) 61 v) 37 vi) 93
______________________ ___________________ ____________________
Prime , composite Prime , composite Prime , composite
Prime factorization
18. Draw a factor tree to show the prime factorization of each.
12 24 49 54
19. Complete each factor tree for 36.
i) ii) iii)
20. Complete each factor tree for the number 40
i) ii) iii)
11
?X?x2
?X22
X 182
36
2X
XX
X ?X?x3
?X33
X 123
36
3
? ?X??
X 94
36
X
?X?x2
?X22
X 202
40
2X
X
?X?x5
?X25
X ?5
40
2X
X ? ?X??
X 104
40
X
21. Complete the following
i) ii) iii)
22. Prime factorise the following number
i) 28 ii) 70 iii) 112 iv ) 144 v) 216 vi) 625
23. Could a prime factorization include 6 as one of the prime factors? Why or Why not?
___________________________________________________________________________
To find H.C.F by prime factorization
24. Find the H.C.F of each group of numbers. (Use prime factorization method).
i) 40,48 ii) 18 , 81 iii) 30 , 75
40 = _________________ 18 = _____________ 30 = ________________
48= ___________________ 81 = _____________ 75 = _________________
H.C.F = ________ = _____ H.C.F. = __________ = _____ H.C.F = __________= _____
iv) 32, 96 v) 49, 98 vi) 60 , 90
32 = _________________ 49 = _____________ 60 = ________________
96= ___________________ 98 = _____________ 90 = _________________
H.C.F = __________ = _____ H.C.F. = __________ = _____ H.C.F = ___________ = _____
vii) 16,28 , 36 viii) 20 , 40, 80 ix) 16 , 48,112
16 = _________________ 20 = _____________ 16 = ________________
28= ___________________ 40 = _____________ 48 = _________________
12
1
7
2 14
28
2 56
2
1
25
2 100
51
7
21
2 84
36 = __________________ 80 = ______________ 112= _________________
H.C.F = __________ = _____ H.C.F. = __________ = _____ H.C.F = ___________ = _____
Problem solving* reasoning
25. The H.C.F. of two numbers is 1. What do you know about the numbers?
____________________________________________________________________________________
_____________________________________________________________________________________
26. What is the H.C.F of two different prime number ?
_______________________________________________
27. The HCF of two consecutive numbers is ____________ .
28. The HCF of two consecutive even numbers is _________ .
29. The HCF of two consecutive odd numbers is ________ .
To find HCF by division method.
30. Fill in the blanks
i) HCF of 20 and 35 ii) HCF of 45 and 30
HCF of 30 and 45 = ______
H.C.F of 20 and 25 = ________
iii) HCF of 24 and 39
13
0
-15
3
155
-15
1
2015
-20
1
3520
__
-30
2
__15
___
1
4530
-----
1159
----
1
24---
-24
---
__24
1
HCF of 24 and 39 = __________
31. Find the HCF of the following group of numbers
i) 44, 55 ii) 37, 48 iii) 100, 140
__________ _______________ ______________
Multiples and Lowest common multiples (LCM)
32. Write the first five multiples of the following numbers.
4 ______________________ 6 _________________ 8 __________________
7 _____________________ 9 _________________ 11 ___________________
33. Determine whether the first number listed is multiple of the second number
I) 297, 3 ii) 495 , 15 iii) 312, 3 iv) 478, 2 v) 1232 , 11 vi) 6709 , 5
_______ ________ _______ ________ _______ ________
34. Find the LCM of each group of numbers. Use prime factorization method.
i) 15, 12 ii) 16, 40 iii) 32,48
15 = _______________ 16= _________________ 32= ________________
12=________________ 40 = ________________ 48 = ________________
LCM= _________ = ___ LCM = ________ =___ LCM= ________ = ___
iv) 14, 20 v) 8, 72 vi) 7, 10
14
14 = _______________ 8= _________________ 7= ________________
20=________________ 72 = ________________ 70 = ________________
LCM= _________ = ___ LCM = ________=___ LCM= __________ = ___
i) 4, 5,6 ii) 2, 8, 12 iii) 18, 27, 6
4 = ____________ 2= _______________ 18= _____________
5=______________ 8 = ________________ 27 = _____________
6= _____________ 12 = ________________ 6 = _____________
LCM= ___________ = ___ LCM = _________ =___ LCM= __________ = ___
Problem solving * reasoning
35. The number of books in Lhamo’s collection is multiple of 2,4,5 and 10. She has more than 11 books and fewer than 25 books. How many books does she have?
_____________________________________________________
36. List all the numbers less than 60 that are multiple of 3,6 and 9
_____________________________________________________
37. Lhayum’s little brother are stacking blocks. Her brother’s blocks are 4cm and her sister’s blocks are 9cm high. How high will their stacks be when they are equal height for the first time?
_____________________________________________________
38. What prime factors do 20 and 30 have in common?
___________________________________________
39. LCM of two consecutive numbers is ___________.
40. LCM of two numbers is 12. What will be the second number if the first number is 4?
Find two possible answers
_______________________________________________________________________
41. Find the pair of numbers whose LCM is 30. Write three possible answers.
____________________________________________________________
15
Fractions
1. A fraction represents a part of a whole. Name the fraction that indicates the shaded part.
I) ____ ii) _____
iii) _____ iv) _____
2. Money problem
i) 50 paisa is what fraction of Re1 ? ______
ii) Rs 25 is what fraction of Rs 200? ________
3. Unit problem (measurement)
i) 1 second is what fraction of a minute? _______
ii) 1m is what fraction of 1km? ______
iii) 1cm is what fraction of 1m? _________
16
iv) What fraction of 1kg is 500 g? _____
5. Time
i) 45 minutes is what fraction of an hour? ______
ii) 8 hours is what fraction of a day? _______
iii) 20 second is what fraction of a minute? ______
6. Change these improper fractions into mixed numbers or whole numbers.
i) 103 = ______ ii)
88 = ______ iii)
256 = ______
iv) 30030 = ______ v)
7570 = ______ vi)
3131 = ______
7. Change these mixed numbers into improper fractions.
i) 1 12 = _____ ii) 2
35 = _____ iii) 15
34 = _____
v) 10 1
10 = _____ vi) 20 38 = _____ v) 1
911 = _____
8. Represent the following fractions on the number line.
17
i) 58
ii) 75
iii) 2 14
iv) 1 57
Equivalent fractions
9. Write two equivalent fractions . (use multiplication)
i ¿ 35 = ______ =__________ ii ¿ 6
7 = ______ =__________ iii¿ 85 = ______ =__________
10. Write two equivalent fractions (use division)
i ¿ 2012 = ______ =__________ ii ¿ 30
55 = ______ =__________ iii¿ 1620 = ______ =__________
11. Write an equivalent fraction with the given denominator.
i ¿ 23= ❑
12 ii¿ 59=❑
27iii¿ 10
32= ❑
16iv ¿ 9
20= ❑
100
v¿ 119
=❑91 vi ¿ 14
21=❑
3vii¿ ❑
42=6
7viii¿ 7
8=❑
80
12. Write an equivalent fraction with given numerator.
18
i ¿ 56=25
❑ ii¿ 311
=30❑ iii¿❑
8=21
24iv ¿ ❑
12=21
36
v¿ 920
=36❑ vi¿ 3
❑=4560
vii¿ 1025
=30❑ viii¿ 64
72= 8
❑
13. Write the equivalent fraction of the following fractions with denominator 60.
12, 23, 34, 45, 56, 7
10 ,1112 ,
715
_________________________________________________________________________________
_______________________________________________________________________________
14. Write each fraction in its simplest form.
i ¿ 3848
=❑❑ ii¿ 28
42=❑
❑ ii i¿ 3090
=❑❑ iv ¿ 33
44=❑
❑
v¿ 60100
=❑❑ v i ¿ 18
54=❑
❑ vii¿ 1218
=❑❑ viii ¿ 108
90=❑
❑
15. Write the missing denominator or numerator.
i ¿ 1624
= 2❑ ii¿ 8
28=❑
7iii¿ 15
45= 1
❑ iv ¿ 981
=❑9
v¿ 1239
= 4❑ vi¿ 25
55=❑
11vii¿ 21
42=❑
2viii¿ 18
42= 3
❑
Comparison of fractions
16. Compare. Write ¿ ,<¿=¿ for each
i ¿ 13
14
ii¿ 37
35
iii¿ 25
35 iv ¿ 7
8
79
v¿ 13
24
vi¿ 410
56
vii¿ 23
36 viii¿ 15
16
3132
19
ix ¿ 920
1840
x¿ 512
1536
xi ¿ 67
76 xii¿ 12
8
1
17. Which fraction is the largest in its group?
i ¿ 14∨1
2∨2
7ii¿ 3
7∨33
77∨ 9
21iii¿ 1
10∨ 11
100∨ 99
1000
iv ¿ 56∨11
15∨17
30
_____________ _____________ _________________ _______________
18. Order from the least to greatest.
i ¿ 316, 18, 29 ii¿ 11
18, 16, 3
4 iii¿ 1720, 38, 25
_______________ ________________ _________________19. Algebra* Expressions Compare. Write ¿ ,<¿=¿ for each
i ¿ x5 37 ,given x =2 ii¿ 1
3 y5 ,given= 1
iii¿ 2x
39, given x=3 iv ¿ x6
9y , given x=1,y=9
Problem solving* Reasoning
20. Tenzin sold cookies for her club. 32 of the 128 boxes she sold were chocolate chip. Express this portion of her sale as a fraction. Then write two equivalent fractions.
____________________________________________________________________
21. Mr Nathulal’s store has 380 fish in stock. Acha Lhamo bought 20 fish. What fraction of the store’s fish did acha Lhamo buy? Write your answer in the simplest form.
_______________________________________________________
22. Penpa has a collection of 36 baseball caps. 30 of the caps have the name of a sports team on them. In the simplest form, what fraction of the caps in Penpa’s collection have the name of a sports team on them?
__________________________________________________________
23. Tsering has read 27 of the books in the school library. Pelmo has read
39 of the books in the library.
Who has read a greater fraction of books?
______________________________________________
24. Lhayum planted 715 of the tomato plants in the home garden. Her home mother planted
1630 of the
tomato plants. Who planted fewer tomato plants?
_______________________________________________
20
Addition and subtraction of fractions
25. Find the sum or difference. Write your answer in simplest form.
i ¿ 13+1
3ii¿ 2
5+ 4
5 iii¿ 34−1
4iv ¿ 5
6−2
6
________ _________ _____________ __________
v¿1 25+2 1
5vi¿2 3
4−1 1
4vii¿3 5
8+2 3
8viii¿1 7
8−1 1
8
___________ _________ ________ ________
ix ¿2+35
x¿1−38
________ __________
26. Add and reduce.
i ¿ 25+ 3
10 = ________ ii¿ 47+ 1
3 = ________
_________ _________
iii¿ 79+2
3 = ____________ iv ¿ 89+ 5
6 = ____________
___________ _________
v¿ 25+ 3
10 = ___________ vi¿ 47+ 1
3 = ___________
_________ ___________
vii¿ 79+ 2
3 = ____________ viii¿ 89+ 5
6 = _____________
_____________ __________
ix ¿ 79−1
3 = ____________ x¿ 815
−16 = _____________
_____________ __________
xi ¿ 34−5
8 = ____________ xii¿ 811
−47 = _____________
_____________ __________
21
27. Find the sum.
i ¿2+1 23 = ____________ ii¿2+1 5
6 = _____________
_____________ __________
iii¿1 12+2 2
3 = ____________ iv ¿3 34+2 2
3 = _____________
_____________ __________
v¿1 79+3 2
3 = ____________ vi¿1 29+ 5
6 = _____________
_____________ __________
28. Find the sum. Express your answer in the simplest form.
i ¿ 79+ 2
3+ 1
2 = ____________ ii ¿ 815
+ 56+ 2
3 = _____________
_____________ __________
iii¿1 78+ 3
4+2 = ____________ iv ¿1 1
5+2 3
4+ 1
10 = _____________
_____________ __________
v¿2 34+3 1
3+1 1
2 = ____________ viii¿4 815
+ 56+3 1
5 = _____________
_____________ __________
29. Find the difference. Express your answer in the simplest form.
i ¿ 45− 7
15 = _____________ ii¿ 32−7
8=¿ iii¿
13−4
9=¿¿ ______________
______________ _______________
iv ¿ 34−2
3 = _____________ v¿1 12−1
2=¿vi ¿3 3
4−2=¿¿ ______________
______________ _______________
22
vii¿2−1 27 = ___________ viii¿3 5
6−1
4=¿ ix ¿2 2
5−1 6
7=¿¿ ___________
__________ ___________
x¿ 8 610
−2 215 = __________ xi ¿7 1
2−5 5
6=¿¿9 3
4−7 8
9=¿¿ __________
__________ _____________
___________ _________ ____________
Problem solving * Reasoning
30. i)Tenzin made a jewelry box 8 58 inches long and 8 1
8 inches wide. How much greater is the length
than the width of the jewelry box?
____________________________________________________________________________
ii) One fifth of the jewelry box is designed for earings. Three fifths is for necklaces. What part of the
jewelry box is for earings and necklaces?
____________________________________________________________________
31. Lhakpa recorded a 3 12 hour Hindi movie and a 2 1
4 hour of English movie on one pen drive.
How many hours of movies are on the pen drive?
______________________________________________________________________
32. One third of Tsering’s video collection is action videos. One fourth is adventure video and rest were Romantic videos. What part of Tsering’s video collection are action and adventure videos? What part of the collection is Romantic video?
______________________________________________________________________
________________________________________________________________________
33. i) The rain fall in Dharamsala totaled7 38 inches in march and 13 1
5 inches in April.
How much more rain fell in April?
__________________________________________________________________________________
ii) Four inches of snow were predicted for the month of January, but only 2 13 inches actually fell.
What isthe difference between the predicted snowfall and the actual snowfall?
__________________________________________________________________________________
23
34. Meela read 50 pages of a book containing 200 pages. Dolma read 25 of the same book. Who read
more?
____________________________________________________________________________________
35. Tendar exercised for 710 of an hour, while Dhargyal exercised for
34 of an hour. Who exercised for
longer time?
____________________________________________________________________________________
36. Diki takes 2 15 minutes to walk across the school ground. Dorjee takes
74 minutes to do the same.
Who takes less time and by what fraction?
____________________________________________________________________________________
Multiply fractions
37. Multiply. Write each product in simplest form.
i ¿ 34× 8
9 = __________ ii¿ 25× 15
4 = ___________
__________ ___________
iii¿ 110× 1
10 = __________ iv ¿ 114× 7
8 = __________
_______ __________
v¿ 25× 15
4 = ___________ vi¿ 1236× 27
30 = ___________
__________ ___________
vii¿ 724× 32
63 = ___________ viii¿ 15× 2
3× 5
2 = ___________
__________ ___________
ix ¿ 200700
× 1003× 300
5000 = ___________ x¿ 813× 52
24 × 34 = ___________
_________ ___________
38. Multiplying fractions by whole numbers.
i ¿5× 78 = ___________ ii¿ 3
4×2 = __________
________ _______
iii¿ 35×10=¿¿ iv ¿ 3
4×2 = ___________
24
_______ ________
v¿ 724×12=¿¿ vi¿5× 3
10×2 = ___________
_______ ________
vii¿ 715×10× 2
21=¿¿ viii¿ 5
9×12× 1
24 = ___________
_______ ________
39. Find the product. Convert products to mixed numbers where applicable.
i ¿2 35×1 1
9=¿¿ ii¿1 3
4× 2
7 = ___________
_______ ________
iii¿2 810× 10
21=¿¿ iv ¿4 1
2×2 1
3 = ___________
_______ ________
v¿ 514×4 9
10=¿¿ vi¿1 1
2×2 2
3×3 3
5 = ___________
_______ ________
Problem solving*Reasoning
40. Tenzin worked 34 of a 40 hour week, how many hours did he work?
______________________________________________________________________
41. i) Tashi travels 2 18 miles each day to deliver newspaper. How many miles does he travel in 5 days?
_______________________________________________________________________
ii) 13 of the newspapers Tashi delivers are to houses on his street. How many newspapers doe she
delivers on his street ?__________________________________________________________________________
42. Ama Tsamchoe needs 2 12 m of fabric to make a backpack. How much fabric does she need to
make 3 backpacks ?__________________________________________________________________________
43. Acha La can make a small bag from 1 18 m of fabric. She needs 1
12 times as much fabric to make a
large bag. How much fabric does acha la need to make a large bag?___________________________________________________________________________
44. Lhakpa reads 13 part of a book in 1 hour. How much part of the book will he read in2 1
2 hours?
25
_____________________________________________________________________________
45. Lhakpa reads a book for 1 16 hours every day. He reads the entire book in 8 days. How many hours
in all were required by him to read the book?
____________________________________________________________________________
46. If milk is available at Rs 2034 per litre.
i) Find the cost of 5 litres of milk _____________________________________________
ii) How much do I have to pay for 7 12 litres of milk?
______________________________________________
47. Diki made 48 skipping ropes . Each ropes is 6 38 feet long. How much rope did she use?
___________________________________________________________________
48. Three eigths of 520 students at TCV School are in sixth grade. How many students are in sixth grade?
_____________________________________________________________________________
Division of fraction
49. Write the reciprocal of the following fractions.
i) 34 ii)
74 iii)
14 iv) 4 v) 2
34
______ ____ _____ ____ _____
vi) 137 vii)
111 VIII) 4
1113 IX) 7
18 X) 1
79
_____ _____ ______ _____ ______50. Divide
i) 75÷ 11
12 ii) 23÷ 5
7iii¿ 11
12÷ 11
12 iv) 23÷ 5
12
______ _______ ______ ______
v) 103÷ 5
3 vi) 13÷ 10
3 vii) 83÷ 10
3 viii) 38÷ 8
9
______ ______ _______ ______
ix) 3 ÷ 34 x) 10 ÷ 5
4 xi) 4 ÷ 43 xii) 12 ÷ 3
4
______ _______ ______ ______
xiii) 43÷4 xiv) 14
9÷7 xv) 5
6÷10 xvi) 3
7÷9
26
______ _______ _______ ________
xvii) 2 13÷ 7
3 xviii) 4 ÷2 18 xix) 8÷2 3
4 xx) 2 14÷ 4
________ ______ _______ _____
xxi) 3 34÷2 xxii) 5 1
2÷2 1
3 xxiii) 3 13÷1 1
3 xxix) 4 12÷1 1
3
_______ ________ ______ ______
Problem solving *Reasoning
51. sonam Lhamo divided 4 12 kg of fruit salad into containers that each hold 1 1
2 kg. Hpw many
containers did she used? ________________________________________________________
52. Dolma poured a 2 12 gallon pitcher of fruit punch into 4 containers. How much fruit punch is in each
container?___________________________________________________________________________
53. Dorjee cut a 36 inch long submarine sandwich into 4 12 inch long pieces. How many pieces did he
cut?
____________________________________________________________________________________
54. A jug holds 58 litre of Pepsi juice. If Tsering pours the Pepsi into
116 litre glasses. How many glasses
of Pepsi will he have? _______________________________________________________________________
Decimal
1. Write out the following decimals in words.i) 0.1 = ________________________________ ii) 0.01 =_____________________________iii) 0.001 = ______________________________ iv) 1.01 = _____________________________v) 72. 15 = ______________________________ vi) 10.05 = _____________________________vii) 0.674 = _____________________________ viii) 2. 123 = _____________________________
2. Write the following as decimals or mixed decimals
i) Six tenth = ______________ ii) Six hundredth = _______________
27
iii) Six thousandth = ______________ iv) Nine and five tenth= ______________
v) Three hundred twenty and seven hundredth =_____ vi) Zero point two three = __________
vii) Eleven point seven two five = _________
3. Change these decimals or mixed decimals to fractions in lowest terms.
i) 0.2 = _______________ ii) 0.02 =_______________
iii) 0.002 = __________ iv) 1.2 = _______________
v) 0.75 = ______________ vi) 20.3 = ______________
4. Change these fractions to decimals.
i) 15 = _______ ii)
12 = _______
iii) 34 = _______ v)
720 = _______
vi) 1310 = _______ vii)
13100 = _______
viii) 1350 = _______ ix)
132 = _______
x) 2 15 = _______ xi) 3
78 = _______
5. Compare. Write¿ ,<¿=¿for each
i) 0.09 0.090 ii) 0.2 0.200
iii) 0.75 0.73 iv) 0.69 0.70
v) 2.125 2.124 vi) 2.215 2.125
vii) 9.9 9.89 viii) 30.456 3.0456
28
6. Order from lowest to highest
i) 0.3, 0.03 , 3.0 , 0.003 _____________________________________
ii) 0.82 ,0.28 , 0.8 , 0.2 ______________________________________
iii) 0.5 , 0.05, 5.5, 5.05 _____________________________________
iv) 46.2, 4.62, 42.6, 4.062 ____________________________________
(unit conversion)
7. Till in the blanks
i) 3.45km = ___km __ m ii) 2.3m = __ m ___cm
iii) 0.456 km = ___ km ___m iv) 3.5mm = ___cm ___mm
v) 10.35m = ___km ___m vi ) 10.035 km = ___km ____m
vii) 1.5kl = ___kl ___l viii) 2.005kl = ___kl ___l
ix) 34.6kg = ___kg ___g x) 67.02kg = ___kg ___g
8. Fill in the blanks
i) 20cm = ______m ii) 20m = ______km
iii) 3m 5cm = ________m iv) 540g = _____kg
v) 1234m = ______km vi) 23mm = ____cm
vii) 2kg 690g = _______kg viii) 45l = ____kl
Adding and subtracting decimals
9. Where should the decimal point be placed in each sum?
i) 7.5 + 3.2 = 107 ii) 1.79+ 0.21 = 200
iii) 9.32 + 4.1 = 1342 iv) 4.05 + 0.6 = 465
v) 7.7 + 2.34 = 1004
29
8. Add the following decimals
i) 1.38 + 2.13 = ____________ ii) 3. 73 + 2.45 = __________
iii) 13.7 + 12.06 = ___________ iv) 11.65 +3.47 = ___________
v) 78.91 + 23.4 = _____________ vi) 1.234 + 5. 6789 = __________
vii) 12.34 + 10 + 8.4 = __________ viii) 100.4 + 10.56 + 3.773 = ____________
ix) 5.3 + 0.779 + 1.66 = _________ x) 11.678 + 3.56+ 7.8 = ________________
9. Find the difference.
i) 10 – 0.7 = ____________ ii) 3.4 – 1.2 = __________
iii) 4.5 – 3.8 = ____________ iv) 21.76 – 13. 9 = _______
v) 0.7 – 0.65 = ___________ vi) 10.8 – 9.762 = _________
vii) 12.6 – 0.789 = ___________ viii) 13.05 – 9.98 = _________
ix ) 11 – 6.75= _________ x) 100 – 90.45= ___________
10. Calculate
i) 35 + 24.06 – 27.89 = ______________ ii) 6.5 – 1.4 – 2.56 = _______________
iii) 100 – 94.45 + 2.7 = _________________ iv) 3.95 + 9.9 – 10.234 = ____________
v) 11.65 + 7.98 – 12 = ________________ vi ) 31.56 – ( 23.6 + 5.87) = ___________
vii) ( 3.45 + 1.7) – 4.1 = ______________ viii) 200 – 190.5 + 3.56 – 2.5 = ____________
Problem solving * Reasoning
10. Dorjee measured two insects during science class. A fly measured 0.08 ft long and spider measured 0.075 ft long. Which insect was longer? By how many ft.
_________________________________________________________________________________________
30
11. Four cities have following populations. City A; 2.78 lakh, City B; 2.87 lakh, City C: 2.8 lakh and City D: 2.7 lakh. Write the population from greatest to least.
__________________________________________________________________________________________
12. On Sunday, the price of petrol was Rs 73.5 per litre ,on Monday the price has been increased by Rs 1.63. how much do we have to pay on Monday for 1 litre of petrol?
13. by how much should 34.79 be increased to get 54.67?
________________________________________________________________________________
14. By how much should 24.4 be decreased to get 18.93?
_________________________________________________________________________________
15. . In a class the height of the tallest child is 56.7 in tall and the shortest child is 50.8 in tall. What is the difference of their height?
____________________________________________________________________________________
16 Ama la bought vegetables weighing 10kg. Out of this 3 kg 500 g is onion, 2kg 75g is tomato and rest is potato. What is the weight of potato?
_____________________________________________________________________________________
17 Dhondup went shopping and bought items priced at Rs 100.5, Rs 79.55, Rs 30.8. How much money did she spend in all?
______________________________________________________________________________
Multiplying decimals
18. Find the products.
I) 23 X 10 = ________ ii) 2.3 X 10 = _______ iii) 0.34 X 10 = _________
31
iv) 1.35 X 10 = _____ v) 7.2 X 100 = ______ vi) 23.45 X 100 = _________
vii) 0.3 X 1000 = _______- viii) 0.34 X 1000 = ________ ix) 1.0324 X 1000 = ________
19. Multiply
i) 24 X 3 = _______ ii) 2.4 X 3 = _______ iii) 0.23 X 3 = _________
iv) 0.6 X 6 = ________ v) 1.6 X 7 = _________ vi) 3.46 X 8 = ________
vii) 12.34 X 67 = ________ viii) 9.78 X 76 = ______ ix) 87 X 6.9 = ________
problem solving* reasoning
20. If a pen cost Rs 43.7. What is the cost of 7 such pens?
____________________________________________
21. The perimeter of a Temple is 2.34km. How far he had travelled for three circumambulate?
__________________________________________________________________________
23. Choekyi wants to buy 5 new books. Each book cost Rs 10.75. She had Rs 50. Does she have enough money to buy the books? How much money does she need?
_____________________________________________________________________________________
24. A bike covers a distance of 55.4km in one litre of petrol. How much distance will it cover in 15 litres of petrol?
______________________________________________________________________________
25. Where will you place the decimal point?
i) 2.3 X 3.2 = 736 ii) 1.03 X 7.8 = 8034 iii) 7.99 x 3.7 = 29563
iv) 8.67 X 4.9 = 42483 v) 6.8 X 2.13 = 14484 vi) 0.6 X 3.45 = 2070
32
26. Find the product.
i) 24.3 X 3.8 ii) 2.9 X 3.6 iii) 4.88 X 1.3
________ __________ ____________
iv) 0.56 X 1.7 v) 0.98 X 2.7 vi) 4.36 X 2.8
________ ________ __________
vii) 12.3 X 12.3 viii) 9.8 X 8.9 ix) 1.8 X 9.3
__________ _________ _________
Problem Solving * Reasoning
27. A two wheeler covers a distance of 55.4km in one litre of petrol. How much distance will it cover in
7.5 litres of petrol? ___________________________________________________________________________
28. If 1kg of pure milk contains 0.25 kg of fat. How much fat is there in 14.4 kg of milk?
_______________________________________________________________
29. one kg of rice costs Rs 52.8. What will be the cost of 18.25 kg of rice?
____________________________________________________________
20. Find the area of a rectangle whose length is 7.6m and breadth is 4.8m.
_________________________________________________________________
Integers
1. The set of numbers -1, -2, -3, -4,… is called ________ integers and the set of numbers 1, 2, 3, 4, … is
called ______ integers.
2. The number ____ is neither positive nor negative integer.
33
3. write the opposite of the following statements:
i) 20km below sea level --- ___________________________
ii) A deposit of Rs 500 in the account --- _____________________
iii) Going 10km east -- _________________________
iv) 280C above zero -- ____________________________
v) A decrease in 100 --________________________________
vi) 10% more --_______________________________
vii) Losing a weight of 7kg -- _________________________
viii) Gain of Rs 3000 -- ________________________________
ix) Gave Rs 50 -- ____________________________
x) Spending Rs 1000 -_____________________
xi) Rs 40 less -- _______________________
4. How would you indicate the following by using + or – sign?
i) Spend Rs 400 -- _______
ii) 100 above 00 --________
iii) Gain of Rs 200 -- _________
iv) A loss of Rs 1000 --___________
v) 70km above sea level -- ___________
vi) 10% increase in price --- ___________
5. mark the following numbers on the number line.
i) -4 ii) 7 iii) -2 iv) 5
34
6. Write all the integers between:
i) -4 and 1 -- _____________________________
ii) -7 and -1 --- _______________________________
iii) 0 and 10 --- _______________________________
iv) -70 and -60 -- __________________________________
7. Which number in each of the pairs is to the left of the other on the number line?
i) 2 , 5 -- ______ ii) 0, -8 --- ______ iii) -10, -12 -- _________
iv) 10, 20 ----_________ v) 0, 7 --- _________ vi ) -90, -99 --- _______
8. Using number line . Write the integer which is
i) 5 more than 2
ii) 3 more than -4
iii) 6 less than 1
iv) 4 less than -4
9. Compare. Write ¿∨¿ for each
i) 0−4 ii) 4−4 iii) −5−4
iv) ) 0 8 v) −10−14 vi) −1−2
viii) −102−94 ix) 1000 999 x) −1000−999
xi) ) −301−300 xii) −701−702 xiii) 1−200
10. Order from greatest to lowest
i) -4 , 3, -2, 1 _________________ ii) -9, 0, -6, -1, -5 ________________
iii) 11, -11, -12, 13, 9, -20, 12 iv) -4, -35, -14, 0, 1, -100______________________ _____________________________
35
11. Arrange the following in ascending order:
i) -4, 7, 8, 0, -2, -5, -10 _________________________________
ii) 5, -5, -4, 4, 10, -78, -89, 2, ___________________________________
12. With the help of number line, give two possible integral values of x if :
i) x ¿2_____________ ii x ¿1¿
iii) x ¿−4¿ iv) x ¿ 4 ___________________
v) 0¿ x<6 ________________ vi) −4<x<2 ________________
Problem solving * Reasoning.
13. Which of the following statements are true and which are false.
i) 2 is an integer. ___________ ii) 0 is a positive integer. __________
iii) Zero is the smallest integer. ___________ iv) -8 is greater than -7 ____________
v) The opposite of -10 is 10. ______________ vi) Every negative integer is less than 2. _________
14. A, B,C, D,E and F represent the change in temperature from 9A.M to 10 A.M at several different
locations.
i) At which location did the temperature increase the most? _________________________________
ii) Which location saw a greater change in temperature C or E ? _______________________________
15. The lowest temperature last January was−120 F. The lowest temperature this January was−90 F. In which year was the lowest temperature lower?_______________________________________
16. Today’s high temperatures from 5 world locations were 200C ,−100C ,00C ,440C∧360C.
Order these temperatures from greatest to least. ___________________________________
17. What integer is 7 units to the left of -3 on a number line? ____________________________
Add integers
18. Use the number line to find the sum.
i) -6 + 5 = ____
36
E
. FDAB ..C.-8 -7 -6 -5 -4 -3 -2 -1 0 10987654321
. .
654321-7 -6 -5 -4 0-3 -2 -1
ii) -7 + 8 = _____
iii) -3 + -2 = _____
iv) - 4 + -3 = ____
19. Add the following:
i) -10 + (-11 )= ______ ii) 19 + ( -100 = _____
iii) 5+ 9 = _____ iv) -5 + (-9) = __________
v) -15 +( -15) =_________ vi ) -15 + 15 = ________
vii) 15 + -15 = _______ viii) 15 + 15 = _______
20. Write the missing addend.
i) -5 + __ = -2 ii) 4 + ___ = -3
iii) 20 -17 = _____ iv) 0 + ___ = -10
v) -12 + ___ = -1 vi) -13 + ____ = 3
vi) ___ + (-5) = -25 vii) ___ +( -5) = 0
viii) -5 + ___ = 12
21. Write the opposite of the following integers:
i) -26 --- _____ ii) 28 -- _____ iii) -40 -- _____
iv) 63 - - ______ v) -2 --- ______ vi) 1 --- _____
37
654321-7 -6 -5 -4 0-3 -2 -1
654321-7 -6 -5 -4 0-3 -2 -1
654321-7 -6 -5 -4 0-3 -2 -1
22. Fill in the blanks
i) The negative of 7 is _____ ii) negative of negative 8 is ______ iii) −(−10 )= _____
iv) +(-100) = _____ v) - (+25)= _____ vi) – (-25)= ____
23. Subtract
i) -10 –(3) = ____ ii) -10 – (-3) = _____ iii) 19 – (-9) = ______
iv) -20 – 0 = ____ v) 0 – ( -10) = _____ v) 700 – (+650) = ______
24. Subtract
i) 15 from -20 __________ ii) -15 from -20 __________
iii) -20 from -15 ___________ iv) 20 from -15 _____________
v) 100 from -98 ___________ vi) -2 from -1 ______________
25. Simplify
i) -11 + 13 – (-2) = ___________ ii) 6 – 7 + 3 = ____________
_____________ ____________
iii) -2 -5 + 6 = ____________ iv) 12 – (-10) – 3 = _________
________ = _________
v) 100 – 300 – (400) = __________ vi) -35 – 25 + ( -30) = ___________
_________ _________
Problem solving * Reasoning
26. the temperature of a freezer is −50C. When the temperature is increased by 80C,is the freezer above or below freezing. Which is 00C? by how much?
38
__________________________________________________________________
27. In a card game, Rabgyal loses 3 points for drawing a club and gain 4 points for drawing a spade. If she has 10 points, then draws a spade and a club, how many points does he have?
____________________________________________________________________
28. At the beginning of the year, a company’s net worth was -17 million. During the year, it lost 5 million. What was the company’s net worth at the end of the year?
______________________________________________________________________
29. A place is 37km above sea level and another is 35km below sea level. What is the difference of level
between the two places?
________________________________________________________________________
30. Rajesh’s check book balance was Rs 1200. He deposited Rs 1000, wrote a check for Rs 2200, and deposited
Rs 500. What was his balance after these transactions?
_________________________________________________________________________
31. The sum of two integers is -337.If one of them is 100, find the other.
____________________________________________________________________________
32. From the sum of -20 and 13 subtract -10.
______________________________________________________________________
Ratio and Proportion
Ratio
1. Fill in the blanks
i) The symbol ___ is used to express a ratio.
39
ii) Ratio exists between ___ things or between _____ units.
iii) The two quantities to be compared are called the _____ of the ratio.
iv) The ____ term of a ratio is called antecedent and the ____ term is called consequent.
v) Ratio has ___ units.
2. Write each of the following as a ratio.
i) 2 parts of lemon juice to 5 parts water __: __
ii) 6 blue marbles to 4 red marbles ____: ___
iii) 3 umbrella to 6 people ____: _____
iv) 1 Tibetan to 200 Chinese ____ : ____
v) 4 teachers to 20 students ____ : ____
vi) In a class there are 35 girls and 25 boys
3. Express the following as ratios in different ways as shown in the examples.
Simplest form
i) 3km to 5km 3/5 3:5 3 is to 5 3:5ii) 50p to Rs 3 50/300 50:300 50 is to 300 1;6iii) 50 marks to 20
marksiv) 10 grams to 5 gramsv) 5 metres to 1cmvi) 20 minutes to 1 hourVii) 8 hours to 1 day
4. Express each of the following ratios in its simplest form.
i) 35 : 49 = ____: _____ ii) 27 : 8 = ___ : ___
iii) 30 minutes to 1 hour = __ : ___ iv) 200m : 1km= ____ : ____
v) 35 days : 3 weeks = __ : ___ vi) 4mm : 2 cm ==___ : ___
5. Determine and state which of the rows have the same ratio of :
i)
40
A
B
C
D
E
ii)
Problem solving * Reasoning
6. There are 160 students in class VI. Of them 75 are girls and the remaining are boys . Find the ratio of i) boys to girls ii) boys to total students iii) girls to total students ____________ _________________ ___________
7. In class VI, 7 out of 30 students got ‘A’ grade in the examination .In class VII . 8 out of 35 students got ‘A’ grade . Which class has a better record of ‘A’ grades?
______________________________________________________8. Two numbers are in the ratio 8:7. Their sum is 60. Find the numbers.____________________________________________________________9. The sum of two angles is 900. Their degrees are in the ratio of 2:3. Find the number of degrees in each angle.___________________________________________________________________________________10. A man divides a sum of Rs 1200, as gift for his two children, in the ratio 5:3 . How much does each child get?_______________________________________________________________________________11. If 3 out of 5 people pass this test, how many will pass the test when 45 people take it?__________________________________________________________________________12. The ratio of male students at Dalai lama college is 4:5. If there are 350 female students, how many male students are there?
_____________________________________________________________________________13. There were 28 people at last week’s board meeting. If the ratio of men to women was 4:3. How many women were at the meeting?_________________________________________________________________________
Unitary Method14. the price of 15 articles is Rs 210. Find the cost of an article.
____________________________________________________________________________
15. Tashi earns Rs 3500 for working 7 days. How much will he earn for 1 day?
41
A
B
C
D
E
_______________________________________________________
16. 20 chocolates cost Rs 320. Find the cost of 35 such chocolates.
_______________________________________________________
17. Railways charge Rs 150 to carry 25 tonnes of weight. What will it charge to carry 15 tonnes?
___________________________________________________________
18. The cost of 40 metres of cloth is Rs 2000. Find the cost of 50 metres of cloth.
___________________________________________________________
19. 25 workers earn Rs 30000 per day. What will be the earning of 20 workers per day at the same rate?
________________________________________________________________________
20. A car travels 178km in 4 hours.
i) How long will it take to travel 445km?
______________________________________________________
ii) How far will it travel in 3.5 hours?
________________________________________________________
Perimeter and Area
Perimeter
1. Find the perimeter of the following figures.
I) ii)
42
2cm
2cm 2cm
2cm
2cm
2cm 4cm
2cm2cm
7cm7cm
4cm
5cm
___________________________ _______________________________
iii) iv)
P = _____ P= ____
2. Fill up the following tables
3. Find the perimeter of the following rectangles
i) ii)
______________ ____________
4. Find the perimeter of the following rectangles whose
i) length = 12cm , breadth = 11cm ii) length = 5.25m , breadth = 1.8m
______________ _______________
iii) length = 10 15 cm, breadth = 9
34 cm iv) length = 12 1
3 cm, breadth = 7 25 cm
________________________ __________________
5. Find the perimeter of the following squares.
i) ii) iii)
__________ ___________ _______
43
4cm
12cm
4cm
4cm
12cm
10ft
14ft
18ft
12ft
9cm10 15
cm
2710 cm10 1
5 2.4cm10 15
3m
7m
15cm
16cm
Rectangle Length (l) Breadth(b) Perimeter = 2( l+b)i) 20cm 10cmii) 8.5m 6.4miii)
234 ft 2
34 ft
6. Find the perimeter of the following square whose side is:
i) 11cm ii) 6.5m iii) 58 cm
________ _____________ ____________
Problem solving * Reasoning
6 Fill up the table
7. A
rectangular piece of lawn is 60m long and 25m wide. Find the length of the fence around it.
_____________________________________________________________
8. The side of a square field is 75m. What is the length of the fence required all around it?
___________________________________________________________________
9. A square piece of land has each side equal to 100m. If 3 layers of metal wire has to be used to fence it. What is the length of the wire needed?
_____________________________________________________________________
10. The dimension of a photograph are 30 cm X 20cm. What length of wooden frame is needed to frame the picture? __________________________________________________________
11. The length of a rectangular field is 100m. If the perimeter is 250m. What is the breadth?
______________________________________________________________________
Area
12. Find the area of figures in square units.
i) ii) iii)
_______ square units ______ square units _______ square units
44
Rectangle Length (l) Breadth(b) Perimeter
i) 20cm 60cm
ii) 6.4m 30.2cm
iii) 25.5cm 72cm
iv) v)
______ square units ____ square units
13. Fill in the blanks
i) ii)
Area = _____ square units
14. Fill up the table.
15. Find the area of the squares
i) ii)
ii)
Area = 16 square unit
= 4 X 4 = 16 sq units Area = _______ square unit
= ___ X ___ = ___ sq units.
16. Find the area of the following squares, if sides=
i) 12cm ii) 10.5m iii) 435 m
______ ____________ ________
Problem solving * Reasoning
45
Area=___ square units
___ X ___ = ___ square units
__ X ___ = ___ square
Rectangle Length(l) Breadth(b) Area = l X bi) 14cm 12cmii) 13.6 m 8miii) 3
2 ft 114 ft
17. Fill up the table
18. Fill up the table
19. The area of a rectangular field is 1125 m2 . If its width is 25 m . What is its length?
_________________________________________________
20. The length and breadth of a room are 6m and 4m respectively. How many square metres of carpet
is required to spread in the room? If the carpet is costing Rs 250 for a square metre, how much will
be the cost for spreading carpet in the entire room?
______________________________________________________
21. Lhakyi’s vegetable garden has a length 35m and perimeter of 120m. What is the area of the
vegetable garden?
Width = _______ Area = ___________
22. If you double the length of the sides of a square, what happens to the areas? Show examples to
support your answer.
____________________________________________________________________________
_______________________________________________________________________
Algebraic Expressions
46
Square Side AreaI) 441cm2
ii) 225cm2
iii) 2.56cm2
Rectangle Length breadth AreaI) 13 130cm2
ii) 20m 220m2
1. Describe a pattern for each sequence. Then use the pattern to write the next three number in the sequence.
a) 4 , 8 , 12 ,16, , ,
Sol 4 ,8 ,12 ,16, , , 16+4 20 +4 24 + 4
b) 30 ,27 ,24 ,21 , , ,
c) 128 , 64,32, 16, ,
2. Observe the letter pattern made by arrows and fill up the table below it.
i)
ii)
Number of Ps formed 1 2 3 4 100 xNumber of arrows required 5 ____ ____ ____ ____ ____
3. Which of the following are expression with number only number only:
i) 3 ii) 2- x iii) 4m iv) m -7 v) 23×7+6 vi)
y+63 vii) z
________________________________________________________________
4. Identify the operations (addition, subtraction, multiplication and division) in the expression formed.
i) 3m ii) p -5 iii y3 iv) 2p- 7
______________________________________________________________________________
5. Match the words expressions with the algebraic expression.
47
282420
Number of Ms formed 1 2 3 4 10Number of arrows required
4 ______ _____ ______ _______
i) 30 more than a number b (a) 97 – wii) 26 less than a number p (b) 45 –qiii) 12 fewer than a number t (c) 55+ niv) Sum of 3.2 and a number s (d) 30 + bv) n fewer than 115 (e) t – 12vi) w less than 97 ( f) p - 26vii) d more than 52 ( g) 3.2 + sviii) 23 more than a number n (h) 23 + nix) q fewer than 45 (i) 115 – nx) Sum of 55 and a number n (j) 52 + d
6. Frame the algebraic expressions for the following .
i) Two times a number increased by three. ________ii) Half of a number added to twelve. ________iii) Twice a number divided by another number.____________iv) Four times a number divided by another number.__________v) Five times a number multiplied by three times another number. ________vi) Thrice a number added to 16. ________vii) Twice a number subtracted from 20. _________viii) A number reduced by 20. _________ix) Five times a number added to 20 is equal to 70. _______x) The cost of an apple cost Rs x . What is the cost such four apples? _______
xi) Tsering is “y” years old. Tenzom is 10 years younger than him. What is the Tenzom’s age? _______
xii) Lhamo had certain number of momos let’s say “p”. She gave 6 pieces to her friend. How
many momos are left with her? __________
xiii) There are “z” number of pencils in the pencil box. I put five more pencils in it. Now, what is
the total number of pencils in the pencil box. _________
xiv) The sum of “n” and “m”. ________
xv) p multiplied by -7 and then 10 is added to the result. _______
xvi) Twice a number reduced by 9 is equal to 25. _______
xvii) Lhakyi is x years old. Tatop is four times Lhakyi’s age . After five years what will be the Tatop’s
age? ___________
48
7. Evaluate x+4 , when value of x is given.
8. Fill up the missing boxes.
i)
ii)
9. Complete the table and by inspection of the table .find the solution to the equations
i) y−7=1
Y = ___ is the solution
ii) 2 x+3=9
x=¿¿ is the solution.
iii) 4m−3= 5
m = ____ is the solution.
Basic Geometrical Ideas
1. the term Geometry is the English word equivalent of the Greek word Geometron,
geo means ____ and metron means ______.
2. A _____ determines a location
49
x 0 1 3 6 7 10
x+4 4 5 ___ ___ ___ ___
x 0 -1 2 -2 4 3
x−5 -5 -6
x 0 1 -2 2 5 100
3x 0 3
y 1 3 5 9 8 9
y−7
x 1 0 -2 3 -1 4
2 x+3
m 1 0 -2 3 2 4
4m−3
3. _____ has no dimension.
4. A line through two points A and B is written as ______.
5. ____ has no ____ point and can extend in both ______.
6. A________ is a section of a line with two end points.
7. The line segment AB is indicated as _____.
8. Line segment has definite _____.
9. We can measure line _____.
10. A ____ is a portion of a line .It starts at one point (called starting point) and
goes endlessly in a direction.
11. If AB is a ray. What is its starting point? ______________________
12. Give one model of a ray. ____________
13. is AB∧ AB same? Justify your answer._______________________________________________
14. The symbol used to indicate an angle is ______.
15. Name the given angle in three different ways.
_________________________________
16. The vertex of the given angle is _____, AB and BC are ____ of the angle.
17. Size of the angle is measured in _________.
18. What is a triangle? _______________________________________________
19. i) Identify the triangles in the figure._____________________
ii) Write the names of six line segment._
50
1B
C
A
R Q
S
P
___________________ iii) Write the names of seven angles.
_________________________ iv) Which two triangles have ∠P as common?
_______________________
20. A______ sided polygon is called a quadrilateral.
21. i) A quadrilateral PQRS has four sides_____________
and four angles __________
ii) Opposite side of PQ is _____
iii) Adjacent sides of QR are ____ and _____.
iv) Opposite angle of ∠ S is ______
v) Adjacent angles of ∠ S are _____ _______
22. In a circle the longest chord is also known as _______.
23. The _____ is a line segment that connect the centre to a point on the circle.
24. The fixed distance between the centre and the circle is called the ______.
25 ______ is double the size of a radius.
26. A line segment joining any two points on the circle is called ____________.
27. A chord that passes through a centre of the circle is called ________.
28. The diameter of a circle divides it into two ___________.
29. from the figure identify :
i) two radii
ii) one diameter
iii) a sector
iv) a segment
v) two points in the circle
vi) one point in the exterior
Understanding Elementary Shapes
1. Fill in the blanks
i) An angle which measures 900 is called a ___________ angle.
51
S
R Q
P
.. .
BY
W
X O
AZ
ii) An angle which measures greater than 00 and less than 900 is called ______ angle.
iii) An angle which measures greater than 1800 and less than 3600 is called _____ angle.
iv) An angle which measures 3600 is called ___________ angle.
v) An angle which measures greater than900 and less than 1800 is called _________ angle.
vi) An angle which measures 1800 is called ___________ angle.
vii) An angle which measures _____ is called zero angle.
2. Classify the following angles:
i) 2010 ii) 1790 iii) 890 iv) 920 v) 3000
________ ________ ____ _____ ________
vi) 3600 vii) 1800 viii) 910 ix) 00 x) 1000
________ __________ ___ _____ ______
xi) 900 xii) 20
___________ ______________
3. In the adjoining figure, name the acute and obtuse angle.
4. Open any two adjacent fingers of your hand. What kind of angles do you get?
To measure an angle with a protractor
5. By looking at each pair of angles given below, state which of the angles in each is greater .
52
71 432
8
5 6
Verify your answer by using protractor.
i) ii)
_____ ¿ _______ _______ ¿ ________
Measurement ∠1=¿¿ ∠2=¿ ¿ ∠3=¿¿ ∠4=¿¿
iii) iv)
_____ ¿ _______ _____ ¿ _______
Measurement ∠5=¿¿ ∠6=¿¿ Measurement ∠7=¿¿ ∠8=¿¿
6. Use protractor and a straightedge to draw each angle.
i) 1800 ii) 420
iii) 1350 iv) 150
6. Construct the following angles with the help of protractor.
i) 350 ii) 1050
iii) 1680 iv) 880
Triangle
7. The _______ sides and three _________ of a triangle taken together are called the ____ parts or _________ of the triangle.
53
2 1
43
658
7
E
F
D
8. The symbol ____ denotes the word triangle.
9. In the given figure :
i) Name the triangle in three different ways
____________________________________________
ii) Name all the sides . ________________________________________
iii) Name all the angles. _________________________________________
iv) Name all the vertices.__________________________________________
v) Name the vertex opposite to EF. ____________________________
vi) Name the side opposite to vertex F.__________________________
10. Look at the given figure and answer the following questions.
i) How many triangles are they? Name all.
________________________________________________________
ii) Name all the triangles which have the point G in their interior.
_____________________________________________________
iii) Name all the triangles which have point F in their exterior.
____________________________________________________
iv) Name all the triangles which have AB as its one side.
____________________________________________________
Fill in the blanks
11. If all the sides of a triangle are unequal in length, it is called ___________ triangle.
12. If two sides of a triangle are equal, it is called _________ triangle.
54
E
..
AB
DC
E G
F
13. If all three sides of a triangle are equal, it is called ______ triangle.
14. A triangle whose all angles are acute is known as an ______________________.
15. A triangle whose one of the angles is a _______ angle is called a right angled triangle.
16. A triangle whose one of the angles is obtuse is called an______ angled triangle.
17. Classify the triangle shown below as scalene, isosceles or equilateral, the lengths of the sides (in cm) are given
on them:
i) ii) iii)
_____________ ________ _______
18. Look at each figure below and state whether it is obtuse, right or acute angled triangle.
i) ii)
_________________ _________________
iii) iv)
_______________ ________________
19. Quadrilateral is a closed figure having ________ sides and _____ vertices.
20. Square is a quadrilateral in which all sides are _____ and angles are ____.
21 Rectangle is a quadrilateral in which _____ sides are equal and angles are _____.
55
5
5 5
8
7
8
53
4
650
250
900
1400
200
200
600600
600 450
550
800
22. Square is a rectangle because ___________________________________________________________
23. Rectangle may not be a square because _____________________________________________________
____________________________________________________________________________________
24. Parallelogram is a quadrilateral in which opposite sides are parallel and ______ .
25. Given figure is a parallelogram:
i) AD = _____
ii) CD = _____
iii) BC is parallel to ______
iv) BA is parallel to _______
26 Why rectangle is a parallelogram?
___________________________________________________________________________________
27. A quadrilateral is which all sides are equal is called ________.
28. Why Square is a rhombus?
___________________________________________________________________________________
29. In a trapezium one pair of opposite sides are _______ to each other.
30. Given figure is a trapezium and which two sides are parallel
_______________________________
Polygon
31. Determine which of the following figures are polygons. Why aren’t the others polygon?
i) ________________________________
56
B
DC
A
D C
BA
ii) _______________________
iii) ___________________________________
iv) ______________________________________
v) ______________________________________
vi) ___________________________________________
vii) ___________________________________________
32. Name each polygon
__________ ___________ ___________
33. Draw a rough sketch :
i) octagon ii) Nonagon iii) Decagon iv) heptagon
Data Handling
1. Fill in the blank
i) A ____ is a collection of numbers gathered to give some information.
57
ii) The data can be arranged in a tabular form using ____ marks.
iii) An observation occurring five times in a data , is represented as _____ using tally marks.
iv) A ________ represents data through pictures of objects.
2. Complete the following table
S.No tally marks Number of observations1. III _____2. II ______3. _____4. _____5. _____6. ____
3. Fill the tables
S.No tally marks Number of observations1. _______ 62. _______ 123. _______ 84. ______ 15. _______ 156. ______ 9
4. The blood group of 25 students are under as
A ,O , AB ,O , AB ,B ,B ,B , A B ,O , A ,B ,B ,B ,O , A , AB , AB , AB , A , A ,O ,B ,B ,O ,
Use the above data to complete the following tables using tally mark.
S.No Blood Group tally marks Number of students
1
2
3
4
A _________ ________
B _________ _______
O _________ ________
AB ________ ________
5. The length s in centimetres of 30 carrot s are given below.
15 ,12,13 ,12,14 ,16 ,22 ,18 ,16 ,22 ,
58
20 ,18 ,12 ,16 ,15 ,20 ,23 ,20 ,16 ,14 ,
20 ,20 ,16 ,17 ,16 ,20 ,13 ,12 ,16 ,18
Arrange the given data in a table using tally marks and answer the following questions.
i) What is the number of carrots which have length more than 20cm?
ii) Which length of carrots occur maximum number of times and minimum number of times?
6. Number of red boxes sold in this week.
i) Find the number of red boxes sold in:
Monday -- Tuesday-- Wednesday--
Thursday -- Friday-- Saturday—
ii) The number of red boxes sold in this week—
7. Jayla asked her friends which sport they liked to play best: soccer, softball, or basketball. The number of Jayla's friends that picked each sport is shown.
59
Soccer
Softball
Basketball
Which sport was picked most by Jayla's friends as their favorite?a. Soccerb. Soft ballc. Soccer
8. The sixth grade students at TCVSchool go on an apple picking field trip. When they return, they create a pictograph showing the number of apples each class picked.
KEY: =10
Ms. Miller's Class:
Mrs. Pena's Class:
Mr. Smith's Class:
Mrs. Quill's Class:?
The sixth grade students pick a total of 250 apples. How many apple symbols should go next to Mrs. Quill's class?
9.
60
i) Find the number of toys sold on each day of the week.
(ii) Find the number of toys sold during the week.
(iii) On which day were the maximum numbers of toys sold?
(iv) On which day were the minimum numbers of toys sold?
(v) What is the difference in number of toys sold on Saturday and Tuesday?
10 .Look at this pictograph:
How many people per television are there in Spain?
11. The numbers of students studying in each of five classes of a secondary school are given below. Draw a pictograph to represent the numerical data:
61
Each = 10 people
Each = 5 people
People per television
North Korea
Peru
Spain
12. At a parking place the following number of scooter were parked on different days. Draw a pictograph to represent the information:
Monday (30) Tuesday (25) Wednesday (35)
Thursday (15) Friday (20) Saturday (40)
13. In a survey it was found that the following number of students of a school uses different brands of soaps. Form a pictograph to represent the data:
Lux (100) Lifebuoy (50) Dove (60) Camay (70)
14. The bar graph shows the weekend activities for the sixth graders at Norling School. Use the bar graph to answer the questions
see a movie go for pizza shop for clothes see a foot ball game
other0
5
10
15
20
25
30
35
40
45scale 1 unit= 5 students
i) What is the most popular weekend activity? _____________
ii) How many students are in the sixth grade? _________________
iii) How many more students saw a football game than shopped clothes? __________
iv) If the students who saw a movie spend Rs 250 each on tickets. What was the total amount of money spent on movie tickets? _______________________________
15. i) Describe the information shown in the bar graph below. _______________________________
62
English Hindi Tibetan Maths Science Social0
10
20
30
40
50
60
70
80
90
100
ii) Which subject had the most entries? _________________________
iii) Which subject had least entries? __________________________
iv) How many more entries were there in Tibetan than Science?______________________
v) How many entries were there altogether? _______________________________
vi) Write the ratio of entries in each subject to the total number.
________________________________________________________________
_________________________________________________________________
___________________________________________________________________
16. Draw a bar graph
17. Draw a bar graph
Favorite Sports
63
Entries in exam subjects
Scale
I unit = 10 students
Day Number of hours of sunshineMondayTuesdayWednesdayThursdayFridaySaturdaySunday
891112743
Basket ball
Football
Swimming
Cricket
Table tennis
21
34
10
12
6
18. In a botanical garden, the number of different types of plants are found as follows.
Types of plants Number of plants
Herbs 50
Shrub 60
Creepers 20
Climbers 45
Trees 95
Draw a bar graph to represent the above information and answer the following questions,
taking scale 1 unit = 5 plants
I) Which type of plants is maximum in number in the garden? ___________
ii) Which type of plant is minimum in the garden?_____________
64
