1 SMART EDUCATIONS
ADDITION..................................................................................................................................... 2
SUBTRACTION.............................................................................................................................3
MULTIPLICATION TABLE............................................................................................................ 4
MULTIPLICATION.........................................................................................................................5
DIVISION.......................................................................................................................................6
BODMAS RULE FOR WHOLE NUMBERS..................................................................................7
INTEGERS.................................................................................................................................... 8
NUMBER SYSTEM..................................................................................................................... 11
RULES OF DIVISIBILITY............................................................................................................13
PRIME FACTORISATION........................................................................................................... 15
LCM AND HCF............................................................................................................................16
RATIONAL NUMBERS............................................................................................................... 18
DECIMAL NUMBERS................................................................................................................. 24
POWERS AND EXPONENTS.....................................................................................................27
ALGEBRA...................................................................................................................................30
IRRATIONAL NUMBER.............................................................................................................. 35
PLAIN FIGURES & 3D FIGURES...............................................................................................36
MENSURATION.......................................................................................................................... 38
GEOMETRY................................................................................................................................ 43
PERCENTAGES..........................................................................................................................47
2 SMART EDUCATIONS
ADDITION
789 855 709 895 659
+654 +765 +562 +854 +369
598 978 825 825 765
+568 +708 +269 +105 + 89
109 706 654 987 809
+100 + 65 +123 +239 +769
777 861 367 852 654
+459 +798 +258 +465 +296
357 369 679 864 655
+159 +264 +569 +623 +289
321 852 753 951 741
+123 +369 +159 +852 + 369
898 353 825 915 765
+454 + 465 +465 +735 +656
848 466 888 709 892
+666 +365 +444 +299 +797
656 644 800 984 964
+626 +536 +586 +369 +536
3 SMART EDUCATIONS
SUBTRACTION
789 855 709 895 659
-654 - 765 - 562 - 854 - 369
598 978 825 825 765
-568 -708 -269 - 105 - 89
109 706 654 987 809
- 100 - 65 - 123 - 239 - 769
777 861 367 852 654
-459 - 798 - 258 - 465 - 296
357 369 679 864 655
-159 - 264 - 569 - 623 - 289
321 852 753 951 741
-123 - 369 - 159 -852 - 369
898 353 825 915 765
- 454 - 465 - 465 - 735 - 656
848 466 888 709 892
- 666 - 365 - 444 - 299 - 797
656 644 800 984 964
- 626 - 536 - 586 - 369 - 536
4 SMART EDUCATIONS
MULTIPLICATION TABLE
2 1 = 2
×
3 1 = 3
×
4 1 = 4
×
5 1 = 5
×
6 1 = 6
×
7 1 = 7
×
8 1 = 8
×
9 1 = 9
×
10 1 = 10
×
2 2 = 4
×
3 2 = 6
×
4 2 = 8
×
5 2 = 10
×
6 2 = 12
×
7 2 = 14
×
8 2 = 16
×
9 2 = 18
×
10 2 = 20
×
2 3 = 6
×
3 3 = 9
×
4 3 = 12
×
5 3 = 15
×
6 3 = 18
×
7 3 = 21
×
8 3 = 24
×
9 3 = 7
×
10 3 = 30
×
2 4 = 8
×
3 4 = 12
×
4 4 = 16
×
5 4 = 20
×
6 4 = 24
×
7 4 = 28
×
8 4 = 32
×
9 4 = 36
×
10 4 = 40
×
2 5 = 10
×
3 5 = 15
×
4 5 = 20
×
5 5 = 25
×
6 5 = 30
×
7 5 = 35
×
8 5 = 40
×
9 5 = 45
×
10 5 = 50
×
2 6 = 12
×
3 6 = 18
×
4 6 = 24
×
5 6 = 30
×
6 6 = 36
×
7 6 = 42
×
8 6 = 48
×
9 6 = 54
×
10 6 = 60
×
2 7 = 14
×
3 7 = 21
×
4 7 = 28
×
5 7 = 35
×
6 7 = 42
×
7 7 = 49
×
8 7 = 56
×
9 7 = 63
×
10 7 = 70
×
2 8 = 16
×
3 8 = 24
×
4 8 = 32
×
5 8 = 40
×
6 8 = 48
×
7 8 = 56
×
8 8 = 64
×
9 8 = 72
×
10 8 = 80
×
2 9 = 18
×
3 9 = 27
×
4 9 = 36
×
5 9 = 45
×
6 9 = 54
×
7 9 = 63
×
8 9 = 72
×
9 9 = 81
×
10 9 = 90
×
2 10 =20
×
3 10 = 30
×
4 10 = 40
×
5 10 = 50
×
6 10 = 60
×
7 10 = 70
×
8 10 = 80
×
9 10 = 90
×
10 10 = 100
×
11 1 = 11
×
12 1 =12
×
13 1 =13
×
14 1 =15
×
15 1 =15
×
16 1 =16
×
17 1 =17
×
18 1 =18
×
19 1 =19
×
20 1 =20
×
11 2 = 22
×
12 2 = 24
×
13 2 = 26
×
14 2 = 28
×
15 2 = 30
×
16 2 = 32
×
17 2 = 34
×
18 2 = 36
×
19 2 = 38
×
20 2 = 40
×
11 3 = 33
×
12 3 =36
×
13 3 =39
×
14 3 =42
×
15 3 =45
×
16 3 =48
×
17 3 =51
×
18 3 = 54
×
19 3 = 57
×
20 3 = 60
×
11 4 = 44
×
12 4 =48
×
13 4 =52
×
14 4 =56
×
15 4 =60
×
16 4 =64
×
17 4 =68
×
18 4 =72
×
19 4 =76
×
20 4 = 80
×
11 5 =55
×
12 5 =60
×
13 5 =65
×
14 5 =70
×
15 5 =75
×
16 5 =80
×
17 5 =85
×
18 5 =90
×
19 5 =95
×
20 5 = 100
×
11 6 =66
×
12 6 =72
×
13 6 =78
×
14 6 =84
×
15 6 =90
×
16 6 =96
×
17 6 =106
×
18 6 =108
×
19 6 =114
×
20 6 = 120
×
11 7 =77
×
12 7 =84
×
13 7 =91
×
14 7 =98
×
15 7 =105
×
16 7 =112
×
17 7 =119
×
18 7 =126
×
19 7 =133
×
20 7 = 140
×
11 8 =88
×
12 8 =96
×
13 8 =104
×
14 8 =112
×
15 8 =120
×
16 8 =128
×
17 8 =136
×
18 8 =114
×
19 8 =152
×
20 8 = 160
×
11 9 =99
×
12 9 =108
×
13 9 =117
×
14 9 =126
×
15 9 =135
×
16 9 =144
×
17 9 =153
×
18 9 =162
×
19 9 =171
×
20 9 = 180
×
11 10=110
×
12 10=120
×
13 10=130
×
14 10 =140
×
15 10 =150
×
16 10 =160
×
17 10 =170
×
18 10 =180
×
19 10 =190
×
20 10 = 200
×
5 SMART EDUCATIONS
MULTIPLICATION
789 855 709 895 659
4 5 2 4 9
× × × × ×
598 978 825 825 765
68 78 69 85 89
× × × × ×
109 706 654 987 809
10 65 123 239 769
× × × × ×
777 861 367 852 654
59 798 258 465 296
× × × × ×
357 369 679 864 655
59 264 569 623 289
× × × × ×
321 852 753 951 741
23 369 159 852 369
× × × × ×
898 353 825 915 765
54 465 465 735 656
× × × × ×
848 466 888 709 892
66 365 444 299 797
× × × × ×
656 644 800 984 964
26 536 586 369 536
× × × × ×
6 SMART EDUCATIONS
DIVISION
684÷2
768÷ 2
908÷2
776÷2
973÷2
9726÷3
522÷3
7837÷3
801÷3
14732÷3
5432÷4
56124÷4
13058÷4
35698÷4
469720÷4
32648÷5
3620÷5
46985÷5
456972÷5
463580÷5
32569÷6
46982÷6
506480÷6
569742÷6
469820÷6
56975÷7
569871÷7
698745÷7
856479÷7
5698705÷7
698745÷8
869756÷8
869426÷8
5698746÷8
869456÷8
569878÷9
56975÷9
8465656÷9
654799÷9
5656646÷9
569750÷10
6549313÷10
68465÷10
554545÷10
654545÷10
64654646÷11
65465464÷11
5156÷11
515151÷11
68546545÷11
4654646÷12
546546÷12
654654÷12
65465456÷12
564654÷12
6584654÷13
846846÷13
654654÷13
65465465÷13
65465465÷13
986464÷14
6565666÷14
658465÷15
65465465÷15
654654÷15
654654÷16
6546565÷16
6546546÷16
5465465÷16
745465÷16
89798546÷17
654÷17
54654÷17
654654÷17
894765÷17
16546÷18
654635÷18
1023654÷18
8465465÷18
21164÷18
2164694÷19
1036654÷19
3213213÷19
231366÷19
651664÷19
132654÷131
5469846÷461
1465465÷141
132132÷331
2316544÷413
131346÷337
654646÷47
6565498÷61
21654646÷71
5456465÷73
66494988÷83
6541687÷37
65498749÷39
6548798÷79
6546984÷113
68476846÷23
6846664÷29
9979791÷37
9878464÷41
64644465÷31
7 SMART EDUCATIONS
BODMAS RULE FOR WHOLE NUMBERS
1)
16+4×3+7−8+12÷3
3)
8×10÷(2+8)−6+21÷3
5)
12+8÷4+6×5−12
7)
13+14÷(5+2)−2+8×6÷3
9)
(10+10)÷10−10+10×10
11)
18÷6+(8×4)÷2+12
13)
20+20÷10+(30+50)÷5
15)
30+5×(8+2)÷2+6×3
17)
321÷(2+1)+8932÷(5−1)
19)
(5+6÷2+3÷3)÷(12÷2−3)
21)
(66÷6+4+15÷5)×(7+6÷3)
23)
[8+{12÷(8−2)+6×4}+6÷2]
25)
20−10÷(3+2)×14÷7+20
27)
{11+9÷9+3×(7−7)+6
29)
13×{8÷4+(2+1)−5}
31)
7−7×12÷12+8+2×6÷3
33)
12+8×4−6÷3+7×6
35)
[{12÷(8+4)+6}×3+2]
37)
[8+6×{(7−7)+5}−19×2]
39)
12+[{(8+2)÷(2+3)+3}÷5]
8 SMART EDUCATIONS
INTEGERS
The numbers which lie on the left side of a number line are smaller than that of the right
side.
For example:-
−6<−4
−4<0
−3 <2
− 𝑎𝑛𝑑 − = +
+ 𝑎𝑛𝑑 + = +
− 𝑎𝑛𝑑 + = −
+ 𝑎𝑛𝑑 − = −
ADDITION AND SUBTRACTION
1)
−7+6
2)
8−12
3)
−10−5
4)
−12+15
5)
−3+5
6)
−5−(−7)
7)
8−(−7)
8)
10+(−5)
9)
5+7
10)
10−20
11)
17−(−20)
12)
−9−5
13)
12−4−6
14)
−1+8−11
15)
−12−5+7
16)
6+(−7)−9
17)
−7+15−5
18)
13−15−5
19)
−12−2+8
20)
25−30+20
21)
−17−7−10
22)
−12−(−6)
23)
−5−5−5
24)
10+(−9)
25)
−18−12−2
26)
−27−7+5
27)
−10+10+5
28)
−12+(−12)
29)
−12+12−5
30)
−5−8+2
31)
−2+12−20
32)
−7+(−7)
33)
−9+1−12
34)
9−(−5)+2
35)
−10+9−19
36)
−5+10−5
37)
9−(−12)+5
38)
−20+5−9
39)
−7+(−12)
40)
15−25+5
41)
−12+(−9)
42)
12−8+2
43)
−7−9+1
44)
−25+37
45)
−12−8−3
46)
11−9+2
47)
19+1−27
48)
−9+2−11
49)
−5−5−10
50)
10−(−12)
51)
−12+(−8)
52)
−3+7−10
53)
−9+1−10
54)
15−5+10
55)
10+(−12)
56)
−15+19
9 SMART EDUCATIONS
57)
−12+8−20
58)
−7+9−12
59)
−1−9+1
60)
−12−10+2
MULTIPLICATION
1)
−7×6
2)
8×12
3)
−10×(−5)
4)
−12×15
5)
−3×5
6)
−5×(−7)
7)
8×(−7)
8)
10×(−5)
9)
−5×7
10)
10×(−20)
11)
−17×(−20)
12)
−9×(−5)
13)
12×(−4)×6
14)
−1×−8
15)
−12×5
16)
6×(−7)
17)
−7×(−5)
18)
−15×(−5)
19)
−12×2
20)
−30×20
21)
−17×7×−10
22)
−12×(−6)
23)
−5×5
24)
10×(−9)
25)
−18×12
26)
−27×(−7)
27)
−10×10
28)
−12×(−12)
29)
−12×12×5
30)
−5×(−8)
31)
−2×12
32)
−7×(−7)
33)
−9×0
34)
0×(−5)
35)
−10×0
36)
−5×10
37)
9×(−12)
38)
−20×5
39)
−7×(−12)
40)
15×(−25)
41)
−12×(−9)
42)
12×8
43)
−7×(−9)
44)
−25×37
45)
−12×−8
46)
11×(−9)
47)
19×(−27)
48)
−9×21
49)
−5×(−10)
50)
10−(−12)
51)
−12×(−8)
52)
−3×7
53)
−9×1
54)
−15×50
55)
10×(−12)
56)
−15×19
57)
−12×80
58)
−7×9
59)
−1×(−9)
60)
−12×10
DIVISION
1)
−12÷4
2)
−10÷5
3)
−18÷(−2)
4)
20÷(−4)
5)
16÷(−4)
6) )
25÷(−5
7)
−36÷(−9)
8)
−27÷9
9)
−63÷7
10)
−42÷(−7)
11)
−28÷7
12)
−24÷6
13)
−44÷11
14)
72÷(−8)
15)
123÷(−3)
16)
−156÷(−6)
17)
−49÷7
18)
−44÷11
19)
108÷(−9)
20)
−33÷3
21)
−21÷7
22)
−625÷(−5)
23)
−46÷23
24)
−10÷5
25)
0÷(−8)
26)
0÷5
27)
7÷0
28)
−12÷0
10 SMART EDUCATIONS
29)
−11÷11
30)
−17÷(−17)
31)
−130÷13
32)
−430÷10
BODMAS RULE
1)
−16−4×3+7−8−12÷3
3)
8×(−10)÷(2+8)−6−21÷3
5)
12−8÷4+6×(−5)−12
7)
13−14÷(5+2)−2+8×(−6)÷3
9)
(10−30)÷(−10)−10−10×10
11)
18÷6+(8×4)÷2+12
13)
20+20÷10+(30+50)÷5
15)
30+5×(8+2)÷2+6×3
17)
321÷(2+1)−8932÷(5−9)
19)
(5−6÷2−3÷3)÷(−12÷2−3)
21)
(66÷6+4−15÷5)×(7−6÷3)
23)
[8−{12÷(8−10)−6×4}+6÷2]
25)
20−40÷(3+2)×(−14)÷7+20
27)
{11−9÷9+3×(7−17)+6
29)
13×{−8÷4+(2+1)−5}
31)
7−7×(−12)÷12+8+2×6÷3
33)
12−8×4−6÷(−3)+7×6
35)
[{12÷(8−10)+6}×3−2]
37)
[8+6×{(7−17)−5}−19×2]
39)
12+[{(8−12)÷(2−4)+3}÷5]
11 SMART EDUCATIONS
NUMBER SYSTEM
Natural Numbers:- 1,2,3,4,5,6,7,8,9,10………………….∞
Whole Numbers:- 0,1,2,3,4,5,6,7,8,9,10………………….∞
Integers:- ∞………….-7,-6,5,-4,-3,-2,-1,0,1,2,3,4,5,6,7………………….∞
Q. Write a number which is a whole number but not a natural number.
Q. Write a number greater than -1.
Q. Write a number which is neither negative nor positive.
Q. Write a number smaller than -6.
Q. Write a number which is an integer but not a whole number.
Q. Which number is greater -12 or -5?
Q. Which of the following are even numbers?
8
12
9
18
11
17
19
13
10
15
5
16
14
0
14
21
63
36
20
39
24
20
19
25
37
42
Q. Which of the following are odd numbers?
81
2
19
17
15
42
32
13
16
5
1
0
14
23
13
9
3
7
11
39
30
20
14
6
37
42
Q. Which of the following are prime numbers?
8
12
9
18
11
17
19
13
10
15
5
16
14
22
14
21
63
36
20
39
24
20
19
25
37
42
Q. Which of the following are composite numbers?
81
2
19
17
15
42
32
13
16
5
1
0
14
23
13
9
3
7
11
39
30
20
14
6
37
42
Q. Which of the following are odd prime numbers?
12 SMART EDUCATIONS
81
2
19
17
15
42
32
13
16
5
1
0
14
23
13
9
3
7
11
39
30
20
14
6
37
42
Q. Which of the following are even prime numbers?
8
12
9
18
11
17
19
13
10
15
5
16
14
22
14
21
63
36
20
39
24
20
19
25
37
42
Q. Which of the following are odd composite numbers?
8
12
9
18
11
17
19
13
10
15
5
16
14
22
14
21
63
36
20
39
24
20
19
25
37
42
13 SMART EDUCATIONS
RULES OF DIVISIBILITY
Q. Which of the following numbers are divisible by 2?
132
161
268
136
220
72
29
227
335
562
1395
1216
2113
5655
6880
3389
7600
6986
6351
4597
35003
46521
63131
13565
78901
95836
46694
49377
39468
48668
Q. Which of the following numbers are divisible by 3?
132
161
268
136
220
72
29
227
335
561
1395
1206
2113
5655
6880
3389
7600
6986
6351
4597
35003
46521
63131
13565
78901
95826
46695
49377
39468
48668
Q. Which of the following numbers are divisible by 4?
16
61
36
44
42
47
98
96
52
132
1000
3212
5203
648
6743
5498
6630
8590
8364
1984
36495
62354
89464
59804
65984
46632
45600
56982
46324
46540
Q. Which of the following numbers are divisible by 5?
132
161
268
136
220
72
29
227
335
562
1395
1216
2113
5655
6880
3389
7600
6986
6351
4597
35003
46521
63131
13565
78901
95836
46694
49377
39468
48668
Q. Which of the following numbers are divisible by 6?
16
61
36
44
42
47
98
96
52
132
1000
3212
5203
648
6743
5498
6630
8590
8364
1984
36495
62354
89464
59804
65984
46632
45600
56982
46324
46540
14 SMART EDUCATIONS
Q. Which of the following numbers are divisible by 7?
16
61
36
44
42
47
98
96
52
132
1000
3212
5203
648
6743
5498
6630
8590
8364
1984
36495
62354
89464
59804
65984
46632
45600
56982
46324
46540
Q. Which of the following numbers are divisible by 8?
132
161
268
136
220
72
29
227
335
561
1395
1206
2113
5655
6880
3389
7600
6986
6351
4597
35003
46521
63131
13565
78901
95826
46695
49377
39468
48668
Q. Which of the following numbers are divisible by 9?
132
161
268
136
220
72
29
227
335
562
1395
1216
2113
5655
6880
3389
7600
6986
6351
4597
35003
46521
63131
13565
78901
95836
46694
49377
39468
48668
Q. Which of the following numbers are divisible by 10?
16
61
36
44
42
47
98
96
52
132
1000
3212
5203
648
6743
5498
6630
8590
8364
1984
36495
62354
89464
59804
65984
46632
45600
56982
46324
46540
Q. Which of the following numbers are divisible by 11?
121
1321
1232
663
781
633
544
890
7084
9632
12321
10001
10010
10109
11111
13200
69843
63206
13268
56354
79865
12345
10021
78973
36505
46987
15697
23689
16587
65987
15 SMART EDUCATIONS
PRIME FACTORISATION
Q. Find the prime factorisation of the following numbers.
16
61
36
44
42
47
98
96
52
132
1000
3212
5203
648
6743
5498
6630
8590
8364
1984
36495
62354
89464
59804
65984
46632
45600
56982
46324
46540
121
1321
1232
663
781
633
544
890
7084
9632
12321
10001
10010
10109
11111
13200
69843
63206
13268
56354
79865
12345
10021
78973
36505
46987
15697
23689
16587
65987
132
161
268
136
220
72
29
227
335
562
1395
1216
2113
5655
6880
3389
7600
6986
6351
4597
35003
46521
63131
13565
78901
95836
46694
49377
39468
48668
16 SMART EDUCATIONS
LCM AND HCF
Q. Find the HCF of the following.
1) 16 and 18
2) 28 and 36
3) 32 and 40
4) 112 and 216
5) 343 and 77
6) 512 and 96
7) 216 and 312
8) 456 and 724
9) 810 and 117
10) 336 and 512
11) 777 and 333
12) 309 and 123
13) 910 and 210
14) 712 and 225
15) 432 and 900
16) 756 and 729
17) 187 and 231
18) 111 and 341
19) 342 and 763
20) 329 and 161
21) 943 and 851
22) 1147 and 1271
23) 16, 56 and 12
24) 36, 15 and 21
25) 100 and 50
26) 512 and 696
27) 136 and 628
28) 329 and 147
29) 333 and 129
30) 321 and 438
31) 546 and 225
32) 798 and 636
33) 635 and 625
34) 86, 129 and 301
35) 1205 and 300
36) 637 and 301
37) 221 and 299
38) 391 and 527
39) 437 and 703
40) 561 and 648
41) 12, 18 and 26
42) 17, 19 and 23
43) 125, 343 and 1331
44) 27,36 and 63
45) 15, 20 and 30
Q. Find the LCM of the following:
1) 12, 18 and 16
2) 8, 6 ,12 and 4
3) 12 ,18 and 15
4) 15, 21, 18 and 25
5) 15, 14 and 35
6) 11 and 22
7) 35 and 55
8) 8, 6 and 12
9) 22, 33 and 12
10) 336 and 512
11) 777 and 333
12) 309 and 123
13) 910 and 210
14) 712 and 225
15) 432 and 900
16) 756 and 729
17) 187 and 231
18) 111 and 341
19) 342 and 763
20) 329 and 161
21) 943 and 851
17 SMART EDUCATIONS
22) 22, 30 and 132
23) 21, 63 and 36
24) 50, 25 and 40
25) 32, 28 and 21
26) 33, 36 and 55
27) 15, 45 and 36
28) 10, 12, 18 and 20
29) 33 and 86
30) 125 and 343
31) 336 and 512
32) 777 and 333
33) 309 and 123
34) 910 and 210
35) 712 and 225
36) 432 and 900
37) 756 and 729
38) 187 and 231
39) 111 and 341
40) 342 and 763
41) 329 and 161
42) 943 and 851
43) 21, 49 and 119
44) 117, 51 and 34
45) 27, 512 and 343
18 SMART EDUCATIONS
RATIONAL NUMBERS
Q. Compare the following numbers:-
1)
7
6
𝑎𝑛𝑑
3
2
2)
5
6
𝑎𝑛𝑑
1
2
3)
7
8
𝑎𝑛𝑑
3
2
4)
11
9
𝑎𝑛𝑑
3
2
5)
1
6
𝑎𝑛𝑑
3
16
6)
11
6
𝑎𝑛𝑑
13
2
7)
1 𝑎𝑛𝑑
3
2
8)
12
5
𝑎𝑛𝑑
11
10
9)
1
3
𝑎𝑛𝑑
5
6
10)
1
2
𝑎𝑛𝑑
3
2
11)
5
6
𝑎𝑛𝑑
3
2
12)
1
3
𝑎𝑛𝑑
3
2
13)
7
5
𝑎𝑛𝑑
3
2
14)
8
5
𝑎𝑛𝑑
17
2
15)
10
9
𝑎𝑛𝑑
15
17
16)
17
8
𝑎𝑛𝑑
17
6
17)
15
14
𝑎𝑛𝑑
15
21
18)
18
11
𝑎𝑛𝑑
35
22
19)
12
5
𝑎𝑛𝑑
3
2
20)
17
6
𝑎𝑛𝑑
13
8
Q. Convert into like fraction:-
1.
7
6
𝑎𝑛𝑑
3
2
2.
5
6
𝑎𝑛𝑑
1
2
3.
7
8
𝑎𝑛𝑑
3
2
4.
11
9
𝑎𝑛𝑑
3
2
5.
1
6
𝑎𝑛𝑑
3
16
6.
11
6
𝑎𝑛𝑑
13
2
7.
1 𝑎𝑛𝑑
3
2
8.
12
5
𝑎𝑛𝑑
11
10
9.
1
3
𝑎𝑛𝑑
5
6
10.
1
2
𝑎𝑛𝑑
3
2
11.
5
6
𝑎𝑛𝑑
3
2
12.
1
3
𝑎𝑛𝑑
3
2
13.
7
5
𝑎𝑛𝑑
3
2
14.
8
5
𝑎𝑛𝑑
17
2
15.
10
9
𝑎𝑛𝑑
15
17
16.
17
8
𝑎𝑛𝑑
17
6
17.
15
14
𝑎𝑛𝑑
15
21
18.
18
11
𝑎𝑛𝑑
35
22
19.
12
5
𝑎𝑛𝑑
3
2
20.
17
6
𝑎𝑛𝑑
13
8
Q. Convert into mixed fraction:-
1)
7
2
2)
13
3
3)
19
3
4)
17
4
5)
23
4
6)
17
5
7)
22
5
8)
31
5
9)
33
7
10)
37
6
11)
37
4
12)
38
5
13)
37
4
14)
36
7
15)
42
8
16)
65
8
17)
66
8
18)
67
8
19)
73
11
20)
35
12
19 SMART EDUCATIONS
21)
11
5
22)
6
5
23)
13
5
24)
19
4
25)
23
4
Q. Convert into improper fraction:-
1)
7
3
5
2)
6
1
2
3)
8
3
7
4)
11
3
8
5)
7
8
9
6)
5
3
8
7)
3
2
3
8)
5
3
4
9)
8
6
7
10)
9
5
8
11)
17
5
11
12)
16
10
13
13)
15
3
10
14)
19
5
11
15)
7
13
17
16)
11
11
13
17)
9
7
9
18)
11
13
15
19)
13
7
12
20)
8
11
16
21)
8
7
11
22)
7
3
5
23)
6
8
9
24)
7
5
9
25)
23
25
29
Q. Convert into simplest form:-
1)
15
18
2)
21
28
3)
14
12
4)
35
28
5)
33
36
6)
16
18
7)
26
12
8)
18
20
9)
46
69
10)
21
63
11)
25
15
12)
20
24
13)
30
12
14)
35
14
15)
40
15
16)
312
126
17)
132
33
18)
69
46
19)
225
63
20)
335
45
21)
460
69
22)
130
45
23)
112
28
24)
112
144
25)
343
147
Q. Find the ratio for the following:-
1) 6 girls and 8 boys
2) Rs10 and Rs15
3) 15kg and 6kg
4) 30 chair and 18 tables
5) 25cm and 40cm
6) 21 trees and 56 plants
7) 49 pens and 28 pencils
8) 12m and 21m
9) 18 books and 30 copies
10) 20 pass and 12 fail
11) 35 km and 25km
12) 40 poor and 16 rich
20 SMART EDUCATIONS
Q.Find the multiplicative inverse or reciprocal of the following:
1)
7
2
2)
13
3
3)
19
3
4)
17
4
5)
−23
4
6)
17
5
7)
−22
5
8)
−31
5
9)
7
10)
5
11)
−
1
4
12)
38
5
13)
0
14)
1
7
15)
42
8
16)
65
8
17)
−66
8
18)
67
8
19)
−73
11
20)
13
21)
11
5
22)
6
5
23)
13
−5
24)
19
4
25)
23
−4
Q. Solve the following:-
1)
7
6
+
3
2
2)
5
6
+
1
2
3)
7
8
+
3
2
4)
11
9
+
3
2
5)
1
6
+
3
16
6)
11
6
+
13
2
7)
1 +
3
2
8)
12
5
−
11
10
9)
1
3
+
5
6
10)
1
2
+
3
2
11)
5
6
+
3
2
12)
1
3
+
3
2
13)
7
5
+
3
2
14)
8
5
−
17
2
15)
10
9
+
15
17
16)
17
8
+
17
6
17)
15
14
+
15
21
18)
18
11
+
35
22
19)
12
5
+
3
2
20)
17
6
+
13
8
21)
7
8
+
11
6
+
5
4
22)
7
9
+
11
12
+
7
15
23)
1
5
+
7
10
+
5
15
24)
11
8
+
7
12
+
5
21
25)
5
12
+
7
15
26)
11
15
+
11
18
27)
13
5
+
13
5
28)
17
21
+
13
15
29)
16
21
+
17
28
30)
10
21
+
19
12
31)
9
5
+
1
6
32)
13
18
+
17
15
33)
7
3
8
+3
5
12
34)
3
5
6
+1
1
4
35)
8
2
15
+4
7
12
36)
1
9
10
+5
3
5
37)
6
9
12
+2
5
6
38)
11
3
9
+5
7
12
39)
17
12
+
15
7
40)
13
17
+
7
5
41)
13
8
+
5
9
42)
11
12
+
12
17
43)
11
5
+
13
7
44)
10
13
+
7
17
21 SMART EDUCATIONS
45)
15
14
+
17
21
46)
1
12
+
7
12
47)
19
17
+
17
19
48)
11
13
+
13
11
49)
17
20
+
18
25
50)
19
18
+
17
12
51)
11
8
+
17
6
52)
8+
7
6
53)
1+
13
15
54)
11
12
+12
55)
5+
5
10
56)
13
15
+
17
18
57)
7
22
+
15
11
+7
58)
7
6
+
6
7
+6
59)
23
13
+
15
26
60)
19
18
+
7
15
61)
16
15
+
11
12
62)
23
25
+
17
35
63)
2
15
+
7
20
64)
17
16
+
23
12
65)
13+
12
13
66)
1
5
+5
67)
27
10
+
16
15
68)
11
18
+
11
15
69)
5
3
+
7
6
70)
3
10
+
8
15
71)
20
27
+
13
18
72)
12+
17
15
73)
12
21
−
2
9
74)
17
12
−
11
15
75)
23
8
−
13
12
76)
13
9
−
7
6
77)
17
14
−
13
21
78)
9−
3
8
79)
13
18
−
1
2
80)
11
15
−
7
12
81)
7
3
2
−4
3
5
82)
7−4
3
4
83)
1
2
−
3
7
84)
13
15
−
15
13
85)
11−11
2
3
86)
7
3
14
−3
1
21
87)
7
3
10
−4
7
15
88)
13−5
3
10
89)
112
15
−
100
15
90)
43
25
−
23
30
91)
33
23
−
19
13
92)
0−
13
15
93)
0−
19
25
94)
0−
13
10
95)
16
15
−0
96)
13
12
−
13
12
97)
13
15
+
17
12
−9
98)
19
12
+6−7
99)
7
12
−8−
1
8
100)
9−
12
21
Q. Multiply the following:-
1)
5
12
×
7
15
2)
11
15
×
11
18
3)
13
5
×
13
5
4)
17
21
×
13
15
5)
16
21
×
17
28
6)
10
21
×
19
12
7)
9
5
×
1
6
8)
13
18
×
17
15
9)
13
8
×
5
9
10)
−11
12
×
12
17
11)
11
5
×
13
−7
12)
−10
13
×
7
−17
13)
15
14
×
17
21
14)
1
12
×
7
12
15)
19
17
×
−17
19
16)
11
13
×
13
−11
22 SMART EDUCATIONS
17)
17
20
×
18
25
18)
−
19
18
×
17
12
19)
−11
8
×
17
6
20)
8×
7
6
21)
1×
13
15
22)
11
12
×12
23)
0×
−5
10
24)
−13
15
×
−17
18
25)
5
3
×
7
6
26)
3
−10
×
−8
15
27)
20
27
×
13
18
28)
12×
17
15
29)
12
21
×
2
9
30)
17
12
×
11
15
31)
−23
8
×
13
12
32)
13
9
×
−7
6
33)
17
14
×
13
21
34)
−9×
3
8
35)
−13
18
×
1
2
36)
−11
15
×
7
−12
37)
−7
3
2
×4
3
5
38)
7×−4
3
4
39)
1
2
×
−3
7
40)
13
15
×
15
13
Q. Divide the following:-
1)
5
12
÷
7
15
2)
11
15
÷
11
18
3)
13
5
÷
13
5
4)
17
21
÷
13
15
5)
16
21
÷
17
28
6)
10
21
÷
19
12
7)
9
5
÷
1
6
8)
13
18
÷
17
15
9)
13
8
÷26
10)
−11
12
÷
12
17
11)
11
5
÷0
12)
0÷
7
−17
13)
15
14
÷
17
21
14)
1
12
÷
7
12
15)
19
17
÷
−17
19
16)
11
13
÷
13
−11
17)
17
20
÷
18
25
18)
−
19
18
÷
17
12
19)
−11
8
÷22
20)
8÷
7
6
21)
1÷
13
15
22)
11
12
÷12
23)
0÷
−5
10
24)
−13
15
÷
−17
18
25)
5
3
÷
7
6
26)
3
−10
÷
−8
15
27)
20
27
÷
13
18
28)
12÷
17
15
29)
12
21
÷
2
9
30)
17
12
÷
11
15
31)
−23
8
÷
13
12
32)
13
9
÷
−7
6
33)
17
14
÷
13
21
34)
−9÷
3
8
35)
−13
18
÷
1
2
36)
−11
15
÷
7
−12
37)
−7
3
2
÷4
3
5
38)
7÷−4
3
4
39)
1
2
÷
−3
7
40)
13
15
÷
15
13
23 SMART EDUCATIONS
Q. Solve the following:-
1)
7
6
+
15
8
×4÷
7
2
−1
1
2
( )
+8−
7
4
2)
15
14
+
13
15
÷
26
15
−
26
15
×25−25+
3
14
3)
3
7
𝑜𝑓 21÷
12
21
+4
3
8
+12×
7
8
+3
3
10
4)
13
12
−
13
12
𝑜𝑓 15+
17
15
+
13
20
÷
13
15
− −
7
15
( )
5)
13
12
+
−7
6
( )
×6÷
3
2
×
12
16
−
12
21
−
16
15
( )
×
7
15
−9
6)
7
6
÷14 𝑜𝑓
15
28
+
3
8
−
5
6
( )
+6−
13
15
+
7
15
× −
5
14
( )
7)
7
3
12
+17− −
7
6
−
5
8
( )
÷
12
21
+
17
6
÷34−
16
15
×
6
8
8)
7
15
−7
16
21
+
15
16
+
17
18
( )
−6÷
7
5
+0×
7
6
−
13
15
9)
19
15
× 15
17
19
+
11
12
−
7
8
×
7
6
−
5
8
( ){ }
+
7
6
⎡
⎣
⎤
⎦
−
7
6
÷
5
8
10)
7
3
15
+5− −
5
9
( )
×
13
15
+7
13
18
−
6
14
×
8
15
−7+
19
18
+
16
21
( )
11)
1
19
−9−9×
17
12
−
15
12
−
17
15
( )
+1
2
3
𝑜𝑓 9÷9
3
18
−
7
6
12)
21−
17
15
×
3
5
−8+6×3
1
5
×
13
16
−
5
8
( )
+9
1
2
−
19
2
×6
13)
11
3
5
+5
3
8
−13+13×
15
39
+
17
15
÷34−5+
7
12
14)
13
15
+8
16
21
−7÷
5
14
+
13
18
+
19
18
×12÷
7
6
−8
12
13
15)
11
8
−
13
21
+6− −
7
12
−4
15
21
( )
+
13
19
+9
3
8
−
13
17
×51
16)
3
1
2
÷
7
5
𝑜𝑓 13 +
11
15
+ −
9
8
+
13
12
( )
−
6
11
×
22
15
+8
17)
3
11
15
+
13
18
+7÷
13
15
+
11
15
×7÷
14
18
+9−
13
16
+
13
16
×4
18)
11
15
+7−
−15
14
+7
11
21
( )
−5×
7
11
+
−7
8
( )
×
9
−15
19)
13+
7
6
×
12
21
−
12
21
×6÷
6
7
+11+5
3
8
−11×
25
21
20)
19
12
÷
1
12
+6×
17
15
+7
4
9
×
13
67
+
−11
18
÷
5
9
+
7
12
21)
11
21
−
1
2
𝑜𝑓 18 −18×
7
12
+
19
15
×15−
17
12
−
13
8
( )
×
24
11
22)
9
11
15
−
7
12
×15−15+
11
15
+
−23
15
( )
+
7
9
+
−5
6
23)
99−
5
12
+
−5
8
+
−7
6
×
−5
21
( )
+6 𝑜𝑓
14
15
−7 −
9
10
24)
1
5
9
−
−7
6
( )
+
7
6
×
15
9
−1
1
6
÷
6
7
+
3
5
𝑜𝑓 13 −13
25)
7
12
−8×
15
4
−
11
12
+
7
9
÷
21
12
+5
7
12
−
−7
5
+
−7
12
( )
×60
24 SMART EDUCATIONS
DECIMAL NUMBERS
Q. Convert the following numbers into decimal:-
1)
17
8
2)
11
5
3)
11
4
4)
23
16
5)
13
2
6)
17
10
7)
23
10
8)
29
10
9)
113
10
10)
171
10
11)
15
6
12)
21
12
13)
1
10
14)
2
25
15)
3
1
4
16)
112
100
17)
217
100
18)
139
100
19)
874
100
20)
1369
100
21)
13
5
22)
1
100
23)
7
25
24)
13
16
25)
12
25
26)
3
4
27)
1354
1000
28)
77
100
29)
7
1000
30)
1365
25
31)
13
8
32)
1
16
33)
13
25
34)
81
6
35)
135
8
36)
1
8
37)
7
100
38)
17
8
39)
13
16
40)
55
16
Q. Convert the following into a fraction number:-
1)
13. 25
2)
12. 5
3)
7. 2
4)
3. 5
5)
11. 63
6)
17. 26
7)
0. 0025
8)
0. 026
9)
0. 0001
10)
13. 58
11)
10. 10
12)
0. 10
13)
1. 10
14)
10. 1
15)
0. 0010
16)
13. 65
17)
11. 32
18)
0. 25
19)
0. 025
20)
0. 125
21)
11. 11
22)
1. 11
23)
11. 1
24)
19. 2
25)
17. 5
26)
1. 01
27)
7. 77
28)
15. 5
29)
11. 225
30)
1. 2222
31)
0. 325
32)
0. 1325
33)
0. 01010
34)
137. 25
35)
11. 23
36)
77. 25
37)
13. 5
38)
10. 5
39)
23. 5
40)
14. 25
Q. Convert into like fraction and compare the following:-
1) 1.5 and 1.25
2) 2.03 and 2.2
3) 3.125 and 3.2
4) 5.7 and 5.458
5) 8.10 and 8.2
6) 6.005 and 6.02
25 SMART EDUCATIONS
7) 4.25 and 4.4
8) 7.9 and 7.90
9) 4.500 and 4.5
10) 0.0005 and 0.005
11) 8.050 and 8.5
12) 9.325 and 9.40
13) 4.505 and 4.3000
14) 0.00400 and 0.004
15) 0.005 and 0.5
Q. Solve the following numbers:-
1)
0. 15+0. 5
2)
0. 25+5. 5
3)
12. 5+1. 50
4)
31. 25+21. 25
5)
0. 005+0. 5
6)
0. 112+12. 2
7)
10. 10+0. 9
8)
13. 256+125
9)
132. 255+25
10)
0. 19+0. 1
11)
1235. 2+12. 80
12)
111. 2564+13. 23
13)
14. 99+15. 1
14)
17. 0236+14. 5
15)
13. 25+25
16)
17. 25−12. 5
17)
10. 25−5. 5
18)
23. 550−0. 35
19)
19. 2565−12. 5
20)
120. 0005−12. 55
21)
18. 225−17
22)
19−12.5
23)
20−13.65
24)
25−16.95
25)
37−15.3587
26)
42−40.985487
27)
12. 68456−10. 56
28)
135−13.5
29)
265−0.265
30)
30−0.30
Q. Multiply the following:-
1)
0. 15+0. 5
2)
0. 25+5. 5
3)
12. 5+1. 50
4)
31. 25+21. 25
5)
0. 005+0. 5
6)
0. 112+12. 2
7)
18. 25×0. 5
8)
36. 5×1. 2
9)
135×0.25
10)
19. 5×0. 005
11)
13. 5×5
12)
17. 5×0. 5
13)
10. 5×17
14)
14. 58×1. 6
15)
46. 55×0. 0005
16)
126. 256×10
17)
126. 256×100
18)
126. 256×1000
19)
126. 256×10000
20)
0. 00005×10
21)
0. 00005×100
22)
0. 00005×1000
23)
0. 00005×10000
24)
13. 25×10
25)
0. 00025×10
26)
13. 25×100
27)
0. 00025×100
28)
13. 255×100
29)
13. 255×12
30)
100×17.25698
26 SMART EDUCATIONS
Q. Divide the following:-
1)
12. 5÷0. 5
2)
13. 5÷5
3)
0. 824÷0. 004
4)
12. 5÷0. 25
5)
12. 25÷10
6)
12. 25÷100
7)
12. 25÷1000
8)
12. 25÷10000
9)
1236. 225÷25
10)
16. 9÷1. 3
11)
34. 3÷0. 49
12)
8. 19÷0. 009
13)
0. 289÷1. 7
14)
0. 0086÷0. 43
15)
164÷0.41
16)
0. 156÷100
17)
1. 89÷21
18)
0. 00001÷0. 1
19)
0. 1÷0. 0001
20)
0. 0004÷0. 2
21)
0. 0098÷0. 98
22)
13. 13÷13
23)
1. 616÷16
24)
19. 019÷1. 9
25)
0. 0001÷10
26)
15. 00015÷0. 5
27)
13. 5÷15
28)
200÷0.200
29)
17÷0.17
30)
0. 0005÷0. 5
Q. Solve the following:-
1)
9
5
+0. 75×
7
2
2)
−7. 458÷
11
8
3)
13
2
÷4. 55
4)
−1
16
−3. 225
5)
−4÷3. 45+
8
5
6)
17
5
×7. 55÷
5
4
7)
7. 45−7. 45÷
5
8
8)
−7. 5−5.25+
5.
2
9)
7
5
×(−6.65)×
−5
16
10)
8
5
−0. 45×3.25
11)
0. 45÷3. 5+
7
8
12)
11. 45×3. 2−
6
15
13)
−2. 5−
7
2
×
5
8
14)
1
16
−0. 25÷3.25
15)
−2. 25+2.25×0.25
27 SMART EDUCATIONS
POWERS AND EXPONENTS
Q. Solve the following:-
1)
5
2
2)
7
3
3)
8
3
4)
(−3)
5
5)
(−1)
3
6)
(−1)
4
7)
(−1)
7
8)
7
0
9)
7
1
10)
(0. 3)
3
11)
7
2
( )
4
12)
3
2
5
2
13)
7
3
5
2
14)
11
9
( )
0
15)
3
5
( )
2
16)
0. 25( )
2
17)
7
5
2
18)
(−3)
0
19)
𝑏
0
20)
(0. 04)
2
21)
7( )
−2
22)
5( )
−3
23)
−3( )
−1
24)
7
5
( )
−3
25)
−5
2
( )
−1
26)
−5( )
−4
27)
−1( )
−4
28)
−1( )
−5
29)
5( )
−1
30)
1( )
−3
Q. Convert into exponential form:-
1)
16
2)
25
3)
343
4)
169
5)
289
6)
32
7)
125
8)
512
9)
64
10)
49
11)
819
12)
27
13)
216
14)
64
289
15)
0. 64
16)
0. 0064
17)
0. 125
18)
0. 00032
19)
0. 36
20)
36
49
Q. Multiply and write the following into exponent form.
1)
5
2
×5
4
2)
3
2
×3
2
3)
7
2
×7
3
4)
13
2
×13
1
5)
3×3
4
6)
2×2
5
7)
4
3
×4
3
8)
5
2
×5
2
9)
2
3
×2
3
10)
3
2
×3
2
28 SMART EDUCATIONS
Q. Divide and write the following into exponent form.
1)
5
7
÷5
3
2)
7
4
7
2
3)
2
8
2
5
4)
3
5
3
4
5)
11
2
11
2
6)
11
5
11
2
7)
−3( )
5
−3( )
2
8)
−2( )
7
−2( )
3
9)
7
5
7
10)
9
3
9
Q. Find the square of the following:-
1)
0
2) 1
3) -1
4) 2
5) -2
6) 3
7) -3
8) 4
9) -4
10) 5
11) -5
12) 6
13) -6
14) 7
15) -7
16) 0.1
17) 0.8
18) 15
19) 13
20) 17
21) 25
22) 19
23) 21
24) 10
25) 100
26) 1000
27) 30
28) 300
29) 29
30) 23
Q. Find the square root of the following numbers:-
1) 7
2) 13
3) 132
4) 224
5) 749
6) 1296
7) 1325
8) 725
9) 625
10) 99
11) 117
12) 111
13) 101
14) 50
15) 72
16) 120169
17) 123.5
18) 1.9
19) 2.5
20) 3.6
21) 6.25
22) 4.9
23) 566.25
24) 1
25) 3
26) 2
27) 22
28) 20
29) 6
30) 8
Q. Find the cube of the following:-
31)
0
32)1
33)-1
34)2
35) -2
36)3
37)-3
38)4
39) -4
40) 5
41) -5
42) 6
43) -6
44) 7
45) -7
29 SMART EDUCATIONS
46) 0.1
47) 0.8
48) 15
49) 13
50) 17
51) 25
52) 19
53) 21
54) 10
55) 100
56) 1000
57) 30
58) 300
59) 29
60) 23
Q. Find the cube root of the following numbers:-
1) 125
2) 8
3) 373
4) 512
5) 1000
6) 216
7) 819
8) 1331
9) 1
10) 0
11) 27
12) 64
13) 12167
14)
15) 2197
30 SMART EDUCATIONS
ALGEBRA
Q. Solve the following:-
1)
5𝑥+2𝑥
2)
7𝑥+3𝑥
3)
𝑥+𝑥
4)
11𝑥+𝑥
5)
7𝑥+3𝑦
6)
9𝑥𝑦+𝑥𝑦
7)
9𝑥𝑦+5𝑥𝑦
8)
11𝑥𝑦+𝑥
9)
13𝑥𝑦+2𝑦𝑥
10)
17𝑥
2
+3𝑥
2
11)
5𝑥
2
+𝑥
12)
17𝑥
2
𝑦−2𝑥
2
𝑦
13)
10𝑥
2
𝑦−5𝑦𝑥
2
14)
12𝑥𝑦
2
+2𝑥
2
𝑦
15)
𝑥𝑦
2
+𝑥𝑦
2
16)
5𝑥
3
−2𝑥
2
17)
7𝑥
3
+2𝑥
3
18)
𝑥
3
+𝑥
3
19)
−7𝑥
2
+5𝑥
2
20)
−𝑥
3
−𝑥
3
21)
−2𝑥−(−5𝑥)
22)
3𝑥−(−3𝑥)
23)
11𝑥+(−15𝑥)
24)
−𝑥−𝑥
25)
5𝑥
2
+(−7𝑥)
26)
−9𝑥𝑦
2
+5𝑥𝑦
2
27)
10𝑥+10
28)
−9+𝑥
29)
8−8𝑦
30)
−2𝑦+2
Q. Multiply the following:-
1)
5𝑥×2𝑥
2)
7×3𝑥
3)
𝑥×𝑥
4)
−9×𝑥
5)
8×8𝑦
6)
−2𝑦×2
7)
11𝑥×𝑥
8)
7𝑥×3𝑦
9)
9𝑥𝑦×𝑥𝑦
10)
9𝑥𝑦×5𝑥𝑦
11)
11𝑥𝑦×𝑥
12)
13𝑥𝑦×2𝑦𝑥
13)
17𝑥
2
×3𝑥
3
14)
5𝑥
2
×𝑥
15)
17𝑥
2
𝑦×2𝑥
2
𝑦
16)
10𝑥
2
𝑦×5𝑦𝑥
2
17)
12𝑥𝑦
2
×2𝑥
2
𝑦
18)
𝑥𝑦
2
×𝑥𝑦
2
19)
5𝑥
3
×2𝑥
2
20)
7𝑥
3
×2𝑥
3
21)
𝑥
3
×𝑥
3
22)
−7𝑥
2
×5𝑥
2
23)
−𝑥
3
×𝑥
3
24)
−2𝑥×(−5𝑥)
25)
3𝑥×(−3𝑥)
26)
11𝑥×(−15𝑥)
27)
−𝑥×(−𝑥)
28)
5𝑥
2
×(−7𝑥)
29)
−9𝑥𝑦
2
×5𝑥𝑦
2
30)
10𝑥×10
31 SMART EDUCATIONS
Q. Divide the following:-
1)
7𝑥
3
÷7𝑥
2)
25𝑥
5
÷5𝑥
2
3)
8𝑥
2
𝑦÷2𝑥
4)
14𝑥
3
𝑦
2
÷7𝑥𝑦
5)
27𝑥𝑦
4
𝑧
3
÷3𝑥𝑦
2
𝑧
2
6)
10𝑥
2
𝑦÷5𝑥
2
7)
24𝑥𝑦÷3𝑥𝑦
8)
14𝑥𝑦
3
÷7𝑥𝑦
9)
0. 25𝑥÷0.5𝑥
10)
1. 24𝑥
2
𝑦÷4𝑥
11)
7𝑥
3
2𝑦
2
÷
7𝑥
2𝑦
12)
8𝑥
3
5
÷
4𝑥
2
15
13)
−16𝑥
5
÷2𝑥
2
14)
−25𝑥
3
𝑦÷(−5𝑦)
15)
𝑥
7
𝑦
5
𝑧
3
÷𝑥
2
𝑦
2
𝑧
2
Q. Solve the following:-
1)
5𝑥
3
+2𝑥×2𝑥
2
+14𝑥
5
÷7𝑥
2
−4𝑥
3
2)
−7𝑥+2𝑥×5−9𝑥×2𝑥÷𝑥+5𝑥
2
3)
9𝑥
3
×2𝑥−2𝑥+7𝑥
3
÷𝑥
2
−12𝑥
4
−4𝑥
4)
−11𝑥+5𝑥×(−2)+12𝑥
3
÷(−2𝑥
2
)+10𝑥
5)
5𝑥𝑦
2
×2𝑥𝑦−7𝑥𝑦+2𝑥
2
𝑦−8𝑥
2
𝑦
2
×𝑦+5𝑥𝑦−8𝑥
2
𝑦
6)
5𝑥𝑧
2
7
−7𝑥𝑧×
5𝑧
2
+7𝑧−0.25𝑥×
2𝑧
2
3
+13. 29𝑧×
5
7
7)
8𝑥
3
𝑧
2
9𝑦
÷
4𝑥𝑧
3𝑦
+
7𝑥
8
×
2𝑥𝑦
21
−
7𝑥
2
15
+
11𝑥
2
6
( )
×0. 25𝑧+(−1. 36𝑥
2
𝑧)
8)
−2. 25𝑝+7. 5𝑞×
2𝑝𝑞
15
−
8𝑝
5
+
7𝑝
5
÷14−14+4. 5𝑝
2
𝑞
9)
11
2
+7𝑥−5𝑥×
15𝑥𝑦
2
4
−0. 35+
7𝑥
2
5
×1. 5𝑦
2
+7𝑥−5
10)
5𝑥𝑦
6
−
9𝑥𝑦
4
( )
×4. 5÷
9
4𝑥𝑦
+6. 5𝑥−6. 5𝑥𝑦+6. 5+
3𝑥
2
Q. Multiply the following:-
1)
5(7𝑥+2)
2)
8(5𝑝−2)
3)
−2(5𝑦+6)
4)
−3(2𝑞−7)
5)
(9𝑥𝑦−7𝑥)4𝑥
6)
−5𝑥(9𝑥+4)
7)
−5𝑝𝑞(−2𝑝
2
−7𝑞
2
)
8)
−7𝑥
2
(5𝑦+4𝑥
2
𝑦)
9)
7𝑥
5
7𝑥
2
−5𝑦
( )
10)
0. 2𝑥(2.5𝑥
2
𝑦−5)
11)
−1. 2(5𝑥−7𝑦)
12)
2𝑥(7𝑥𝑦−2𝑦−7𝑥)
32 SMART EDUCATIONS
13)
−3𝑥𝑦(5−2𝑥+𝑦)
14)
−
2𝑥𝑦
3
9𝑥
5
−9𝑥
2
𝑦
( )
15)
−5(
7𝑥
2
−𝑥−2)
16)
−7𝑥𝑦(2𝑥
2
𝑦−5𝑥𝑦
2
−4𝑥𝑦)
17)
(2𝑥+5𝑦)(7𝑥−5)
18)
(−2𝑥−5𝑦)(4𝑥
2
𝑦+5𝑥𝑦)
19)
5𝑥
2
𝑦(−3𝑥+2𝑥𝑦−3𝑥
2
𝑦)
20)
(5𝑦−7𝑥𝑦)(−2𝑥+5𝑥𝑦−2𝑦)
21)
(−2𝑥𝑦−7𝑥
2
)(5𝑦
2
−7𝑥𝑦
2
)
22)
(7𝑥−2𝑥𝑦)(−2𝑥+7𝑥𝑦−2𝑦)
23)
(2𝑥−7𝑥𝑦−3𝑥
2
)(−5𝑥𝑦+5𝑥)
24)
5𝑥𝑦
2
−7𝑥+
5𝑦
2
( )
5𝑥
2
3
−2𝑥𝑦
( )
25)
7𝑥
2
5
−
2𝑥𝑦
3
( )
2𝑥𝑦
2
3
−2𝑥𝑦+
5
3
( )
26)
−7𝑥
2
𝑦(5𝑥𝑦−2𝑥𝑦
2
)+ 2𝑥𝑦−5𝑥
2
( )
(−4𝑥
2
−4𝑥𝑦+7𝑥)
27)
2𝑥−7𝑦( )−5𝑥+2𝑥𝑦−3( )− 2𝑥+7𝑦( )11𝑦−5+2𝑥𝑦( ) +2𝑥𝑦
28)
−2𝑝𝑞
5
+
5𝑝
8
( )
7
6
−
𝑝𝑞
2
( )
−
3𝑝
2
5
−2𝑝𝑞−
7
3
( )
2𝑝𝑞
3
−
7𝑝
2
𝑞
2
5
−2𝑝𝑞
( )
−7𝑝𝑞+5𝑞
29)
2𝑝𝑥
5
−
7𝑝𝑞𝑥
2
+
5𝑥
3
( )
7𝑝𝑞
2
+
3𝑞𝑥
4
( )
−
8𝑝𝑞
7
−
9
8
( )
−8𝑥
5
+𝑥𝑝−
7𝑥
2
3
( )
−2𝑝𝑥+𝑥
2
30)
−
7𝑞𝑥𝑧
3
+
5𝑥
3
( )
7𝑥𝑦
4
−
2𝑥𝑞
3
+
7𝑝𝑞𝑥
6
( )
−
5𝑝𝑥
3
−
2𝑧𝑥
5
( )
𝑝𝑞𝑥𝑦𝑧
5
−
2𝑝𝑥𝑦
3
+
8𝑝𝑥𝑧
3
( )
Q.
𝑆𝑜𝑙𝑣𝑒 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔. 𝐼𝑓 𝑥=2, 𝑦=−2, 𝑧=1, 𝑝=−3 𝑎𝑛𝑑 𝑞=0
1)
5𝑥
3
+2𝑥×2𝑥
2
+14𝑥
5
÷7𝑥
2
−4𝑥
3
2)
−7𝑥+2𝑥×5−9𝑥×2𝑥÷𝑥+5𝑥
2
3)
9𝑥
3
×2𝑥−2𝑥+7𝑥
3
÷𝑥
2
−12𝑥
4
−4𝑥
4)
−11𝑥+5𝑥×(−2)+12𝑥
3
÷(−2𝑥
2
)+10𝑥
5)
5𝑥𝑦
2
×2𝑥𝑦−7𝑥𝑦+2𝑥
2
𝑦−8𝑥
2
𝑦
2
×𝑦+5𝑥𝑦−8𝑥
2
𝑦
6)
5𝑥𝑧
2
7
−7𝑥𝑧×
5𝑧
2
+7𝑧−0.25𝑥×
2𝑧
2
3
+13. 29𝑧×
5
7
7)
8𝑥
3
𝑧
2
9𝑦
÷
4𝑥𝑧
3𝑦
+
7𝑥
8
×
2𝑥𝑦
21
−
7𝑥
2
15
+
11𝑥
2
6
( )
×0. 25𝑧+(−1. 36𝑥
2
𝑧)
8)
−2. 25𝑝+7. 5𝑞×
2𝑝𝑞
15
−
8𝑝
5
+
7𝑝
5
÷14−14+4. 5𝑝
2
𝑞
9)
11
2
+7𝑥−5𝑥×
15𝑥𝑦
2
4
−0. 35+
7𝑥
2
5
×1. 5𝑦
2
+7𝑥−5
10)
5𝑥𝑦
6
−
9𝑥𝑦
4
( )
×4. 5÷
9
4𝑥𝑦
+6. 5𝑥−6. 5𝑥𝑦+6. 5+
3𝑥
2
33 SMART EDUCATIONS
Q.
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔: −
1)
𝑥+8=12
2)
𝑥−7=20
3)
2𝑥=24
4)
𝑥
2
=10
5)
2𝑥+5=13
6)
3𝑥−8=4
7)
𝑥
3
−5=7
8)
𝑥
4
+7=8
9)
2𝑥
5
−7=3
10)
7𝑥
3
+8=22
11)
5𝑥+7=8+4𝑥
12)
3𝑥−9=11−𝑥
13)
3𝑥
8
−
5
2
=
𝑥
6
−
7
6
14)
7𝑥−
5
6
+
2𝑥
5
=
3
8
−
−7𝑥
6
15)
−5
9
+
4𝑥
9
−𝑥=5−𝑥−
7𝑥
6
+
5𝑥
6
16)
5𝑦
3
+8−
9
10
=
−7𝑦
6
+
𝑦
8
+
3
5
17)
7𝑥+8
−2𝑥−6
=
−5
3
18)
3𝑥+5
6−8𝑥
=
7
−8
19)
−4𝑥−7
3−5𝑥
=
3
8
+
5
6
20)
7
3
=
5𝑥 − 7
−𝑥+8
21)
11𝑥
7
=
−5𝑥
8
+
−7
6
22)
−2𝑥−9
9−2𝑥
=
−5
3
23)
−5(7−𝑥)=7(−𝑥+4)
24)
3(3−2𝑥)=−4(−8𝑥+9)
25)
7(8+5𝑥)= 7(4𝑥−9)
26)
4(3𝑥−5)
3
=
−9(4−2𝑥)
5
27)
8(5−3𝑥)
7
=
4(−7−5𝑥)
3
28)
−3(2−7𝑥)
−5
=
2(−3−3𝑥)
7
29)
4(5−3𝑥)
9
−
4(7−2𝑥)
3
=
3(7−𝑥)
8
−
5(−3−2𝑥)
6
34 SMART EDUCATIONS
30)
−5(6−7𝑥)
8
+
5(𝑥−1)
6
=−7+
2(7−𝑥)
9
−
5(6−𝑥)
6
Q. Solve the following using identities.
1)
5𝑥+2( )
2
2)
2𝑥+3𝑦( )
2
3)
𝑥+5𝑥𝑦( )
2
4)
7𝑥𝑦+2𝑥( )
2
5)
7𝑥−2( )
2
6)
9𝑥−5𝑥𝑦( )
2
7)
4𝑥−2𝑥𝑧( )
8)
6𝑥
2
−2𝑥
( )
2
9)
(5𝑥+2𝑦)(5𝑥−2𝑦)
10)
(7𝑥−3)(7𝑥+3)
11)
(4𝑥
2
−4𝑥)(4𝑥
2
+4𝑥)
12)
(6𝑥𝑦+5𝑥)(6𝑥𝑦−5𝑥)
13)
7𝑥
3
+2𝑥
2
( )
2
+ 4𝑥
3
−3𝑥
2
( )
2
14)
6𝑥
4
+𝑥
3
( )
2
− 5𝑥
4
−8𝑥
3
( )
2
15)
(9𝑥+7𝑦)(9𝑥−7𝑦)+ 2𝑥+3𝑦( )
2
− 9𝑥−5𝑥𝑦( )
2
−(2𝑥𝑦−7𝑥)
2
+5𝑥
2
𝑦
35 SMART EDUCATIONS
IRRATIONAL NUMBER
IRRATIONAL NUMBER:-
2, 3, 5, 6, ..........π.......
Q. Solve the following:-
1)
3 5+5 5
2)
7 3−2 3+8 3
3)
4 2+ 2−3 2
4)
7+ 7
5)
5 7+2 5−3 7
6)
− 5+3− 5
7)
7−7 3+5 3
8)
5 5−7 3+ 3
9)
3 8+2 2− 2
10)
8+ 8+ 8− 2
11)
7 18+3 3+ 18
12)
7+ 7+2 28
13)
7 20−3 5+4 45
14)
− 8+7 28+ 18
15)
28− 8+ 2
16)
3× 3
17)
5× 5
18)
7× 7
19)
5 3×2 3
20)
−7 2×5 2
21)
3 3×5 2
22)
6 5×3 2
23)
5 14×3 2
24)
5× 3
25)
4 3×3 5×2 7
26)
5( 7− 3)
27)
−35 2−2 3
( )
28)
42 7+2 5
( )
29)
2 33 2−5 7
( )
+ 6
30)
−3 22 3−5 7
( )
31)
3 3 5+2 7− 3
( )
32)
−2 32 5+7 3
( )
33)
5 22 5−7 3
( )
34)
2 3+3 2
( )
5 3+7 2
( )
35)
7 3−5 2
( )
3 2−2 3
( )
36)
2 7−5 2
( )
2 5−7 2
( )
−2 10
37)
−2 3+2 6
( )
7 2− 2+8 5
( )
38)
2 6+5 3−7
( )
3 2−7+2 3
( )
39)
2 7−5 5
( )
−4 3−5 7+ 5
( )
40)
−5 23 2−5 3
( )
−2 37 2−6 3
( )
+ 6+3
( )
−4 3−2 5
( )
− 2− 3+ 6
36 SMART EDUCATIONS
PLAIN FIGURES & 3D FIGURES
1. PLAIN FIGURES
Name
Figure
Properties
Dimensions
CIRCLE
Radius = r
Diameter = d
TRIANGLE
Side
1
= a
Side
2
= b
Side
3
= c
QUADRILATERAL
Side
1
= a
Side
2
= b
Side
3
= c
Side
4
= d
PARALLELOGRAM
* Opposite sides are
parallel.
* Opposite sides are
equal.
Side
1
= a
Adjacent Side = b
RECTANGLE
* Opposite sides are
equal.
* All angles are 90
0
.
Length = l
Breadth = b
SQUARE
* All sides are equal.
* All angles are 90
0
.
Side = a
RHOMBUS
* All sides are equal.
Side = a
KITE
* Adjacent sides are
equal.
Side
1
= a
Opposite Side = b
TRAPEZIUM
* One pair of opposite
sides are parallel.
Parallel side
1
= p
1
Parallel side
2
= p
2
Non Parallel side
1
= a
Non Parallel side
2
= b
37 SMART EDUCATIONS
2. 3D FIGURES
Name
Figure
Properties
Dimensions
Cuboid
* 6 Rectangular
faces
* 12 Edges
* 8 Vertices
Length = l
Breadth = b
Height = h
Cube
* 6 Square faces
* 12 Edges
* 8 Vertices
Edges/Sides = a
Cylinder
* 2 circular faces
and 1 Curved Face
Radius = r
Diameter = d
Height = h
Cone
* 1 circular face and
1 Curved Face
Radius = r
Diameter = d
Height = h
Slant height = l
Sphere
* Curved Face
Radius = r
Diameter = d
Hemisphere
* 1 circular and 1
Curved Face
Radius = r
Diameter = d
38 SMART EDUCATIONS
MENSURATION
Name
Figure
Perimeter
Area
CIRCLE
2π𝑟
Note:-
𝑟=
𝑑
2
π𝑟
2
TRIANGLE
* Isosceles Triangle = 2 sides are equal.
* Equilateral Triangle = 3 sides are
equal
* Right Triangle = 1 angle is 90
0
𝑎+𝑏+𝑐
[For Right Triangle:-
]
ℎ
2
=𝑝
2
+𝑏
2
1
2
×𝑏𝑎𝑠𝑒×ℎ𝑒𝑖𝑔ℎ𝑡
QUADRILATERAL
𝑎+𝑏+𝑐+𝑑
1
2
×𝑐𝑜𝑚𝑚𝑜𝑛 𝑏𝑎𝑠𝑒
× 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 ℎ
1
+ℎ
2
( )
PARALLELOGRAM
2(𝑎+𝑏)
𝑏𝑎𝑠𝑒×𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 ℎ𝑒𝑖𝑔ℎ𝑡
RECTANGLE
2(𝑙+𝑏)
𝑙×𝑏
SQUARE
4×𝑠𝑖𝑑𝑒𝑠
𝑠𝑖𝑑𝑒×𝑠𝑖𝑑𝑒
RHOMBUS
4×𝑠𝑖𝑑𝑒𝑠
𝑏𝑎𝑠𝑒×ℎ𝑒𝑖𝑔ℎ𝑡
1
2
× 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙
1
×𝑑
2
KITE
2(𝑎+𝑏)
1
2
× 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙
1
×𝑑
2
TRAPEZIUM
𝑎+𝑏+𝑝
1
+𝑝
2
1
2
×ℎ× 𝑝
1
+𝑝
2
( )
39 SMART EDUCATIONS
Name
Perimeter
Area
Volume
Cuboid
4𝑙+𝑏+ℎ( )
* For 6 Faces
2𝑙𝑏+𝑏ℎ+ℎ𝑙( )
* For 4 Faces[LSA]
2𝑙+𝑏( )ℎ
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟×ℎ
* For 5 Faces
2𝑙+𝑏( )ℎ+𝑙𝑏
𝑙×𝑏×ℎ
Cube
12×𝑎
* For 6 Faces
6𝑎
2
* For 4 Faces[LSA]
4𝑎
2
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟×ℎ
* For 5 Faces
5𝑎
2
𝑎
3
Cylinder
* For 2 Caps
2π𝑟𝑟+ℎ( )
* For 1 Cap
π𝑟2ℎ+𝑟( )
* For 0 Cap[CSA]
2π𝑟ℎ
π𝑟
2
ℎ
Cone
* For 1 Cap
π𝑟𝑟+𝑙( )
* For 0 Cap
π𝑟𝑙
𝑙
2
=𝑟
2
+ℎ
2
𝑣𝑜𝑙𝑢𝑚𝑒=
1
3
π𝑟
2
ℎ
Sphere
4π𝑟
2
4
3
π𝑟
3
Hemisphere
*For 1 Cap
3π𝑟
2
For 0 Cap
2π𝑟
2
2
3
π𝑟
3
40 SMART EDUCATIONS
Q. Convert the following unit as directed below:-
1) 120 cm to m
2) 5 m to cm
3) 6 km to m
4) 1250 m to km
5) 7 cm to mm
6) 70 cm to m
7) 8 kg to gm
8) 6 l to ml
9) 1500 gm to kg
10) 3600 ml to l
11) 750 paise to Rs
12) 1200 gm to kg
13) 80 cm to m
14) 4 m to cm
15) 6 km to m
1. Find the area of the circle whose diameter is 10 cm.
2. Find the area of the circle whose circumference is 22 cm.
3. If area and circumference of a circle are numerically equal then find its diameter.
4. If the area of a circle is 154 cm
2
then find its circumference.
5. If the radius of a circle is doubled then how many times will the area increase?
6. If the radius of a circle is increased by 3.5 cm then by how much will the circumference
of the circle increase?
7. If the radius of a circle is decreased by 7 cm then by how much will the circumference of
the circle decrease?
8. If the radii of two circles are 5 cm and 8 cm then find the ratio of their circumference.
9. If the ratio of the radii of the two circles are 6:2 then find the ratio of their circumference.
10. While finding the area of a circle with radius 8 cm but it was misread as 6 cm then what
is the difference between the right answer and wrong answer?
11. Find the perimeter of the triangle whose sides are 3 cm, 4 cm and 5 cm.
12. If the perimeter of the triangle is 24 cm and the measure of the two sides are 8 cm and
10 cm then find the third side.
13. Find the area of a triangle whose base is 6 cm and the height is 5 cm.
14. Find the height of a triangle whose area is 24 cm
2
and the base is 6 cm.
15. Find the base of a triangle whose area is 52 cm
2
and the height is 8 cm.
16. Find the base of a triangle whose area is 48 cm
2
and the base of the triangle 2 more
than the two times of the height.
17. In a right triangle if the base and perpendicular are 7 cm and 24 cm respectively then
find the hypotenuse.
18. In a right triangle if the base and hypotenuse are 8 cm and 10 cm respectively then find
the perpendicular. 12 5 13
19. If the sum of two sides (other than hypotenuse) is 17 cm and the hypotenuse is 13 cm
then find the other two sides of the right triangle.
20. Find the area of a parallelogram whose base and height are 5 cm and 12 cm.
41 SMART EDUCATIONS
21. Find the base of a parallelogram whose area is 20 cm
2
and the height is 5 cm.
22. One side of a parallelogram is 8 cm and the perimeter is 36 cm. If the height of the
parallelogram corresponding to the shorter side is 5 cm then find the height
corresponding to the longer side.
23. FInd the area of a rectangle whose length and breadth are 5 cm and 7 cm.
24. Find the Perimeter of a rectangle whose length is 8 cm and the breadth is 4 more than
the length.
25. If the perimeter of a rectangle is 24 cm and the breadth is 10 cm then find its area.
26. If the area of a rectangle is 60 cm
2
and the base is 12 cm then find its diagonal.
27. If the length and breadth of a rectangle are doubled then what does change in area?
28. Find the area of the square whose one side is 5 cm.
29. Find the perimeter of the square whose one side is 8 cm.
30. If the perimeter of a square is 28 cm then find its area.
31. If the area of a square is 169 cm then find its perimeter.
32. If the perimeter of a square is numerically equal to that of area then find its side.
33. If the side of the square is tripled then how many times will the area increase?
34. If the perimeter of a circle with radius 7 cm and that of a square are equal then find the
area of the square.
35. Find the area of a rhombus whose diagonals are 8 cm and 6 cm.
36. If the area of a rhombus is 56 cm
2
and one diagonal is 8 cm then find the other diagonal.
37. FInd the area of a rhombus whose side and one diagonal are 5 cm and 8 cm
respectively.
38. FInd the area of a trapezium whose parallel sides are 8 cm and 6 cm and height of the
trapezium is 5 cm.
39. If the area of a trapezium is 98 cm
2
and the two parallel sides are 15 cm and 13 cm then
find the height.
40. If the area of a trapezium is 144 cm
2
and one parallel side is 18 cm and the distance
between the two parallel lines is 9 cm then find the other parallel side.
41. Find the total surface area of a cuboid whose dimensions are 8 cm, 6 cm and 5 cm.
42. Find the lateral surface area of a cuboid whose dimensions are 8 cm, 6 cm and 5 cm.
43. Find the total surface area of a cuboidal box which is open on top whose dimensions are
8 cm, 6 cm and 5 cm.
44. Find the volume of a cuboid whose dimensions are 8 cm, 6 cm and 5 cm.
45. Find the total surface area of a cube whose one side is 8 cm.
46. Find the lateral surface area of a cube whose one side is 8 cm.
47. Find the total surface area of a cubical box which is open on top whose one side is 8 cm.
48. FInd the volume of the cube whose edges are 7 cm.
49. Find the total surface area of a cylinder whose diameter is 14 cm and the height is 10cm.
50. Find the curved surface area of a cylinder whose radius is 14 cm and the height is 10cm.
51. Find the total surface area of a cylindrical container which is open on the top whose
circumference of the base is 14 cm and the height is 10 cm.
52. FInd the volume of the cylinder whose radius and height are 3.5 cm and 8 cm
respectively.
53. Find the total surface area of a cone whose slant height is 14 cm and the radius is 5 cm
42 SMART EDUCATIONS
54. Find the curved surface area of a cone whose slant height is 14 cm and area of the base
is 154 cm
2
55. FInd the volume of the cone whose slant height is 13 cm and radius is 5 cm.
56. Find the surface area of a sphere whose radius is 14 cm.
57. Find the volume of a sphere whose diameter is 14 cm.
58. Find the total surface area of a hemi sphere whose radius is 14 cm.
59. Find the curved surface area of a hemi sphere whose radius is 3.5 cm.
60. Find the volume of a hemi sphere whose diameter is 14 cm.
43 SMART EDUCATIONS
GEOMETRY
1. A line segment has ………….. end points.
2. An angle has ……………. arms.
3. Sum of linear pair angles is……………
4. Vertically opposite angles are………….
5. Co - interior angles are ……………..
6. Alternate interior angles are ……………..
7. Corresponding angles are ………………..
8. Name the angle which is less than 90
o
.
9. Name the angle which is less than 360
o
but more than 180
o
.
10. Name the angle which is equal to 90
o
.
11. Name the angle which is less than 180
o
but more than 90
o
.
12. Name the angle whose measure is 180
o
.
13. If the sum of the two angles is 180
o
then what are they called?
14. If the sum of the two angles is 90
o
then what are they called?
15. What does perpendicular mean?
16. Find the complement of 30
o
.
17. Find the supplement of 70
o
.
18. If a ray divides an angle into two equal angles then what is the line called?
19. What is the sum of exterior angles in a triangle?
20. What is the sum of interior angles in a triangle?
21. If two sides of a triangle are equal then what type of triangle is this?
22. Find the measure of all angles of an equilateral triangle.
23. Find the measure of all angles of a right angled isosceles triangle.
24. Name all the marked angles in the following figure:-
25. Find ㄥACB in the following figure.
44 SMART EDUCATIONS
26. Find in the following figure:-
𝑥
27. Find all the other angles in the following figure:-
28. If two angles of a triangle are 60
o
and 50
o
then find the other angle.
29. Let ㄥAOB and ㄥOBC are alternate interior angles and ㄥAOB = 50
o
then find ㄥOBC.
30. Let ㄥAOB and ㄥOBC are co-interior angles and ㄥAOB = 60
o
then find ㄥOBC.
31. Let ㄥAOB and ㄥOCD are corresponding angles and ㄥAOB = 450
o
then find ㄥOBC.
32. Let ㄥAOB and ㄥOBC are linear angles and ㄥAOB = 80
o
then find ㄥOBC.
33. Let ㄥAOB and ㄥCOD are vertically opposite angles and ㄥAOB = 70
o
then find ㄥOBC.
34. Find all the other angles in the following figure:-
45 SMART EDUCATIONS
35. Find all the other angles in the following figure:-
36. Find all the other angles in the following figure:-
37. Find all the other angles in the following figure if ㄥADB = 100
o
, ㄥDAE = 35
o
, ㄥBCF =
80
o
and AE ∥ BC
38. In the following figure ㄥPAD = 55
o
and PK and DK are the bisectors of ㄥAPD and
ㄥADP respectively then find the ㄥPKD :-
39. In the following figure AP = AD, ㄥPAD = 55
o
and PK and DK are the equal bisectors of
ㄥAPD and ㄥADP respectively then find all the other angles.
46 SMART EDUCATIONS
40. In the following figure AK = BK, DB = NB, ㄥAKB = 70 and ㄥKBM = 35
o
then find all the
other angles :-
47 SMART EDUCATIONS
PERCENTAGES
1. Solve the following:-
1) 5% of 1200
2) 6% of 1800
3) 15% of 2500
4) 9% of 2200
5) 33% of 500
6) 30% of 20
7) 12% 2300
8) 15% of 12000
9) 18% of 4000
10) 28% of 46500
11) 8% of 1800
12) 45% of 12000
13) 11% of 34000
14) 17% of 6500
15) 2% of 3650
2. Convert the following into percentage:-
1) 30 out of 150
2) 70 out of 120
3) 40 out of 80
4) 400 out of 500
5) 200 out of 250
6) 7 out of 10
7) 1 out of 10
8) 12 out of 30
9) 18 out of 25
10) 12 out of 20
11) 18 out of 20
12) 1300 out of 5000
13) 600 out of 4500
14) 3 out of 15
15) 14 out of 15
3. If a mall allows a 20% discount on every item then what price should a buyer pay
for the following:-
1) Price of a jeans = 1200
2) Price of a shirt = 800
3) Price of a shoe = 700
4) Price of a cap = 150
5) Price of a Tie = 80
6) Price of a bag = 1600
7) Price of a saree = 3000
8) Price of a kurti = 1800
9) Price of a skirt = 2000
10) Price of a raincoat = 700
11) Price of a sweater = 900
12) Price of a towel = 250
13) Price of a curtain = 1900
14) Price of a gloves = 300
4. If a mall allows a 20% tax on every item then what price should a buyer pay for
the following:-
48 SMART EDUCATIONS
1) Price of a jeans = 1200
2) Price of a shirt = 800
3) Price of a shoe = 700
4) Price of a cap = 150
5) Price of a Tie = 80
6) Price of a bag = 1600
7) Price of a saree = 3000
8) Price of a kurti = 1800
9) Price of a skirt = 2000
10) Price of a raincoat = 700
11) Price of a sweater = 900
12) Price of a towel = 250
13) Price of a curtain = 1900
14) Price of a gloves = 300
5. If 40% is needed to pass the following exams with different total marks then find
the passing marks for each:-
1) Out of 700
2) Out of 1200
3) Out of 500
4) Out of 250
5) Out of 800
6) Out of 1500
6. If the marks obtained by a student in following exams with different total marks
are given then find the percentage in each exam:-
7) 500 out of 700
8) 700 out of 1200
9) 200 out of 500
10) 100 out of 250
11) 700 out of 800
12) 400 out of 1500
7. In an office 5% salary is increased for every employee then find the new salary if
the old salary is given for every employee.
1) 12000
2) 18000
3) 15000
4) 10000
5) 8000
6) 22000
7) 21000
8) 20000
9) 25000
10) 9000
11) 17000
12) 19000
13) 30000
14) 35000
15) 55000
49 SMART EDUCATIONS
8. In an office 5% salary is increased for every employee then find the old salary if
the new salary is given for every employee.
1) 12000
2) 18000
3) 15000
4) 10000
5) 8000
6) 22000
7) 21000
8) 20000
9) 25000
10) 9000
11) 17000
12) 19000
13) 30000
14) 35000
15) 55000
9. In an office the salary of all employees changed as given below, then find the
percentage of increase or decrease in their salaries.
1) 12000 to 14000
2) 18000 to 22000
3) 10000 to 15000
4) 8000 to 14000
5) 21000 to 18000
6) 20000 to 22000
7) 9000 to 15000
8) 17000 to 15000
9) 30000 to 24000
10) 35000 to 28000
11) 15000 to 18000
12) 25000 to 21000
13) 22000 to 25000
14) 19000 to 20000
10. Find the Profit or Loss percentage in the following situation:-
1) CP = 800
SP = 900
2) CP = 1200
SP = 1250
3) CP = 1800
SP = 2000
4) CP = 1400
SP = 1200
5) CP = 700
SP = 650
6) CP = 900
SP = 1000
7) CP = 1250
SP = 1500
8) CP = 1100
SP = 1350
9) CP = 2000
SP = 1920
10) CP = 180
SP = 210
11) CP = 110
SP = 105
12) CP = 1700
SP = 1785
13) CP = 2300
SP = 2290
14) CP = 450
SP = 555
15) CP = 7360
SP = 7500
50 SMART EDUCATIONS
11. If a shopkeeper wants to earn 8% on each item then at how much price should
he sell the following items:-
1) Price of a jeans = 1200
2) Price of a shirt = 800
3) Price of a shoe = 700
4) Price of a cap = 150
5) Price of a Tie = 80
6) Price of a bag = 1600
7) Price of a saree = 3000
8) Price of a kurti = 1800
9) Price of a skirt = 2000
10) Price of a raincoat = 700
11) Price of a sweater = 900
12) Price of a towel = 250
13) Price of a curtain = 1900
14) Price of a gloves = 300
12. If the rate of interest in a bank is 7% annually as simple interest in saving account
then find the following:-
1) P = 7000
t = 2 Years
A = ?
2) P = 1200
t = 3 Years
A = ?
3) P = 12000
t = 3 Years
SI = ?
4) P = 6500
t = 2 Years
SI = ?
5) P = 25000
t = 3 Years
A = ?
6) P = 12500
t = 2 Years
SI = ?
7) P = 13525
t = 3 Years
A = ?
8) P = 16352
t = 2 Years
SI = ?
9) P = 7525
t = 4 Years
A = ?
10) P = 10568
t = 2 Years
A = ?
51 SMART EDUCATIONS
13. If the rate of interest of a loan company is 3% p.a as compound interest then find
the following:-
11) P = 7000
t = 2 Years
A = ?
(Compounded annually)
12) P = 1200
t = 3 Years
A = ?
(Compounded half yearly)
13) P = 12000
t = 3 Years
CI = ?
(Compounded annually)
14) P = 6500
t = 2 Years
CI = ?
(Compounded half yearly)
15) P = 25000
t = 3 Years
A = ?
(Compounded quarterly)
16) P = 12500
t = 2 Years
CI = ?
(Compounded half yearly)
17) P = 13525
t = 3 Years
A = ?
(Compounded annually)
18) P = 16352
t = 2 Years
CI = ?
(Compounded quarterly)
19) P = 7525
t = 4 Years
A = ?
(Compounded half yearly)
20) P = 10568
t = 2 Years
A = ?
(Compounded quarterly)
14. If the rate of production of viruses is 5% per hour then find the total number of
viruses if the current number of viruses are given:-
1) P = 300
t = 2 hr
2) P = 40
t = 3 hr
3) P = 700
t = 3 hr
4) P = 500
t = 4 hr
5) P = 400
t = 1 hr
6) P = 1225
t = 4 hr
7) P = 1700
t = 5 hr
8) P = 1200
t = 3 hr
9) P = 1850
t = 2 hr