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Answers

Chapter 1: Patterns in Mathematics Practice Time 1C
1. 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
Let’s Recall Multiplying by 6 and adding 1 will give a centred hexagonal number
starting from 7.
2. 64 3. Pair of triangular numbers
1. , ; 1 1 1 1 1 1, yes 4. An even number
6. 100th triangular number = 5050
1000th triangular number = 500500
1
2. , ; 1 2 3 4 5 6, yes Triangular number = 2 × Product of dots along length and breadth of
the rectangle so formed.
8. 65 = 8 + 1 = 7 + 4 2
2
2
2
3. ; 3 5 7 9 11, yes 11. 99999 × 2 = 199998
9999999 × 2 = 19999998
12. 11111 × 88888 = 987634568
4. ; 4 7 10 13 16, yes 111111 × 888888 = 98765234568
1111111 × 8888888 = 9876541234568
13. 12345 × 8 + 5 = 98765
123456 × 8 + 6 = 987654
5. ; 5 9 13 17 21, yes 1234567 × 8 + 7 = 9876543
12345678 × 8 + 8 = 98765432
14. 65359477124183 × 68 = 4444 4444 4444 4444
65359477124183 × 85 = 5555 5555 5555 5555
Practice Time 1A 65359477124183 × 102 = 6666 6666 6666 6666
1. (a) 12, 28 (b) 11, 22, 29, 37 2. (a) 30, 28 (b) 73, 66, 55 65359477124183 × 119 = 7777 7777 7777 7777
3. 987654321 × 9 = 8888888889 65359477124183 × 153 = 9999 9999 9999 9999
987654321 × 18 = 17777777778 Practice Time 1D
987654321 × 27 = 26666666667 1. Nonagon, decagon 2. Brick walls
987654321 × 36 = 35555555556 3. 3, 4, 5, 6, ...
987654321 × 45 = 44444444445 4. 1, 4, 9, 16, 25
987654321 × 54 = 53333333334 This is the sequence of square numbers.
987654321 × 63 = 62222222223 7. A honeycomb is hexagonal because hexagons efficiently cover a surface
987654321 × 72 = 71111111112 without leaving gaps, using the least amount of material to enclose
987654321 × 81 = 80000000001 the maximum area. One can create a similar pattern using triangles or
4. 5 = 1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 2 = 1 + 1 + 2 + 1 = 1 + 2 + 1 + 1 squares.
= 2 + 1 + 1 + 1 = 1 + 2 + 2 = 2 + 1 + 2 = 2 + 2 + 1 = 1 + 1 + 3 8. 3, 12, 48, ... Next number is obtained by multiplying previous number by 4.
= 1 + 3 + 1 = 3 + 1 + 1 = 2 + 3 = 3 + 2 = 1 + 4 = 4 + 1 Brain Sizzlers
5. 89 ways
Think and Answer

1 3 6 10 15; triangular numbers
Mental Maths
1. Even numbers 2. 343 3. Hexagonal
Maths Fun
1 6 16 31 51
Practice Time 1B
1. (a) 10, 66, 100, 28, 64 (b) 25, 81, 35, 55, 49, 27, 15 13
(c) 10, 15, 28, 55, 66 (d) 25, 81, 100, 64, 49
(e) 64, 27 ( f ) 35 (g) 15, 28, 66
21
3 2 1 8
1
4. 5
Chapter Assessment
A. 1. (c) 2. (d) 3. (b) 4. (a) 5. (a)
36
36 B. 1. Virahanka number 2. 8 3. a square number
The numbers 1 and 1225 are triangular as well as square. 4. 25 + 16 + 9 + 4 + 1 = 55 5. triangular
6. Sum of consecutive centred hexagonal numbers is a cubic number. C. 1. False 2. False 3. False 4. True
Quick Check D. 1. (c) 2. (d) 3. (a) 4. (b)
E. 1. 9 × 9 = 81
99 × 99 = 9801
999 × 999 = 998001
9999 × 9999 = 99980001
99999 × 99999 = 9999800001

309 Answers