Integrated mathematics scheme: IMS T2 - National STEM Centre

Answers
M41 A. 1.
5.
9.
13.
Some of the facts which should appear from exploration
are:
(i) xn~ 00 as n~ 00 if x> 1
(ii) x n ~ 0 as n ~ 00 if x < 1
(iii) XO = 1
(iv) x m • x n = x m + n
(v) (xmt = x mxn = (xn)m
4 2 2. 7 2 3. 52 4. 6 2
(2·5)2 6. 9x9 7. 10x10 8. 12 x 12
8 3 10. 11x11x11 11. 53 12. 6 3
(4'5)3 14. (2·8) cubed 15. 31 x 31 x 31
B. 1.
6.
11.
C. 1.
2.
3.
8 2. 9 3. 125 4. 64 5. 1000
2·25 7. 484 8. 4913 9. 18·49 10. 1936
175·616 12. 0·64 13. 0·343 14. 0·04 15. 0·027
6 2 7 2 8 2 9 2 10 2
36 49 64 81 100
11 13 15 17 19 ~ differences
20 2 21 2 22 2 23 2 . .. etc.
400 441 484 529
41 43 45
1.1 2 1.2 2 1.3 2 1.4 2 . .. etc.
1·21 1·44 1·69 1·96
0·23 0·25 0·27 ... etc.
4. (a) Cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
(b) 7 19 37 61 91 ~ differences
12 18 24 30. . . etc.
666
(c) The 6 times table appears. Differences of this are all 6s.
M42 A. 1. (a) 7 7 = 823543 (b) Also 7 7 in fact 7 8 -T 7 (c) Also gives 7 7
2. (a) 3 8 (b) 3 16 (c) 3 8 = 6561
3. (a) (1·6)10 (b) (1·6)18 (c) (1·6)10
4. (a) (0·9)12= 0·2824295 (b) (0·9)12 (c) (0·9)16
B. Some calculators will set in the constant multiplier automatically.
Others will require a double press on the [K] button. There are also
other systems. This should be checked before starting the exercise.
1. See above
2. (a) 20·4, 27,2, 37·4, 54·4, 27·88
(b) 2401 (c) 32 768 (d) 15·625 (e) 0·03125
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