Transition Year Maths 9. Pi
1. 3.18918 2. 15.700m 3. 15.714m 4. 15.708m 5. 0·159; 0·796; 1·591; 3·183 6. 0·1736; 0·3420; 0·8415; 0·9092 7. 0·8415; 0·9093; 0·1411; –0·7568 8. Because 1 radian = 57·3° 9. Yes
10.
22 7
11. Plot (1, 1); (1, –1); (2, 0·5); (2, –0·5); (3, 0·33) . . . and so on
8. 2,598,960; 1,287; 575,757; 65,780; 249,900; 2,349,060; 1,712,304; 48 + 3x2
9. (a) x3 (b) x5 (c) x4
+ 10x4 + 8x3
(d) 8x3
y + 3xy2 + 40x3
y + 24x2 –36x2 (e) 1 + 10x + 40x2 + y3 + 80x2 y2 y + 54xy2 + 80x3
+ 32xy3 –27y3
+ 80x + 32 + 16y4
+ 80x4 + 32x5
12. Fermat’s Last Theorem 1. 93
2. 53 3.
4.
10. Probability 1. 1 in 6; 1 in 6; 1 in 2; 5 in 6; 2 in 6
2. 3.
4. 5.
7. 8.
9. 10.
1 6
1 2 1 6
1 8
;;; 1 3
1 6
1 52 ;;; ; ;;;5 1 52
;;; ;; ; 1 3
1 36 ;;;;
3 8
6
8 1 8
16 ;
16 6 16
; 11. Combinations and Permutations
1. 4, 12, 24, 24 2. 4, 6, 4, 1 3. 40,320 4. 88
= 16,777,216
5. 65,780 6. 24; 13,824; 12,144 7. 210; 126; 112
3 8
11 36 0 25
1 8 0
36 1 5 52
1 2
3 4
48 52
8 52
1 6
;
1 3
12 52
; 1 26 13. Chaos
1. –·91, –·17, –·97, –·06, –·99, . . . . . . –1, 0, –1, 0
2. 3, 8, 63, 3968, . . . . . . most calculators will do about 8
3. –1·84, 1·38, –0·08, –1·99, 1·97, 1·89, 1·6, 0·57, –1·67, . . . . . .
4. (a) 0·25, 0·0625, . . . . . . (b) 0·125, 0·0019, . . . . . . (c) 2, 0·5, 2, 0·5, 2, 0·5, . . . . . . (f) chaotic (g) chaotic
5. (a) oscillator (b) chaotic
(c) oscillator (h) stable (d) stable
(e) oscillator
6. 500, 250, 125, 62·5, 31·25, 15·625, . . . . . . 7. 0·078, 0·289, 0·822, 0·585, 0·970, . . . . . . Chaotic
8. 0·059, 0·016, 0·415, 0·728, . . . . . . 0·61, 0·70, 0·61, 0·70, . . . . . . oscillator
9. 0·039, 0·075, 0·139, 0·239, . . . . . . 0·5, 0·5, 0·5, . . . . . . stable
164 (i) oscillator
= 83 + 63
+ 63 = 73 + 13 –2
It’s the only number between a cube and a square
(i) 1, 1, 2, 2 (ii) 6, 5, 3, 10 (iii) 3, 3, 3, 4 or 1, 1, 1, 2 (iv) 5, 5, 2, 6
5. Eight 6. 1, 32, 243, 1024, 3125, 7776. 16807, 32768, 59049, 100,000 95
+ 85 + 65 + 407 = 105
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