Integrated mathematics scheme: IMS T2 - National STEM Centre

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B. 1. 484 2. 1296 3. 1936 4. 3249 5. 3721 6. 77·44 7. 56·25 8. 4·84 9. 75·69 10. 98·01 c. It is true because the squares end in 0, 1, 4, 5, 6 or 9. M32 A. 1. 0·09 2. 0·49 3. 0·81 4. 0·36 5. 0·64 6. 0·7225 7. 0·3969 8. 0·1764 9. 0·0225 10. 0·0064 B. 1. 0·04 2. 0·16 3. 0·25 4. 0·0484 5. 0·5625 6. 0·6724 7. 0·8836 8. 0·0324 9. 0·0064 10. 0·0036 c. 0·2~0·04 0·71 ~ 0·50 0·4~0·16 0·5~ 0·25 0·63~0·40 0·3~0·09 0·25~0·06 M33 A. 1. 49 2. 144 3. 144 4. 324 5. 900 6. 36 7. 22·09 8. 88·36 9. 156·25 10. 174·24 B. If you have a calculator without I x 2 1 or brackets you will have to use something like ~ [K] la El ~ [±] ~ 5J ~ ~ for the decimal squares.* 1. 25 (appears as 24·999999.) 2. 74 3. 72 4. 170 5. 452 6. 18·72 7. 11·45 8. 44·26 9. 79·93 10. 101·7 (a + b)2 = a 2 + b 2 is only true if a = 0 or b = O. c. 1. II III IV V VI VII VIII (col lv-col VII) a b a+b (a + b)2 a 2 b 2 a 2 + b 2 (a + b)2 - (a 2 + b 2 ) 2 3 5 25 4 9 13 12 4 7 11 121 16 49 65 56 5 3 8 64 25 9 34 30 2·5 4 6·5 42·25 6·25 16 22·25 20 1·7 2·8 4·5 20·25 2·89 7·84 10·73 9·52 3·6 6·6 10·2 104·04 12·96 43·56 56·52 47·52 4·2 0·8 5·0 25 17·64 0·64 18·28 6·72 2. The numbers in col VIII are twice the product of a and b, e.g. (2 x 3) x 2 = 12, (1·7 x 2·8) x 2 = 9·52. This is explained in the next section. *If you press ~ [K] [;] [±] [ft] [K] [;] you get the square of (a 2 + b). 27
M34 A. All drawings. B. These should be demonstrated by the teacher and related to drawings. The actual steps are quite simple, but important. C. 1. They are all examples of (a + b)2 where a + b = 10. 2. (c) should be d + 14c +49. 3. This exercise shows that one can get by sometimes without using a calculator. P22 A. 1. 14~ 196 7·6~57·76 33~ 49~2401 3·7~ 13·69 2-3~ 5·29 8·8~ 77·44 60~3600 0·83~ 0·6889 0·35 ~ 0·1225 2. (a) 84100 (b) 8-41 (c) 0-0841 (d) 0·000841 3. (a) 532900 (b) 53-29 (c) 0·5329 (d) 0·005329 4. (a) 1444 (b) 144400 (c) 0·1444 (d) 0·001444 B. 1. 16 2. 5041 3. 4624 4. 1369 5. There isn't one unless you count 7744. C. 1. 44 2. 65 3. 9·3 4. 9·8 5. 22 6. 20 7. 1·5 8. 0·43 9. 0-66 10. 0-75 P23 This exercise introduces the new concept of a square root. If a calculator with a ) button is not available tables will be needed. The best type are Basic Mathematical Tables (Bell & Hyman) which give) together with other functions in a form suited to calculator use. Some care will be needed where, for example, square roots of 3 figure numbers are to be found. The tables will give the square root of 8,3, 83 and 830 but if )835 is 28 required we use )8·3 = 2,881, )8·4 = 2·898 so )8·35 = 2·890 (about halfway). Thus )835= 28·9. A more complicated method of finding square roots using the multiplication tables or 4 function calculator is divide and average, taking a rough estimate from the ) tables. E.g. wanted ) n. Estimate x. Now follow the sequence [Q] El [K] [±] [K] El [2J ~. This gives at least two more decimal places of the square root. The process is repeated with the latest answer used for x and so on until a constant result is achieved. (This may not be as easy as it sounds.) A. B. 1. 7 2. 11 3. 22 4. 40 5. 44 6. 85 7. 58 8. 92 9. 4·1 10. 7·5 11. 6-1 12. 5·8 13. 1·3 14. 1·9 15. 1-2 16. 2·1 17. 0-46 18. 0·85 19. 0·9 20. 0-49 1. 7 2. 17 3. 21 4. 23 5. 25 6. 32 (31-62) 7. 57 8. 75 (74-53)
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Integrated mathematics scheme: IMS T2 - National STEM Centre

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