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Friday, January 25, 2013                           AIRIL AHMAD
Friday, January 25, 2013                           INDICES               HJ. AIRIL AHMAD                                  ...
Friday, January 25, 2013                                          6                                      2      23= 2 x 2 ...
Friday, January 25, 2013     Indices                       is read as 3 to the power              4     3                 ...
Friday, January 25, 2013       Repeated Multiplication        63= 6 x 6 x 6        25= 2 x 2 x 2 x 2 x 2        (-g)4= ...
Friday, January 25, 2013       Repeated Multiplication       9  x9x9=       25 x 25 x 25 x 25 x 25 =        (-kg) x (-k...
Friday, January 25, 2013  By using the calculator find the values         of the following indices       1. 65 =          ...
Friday, January 25, 2013       Expressing a certain number in the       index notation.   Example 1: Express 32          ...
Friday, January 25, 2013  Exercise  Express each of the following in the index notation   with the base given in the brac...
Friday, January 25, 2013              MULTIPLICATION               OF NUMBERS IN              INDEX NOTATION              ...
Friday, January 25, 2013     Example:   1.     32 x 33 =       3 ×x 3 × 33                           3 x 3× 3 × 3     ...
Friday, January 25, 2013       Example: 3.   g 4 x g5 =          g × g × g × g ×xgg×xgg×xgg×xgg xgg                      ...
Friday, January 25, 2013       Verify a x a = a    m    n         m+n   1.          5 x 5 =                   4       5  ...
Friday, January 25, 2013       Exercise       Pg 103       Ex.5.2A       1abcdef       2abc                           ...
Friday, January 25, 2013             MULTIPLICATION OF               NUMBERS OR             ALGEBRAIC TERMS            WIT...
Friday, January 25, 2013 Example:1. 3a2 x                  2a =                             3  (3x2) a2+3 =6a52.      6f...
Friday, January 25, 2013 Exercise:1. 9d2 x 2d10= (9x2) d2+10 =18d122.     10n4 x 2n3=        (10x2) n4+3   =20n73.     ...
Friday, January 25, 2013     Simplify multiplication of numbers or     algebraic terms with different bases       Example:...
Friday, January 25, 2013       Exercise       Pg 104       Ex.5.2B       1-10                           AIRIL AHMAD
Friday, January 25, 2013            DIVISION OF          NUMBERS IN INDEX             NOTATION              HJ. AIRIL AHMA...
Friday, January 25, 2013       Verify a ÷ a = a        m    n         m-n   1.          5  7                       ÷   5 ...
Friday, January 25, 2013       Example:                1. 35 ÷ 33 =                2. k14 ÷ k5 =                3. 99 ÷ 94...
Friday, January 25, 2013       Exercise       Pg 106       Ex.5.3A       1abcdef       2ab                           A...
Friday, January 25, 2013 Exercise:  1. 9d ÷ 3d =   12        2    (9 ÷3) d12-2     =3d10  2. 10n4 ÷ 2n3=               (10...
Friday, January 25, 2013       Exercise       Pg 106       Ex.5.3A       2cdefgh       3abcd                          ...
Friday, January 25, 2013           RAISING NUMBERS            AND ALGEBRAIC            TERMS IN INDEX               NOTATI...
Friday, January 25, 2013       Verify (a ) = a     m n        mn   1.          (5 ) =                     7 5         57x...
Friday, January 25, 2013   3. (2c ) =      7 5                           2   1x5   c7x5 =   25c35  4. (32h8)8 =           ...
Friday, January 25, 2013       Exercise       Pg  108       Ex.5.4A       1-8                           AIRIL AHMAD
Friday, January 25, 2013       Exercise       Pg  109       Ex.5.4B       Question 1        only                       ...
Friday, January 25, 2013                           AIRIL AHMAD
Friday, January 25, 2013            COMPUTATIONS              INVOLVING           NEGATIVE INDICES              HJ. AIRIL ...
Friday, January 25, 2013                                      1       Verify a =          -n                              ...
Friday, January 25, 2013       Exercise       Pg 112       Ex.5.5A       1 AND 2                           AIRIL AHMAD
Friday, January 25, 2013PERFORM COMPUTATIONSINVOLVING NEGATIVE INDICES  Example:  1. 2-2 x 2-4 =           2-2+ (-4) =    ...
Friday, January 25, 2013       E xercise       Pg 113       Ex.5.5B       Question        1-8                          ...
Friday, January 25, 2013                           AIRIL AHMAD
Friday, January 25, 2013            COMPUTATIONS              INVOLVING           FRACTION INDICES              HJ. AIRIL ...
Friday, January 25, 2013                                   ( a)                               m                           ...
Friday, January 25, 2013                                    ( a)                            m                             ...
Friday, January 25, 2013          Change to root notation:     1.                  1        2.                            ...
Friday, January 25, 2013       Calculate the values using calculator:                           ( 81)                     ...
Friday, January 25, 2013                                   1.Press 4                           ( 81)  2.              1   ...
Friday, January 25, 2013          Example: Calculate the values:     1.             1      2.        1             25     ...
Friday, January 25, 2013       Exercise       Pg  118       Ex.5.6D       1 - 10                           AIRIL AHMAD
Friday, January 25, 2013       Exercise       Pg 117       Ex.5.6C       1 2 3 5 6 7 8                           AIRIL ...
Friday, January 25, 2013       Exercise       Pg  117       Ex.5.6C       1 - 8                           AIRIL AHMAD
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NOTE MATH FORM 3 - INDICES

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NOTE MATH FORM 3 - INDICES

  1. 1. Friday, January 25, 2013 AIRIL AHMAD
  2. 2. Friday, January 25, 2013 INDICES HJ. AIRIL AHMAD AIRIL AHMAD
  3. 3. Friday, January 25, 2013 6 2 23= 2 x 2 x 2 8 4 3 2.5 x 2.5 x 2.5 7 5x5x5x5x5x5x5 AIRIL AHMAD
  4. 4. Friday, January 25, 2013 Indices is read as 3 to the power 4 3 of 4 where 3 is the base and 4 is the index. AIRIL AHMAD
  5. 5. Friday, January 25, 2013 Repeated Multiplication  63= 6 x 6 x 6  25= 2 x 2 x 2 x 2 x 2  (-g)4= (-g) x (-g) x (-g) x (-g)  (3y)3= (3y) x (3y) x (3y) AIRIL AHMAD
  6. 6. Friday, January 25, 2013 Repeated Multiplication 9 x9x9= 25 x 25 x 25 x 25 x 25 =  (-kg) x (-kg) x (-kg) x (-kg)=  (6w) x (6w) x (6w) = AIRIL AHMAD
  7. 7. Friday, January 25, 2013 By using the calculator find the values of the following indices 1. 65 = 6. (½)5 = 2. (-12)4 = 7. (-¼) 4 = 3. (2.4)4 = 8. (¾)4 = 4. 153 = 9. (²/3)3 = 5. (32.9)2 = 10. (50)4 = AIRIL AHMAD
  8. 8. Friday, January 25, 2013 Expressing a certain number in the index notation. Example 1: Express 32  Example 2: Express 625 in in the index notation the index notation with with base 2. base 5. 2 32 5 625 2 16 5 125 2 8 5 25 2 2 4 2 1 2 5 5 5 1 5 4 AIRIL AHMAD
  9. 9. Friday, January 25, 2013 Exercise Express each of the following in the index notation with the base given in the brackets 1. 16 (base 2) 6. 243 (base 3) 2. 81 (base 3) 7. 216 (base 6) 3. 64 (base 2) 8. 343 (base 7) 4. 125 (base 5) 9. 128 (base 2) 5. 256 (base 4) 10. 10 000 (base 10) AIRIL AHMAD
  10. 10. Friday, January 25, 2013 MULTIPLICATION OF NUMBERS IN INDEX NOTATION HJ. AIRIL AHMAD AIRIL AHMAD
  11. 11. Friday, January 25, 2013 Example:  1. 32 x 33 = 3 ×x 3 × 33 3 x 3× 3 × 3  3  x 3  x =35 5times  2. 93 x 94 = 9 × 9 × 9 × 9 × 9 × 9 × 9 =97 x x x x x x     7 times AIRIL AHMAD
  12. 12. Friday, January 25, 2013 Example: 3. g 4 x g5 = g × g × g × g ×xgg×xgg×xgg×xgg xgg gxgxgxg × =g9   9 times 4. 1518 x 1514 = AIRIL AHMAD
  13. 13. Friday, January 25, 2013 Verify a x a = a m n m+n 1. 5 x 5 = 4 5 54+5 = 59 2. h11 x h18 = h11+18 = h29 AIRIL AHMAD
  14. 14. Friday, January 25, 2013 Exercise Pg 103 Ex.5.2A 1abcdef 2abc AIRIL AHMAD
  15. 15. Friday, January 25, 2013 MULTIPLICATION OF NUMBERS OR ALGEBRAIC TERMS WITH THE SAME BASE HJ. AIRIL AHMAD AIRIL AHMAD
  16. 16. Friday, January 25, 2013 Example:1. 3a2 x 2a = 3 (3x2) a2+3 =6a52. 6f5 x 2f3= (6x2) f5+3 =12f83. 4m2 x 2m9= (4x2) m2+9 =8m114. 8z9 x 3z3= (8x3) z9+3 =24z12 AIRIL AHMAD
  17. 17. Friday, January 25, 2013 Exercise:1. 9d2 x 2d10= (9x2) d2+10 =18d122. 10n4 x 2n3= (10x2) n4+3 =20n73. 4w2 x w14= (4x1) w2+14 =4w164. z19 x 34z3= (1x34) z19+3 =34z22 AIRIL AHMAD
  18. 18. Friday, January 25, 2013 Simplify multiplication of numbers or algebraic terms with different bases Example: 1. 32 x 23 x 34 x 27= 3 2+4 x 23+7 =36 x 210 2. k x m x k x m= 5 6 8 7 k 5+8 x m6+7 =k13 x m13 3. (½)9 x (½)4 x (¼)12 x (¼)9= AIRIL AHMAD
  19. 19. Friday, January 25, 2013 Exercise Pg 104 Ex.5.2B 1-10 AIRIL AHMAD
  20. 20. Friday, January 25, 2013 DIVISION OF NUMBERS IN INDEX NOTATION HJ. AIRIL AHMAD AIRIL AHMAD
  21. 21. Friday, January 25, 2013 Verify a ÷ a = a m n m-n 1. 5 7 ÷ 5 = 5 57-5 = 52 2. h21 ÷ h18 = h21-18 = h3 AIRIL AHMAD
  22. 22. Friday, January 25, 2013 Example: 1. 35 ÷ 33 = 2. k14 ÷ k5 = 3. 99 ÷ 94 = 4. 1518 ÷ 1514 = AIRIL AHMAD
  23. 23. Friday, January 25, 2013 Exercise Pg 106 Ex.5.3A 1abcdef 2ab AIRIL AHMAD
  24. 24. Friday, January 25, 2013 Exercise: 1. 9d ÷ 3d = 12 2 (9 ÷3) d12-2 =3d10 2. 10n4 ÷ 2n3= (10 ÷ 2) n4-3 =5n1 3. 40w27 ÷ 4w14= (40 ÷ 4) w27-14 =10w13 4. 25z19 ÷ 5z3= (25 ÷5) Z19-3 =5z16 AIRIL AHMAD
  25. 25. Friday, January 25, 2013 Exercise Pg 106 Ex.5.3A 2cdefgh 3abcd AIRIL AHMAD
  26. 26. Friday, January 25, 2013 RAISING NUMBERS AND ALGEBRAIC TERMS IN INDEX NOTATION AIRIL AHMAD AIRIL AHMAD
  27. 27. Friday, January 25, 2013 Verify (a ) = a m n mn 1. (5 ) = 7 5 57x5 = 535 2. (h20)8 = h20x8 = h160 AIRIL AHMAD
  28. 28. Friday, January 25, 2013 3. (2c ) = 7 5 2 1x5 c7x5 = 25c35 4. (32h8)8 = 3 2x8 h8x8 = 316h64 AIRIL AHMAD
  29. 29. Friday, January 25, 2013 Exercise Pg 108 Ex.5.4A 1-8 AIRIL AHMAD
  30. 30. Friday, January 25, 2013 Exercise Pg 109 Ex.5.4B Question 1 only AIRIL AHMAD
  31. 31. Friday, January 25, 2013 AIRIL AHMAD
  32. 32. Friday, January 25, 2013 COMPUTATIONS INVOLVING NEGATIVE INDICES HJ. AIRIL AHMAD AIRIL AHMAD
  33. 33. Friday, January 25, 2013 1 Verify a = -n an 1. 1 8 = -7 7 8 2. f -2 = 1 2 f AIRIL AHMAD
  34. 34. Friday, January 25, 2013 Exercise Pg 112 Ex.5.5A 1 AND 2 AIRIL AHMAD
  35. 35. Friday, January 25, 2013PERFORM COMPUTATIONSINVOLVING NEGATIVE INDICES Example: 1. 2-2 x 2-4 = 2-2+ (-4) = 2-2-4 = 2-6 2. 7-5 ÷ 7-2 = 7-5 - (-2) = 7-5+2 = 7-3 3. (8-2)-4 = 8-2 x (-4) = 88 AIRIL AHMAD
  36. 36. Friday, January 25, 2013 E xercise Pg 113 Ex.5.5B Question 1-8 AIRIL AHMAD
  37. 37. Friday, January 25, 2013 AIRIL AHMAD
  38. 38. Friday, January 25, 2013 COMPUTATIONS INVOLVING FRACTION INDICES HJ. AIRIL AHMAD AIRIL AHMAD
  39. 39. Friday, January 25, 2013 ( a) m m n Verify a = n m power a n root AIRIL AHMAD
  40. 40. Friday, January 25, 2013 ( a) m m n Verify a = n 1. 8 = ¼ ( 8) 4 1 2. f ¾ = ( f) 4 3 AIRIL AHMAD
  41. 41. Friday, January 25, 2013 Change to root notation: 1. 1 2. 1 25 = 2 27 = 3 3. 1 4. 1 32 = 5 49 = 2 AIRIL AHMAD
  42. 42. Friday, January 25, 2013 Calculate the values using calculator: ( 81) 1.Press √¯¯ 1. 1 1 81 = 2.Press 81 2 2 3.Press = 4.Press ^ =9 5.Press 1 6.Press = AIRIL AHMAD
  43. 43. Friday, January 25, 2013 1.Press 4 ( 81) 2. 1 2.Press shift ^ 1 81 = 4 4 3.Press 81 4.Press = 5.Press ^ =3 6.Press 1 7.Press = AIRIL AHMAD
  44. 44. Friday, January 25, 2013 Example: Calculate the values: 1. 1 2. 1 25 2 27 3 3. 1 4. 1 32 5 49 2 AIRIL AHMAD
  45. 45. Friday, January 25, 2013 Exercise Pg 118 Ex.5.6D 1 - 10 AIRIL AHMAD
  46. 46. Friday, January 25, 2013 Exercise Pg 117 Ex.5.6C 1 2 3 5 6 7 8 AIRIL AHMAD
  47. 47. Friday, January 25, 2013 Exercise Pg 117 Ex.5.6C 1 - 8 AIRIL AHMAD

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