NOTE MATH FORM 3 - ALGEBRAIC

32,229 views

Published on

4 Comments
27 Likes
Statistics
Notes
No Downloads
Views
Total views
32,229
On SlideShare
0
From Embeds
0
Number of Embeds
193
Actions
Shares
0
Downloads
660
Comments
4
Likes
27
Embeds 0
No embeds

No notes for slide

NOTE MATH FORM 3 - ALGEBRAIC

  1. 1. Friday, January 25, 2013 AIRIL AHMAD
  2. 2. Friday, January 25, 2013 Expand a single pair of brackets Example 1: Expand w (x + y) w ( x + y ) = w x x + w x y = wx + wy AIRIL AHMAD
  3. 3. Friday, January 25, 2013 Example 2: Expand 3 (a - c) 3 ( a - c ) = 3 x a - 3 x c = 3a - 3c AIRIL AHMAD
  4. 4. Friday, January 25, 2013 Example 3: Expand 7g (m + 2n) 7g ( m + 2n ) = 7g x m + 7g x 2n = 7gm + 14gn AIRIL AHMAD
  5. 5. Friday, January 25, 2013 Example 4: Expand 4e ( r + 2s – 8t) 4e ( r + 2s - 8t ) = 4e x r + 4e x 2s - 4e x 8t = 4er + 8es - 32et AIRIL AHMAD
  6. 6. Friday, January 25, 2013 AIRIL AHMAD
  7. 7. Friday, January 25, 2013 ALGEBRAIC EXPRESSIONS EXPAND DOUBLE PAIRS OF BRACKETS HJ. AIRIL AHMAD AIRIL AHMAD
  8. 8. Friday, January 25, 2013 Expand double pairs of brackets Example 1: Expand (w + v)(x + y) ( w + v ) ( x + y ) = wxx + w x y +vxx + vxy = wx + wy + vx + vy AIRIL AHMAD
  9. 9. Friday, January 25, 2013 Expand double pairs of brackets Example 2: Expand (2e + f)(c + d) ( 2e + f ) ( c + d )= 2e x c + 2e x d +fxc + fxd= 2ce + 2de + cf + df AIRIL AHMAD
  10. 10. Friday, January 25, 2013 Expand double pairs of brackets Example 3: Expand (2m + n)(p - s) ( 2m + n ) ( p - s )= 2m x p + 2m x (-s) + n x p + n x (-s)= 2mp - 2ms + np - ns AIRIL AHMAD
  11. 11. Friday, January 25, 2013 EXPAND DOUBLE PAIRS OF BRACKETS HJ. AIRIL AHMAD AIRIL AHMAD
  12. 12. Friday, January 25, 2013Expand double pairs of brackets Example 1: Expand (r + 4)(r + 3) ( r + 4 ) ( r + 3 ) = rxr + r x 3 +4xr + 4x3 = r2 + 3r + 4r + 12 = r2 + 7r + 12 AIRIL AHMAD
  13. 13. Friday, January 25, 2013Expand double pairs of brackets Example 2: Expand (2e + f)(e + 2f) ( 2e + f ) ( e + 2f ) = 2e x e + 2e x 2f +fxe + f x 2f = 2e2 + 4ef + ef + 2f2 = 2e2 + 5ef + 2f2 AIRIL AHMAD
  14. 14. Friday, January 25, 2013 EXERCISE AIRIL AHMAD
  15. 15. Friday, January 25, 2013Expand double pairs of brackets Example 3: Expand (w + 4)(w - 3) ( w + 4 ) ( w - 3 ) = wxw + w x (-3) + 4 x w + 4 x (-3) = w2 - 3w + 4w - 12 = w2 + w - 12 AIRIL AHMAD
  16. 16. Friday, January 25, 2013 EXPAND DOUBLE PAIRS OF BRACKETS In general , (a+b)2= a2 + 2ab + b2 or (a-b)2= a2 - 2ab + b2 HJ. AIRIL AHMAD AIRIL AHMAD
  17. 17. Friday, January 25, 2013 Expand same pairs of brackets Example 1: Expand (r + 4)2 ( r + 4 ) ( r + 4 ) = rxr + r x 4 +4xr + 4x4 = r2 + 4r + 4r + 16 = r2 + 8r + 16 AIRIL AHMAD
  18. 18. Friday, January 25, 2013 Expand same pairs of brackets Example 2: Expand (2e + f)2 ( 2e + f ) ( 2e + f )= 2e x 2e + 2e x f + f x 2e + f x f = 4e2 + 2ef + 2ef + f2 = 4e2 + 4ef + f2 AIRIL AHMAD
  19. 19. Friday, January 25, 2013 Expand same pairs of brackets Example 3: Expand (w - 4)2 ( w - 4 ) ( w - 4 ) = w x w+ w x (-4) + (-4) x w + -(4) x (-4) = w2 - 4w - 4w + 16 = w2 -8w + 16 AIRIL AHMAD
  20. 20. Friday, January 25, 2013State the factors of an algebraic termExample 1: 2m 1, 2, m, 2mExample 2: 4g 1, 2, 4, g, 2g, 4g AIRIL AHMAD
  21. 21. Friday, January 25, 2013State the factors of an algebraic termExample 3: 12y 1, 2, 3, 4, 6,12, y, 2y, 3y, 4y, 6y, 12yExample 4: 15k 1, 3, 5, 15, k, 3k, 5k, 15k AIRIL AHMAD
  22. 22. Friday, January 25, 2013ExerciseWrite all the factors of the following algebraic terms. 5j1. 5n 3. 2 2. 14 p 4. abc AIRIL AHMAD
  23. 23. Friday, January 25, 2013 CONCEPT OF FACTORISATION OFALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
  24. 24. Friday, January 25, 2013Highest Common Factor (HCF)Find the HCF of the following algebraic terms.Example 1 : Example 2 :6h & 4gh 2pq & 4q 2 6h , 4gh 2 2pq , 4q h 3h , 2gh q pq , 2q 3 , 2g p , 2 HCF = 2 x h HCF = 2 x q = 2h = 2q AIRIL AHMAD
  25. 25. Friday, January 25, 2013Highest Common Factor (HCF)Find the HCF of the following algebraic terms.Example 3 : Example 4 :14v2 & 8v 5cd2 & 10cd 2 14v2 , 8v 5 5cd2 , 10cd v 7v2 , 4v cd cd2 , 2cd 7v , 4 d , 2 HCF = 2 x v HCF = 5 x cd = 2v = 5cd AIRIL AHMAD
  26. 26. Friday, January 25, 2013 EXERCISE AIRIL AHMAD
  27. 27. Friday, January 25, 2013 AIRIL AHMAD
  28. 28. Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
  29. 29. Friday, January 25, 2013Factorise the following algebraic termExample 1: 2pq + 4qr 2 2pq + 4qr q pq + 2qr (p + p 2r 2r) AIRIL AHMAD
  30. 30. Friday, January 25, 2013Factorise the following algebraic termExample 2: mn – mn2 m mn - mn2 n n - n2 (1 - n 1 n) AIRIL AHMAD
  31. 31. Friday, January 25, 2013Factorise the following algebraic termExample 3: 3ab + 6bc - 9b2 3 3ab + 6bc - 9b2 b ab + 2bc - 3b2 ( a + 2c - 3b3b) AIRIL AHMAD
  32. 32. Friday, January 25, 2013 EXERCISE AIRIL AHMAD
  33. 33. Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
  34. 34. Friday, January 25, 2013Factorise ab + ac +bd + cdExample 9: ag + 3a + 2g + 6 (ag + 3) )+ (2g + 6 ) a (g 3a a 2 (g 3)2 (a (g + 3) + 2 (g + 3) ) AIRIL AHMAD
  35. 35. Friday, January 25, 2013Factorise ab + ac +bd + cdExample 10: mn + 4n + 2m + 8 ( mn + 4n) +( 2(m +2 ) (m + 4) n n 2m 8 4) (n (m + 4) + 2 (m + 4) ) AIRIL AHMAD
  36. 36. Friday, January 25, 2013 EXERCISE AIRIL AHMAD
  37. 37. Friday, January 25, 2013Exercise Factorise the following algebraic expressions: 1. ac + ad + bc + bd 2. ax + ay + bx + by 3. gh + 2h + 3g + 6 4. a2 + ab + 2a + 2b 5. de + d2 + ef + df AIRIL AHMAD
  38. 38. Friday, January 25, 2013Factorise a2- b2Example 11: a 2 – b2 ( a 2 – - b2 ) ) (a + b a AIRIL AHMAD
  39. 39. Friday, January 25, 2013Factorise a2- b2Example 12: m 2 – n2 ((m2 –- n2 ) ) m + n n AIRIL AHMAD
  40. 40. Friday, January 25, 2013Factorise a2- b2Example 13: 16m2 – 25n2 16m2 – 25n2 ( 42m2 – -5n ) ) (4m + 55n 4m n 2 2 AIRIL AHMAD
  41. 41. Friday, January 25, 2013 EXERCISE AIRIL AHMAD
  42. 42. Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
  43. 43. Friday, January 25, 2013Factorise a2 + 2ab + b2Example 1: y2 + 8y + 16 41st Step: 16 = 1 x 16 (y 4) + +4y 16 = 2 x 8 16 = 4 x 42nd Step: + +4y 8= 4+ 4 (y + 4) AIRIL AHMAD
  44. 44. Friday, January 25, 2013Example 2: 7 2 y2 + 9y + 141st Step: 14 = 1 x 14 (y 2) + +2y 14 = 2 x 72nd Step: + +7y 9= 2+ 7 (y + 7) AIRIL AHMAD
  45. 45. Friday, January 25, 2013 Exercise: • Page 135 • Ex.6.2C •1 - 8 AIRIL AHMAD
  46. 46. Friday, January 25, 2013Factorise completely (Factorise a2 + 2ab + b2) 1. m2 + 12m + 36 2. a2 + 4a +4 3. j2 + 4j +3 4. k2 + 7k +12 5. b2 + 8b +15 6. f2 + 6f +8 7. g2 + 9g +14 8. s2 + 10s +16 9. h2 + 5h +6 10. r2 + 7r +10 AIRIL AHMAD
  47. 47. Friday, January 25, 2013Example 3: y2 - 6y + - 2 841st Step: 8= 1x8 (y -2) -2y 8= 2x42nd Step: -4y -6 = -2 - 4 (y - 4) AIRIL AHMAD
  48. 48. Friday, January 25, 2013Example 4: y2 - 10y + - 3 7 211st Step: 21 = 1 x 21 (y -3) -3y 21 = 3 x 72nd Step: -7y -10 = -3 - 7 (y - 7) AIRIL AHMAD
  49. 49. Friday, January 25, 2013 Exercise Factorise the following algebraic expressions: 1. y2 – 3y + 2 6. y2 – 8y + 15 2. y2 – 5y + 6 7. y2 – 9y + 18 3. y2 – 7y + 12 8. y2 – 8y + 12 4. y2 – 7y + 10 9. y2 – 12y + 35 5. y2 – 9y + 14 10. y2 – 14y + 45 AIRIL AHMAD
  50. 50. Friday, January 25, 2013 Exercise: • Page 134 • Ex.6.2B • 1 - 15 AIRIL AHMAD
  51. 51. Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
  52. 52. Friday, January 25, 2013Factorise a2 + 2ab - b2Example 5: y2 + 5y - 36 +9 -41st Step: 36 = 1 x 36 (y +9) 36 = 2 x 18 +9y 36 = 3 x 12 36 = 4x 9 36 = 6x 6 -4y2 Step: nd 5= 9- 4 (y - 4) AIRIL AHMAD
  53. 53. Friday, January 25, 2013Example 6: y2 + 4y - 21 +7 -31st Step: 21 = 1 x 21 (y +7) 21 = 3 x 7 +7y2nd Step: 4= 7- 3 -3y (y - 3) AIRIL AHMAD
  54. 54. Friday, January 25, 2013 Exercise Factorise the following algebraic expressions: 1. y2 + y – 6 6. y2 + 4y – 12 2. y2 + 2y – 15 7. y2 + y – 42 3. y2 + 6y – 27 8. y2 + 4y – 21 4. y2 + 3y – 10 9. y2 + 7y – 30 5. y2 + 3y – 18 10. y2 + 10y – 24 AIRIL AHMAD
  55. 55. Friday, January 25, 2013Factorise a2 + 2ab + b2Example 7: y2 - 3y - 10 +2 -51st Step: 10 = 1 x 10 (y -5) 10 = 2 x 5 -5y2nd Step: -3 = - 5 + 2 +2y (y +2) AIRIL AHMAD
  56. 56. Friday, January 25, 2013Factorise a2 + 2ab + b2Example 8: y2 - 3y - 28 +4 -71st Step: 28 = 1 x 28 (y -7) 28 = 2 x 14 -7y 28 = 4 x 72nd Step: -3 = - 7 + 4 +4y (y + 4) AIRIL AHMAD
  57. 57. Friday, January 25, 2013 Exercise Factorise the following algebraic expressions: 1. y2 – 2y – 8 6. y2 – 5y – 36 2. y2 – 3y – 18 7. y2 – y – 12 3. y2 – 5y – 14 8. y2 – 2y – 24 4. y2 – 7y – 30 9. y2 – 6y – 7 5. y2 – y – 20 10. y2 – y – 6 AIRIL AHMAD
  58. 58. Friday, January 25, 2013FACTORISE AND SIMPLIFY ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
  59. 59. Friday, January 25, 2013 Simplify the following expressions: Example 1: 4 8 xy 4y = = 4y 1 2x 1 AIRIL AHMAD
  60. 60. Friday, January 25, 2013 Example 2: 5 a 2 20a b 5a 4ab = 1 = 5a 1 AIRIL AHMAD
  61. 61. Friday, January 25, 2013 Exercise Page 138 Ex. 6.2F No. 1 abcd AIRIL AHMAD
  62. 62. Friday, January 25, 2013Simplify the following algebraicfractions to the lowest terms Working Space Example 3: 1 2 6g + 46g + 4 2(3g + 2) = 3g + 2 4 42 3g + 2 2 ( 3g + 2 ) = 2 AIRIL AHMAD
  63. 63. Friday, January 25, 2013 Working Space Example 4: 2 2a - 8b2a − 8b 2(a − 4b) = a - 4b 2c 2c 2 ( a – 4b ) a − 4b = c AIRIL AHMAD
  64. 64. Friday, January 25, 2013 Exercise Page 138 Ex.6.2F No. 2 only AIRIL AHMAD
  65. 65. Friday, January 25, 2013 ADDITION OF ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
  66. 66. Friday, January 25, 2013Simplify the following:Example 1: 3x 2 x 3x + 2 x 5x + = = 7 7 7 7 AIRIL AHMAD
  67. 67. Friday, January 25, 2013Example 2: g + 3 2g + 4 + 3 3 g + 3 + 2g + 4 = 3 3g + 7 = 3 AIRIL AHMAD
  68. 68. Friday, January 25, 2013 Exercise AIRIL AHMAD
  69. 69. Friday, January 25, 2013 SUBTRACTION OF ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
  70. 70. Friday, January 25, 2013Simplify the following:Example 1: 9p 2p 9p −2p 7p − = = 10 10 10 10 AIRIL AHMAD
  71. 71. Friday, January 25, 2013Example 2: 9 f +8 2 f +5 − hk hk 9 f + 8 − 2f - 5 = hk 7f +3 = hk AIRIL AHMAD
  72. 72. Friday, January 25, 2013 8k + 7 7k − 2Example 3: − 2abc 2abc 8k + 7 − 7k + 2 = 2abc k+9 = 2abc AIRIL AHMAD
  73. 73. Friday, January 25, 2013 Exercise AIRIL AHMAD
  74. 74. Friday, January 25, 2013 Exercise Page 139 Ex. 6.3A No. 1,2,3,5,10,11,12, 13,14,15 AIRIL AHMAD
  75. 75. Friday, January 25, 2013 ADD OR SUBTRACT TWOALGEBRAIC FRACTIONS WITH ONE DENOMINATOR AS A MULTIPLE OF THE OTHER DENOMINATOR AIRIL AHMAD AIRIL AHMAD
  76. 76. Friday, January 25, 2013Simplify the following:Example 1: 3 xx2 2 x + 2 x2 4 =6 x+ 2x 4 4 8x = = 2x 4 AIRIL AHMAD
  77. 77. Friday, January 25, 2013 4h x 3 2hExample 2: + 5 x 3 15 12h +2h = 15 15 12h + 2h 14h = = 15 15 AIRIL AHMAD
  78. 78. Friday, January 25, 2013 5hx 2 2 hExample 3: − 6 x 2 12 10h −2h = 12 12 10h − 2h 8h 2h = = = 12 12 3 AIRIL AHMAD
  79. 79. Friday, January 25, 2013 Exercise AIRIL AHMAD
  80. 80. Friday, January 25, 2013 ADD AND SUBTRACT ALGEBRAIC FRACTIONS WITHOUT ANY COMMON FACTORS AIRIL AHMAD AIRIL AHMAD
  81. 81. Friday, January 25, 2013 Simplify the following: Example 1:3 p 5 2r 2 x x 15 p − 4r − = 2x5 5x 2 10 AIRIL AHMAD
  82. 82. Friday, January 25, 2013 8x n f + x m 5Example 2: − m n x nx m 8n − fm – 5m = mn 8n − fm − 5m = mn AIRIL AHMAD
  83. 83. Friday, January 25, 2013 2 − x y 3 xx x xExample 3: + xxy yx x 2y - xy + 3x2 = xy 2 y − xy + 3x 2 = xy AIRIL AHMAD
  84. 84. Friday, January 25, 2013 Exercise AIRIL AHMAD
  85. 85. Friday, January 25, 2013 Exercise Page 142&143 ALL Ex.6.3C AIRIL AHMAD
  86. 86. Friday, January 25, 2013 MULTIPLICATION ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
  87. 87. Friday, January 25, 2013 Simplify the following: Example 1: 3 2 3× 2 6 × = = 5 7 5 × 7 35 AIRIL AHMAD
  88. 88. Friday, January 25, 2013 Example 2:m p m × p mp × = =n q n × q nq AIRIL AHMAD
  89. 89. Friday, January 25, 2013 5p Example 3: 1r ×5p = r ×5p 5 pr2 = 2 2 AIRIL AHMAD
  90. 90. Friday, January 25, 2013 ( x + y) 4g Example 4: × h (e − f ) ( x + y) × 4 g = h × (e − f ) 4 g ( x + y) = h (e − f ) AIRIL AHMAD
  91. 91. Friday, January 25, 2013 Exercise AIRIL AHMAD
  92. 92. Friday, January 25, 2013 Exercise Page 85 Ex.7 No. 1 to 12 AIRIL AHMAD
  93. 93. Friday, January 25, 2013 DIVISION OF TWO ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
  94. 94. Friday, January 25, 2013 Simplify the following: Example 1: × 3 2 3 ÷ = 5 7 5 7 3 × 7 21 = = 2 5 × 2 10 AIRIL AHMAD
  95. 95. Friday, January 25, 2013 5p Example 2: 1r2 × ÷5p = r 2 1 5p r ×1 r = = 2×5 p 10 p AIRIL AHMAD
  96. 96. Friday, January 25, 2013 Example 3: ÷ = × 2c 5 2c 3d 4e 3d 4e 5 2c × 4e 8ce = = 3d × 5 15d AIRIL AHMAD
  97. 97. Friday, January 25, 2013 Exercise Page 85 Ex.7 No. 13 to 29 AIRIL AHMAD

×