Like this presentation? Why not share!

# NOTE MATH FORM 3 - ALGEBRAIC

## on Jan 25, 2013

• 8,798 views

### Views

Total Views
8,798
Views on SlideShare
8,670
Embed Views
128

Likes
6
175
3

### Report content

• Comment goes here.
Are you sure you want to
• Simple
Are you sure you want to
• juz for easy my students n me can understand
Are you sure you want to
• simple
Are you sure you want to

## NOTE MATH FORM 3 - ALGEBRAICPresentation Transcript

• Friday, January 25, 2013 AIRIL AHMAD
• 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
• Friday, January 25, 2013 Example 2: Expand 3 (a - c) 3 ( a - c ) = 3 x a - 3 x c = 3a - 3c AIRIL AHMAD
• Friday, January 25, 2013 Example 3: Expand 7g (m + 2n) 7g ( m + 2n ) = 7g x m + 7g x 2n = 7gm + 14gn AIRIL AHMAD
• 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
• Friday, January 25, 2013 AIRIL AHMAD
• Friday, January 25, 2013 ALGEBRAIC EXPRESSIONS EXPAND DOUBLE PAIRS OF BRACKETS HJ. AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• 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
• Friday, January 25, 2013 EXPAND DOUBLE PAIRS OF BRACKETS HJ. AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• Friday, January 25, 2013 EXERCISE AIRIL AHMAD
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Friday, January 25, 2013ExerciseWrite all the factors of the following algebraic terms. 5j1. 5n 3. 2 2. 14 p 4. abc AIRIL AHMAD
• Friday, January 25, 2013 CONCEPT OF FACTORISATION OFALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• Friday, January 25, 2013 EXERCISE AIRIL AHMAD
• Friday, January 25, 2013 AIRIL AHMAD
• Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
• Friday, January 25, 2013Factorise the following algebraic termExample 1: 2pq + 4qr 2 2pq + 4qr q pq + 2qr (p + p 2r 2r) AIRIL AHMAD
• Friday, January 25, 2013Factorise the following algebraic termExample 2: mn – mn2 m mn - mn2 n n - n2 (1 - n 1 n) AIRIL AHMAD
• 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
• Friday, January 25, 2013 EXERCISE AIRIL AHMAD
• Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• Friday, January 25, 2013 EXERCISE AIRIL AHMAD
• 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
• Friday, January 25, 2013Factorise a2- b2Example 11: a 2 – b2 ( a 2 – - b2 ) ) (a + b a AIRIL AHMAD
• Friday, January 25, 2013Factorise a2- b2Example 12: m 2 – n2 ((m2 –- n2 ) ) m + n n AIRIL AHMAD
• Friday, January 25, 2013Factorise a2- b2Example 13: 16m2 – 25n2 16m2 – 25n2 ( 42m2 – -5n ) ) (4m + 55n 4m n 2 2 AIRIL AHMAD
• Friday, January 25, 2013 EXERCISE AIRIL AHMAD
• Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• Friday, January 25, 2013 Exercise: • Page 135 • Ex.6.2C •1 - 8 AIRIL AHMAD
• 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
• 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
• 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
• 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
• Friday, January 25, 2013 Exercise: • Page 134 • Ex.6.2B • 1 - 15 AIRIL AHMAD
• Friday, January 25, 2013 FACTORISE ALGEBRAIC EXPRESSIONS AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• 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
• 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
• 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
• 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
• Friday, January 25, 2013FACTORISE AND SIMPLIFY ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
• Friday, January 25, 2013 Simplify the following expressions: Example 1: 4 8 xy 4y = = 4y 1 2x 1 AIRIL AHMAD
• Friday, January 25, 2013 Example 2: 5 a 2 20a b 5a 4ab = 1 = 5a 1 AIRIL AHMAD
• Friday, January 25, 2013 Exercise Page 138 Ex. 6.2F No. 1 abcd AIRIL AHMAD
• 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
• 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
• Friday, January 25, 2013 Exercise Page 138 Ex.6.2F No. 2 only AIRIL AHMAD
• Friday, January 25, 2013Simplify the following:Example 1: 3x 2 x 3x + 2 x 5x + = = 7 7 7 7 AIRIL AHMAD
• Friday, January 25, 2013Example 2: g + 3 2g + 4 + 3 3 g + 3 + 2g + 4 = 3 3g + 7 = 3 AIRIL AHMAD
• Friday, January 25, 2013 Exercise AIRIL AHMAD
• Friday, January 25, 2013 SUBTRACTION OF ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
• Friday, January 25, 2013Simplify the following:Example 1: 9p 2p 9p −2p 7p − = = 10 10 10 10 AIRIL AHMAD
• Friday, January 25, 2013Example 2: 9 f +8 2 f +5 − hk hk 9 f + 8 − 2f - 5 = hk 7f +3 = hk AIRIL AHMAD
• Friday, January 25, 2013 8k + 7 7k − 2Example 3: − 2abc 2abc 8k + 7 − 7k + 2 = 2abc k+9 = 2abc AIRIL AHMAD
• Friday, January 25, 2013 Exercise AIRIL AHMAD
• Friday, January 25, 2013 Exercise Page 139 Ex. 6.3A No. 1,2,3,5,10,11,12, 13,14,15 AIRIL AHMAD
• Friday, January 25, 2013 ADD OR SUBTRACT TWOALGEBRAIC FRACTIONS WITH ONE DENOMINATOR AS A MULTIPLE OF THE OTHER DENOMINATOR AIRIL AHMAD AIRIL AHMAD
• 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
• Friday, January 25, 2013 4h x 3 2hExample 2: + 5 x 3 15 12h +2h = 15 15 12h + 2h 14h = = 15 15 AIRIL AHMAD
• 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
• Friday, January 25, 2013 Exercise AIRIL AHMAD
• Friday, January 25, 2013 ADD AND SUBTRACT ALGEBRAIC FRACTIONS WITHOUT ANY COMMON FACTORS AIRIL AHMAD AIRIL AHMAD
• 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
• 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
• 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
• Friday, January 25, 2013 Exercise AIRIL AHMAD
• Friday, January 25, 2013 Exercise Page 142&143 ALL Ex.6.3C AIRIL AHMAD
• Friday, January 25, 2013 MULTIPLICATION ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
• Friday, January 25, 2013 Simplify the following: Example 1: 3 2 3× 2 6 × = = 5 7 5 × 7 35 AIRIL AHMAD
• Friday, January 25, 2013 Example 2:m p m × p mp × = =n q n × q nq AIRIL AHMAD
• Friday, January 25, 2013 5p Example 3: 1r ×5p = r ×5p 5 pr2 = 2 2 AIRIL AHMAD
• 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
• Friday, January 25, 2013 Exercise AIRIL AHMAD
• Friday, January 25, 2013 Exercise Page 85 Ex.7 No. 1 to 12 AIRIL AHMAD
• Friday, January 25, 2013 DIVISION OF TWO ALGEBRAIC FRACTIONS AIRIL AHMAD AIRIL AHMAD
• 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
• Friday, January 25, 2013 5p Example 2: 1r2 × ÷5p = r 2 1 5p r ×1 r = = 2×5 p 10 p AIRIL AHMAD
• Friday, January 25, 2013 Example 3: ÷ = × 2c 5 2c 3d 4e 3d 4e 5 2c × 4e 8ce = = 3d × 5 15d AIRIL AHMAD
• Friday, January 25, 2013 Exercise Page 85 Ex.7 No. 13 to 29 AIRIL AHMAD