Chapter 7 Algebraaic Expressions

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CHAPTER 7 : ALGEBRAIC EXPRESSIONS

A. Unknown

*An unknown is a quantity whose value has not been determined. *Letters can be used to represent unknowns or objects.

Example Exercise1. The teacher gives some

pencils to the studentsSolution : The unknown is the number of pencils

2. There are x students in m class Solution : x is unknown m is object

1. I bought some books Solution : ……………………………

2. There are many monkeys in the garden. Solution : …………………………….

3. Azman bought y durian in z shop yesterday.

Solution : unknown…………….. object ……………….

4. Mr a sold his car for k ringgit Solution : unknown ……………….. object :…………………..

B Algebraic Terms

i) Algebraic Term with one unknown - is the product of an unknown and a number. Example : 4y is called an algebraic term 4y = 4 x y = y + y + y + y 4y

Number unknown * Identify coefficients in given algebraic term - Coefficient is the number that multiply the unknown

Example Exercise1) 7m : coefficient of m is 7

2) coefficient of r is

3) – y : coefficient of y is -1

1) -3z : coefficient of z is……………

2) : coefficient of x is …………..

3) 0.7 h : coefficient of h is …………

4) p : coefficient of p is …………..

Algebraic Expressions 77

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(ii) Like and Unlike Algebraic Terms * Like term : terms with the same unknowns * Unlike terms : terms with different unknowns.

Example Exercise

1. 3m and -4m Like term 2. 4x and ¼ x (same unknown)3. 0.9z and 5z

1. 2w and 8h unlike term2, -5f and ½g (different unknown)3. 1.2q and 3.5g

Determine whether each of the following pairs of algebraic terms are like term / unlike term

1. 6s , - t : ……………………

2. , 8y : ……………………..

3. 19 d , 19e : ……………………

4. , 4e : ………………………..

C Algebraic Expressions An algebraic expression is a combination of two or more algebraic

terms by addition, subtraction or both

Examples : 2x + 4y , 6r – 3s + 6z

(i) Number of terms in a given algebraic expression

Example ExerciseDetermine the number of terms in the algebraic expressions below :

1. 3x + 6y : 2 terms

2. 7p + 5q – 9 : 3 terms

3. w – 2z – 8y + 1 : 4 terms

Determine the number of termsin the algebraic expressions below :

1. 6m + 8n – 9 : …………………..

2. 3b + 2e – 10b -5e : …………….

3. 2s – 4s + 5s + 3 – w :………….

(ii) Simplifying Algebraic Expressions - Group all the like terms together - Add / subtract the coefficient of the terms - unlike terms cannot be simplified


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Examples Exercise1. 6m – 2n + 4m – 5n = 6m + 4m -2n -5n (group like terms)

= 10m – 7n

2. -7x + 4y + 3y + 2x = -7x + 2x + 4y + 3y = -5x + 7y

3. ( 12a – 4b) + ( 5a + 7b) = 12a+ 5a – 4b + 7b = 17a + 3b

4. ( 9q + 2p) – ( 4q – 6p) = 9q + 2p – 4q + 6p = 9q – 4q + 2p + 6p = 5q + 8p

5. 8x – ( - 4x) + x = 8x + 4x + x = 13x

6. -3c –(- d) +(-2d) = -3c +d – 2d =-3d -d

.1. 2x – 7y + 5x – y =

2. 11z -3w - 8z- 8w =

3. ( 6r + 9s) + ( 3r – 2s) =

4. ( 5k -3) – ( 7k + 2) =

5. (2t +4s) – (7t – 3s) =

6. – 3s – (- 5s + 1) =

7. -14w –(-3w) -7w =

D. Algebraic Terms in two or more unknowns

Is the multiplying factors of the term Examples : 3xy , ½abc, 0.8 def

* Identifying the coefficient of an unknown

Example ExerciseIn the term 8xy2

* 8y(xy) the coefficient of xy is 8y* 8x(y2) the coefficient of y2 is 8x* 8y2 (x) the coefficient of x is 8y2

* 8(xy2) the coefficient of xy2 is 8

1. in the term -3ab2c* the coefficient of abc =………………..* the coefficient of ab2 = ………………..* the coefficient of ab2c =……………..* the coefficient of ac = ……………….


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E. Multiplication & Division of 2 or more terms (i) Finding the product of 2 algebraic terms - collect all numbers and similar unknowns together - then multiply the numbers and the unknown separately.

Example Exercise1. 2ab x 4b2c = 2 x a x b x 4 x b x b x c = 2 x 4 x a x b x b x b x c = 8 x a x b2 x c = 8ab3c

2. 4m2 x ½ mn2

= 4 x ½ x m x m x m x n x n = 2 x m3 x n2

= 2 m3 n2

Exercise

6. =

7. (-3m2hk3)x (-7m2hk2) =

1. ab x a2b

=

2. 3xy x (-2 yz)

=

3.. 6ab2c x (½ bc3)

=

4. (-8p3qr) x ( -7pqr2)

=

5.

=


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(ii) Finding the quotient of two algebraic terms - Express the division in fraction form - cancel similar unknowns that are found in both numerator and denominator

Example Exercise

1.

=

= 2y

2. 12m2n ÷ 3mn

=

= 4m

3. -5cd2e ÷ 15c2de

=

=

1. 24pq2z ÷ 8qr =

2.

=

3. 12abc ÷ (-18cd) =

4. (- 18sr3t2) ÷ 6sr2t =

iii) Multiplication and Division involving algebraic terms

Example Exercise1. 4p x 6q2 ÷ 3pq

= 8q

2.

=

= -2 x c x d x 3 x c x d x e = -2 x 3 x c x c x d x d x e = -6c2d2e

1. 6p2qr ÷ 3pq x 8pr =

2.

=

3. 10a2b3 x (-2b2c) ÷ 5abc


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F ) Computations involving Algebraic Expressions

* In Multiplication / division of algebraic expressions by a number, every term In the expression is multiply/ divide by the same number Example Exercise1. 3 ( 2a –b) = 3 x 2a – 3 x b = 6a – 3b

3. h – 9(h – 2) = h – 9h + 18 = -8h +18

4. 2 (4e +y) – 5( 2e – 3y) = 2 x 4e + 2 x y – 5 x 2e + 5 x 3y = 8e + 2y – 10e + 15y = 8e -10e +2y + 15y = -2e + 17y

5. (6ab – 4bc) ÷ 2b = 6ab ÷ 2b – 4bc ÷ 2b = 3a – 2c

7. 5(2x – 1) -

= 10x -5 – (3x - 1) = 10x -5 -3x + 1 = 10x -3x -5 + 1 = 7x -4

1. 8 ( 5m -2) =

2. - ½ ( 4a + 12b) =

3. – p – 7 ( p -3 ) =

4. – 5 ( t -2) + 8t =

5. 3 ( 2s -7) – 4( s + 3) =

6. . ( -12pq + 8qr – 4pqr) ÷ 4 =

7.

=

8.

=

9.

=


2

6

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Common Errors

Errors Correct Steps1. 7pq x 3pq = 21 pq

2. 2 ( 4e – 3 d) = 8e – 3d

3. (6de2 – 4ef) ÷ 2e = 3de – 4ef

4. (x – 4y) – ( 2x + y) = x – 4y – 2x + y = x -2x -4y + y = -x-3y

5. -2p ( pq – 3) = - 2pq – 6p

6. 10abc – 4 abc = 6

7. 3a +6b – 8a – 3b = 3a + 8a - 6b -3b = 11a – 9b

8. ( - 4rs2t) x 5r3st2

= (-4) x 5 x r x r3 x s2 x s x t x t2 = 20r3s2t2

9. -5s - ( 3t – 2)

= +15st -10s

1. 7pq x 3pq = 7 x 3 x p x p x q x q = 21 p2q2

2. 2( 4e – 3d) = 2 x 4e – 2 x 3d = 8e – 6d

3. (6de2 – 4ef) ÷ 2e = 6de 2 ÷ 2e – 4ef ÷ 2e = 3de – 2f

4. (x – 4y) – ( 2x + y) = x – 4y – 2x - y = x -2y -4y - y = - x - 5y

5. -2p ( pq – 3) = - 2p2q + 6p

6. 10abc – 4 abc = 6abc

7. 3a +6b – 8a – 3b = 3a - 8a + 6b -3b = -5a +3b

8. ( - 4rs2t) x 5r3st2

= (-4) x 5 x r x r3 x s2 x s x t x t2 = -20r4s3t3

9. -5s - ( 3t – 2)

= -5s -3t +2


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(G) Expanding single Brackets

* Expanding algebraic expressions by multiplying each term inside the bracket by the number or term outside

Example Exercise1. 2p (p – 3q) = 2p x p – 2p x 3q = 2p2 – 6pq

2. -4b(2a + b) = -4b x 2a -4b x b = -8ab – 4b2

3. (6a – 9c)

= x 6 2a - x 9c

= 4ab -6bc

1. y ( w + y) =

2. -5e ( 3f + 2g) =

3.

=

4. xy ( 4z – 2w + xy) =

5.

=

6. - 7ab(2a – 4b + c) =


* p(q + r)= p q + p r = pq + pr

3

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(H) Expanding double brackets

* Expanding algebraic Expressions by multiplying each term within the first pair of brackets by every term within the second pair of brackets ( a + b)(x + y) = a( x +y) + b( x+y) = ax + ay + bx + by

Example Exercise1. (x -3)(y+5) = x (y + 5) – 3(y + 5) = xy + 5x – 3y – 15

2. (2k -1)(k – 3) = 2k(k -3) – 1(k -3) = 2k2- 6k – k + 3 = 2k2 -7k + 3

3. (p – 3q)2

= (p – 3q)(p -3q) = p(p-3q) – 3q (p-3q) = p2 – 3pq – 3pq + 9q2

= p2 – 6pq + 9q2

4. (2a +b)2

= (2a+b)(2a+b) = 2a(2a+b) + b(2a+b) = 4a2 +2ab +2ab + b2

= 4a2 +4ab +b2

1. (a -2)(b +1) =

2. (m +3)( 3m – n) =

3. (-2s -5)( 3t + 4) =

4. ( a -3)2

=

5. (3m –n)2

=

6. ( 5x +2)2

=


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7. (y + 4d)2

=

Common Errors

Errors Correct Steps1. 2x(x-3)

= 2x2 -3

2. (a+b)2

= a2 + b2

3. ( a – b)2

= a2 – b2

4 2m2(3m2n – 4 mn3)

= 6m4n – 4m2n3

5. -4 ( 3de – 2rst2)

= - 12de – 2rst2

6. ( x -3)2

= x2 – 9

7. 4a2 –(a + b)2

= 4a 2 –a2 + b2

= 3a2 + b2

8. (2x -3)(x + 4)

= 2x( x+4) – 3 (x + 4)

= 2x2 + 8x – 3x + 12

1. 2x(x-3)

= 2x2 – 6

2. (a+b)2

= a2 +2ab + b2

3.. ( a – b)2

= a2 – 2ab + b2

4. 2m2(3m2n – 4 mn3)

= 6m4n – 8m3n3

5. -4 ( 3de – 2rst2)

= - 12de + 8rst2

6. ( x -3)2

= x2 – 6x + 9

7. 4a2 –(a + b)2

= 4a 2 –( a2 +2ab + b2 )

= 4a2 – a2 - 2ab - b2

= 3a2 -2ab –b2

8. (2x -3)(x + 4)

= 2x( x+4) – 3 (x + 4)

= 2x2 + 8x – 3x - 12


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= 2x2 +5x + 12 = 2x2 +5x – 12

(I ) Factorization

* Process of writing an expression as a product of two or more factors.

- List out common factors for each alg. term , determine the HCF of the terms .

- Write as the product of 2 factors

Example Exercise1. st – sr = s( t – r )

2. 4m + 12mn – 16m2

= 4 xm + 4 x 3x mxn- 4 x 4 x m x m = 4m ( 1 + 3n – 4m)

3. 6d2 – 3d = 3 x 2 x d xd – 3 x d = 3d ( 2d – 1)

4. 10mn – 15m2

= 5 x 2 x m x n – 5 x 3 x m x m = 5m ( 2n – 3m )

1. 6a – 24c =

2. 4m3 – 6m2

=

3. 8ax + 4bx – 2cx =

4. x2yz – xy2z =

5. 3st2 – 15 stw =

6. 2yz – 4yz2 + 6xyz =


ab – ac = a ( b – c) a = common factor

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*Factorize an expression by using the difference between 2 squares i) expressions which consist of 2 terms :

Example Exercise1 9 – a2

= 32 – a2

= ( 3-a)(3+a)

2. 4x2 – 25y2

= 22 x2 – 52 y2 = ( 2x)2 – (5y)2

= ( 2x – 5y)( 2x + 5y)

3. 8g2 – 18h2

= 2 ( 4g2 – 9h2 ) = 2 [ ( 2g)2 – ( 3h)2 ] = 2 (2g -3h) (2g + 3h)

1. w2 – 25 =

2. 5x2 -5 =

3. 12d2 – 75 =

4. 36c2 -100e2

=

ii) expressions which consist of 3 terms

Example Exercise1. 9x2 + 6xy + y2

= (3x2) + 2 (3x)(y) + y2

= ( 3x + y)2

2. p2 – 4pq + q2 = p2 – 2(p)(q) + q2

= (p – q)2

3. 16p2 – 24pq + 9q2

1. a2 + 4ab + b2

=

2. 4x2- 20x + 25 =


a2 – b2 = ( a – b)( a + b)

a2 + 2ab + b2 = (a + b)2

a2 - 2ab + b2 = (a - b)2

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= (4p)2 – 2(4p)(3q) +(3q)2

= (4p –3q)2 3. 9e2 – 12 ef + 4f2

=

iii) expressions which consist of 4 terms

Example Exercise1. w2 + wz + 6w + 6z

= (w2 + wz) +( 6w + 6z)

= w(w+z) + 6(w+z)

= (w + 6)(w+z)

2. a2b2 + a2b + b+1

= (a2b2 + a2b) + (b+1)

= a2b (b + 1) + 1(b+1)

= (a2b +1)(b+1)

3. 2x2 - 4xy + 6y – 3x

=(2x2 - 4xy) + (6y – 3x)

= 2x (x -2y) + 3 (2y- x)

= 2x(x – 2y) – 3(x - 2y)

= (2x - 3)( x - 2y)

4. ab + bc – ad – dc

= (ab + bc) – (ad + dc)

= b(a+c) – d(a+c)

= (b– d)(a+c)

1. pq + qr + ps + rs

=

2. 2ab + bc + 6ad + 3cd

=

3. de – de2 + 7de – 7d

=

4. 10 + 3ab – 15a – 2b

=


ax + ay + bx + by = (ax + ay) + (bx + by) = a( x+y) + b(x+y) = (a+b)(x+y)

ax + ay - bx - by = (ax + ay) -(bx + by) = a( x+y) - b(x+ y) = (a -b)(x + y)

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Common Errors

Errors Correct Steps

1.

=

2.

=

= x – 3

3. x2 – 9

= (x + 9 ) ( x – 9)

4. y2 - 62

= ( y – 6 )2

1.

=

=

2.

=

= x + 3

3. x2 – 9

= x2 - 32

= (x + 3 ) ( x – 3)

4. y2 - 62

= ( y – 6 )( y + 6)

J) Factorizing & Simplifying Algebraic Expressions

* Algebraic Fractions are fractions with either its numerator or

denominator or both having algebraic expressions

Examples :


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I) Simplifying algebraic Expressions

* divide the numerator and denominator by their common factors.

* factorizing the numerator or denominator or both and then divide the

numerator and denominator by their common factors.

Example Exercise

1.

=

=

2.

=

=

3.

=

4.

=

=

=

1.

=

2.

=

3.

=

4.

=


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ii) Addition & Subtraction of Algebraic Expressionsa) Algebraic Fractions with same denominator

Example Exercise

1.

=

2.

=

=

=

=

1.

=

2.

=

b) Algebraic Fractions with different denominatorExample Exercise

1. (LCM = 5b)

= +

=

2. ( LCM =4x2y)

=

=

3. (LCM = 6ab)

=

=

=

1

=

2.

=


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= 3.

=

iii)Multiplication and Division of Algebraic Expressions

a) Multiplication 2 algebraic fractions involving 2 types : * Denominator with one term

Example Exercise

2.

=

=

= 4mn

1.

=

2.

=

3.

* denominator with two terms

Example Exercise

.

2.

1.

=

2.

=


1.

1.

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=

=

.

Division of Algebraic Fractions

* Denominator with one term

Example Exercise

1.

2.

=

=

3.

=

=

=

.

1.

=

2.

=

3.

=

4.


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*Denominator with 2 terms

Example Exercise

2.

=

=

=

3,

=

=

=

1.

=

2.

=

3.

=

4.

=

5.

=


1.

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Common Errors

Errors Correct Steps

1.

=

=

2.

=

=

3 .

= =

4.

1.

=

=

2.

=

=

3.

= = -

4.


5 5

6

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Questions based on PMR Format

(A) Simplify each of the following expressions : 1) 4a – (a – 5) 11. (a – 3)2

2) 10q + ( -6q) -5 12 ( 3x + 2)2

3) 6p – ( -3p) – 2p 13. (5d – t)2

4) 4a – a( b+4) 14. (x – 2)2 – x( x -6)

5) -5m – 4(m – 2) 15. ( 2y + 3)2 – ( 5y - 2)

6) 6b – (b +3) 16. ( 3w –z)2 + z(2w –z)

7) 5x – 3(2 - x) 17) (k-2)2- 8 + 3k


6.

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8) 4k(k – 3m) – 3m(m – 4k) 18) ( 6s -1)2 – ( 4s + 1)

9) 3(x –y ) – 2 ( y – x) 19) 2 ( 3y- 4) + ( y -5)2

10) -3 ( c – d) + 2 ( 4c -2d) 20) (2p +q)2 - q(4p – 2q)

(B) Factorise completely each of the following expressions :1. 12xy – 4x2 11. 4x -3y –xy – 12

2. 6e – 18ef 12, a2 b2 + a2b + b + 1

3. 4x2 -100

13. 2m2 –m + 2mn

4, 75 – 3m2 14 9c2 – 100d2

5. 3y + 12 15 uv + wv –ux –wx


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6. 20 – 5x2 16 ab+ bc –ad-cd

7. 3st – 15st2u 17. k2-14k + 49

8. 36x2 – 81y2 18. g2 -12g + 36

9. m3 – 9m 19. 3x-4y-6wx+8wy

10. 4p2 -1

20. 2pq- 6pz – 3rq + 9rz

(C) Express each of the following expressions as a single fraction in its simplest form

1. 9.

2. 10


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3. 11

4. 12.

5. 13.

6. 14.

7 15.

8. 16.


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(D) Expand each of the following expressions1. 2 (m+1) 10. (p + 2z )( p – x)

2. 3b (b – 3) 11 (n -7)2

3 -2a ( x – 4) 12. ( r – t)2 -4rt

4. 2k2 ( k – 7) 13 (4m -2)2 + 7m

5. – 5x ( x – 2y) 14 (a+ 2d)( a+ 2d)

6. 2e( 4e – f + 7) 15 (3ª +b)(2a- 2c)

7 16 ( x – 3y)( x + 3y)

8. -6pq(2pq + 4p – 3q) 17 . (2a + 1)( b- 3)


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9 4 ( - 3s + 5h) 18. (x -2)( y + 3)

PMR past year questions

2004

1. Simplify (3x-1)2 –(7x + 4) (2 marks)

2. Factorise completely a) 9xy -3x2 b) p2 – 6(p+1) – (8 –p)

( 3 marks)

3. Express as a single fraction in its simplest form

( 3 marks)

2005

4. Simplify (2p- q)2 + q(4p –q) ( 2marks)


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5. Factorise completely each of the following expressions : (a) 4e – 12ef b) 3x - 48 ( 3 marks)

5. Express as a single fraction in its simplest form.

( 3 marks)

2006

6. Factorise completely 50 – 2m2 (2 marks)

7. Simplify 3 (2p -5) + (p – 3)2 ( 2 marks)


(3 marks)

2007Algebraic Expressions 103

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9. Factorise completely each of the following expressions :

a) 2y + 6 b) 12 – 3x2 ( 3 marks)

10. Expand each of the following expressions : (a) q(2 + p) (b) ( 3m –n)2 ( 3 marks)


(3 marks)

2008

12. Simplify 2p – 3q – (p + 5q) ( 2 marks)

13. Expand each of the following expressions :

(a) 2g ( 5 –k) (b) ( h – 5)(3h + 2) ( 3 marks)


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( 3marks)

CHAPTER 7 : ALGEBRAIC EXPRESSIONSANSWERS

A unknown 1. Number of books 2. number of monkeys 3. unknown : y Object : z 4. unknown : k Object : a

B Algebraic terms (i) 1) -3

2)

3) 0.7 4) 1 (ii) 1) unlike term 2) like term 3) unlike term 4) unlike term

C) Algebraic Expressions i) Number of term 1) 3 2) 4 3) 5 ii) simplify Algebraic Exp. 1) 7x – 8y 2) 3z – 11w 3) 9r + 7s 4) -2k-5 5) -5t+7s 6) 2s -1 7) -18w D) Alg Terms in two or more terms * Identify coefficient of unknown -3b , -3c, -3, -3b2

E) Multiplication & division of alg terms

i) find product of 2 alg terms 1) a3b2

2) -6xy2z 3) 3ab3c4

4) 56p4q2r3

5) 6w3z4

6) -

7) 21m ii) find quotient of 2 alg. Terms

1) 3)

2) 4) -3rt

iii) Multiplication &Division of alg terms

1. 16p2r2

2 18k 3. -4ab4

F. Computation involve Alg Exp. 1. 40m – 16 2. -2a – 6b 3. -8p + 21 4 10 + 3t 5 2s - 33 6 -3pq+2qr –pqr 7 x – 3 – 5y 8. -3p2

9. 6u2-12

G. Expanding single Brackets 1. wy + y2


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2. -15ef – 10eg 3 4r – 3rs + rt 4 4xyz – 2xyw + x2y2

H. Expanding double brackets 1. ab + a -2b -1 2. 3m2-mn + 9m -3n 3. -6st – 8s – 15t -20 4. a2 -6a + 9 5. 9m2 -6mn +n2

6. 25x2+20x + 4 7. y2+8dy+16d2

I. Factorization 1. 6( a – 4c) 2. 2m2( 2m -3) 3. 2x ( 4a + 2b –c) 4. xyz( x -y) 5. 3st (t-5w) 6. 2yz( 1- 2z +3x)

i) expressions which consist of 2 terms

1) (w – 5)(w + 5) 2) 5(x – 1)(x + 1) 3) 3(2d-5)(2d +5) 4) (6c -10e)(6c +10e)

ii) expressions which consist of 3 terms

1) (a + b)2

2) (2x – 5)2

3) ( 3e – 2f)2

iii) expressions which consist of 4 terms 1) (q +s)(p + r) 2) (b+ 3d)(2a+c) 3) (de – 7e)(1- e) 4) (5 –b)(2 – 3a )

J) Factorising & simplifying Alg Expressions.

i) Simplifying alg Expressions

1.

2

3.

4

ii) Addition & Subtraction of alg Exp.

a) Alg Fraction with same denominator

1.

2

b)Alg Fraction with different denominator

1.

2.

3.

iii) Mul & division of Alg Exp a) Multiplication of 2 alg

fractions * Denominator with one term

1.

2.

3.

* denominator with 2 terms

1.

2

b) Division of Alg Fractions * Denominator with one term

1.

2.

3.

4.


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* Denominator with 2 terms

1.

2.

3.

4

5.

Questions based on PMR Format

A. Simplify expressions 1. 3a+ 5 2. 4q -5 3. 7p 4. –ab 5. -9m+8 6. 5b -3 7. 8x – 6 8. 4k2 - 3m2

9. 5x – 5y 10. 5c – d 11 a2 - 6a + 9 12 9x2+ 12x +4 13 25d2 -10dt + t2

14 2x + 4 15 4y2 + 7y + 11 16 9w2 - 4wz 17 k3 –k -4 18 36s2 – 16s 19 y2 -4y + 17 20 4p2 + 3q2

B. Factorise Expressions 1 4x( 3y – x) 2. 6e( 1 – 3f) 3 (2x – 10)( 2x + 10) 4. 3 (5 –m)(5+m) 5. 3( y + 4)

6. 5(2-x)(2+x) 7. 3st(1 – 5tu) 8 9(2x -3y)(2x+3y) 9 m(m-3)(m+3) 10 (2p-1)(2p+1) 11 (x+3)(4-y) 12 (a2b+1)(b+1) 13 m(2m-1+2n) 14 (3c-10d)(3c+10d) 15 (v-x)(u+w) 16 (b-d)(a+c) 17 (k -7)2

18 (g – 6)2

19 (3x -4y)( 1-2w) 20 (2p-3r)(q-2)

C) Express expressions as a single fraction in its simplest form

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Module PMR

16.

D Expand expressions 1. 2m+2 2. 3b2 -9b 3. -2ax+ 8x 4.. 2k3 – 14k2

5. -5x2+ 10xy 6. 8e2 -2ef +14e 7. 4sx -8sy +6s

8. -12p2q2 -24p2q +18pq2

9. -12s +20h 10. p2 –px + 2pz – 2zx 11. n2 -14x +49 12. r2 -6rt +t2

13. 16m2 -9m + 4 14, a2 +4ad + 4d2

15. 6a2 -6ac+2ab-2bc 16. x2 + 9y2

17. 2ab- 6ª + b -3 18. xy +3x -2y -6

PMR Past Year Questions

2004

1. 9x2 -13x -32. a) 3x(3y-x)

b) p2- 7p -14

3.

2005

4. 4p2

5. a) 4e(1-3f) b) 3(x-4)(x+4)6.

7.

2006

6. 2(5 –m)(5 +m)7. p2 – 6

8.

2007

9. a) 2(y+3) b) 3(2-x)(2+x)10. a) 2q+pq b) 9m2- 6mn +n2

11.

2008

12. p -8q13. a) 10g -2gh b) 3h2 -12h -10

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Module PMR


Documents

Chapter 7 Algebraaic Expressions