Chapter 4.1 I Algebraic Expressions ENHANCE

8/6/2019 Chapter 4.1 I Algebraic Expressions ENHANCE

1/17

Unknown

Important Concept

An unknown is a quantity whose value has not been determined

4.1.1

Example Exercise1. Azmi bought some durians

Solution:

The unknown is the number ofdurian.

1.

2.

3.

4.

5.

There were a lot of people in the fun fair.

Solution:

Mr.Tan lost a large amount of money

when he dropped his wallet

Solution:

A number of students are studying in the

library.

Solution:

My father bought a few kilograms of

rambutans yesterday.

Solution:

Ketty gained a few kilograms of weight

during the holidays

Solution:

Algebraic term

identifying algebraic terms with one unknown.

Important concept:

An algebraic term with one unknown is the product of a number and an unknown

4.1.2

EXAMPLE EXERCISE

x6 is the multiplication of the number 6 withthe unknownx

1.

2.

Determine the algebraic termwith one unknown for each

of the following.

3e

Solution:

-5t

Solution:

Algebraic Expressions 1

CHAPTER 4

4.1 ALGEBRAIC EXPRESSION I, II, III


2/17

EXERCISE EXERCISE

3. 0.8t

Solution:

4. 80w

Solution

Identify Coefficients in given algebraic term

Important concept:

the numberis known as the coefficient of the unknown

4.1.3

Identify Like Algebraic Term and Unlike algebraic Term.

Important concept:

Like term : are term have that same unknowns

Unlike term : are term that have different unknowns

4.1.4

EXAMPLE EXERCISE

Like Term:

p9 and p same

x8.0 and x4

1 unknowns

y9 and6

y

1.

2.

3.

Determine the term in each of the

following pairs of term given below liketerms or unlike terms.

kmnk 20,56.4

Solution:

10,100

jj

Solution:

39,4 zz

Solution:

Algebraic Expressions

EXAMPLE EXERCISE

1.

2.

3.

x6 : 6 is the coefficient of x

a3 : -3 is the coefficient of a

8

r: 8

1is the coefficient of r

because8

r

p : 1 is the coefficient of p

1.

2.

3.

4.

5.

k8Solution:

q65.0

Solution:

t13Solution:

p8

5

Solution:

j

Solution:

2


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Unlike Term :

p9 and q9 different

x8.0 and y2

1unknowns

w70 and 217 w

4.

5.

qq 5,11

Solution:

tt 8.0,7

Solution:

Algebraic Expressions

Important concept:

group all the like terms together

add/subtract the coefficient of the terms

leave the terms as your answer

4.1.5

EXAMPLE EXERCISE

1.

2.

3.

4.

nm

nmm

mnm

27

26

26

=

=

uk

ukkk

kukk

=

++=

++

22

9310

9310

vu

vuu

uvu

75

74

47

+=

+=

+

bq

bbqq

qbbq

26

351711

173511

=

+=

+

1.

2.

3.

4.

Simplify the following algebraic

expressions.

:129

Solutionyy

:

10811

Solution

nnn

:

84

Solution

xxw

:

9412

Solution

k+

EXERCISE EXERCISE

5.

:

871121

Solution

ddvv + 6.

:

5965

Solution

yu +

An algebraic term in two or more unknowns is a product of two or more

unknowns and a number.



4/17

4.1.6

EXAMPLE EXERCISE

1. xy5

= xy5 The coefficient ofxy is 5= yx5 The coefficient of y is x5= xy5 The coefficient ofx is y5

1.

2.

3.

4.

Write the unknowns in thefollowing algebraic terms.

ab2Solution:

qp 2

Solution :

xyz7

Solution:

5t

Solution:

Finding the product of two algebraic terms.

4.1.7

EXAMPLE EXERCISE

1.

2.

pqr

rpq

rqp

qrp

40

58

58

58

=

=

=

p

n

pppn

ppnn

nppn

=

=

322

1.

2.

3.

4.

22abcab

Solution:

)8(2

1

srs

Solution:

rssr 3

3

Solution:

baba334

26

Solution:



5/17

3.

4.

48

)4(8

)1(424

)12(4

=

+=

+=

x

x

x

x

42

2

8

2

4

2

84

2)84(

=

=

=

x

x

x

x

5.

6.

)5(32 pp +

Solution:

)52(8 nm

Solution:

EXERCISE EXERCISE

7.

9.

2

)46(5 +m

Solution:

6)694( 2 + aabab

Solution:

8.

10.

4)2420( + ppq

Solution:

3

183022 stts +

Solution:

Expanding single brackets and two brackets.

4.1.8

EXAMPLE EXERCISE



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1.

2.

3.

4.

Expanding single bracketsayaxyxa +=+ )(

aaba

abaaa

baa

pqp

qppp

qpp

bnbm

nbmb

nmb

yx

yx

yx

62

62

)62(

1520

3)5(45

)34(5

66

2323

)22(3

55

55

)(5

2

2

+=

+=

+

=

+=

+

=

=

+=

+=

+

1.

2.

3.

4.

:

)94(11

:

)52(7

:

)8(3

:

)2(10

Solution

nm

Solution

bap

Solution

y

Solution

x

+

+

EXERCISE EXERCISE

5.

7.

:

)42(3

Solution

yxyx +

:

)25(22

Solution

dccdc +

6

8.

:

)127(5

Solution

baab +

:

)37(6

Solution

tss

EXAMPLE EXERCISE



7/17

1.

2.

Expanding two brackets;

bybxayax

yxba

+++=

++ ))((

pqnpmqmn

qnpqnm

qnpm

baab

baba

bba

ba

22

)(2)(

))(2(

152068

35453242

)34(5)34(2

)34)(52(

+=

+=

+

+++=

+++=

+++=

++

9.

10

.

11

.

12

.

Solution

yx

Solution

edc

Solution

trqp

Solution

byax

)32)(116(

)12)(2(

:

)75)(3(

:

)2)((

+

+

++

EXERCISE EXERCISE

13

.

15

.

:

)9)(2(

Solution

aa +

:

)105)(3(

Solution

pqp +

14

.

16

.

:

)34)(53(

Solution

xx +

:)37)(54(

Solutionmnm +

EXAMPLE EXERCISE



8/17

3.

4.

22

22

2

2

22

2

25309

)5()5)(3(2)3(

)53(

44

2)2)((2

)2(

nmnm

nnmm

nm

xx

xx

x

+=

+=

++=

++=

+

17

.

18

.

19

.

20

.

:

)52( 2

Solution

ba +

:

)27( 2

Solution

m+

:

)6( 2

Solution

qp

:

)38(2

Solution

r



9/17

Factorising Algebraic Expressions.

4.1.9

EXAMPLE EXERCISE

1

.

2

.

3

.

4

.

5

.

6

.

)912)(912(

)9()12(

81144

)54)(54(

)5()4(

2516

)63(2

62322

1262

)35(6

3656

1830

)13(3

1333

39

)32(2

3222

64

)(

22

22

22

2

2

2

23

22

2

yxyx

yx

yx

aa

a

a

ppp

ppppp

ppp

mnmn

mmnnmn

nmmn

xx

xxx

xx

a

a

a

cbaacab

+=

=

+=

=

+=

+=

+

+=

+=

+

=

=

+=

+=

+

= 1.

2.

3.

4.

5.

6.

:

9225

:

449

:

36

:

153550

:

64

:

408

22

22

2

22

Solution

ba

Solution

yx

Solution

m

Solution

rsrssr

Solution

bxax

Solution

m

+

+

+



10/17

EXAMPLE EXERCISE

7.

8.

)53)(2(

)53(2)53(

)106()53(

106513

)32(

)3()3)(2(2)2(

9124

2

2

2

22

22

nmm

nmnmm

nmmnm

nmmnm

nm

nnmm

nmnm

++=

+++=

+++=

+++

+=

++=

++ 7.

8.

9.

:

2412329

:

3648

:

69

2

22

Solution

xyyx

Solution

ppqpq

Solution

nmnm

+

+

++



11/17

Questions based on examination format

2

2

2

2

2

2

2

2

2

2

2

)6.(

)2)(13.(

)6)(6.(

)6.(

1236.3

181512.

181512.

181512.

181512.

)63)(34.(2

6515.

5615.

5656.

1..

)7)(8.(1

+

+

+

=++

+

+

++

=+

++

++

++

++

=++

mD

mmC

mmB

mA

mm

mmD

mmC

mmB

mmA

mm

nnD

nnC

nnB

nnA

nn

4. Factorize 2592y

)53)(35.(

)53.(

)53.(

)53)(53.(

2

2

+

+

+

yyyD

yC

yB

yyA

611.

67.

57.

65.

)2(38.9

78.

56.

54.

72.

15)2(3.8

10.

2.

10.

2.

)2(56.7

12.

6.

12.

12.

2

134.6

1011.

211.

10.

211.

)2(56.5

+

+

+

+

++

+

+

+

=

+

+

+

=

aD

aC

aB

aA

aa

aD

aC

aB

aA

aa

kD

kC

kB

kA

kk

pqrD

pqrC

qrB

pqA

rqp

yD

yC

yB

yA

yy



12/17

yxC

yxB

yxA

yx

aabD

aabC

aabB

aabA

aba

mtDmtC

mtB

mtA

mt

pxD

xpC

pxB

pxA

p

xpx

xkxD

xkxC

xkxB

xkxA

xkxxkx

53

2.

53

2.

53

2.

)456(

9

1.14

36.

36.

35.

35.

)2(3.13

)4(2.

)4(2.

2.

4.

7

5614.12

)5.(

5.

5.

5.

12

)10(6

.11

33.

33.

23.

23.

)()(2.10

2

2

22

2

2

2

2

2

22

+

=

+

+

=

+

+

=

=

+

+

=

yxD 53

2. +

15. The length of a football field (4h-3) m

and its width is (3h +2) m. The perimeter of

the field, in m, is

214.

212.

110.

17.

+

+

hD

hC

hB

hA

16.If 3=x and 1=r , find the value

of

54.

18.

27.

81.

).6(2

D

C

B

A

xr

x

17.Find the value of )(2xpx when

2=p and 3=x

15.

12.

0.

4.

D

C

B

A

18.Tickets to a circus for child is RM p andfor an adult is RM q . The total price oftickets for 10 children and 2 adults, in RM,

is

qpD

qpC

pqB

pqA

+

+

+

+

.

)(12.

102.

210.

19.The value of efe 322 when 4=e

and21=f is

70.

38.

26.

22.

D

C

B

A

2

2

2

8

3.

)3(4.

8

3.

3(.

8

3

4

120

m

mD

mmC

m

mB

mmA

m

m

m

+

+

=

PAST YEAR SPM QUESTIONS.



13/17

November 2003

1. =+ )2)(3( mpmp

A. 22 253 mpmp + C. 22 273 mpmp +

B. 22 253 mpmp + D. 22 273 mpmp +

November 2004

2. =2)3()2(3 yxyxx

A. 26 yxy + C. 22 66 yxyx +

B. 226 yx D. 22 93 yxyx

November 2005

3. =+ )52)(43( hh

A. 2076 2 + hh C. 20236 2 + hh

B. 2076 2 hh D. 20236 2 hh

Jun 2006

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

A. 2y2 - xy + x2 C. 2y2 + xy - x2

B. 2y2 - xy - x2 D. 2y2 + xy - x2

November 2006

5. 3x2 - x(1 - x) =

A. 2x2 - 1 C. 4x2 - 1

B. 2x2 - x D. 4x2 - x

Jun 2007

6. (x y) (5x + 3y) x(x y) =A. 4x2 xy -3y2 C. 4x2 xy + 3y2

B. 4x2 -3xy 3y2 D. 4x2 -3xy + 3y2

November 2007

7. (2x y)2 x ( x y) =

A.3x2 - 3xy + y2 C. 3x2 + xy y2

B. 3x2 - 5xy + y2 D. 3x2 - 5xy y2

November 2008

8. 5pq 2( 1 pq) =

A. 3pq - 2 C. 6pq - 2

B. 4pq - 2 D. 7pq - 2



14/17

ANSWERS

Chapter 4 Algebraic Expressions

4.1.1

1. a lot of people

2. a large amount of money3. a number of students

4. a few kilograms of rambutans

5. a few kilograms

4.1.2

1.e

2.t3.t

4.w

4.1.3

1. 8

2. 0.65

3.-13

4.8

5

5. -1



15/17

4.1.4

1.unlike terms

2.like terms

3.unlike terms

4.like terms

5. like terms

4.1.51.-3y

2. -7n

3. -4w-9x

4. -4k-3

5. 10v-d6. -3u-15

4.1.6

1.a and b

2. p and q

3. x, y and z

4. t4.1.7

1. 232 cba

2. 24rs

3. 23r

4. 23ab

5. pp 315 2 +

6. nm 4016 +

7. 1015 +m

8. ppq 65 +

9. aabab +2

2

3

3

2

10. stts 610 22 +

4.1.8



16/17

42849.18

25204.17

15351228.16

301510515

151112.14

187.13

33221812.12

12242.11

752115.10

22.92244110.8

51035.7

126.6

1842.5

9944.4

3514.3

24.2

110.1

2

22

2

2

2

2

22

22

2

2

++

++

+

++

+

+

+

+++

+

+

+

+

+

+

mm

baba

mnnmm

qpqpp

xx

aa

yxxy

ddecce

ptqrptpr

abaybxxycdcdc

ababba

xyyx

sts

mnm

bpap

y

x

64489.20

1236.19

2

22

+

+

rr

qpqp

4.19

2

1.8( 500

2.2 (2 3 )

3.5 (10 7 30

4.( 6)( 6)

5.(7 2 )(7 2 )

6.(15 3 )(15 3 )7.(3 )

8.(2 )(4 3 )

9.(3 8)(4 3)

m

x a b

rs r s

m m

x y x y

a b a bm n

q p p

x y

+

+

+

+

+

+

+

+

Examination Format Questions

1. C 11. C

2. B 12. C

3. D 13 D

4. A 14. BAlgebraic Expressions 16


17/17

5. D 15 D

6. C 16 A

7. D 17 D

8. A 18 B

9. A 19 C

10. C 20 B

SPM Past year questions.

1. A 2. B 3. B 4. C 5. D6. A 7. A 8. D


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Chapter 4.1 I Algebraic Expressions ENHANCE