04 (algebraic formulae)

7/29/2019 04 (Algebraic Formulae)

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TOPIC 7 : ALGEBRAIC FORMULAE

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2

1. Given that 5p = 4m + 3 , then m =

Diberi bahawa 5p = 4m + 3 , maka m =

2.If , thenx =

Jika , maka x =

3.

Given that 72

3

12=

q

q, then q =

Diberi bahawa 723

12=

q

q, maka q =

4.Given that then k =

Diberi bahawa maka k =

5. It is given that2

4 xy = . Find the value of y when 3=xDiberi bahawa 24 xy = . Cari nilai y apabila 3=x

6. Given that = + , express u in terms ofw and v

Diberi bahawa = + , ungkapkan u dalam sebutan w dan v


3/11

PMR past year questions

2003

1). Given that 3h = 5k + 4, express k

in terms ofh.

[2 marks]

2004

2). Given that 5

k

3)2(p=

, express p in

terms of k.

[2 marks]

2005

3). Given 2py

3-4y=

+, express yin terms

ofp.

[2 marks]

2006

4). Given5

nk-3n=F , express n in terms of

F and k.

[2 marks]

2007

5). Given that r2+ 7 =p, express rin

terms ofp.

[2 marks]

2008

6). Given qr+ s =p, express rin terms of

p , q and s.

[2 marks]

2009

2010

3


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7.Given that5

3 yyk

=+

,express y in terms of k.

Diberi bahawa5

3 yyk

=+ ,

ungkapkan y dalam sebutan k.

8.Given that yk

=

3

72

,express k in

terms of y.

Diberi bahawa yk

=

3

72

,

ungkapkan k dalam sebutan y.

2011

9. Given 8= kmk ,express m interms of k.

Diberi 8= kmk ,

ungkapkan m dalam sebutan

k.

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ANSWERS

TOPIC 7 : ALGEBRAIC FORMULAE

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

5


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2003

1). 5k = 3h - 4

k =3 4

5

h

1

1

2004

2). 2p - 6 = 5k

2p = 5k + 6

p =5 6

2

k+

1

1

1

2005

3). 4y - 3 = 2y + 2p

2y = 2p + 3

y =2 3

2

p +

1

1

1

2006

4). 5F = 3n - nk

n(3 - k) = 5F

n =5

3

F

k

1

1

1

2007

5). 2r = p - 7

r = 7p

1

1

2008

6). qr = p - s 1

6


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r =p s

q

1

ENRICHMENT

1 Writeyas the subject of the equationy

kx

5=

2 Writexas the subject of the equationtm

xk

26

=

3 Given that a = 5, b = 7, and c = 4, find the value oftin the equation

c

bat

)(2 =

4 Given thatvuf

111+= , find the value of f if u = 3 and v= 4.

5 Given that qxkypx =+27 , writexas the subject of the equation.

6 If 62 += kxxy , then find the value ofyif x= 5 and k = 5.

7 Given that 52 =++ mn , write m as the subject of the equation.

8 If )],5)(3[( += xxky then find the value ofywhen x= 2 and k= 3.

9 If f

yxf 5

2

+

= , writex as the subject of the equation.

10 The price of a ticket to the zoo for an adult is RMxand the ticket price forchildren is half of that. Write an equation for the total amount of moneypaid, T, for 3 adults and 5 children.

7


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2003

1). Given that 3h = 5k + 4, express k

in terms ofh.

[2 marks]

2004

2). Given that 5

k

3)2(p=

, express p in

terms of k.

[2 marks]

2005

3). Given 2py

3-4y=

+, express yin terms

ofp.

[2 marks]

2006

4). Given5

nk-3n=F , express n in terms of

F and k.

[2 marks]

2007

5). Given that r2+ 7 =p, express rin

terms ofp.

[2 marks]

2008

6). Given qr+ s =p, express rin terms of

p , q and s.

[2 marks]

3. ALGEBRAIC FORMULAE

8

TICKET 3(a)

(a) h = 2k 3[k]

(b)2

5+=k

p [k]

(c)r

p

r

q=

21 [r]

(d) 122

= aab

[a]

(e) qr

q=5 [q]

TICKET 3(b)

(a)k

mmk = 5

[m]

(b) a = 1b

b

[b]

(c)3

5 hh

n= [h]

(d) h k(4 + h) = k[h](e)p q(3 p) = q [p]

TICKET 3(c)

(a)p

mmp = 6

[m]

(b)p r(7 +p) = r [p](c) 5h k(5 h) = k

[h]

(d) kkxxk

=

3

6[x]

(e)( )

rk

rk=

+

1

1[k]

TICKET 3(d)

(a)r

ppr = 4 [p]

(b) mkkm

=

5

[m]

(c) xy

x35

6= [y]

(d) mkkm

=5

[k]

(e)u

w

uw =

7[w]

TICKET 3(e)

(a)x(2y + m) = 3y,

[y]

(b) my y= 7,

[y]

(c) x3 = 2y,[x]

(d)2

=

y

yx ,

[y]

TICKET 3(f)

(a)n

nm

2

3+= ,

[n]

(b) mn

m=3 ,

[m]

(c)5

3 ee

d= ,

[e]

(d) p12

+= , [q]

TICKET 3(g)

(a)r

ppq =2 , [p]

(b)( )

2

2

=

n

mnm , [n]

(c)m

p

m

kp =+ , [p]

(d)q

prpq = , [p]

(e)q

r

q

pr =2 , [r]

TICKET 3(h)

(a) 3p = 2m r[m]

(b) m n(4 3m) = n,[n]

(c) kpr

=12

[p]

(d)pr

rk

+

= , [r]

(e) fg

f25 = , [f]

(f) 2m n(3 + m) = n,


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9

TICKET 3(i)

(a)a

baw 23 = , [a]

(b)nm

m

2

5

5=

,

[m]

(c)n

nm

2

4+= ,

[n]

(d) myy

m3

3

5= ,

[m]


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10

TICKET 3(j)

(a) r2 + 7 =p[r]

(b) k= 9 2p2

[p]

(c) kh =13 [h]

(d) 35

=

+ nm

mn,

[n]

(e) 523

32=

pp

[p]

TICKET 3(k)

(a)2

3 pk

= , [p]

(b)

2

=

x

xyd , [x]

(c)3

2 nm

= , [e]

(d)2

31 rp

= [r]

TICKET 3(l)

(a)1+

=

v

vwu [v]

(b) 32=

h

r[r]

(c)2

=

q

pqs [q]

(d)( )

h

mhm

21

12

= [h]

TICKET 3(m)

(a)x= 3y2 + 6[y]

(b) ps

23+ = r2, [s]

(c) 13 = kap , [a]

(d) yxmxy 3=+ , [x]

(e) cd 153= , [c]

(f)d

dkj

3

42 += , [d]

(g) h k(4 + h) = k,[h]

TICKET 3(n)

(a) km = 3(2k + p),[k]

(b)3=

pm ,[p]

(c) 23

22 =

rk , [k]

(d)1+

=

v

vwu ,

[v]

(e)yx

x 2

1

1=

+

,

TICKET 3(0)

(a) 43

52 =

rk [k]

(b)12

2

=

pk

[p]

(c)( )

532=

k

p[p]

(d) 234=

+

py

y

[y]5 mnm

=

TICKET 3(p)

(a)w

wy

+

=

1[w]

(b) 31

2=

n

t

[n]

(c)K

mT

3

1=

[m]

(d)k

kk

3

1

2

2

=

[k]

TICKET 3(q)

(a) mn

m25 = [n]

(b) ( )329

5= xy [x]

(c) 345

=

yx

xy[y]

(d) 51=+

xy [x]

(e) r (2p + q) = 3p,[p]

TICKET 3(r)

(a) dee

d3=

[e]

(b) xyy

x =1

[x]

(c)nm

m 2

2=

[m]

(d) dee

d3

2

5= [d]

(e) 2m n(3 + m) = n

TICKET 3(s)

(a)1

32

+

=

pt [p]

(b)x

yyx

243 = [y]

(c) k

p

r=1

2[p]

(d)5

83

yxy =+ [x]

(e) xxyyx

+=

3

25[x]

TICKET 3(t)

(a)2

=

x

xyd [x]

(b) mnm

43

2= [x]

(c)( )

1

1

+

=

p

mpm

[m]

(d) dee

d3

2

5= [d]

(e)5

83

yxy =+ [y]


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04 (algebraic formulae)

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