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AIIGLICAI\I HIGII PAPER I (2007)edited

This questionpaperconsistsof 6 pages.

For Examiner'sUse

Answer all the questions. 1,

50

Considerthe numbersandusethemto fill in the tablebelow. (Eachnumbercanonly be usedonce.) '

-l

o.r, ,43, 3, tT, L3,-30,33, 1.3 f

t3l

Answer Two prime numbers

77 g, l3 ., -70 6..1

Two integers Two inational numbers

2.

3,rb d3 r

--L _ aw[rtt ^L

/1.

?- t

b ^* -,.dc

-\ ir rat'"2I

(a)

Calculatethe exactvalueof V8* tO6 + J4 .

(b)

of theirprimer""r"rl]lrf;l=1 ,:. 60and126,writtenasproducts Thenumbers 6a=22x3x5,126=2x32x7.Find (D the largestintegerwhichis a factorof both60 and 126,

/0X-:ll'g t -l '5- ! l:'J t1x)(= !,

b,'1. 3 8 x t o b + ,l tt-

=r@+L

: z@rL = t -lf T'/- q * 5 b

+ L

2-sxS-+2 LOL//

Answer (a)

fuL

tll

@(i) (ii)

121

l z bo

tlI

F \

3.

(a)

Evaluatethefollowing.

o)

(i)

(z-s[-to)

(ii)

[-1"(- +)]x2+(-z[*l)

Fill in the boxeswith the correetoperationsto makethe mathematicalsentencetrue.

2 t+ r t f - J 7 - 6 l l j 4 =

3a)Lt "/"

tzl

I

C - z -5 ) ( - t o )

(- +) ( ro)

:

- + o.

rii). [- sxG+)J x: + CzX-3) a

l Z X 2 +

-- >++6 : 4.

6 .

30.

Evaluate

(a)

(b)

7.66+(-o.z)'-(-s.t)

zq*(t-=) ( s r.6)

4a').+ - L b+ C o ' > ) a -[ - 5 , r ) + "6 [ + o ' o + + 5 - l l > ,g

-To

Answer (a)(t

30.

(ii).

t 4b ?.-s \ L l

rrl

€

d-5

-

I

[ + t- H ) | -t J-

rfs

qt,

t)

(+t-6)

9 t 5

(G)

t 2 :

5

tzl

(

: L

,

'

5 : l >

F

6

5

x+

5

= 7 .

Annrter (a) (b)

(2-g 2.

t21 t3l

\ .'\

r:F

/ .// /

s.

(a)

X-

Estimate,correctto onesignificantfigure,thevalueof

'Jffi

t3l

+q,got'

ffi

3 ?w+so' 'W =

lsl ar ftal-

5 + L S

5 5. 6.

(a) (b)

b (e)

t -?O,l r, find thevalueofp whenc =10 andd= 2. (c -3d)" Findthevalueof (2e+ f)(e - f +l) whene = 5 andf: 3. Giventhefsrmula p =

[o- 3(]t- -m--= P zr.,)J' .^

{0- lL

a

r) hl (lo+il@-s+ : ( r * b + 3 ) G - 3 J+ t 1 3x 3

4z

*2

3q

T A

_J* -

- l Answer (a)

(b)

g

t2l

71

t1l

7.

(a)

Given that x is an odd numb€r,find and simplifr an expression,in termsof x, for the sum of the next two evennumbers.

(b)

An approximatemethodto converta temperaturefrom Celsius("C to Fahrenheit ) ("F ) is to doublethe temperature in Celsiusandadd30. Usethis method (D to convert25oCelsiusto Fahrenheit, (ii) to write downa fomrulaexpressing Fin tennsof C.

gurA

7(n)

(W3) n4x+ ) wLw tM)44I"\rI=QC+t) +

*

= Lac*4

) i ) ) 6 ' c= [ r n z s + 3 0 ) ? F = 8o'F

tit)'

2x+4

Answer (a)

F= JL+3o

(b)(i)

Solvethe following equations.

(a) ?*t=? 3 x 5

)

L- D . : -

)?La

)

(b)

: : - l- = 4 3x

C ^+)3 x* 5 = It

X /E

\5Du z

3>c

n z-

5.

tE-X, oh bc'fh Elol'Iz,

= t5:c) L+ L

:lL

I

Lzrc-t) rr\ batn"gtdx

3

* L>c-l)

3

lL>r--+. = lzn

+

Lr+

'L.r.

t0+ *5>c = 6 x 75tc -G*= -lO blx = - t o L

oF tu

h0

F=)Lt3o ru

(i, 8.

tzl

Answer(a) *:

(b),:

_ t0. Lq

+

pl

I2l 4

9.

b )I

Simpliff the following.

ze-ls(e+2d)+6dl

(a)

(b)r-+?

:

nC^)

S e t brLT bA be

Lz

+

t 7 - + b L + S )- q L . L - I \ t7 -9'u'+7 fl^ 4at-)o

k -Dste'+2N+AJ = ) e- [ 5 e * l o d + L o { - 1 )z-l

3 LL-l)

Li S. 3

IL *13** 1 :

lz

Answer (a)

- 3e-lbd r3l

ry

-)

)t , tlrot bz

(b)

t3l

10. Productsof prime factorsof 240and540 areshownbelow. 2 4 A = 2 4x 3 x 5 , 5 4 0= 2 2 x 3 3x 5 Write down asproducts of prime factors (a) the lowestcommonmultiPle,

ttl

(b)

the highestcommonfactor of the two numbersand

tll

(c)

the squareroot ofthe productof240 and 540.

ltl

-. 0..). Lc,r,,r, tr+o, 5qp) 3 )4x 3' x 5 /r

b7, hcr Lz+0,Dry):)'x vx u t)

\

,,

ru

V 2 \ o x 5 4 o = J 2 4 x 3 x s a 7 " 3x 3x b =J 2o<34x5' = 7t x 3' xq

<J.

,,

//

a

11. (a)

a, b andc arepositiveintegerssuchthat a > b > c. If the averagevalueof these integersis 8 and6 = 5, find (i) the greatestpossiblevalueof a if it is a prime, t3l , ,

(ii)

thesmauesrpossible valueofa.W

11

'g

\liltu tc

!7b'"

,T?l!^tryafulu\il^v fa=15 L

asthe rationalnumber wherep andqare integers. ./Of canbe expressed q \l 4 q. Find the valueofp andof t-

[ur.,/5t

t tCa)00 \ > 5 > C , 7 o 0-t b + g = 9 Y 3 L .

p --

i-+ &. is

Pn@,

-_L

-Ll

q/

---

L )

& a- is l+. %rorqi"+,+ra,fu^{-

Ce4nn'ot-

ry P-S L ) 1/--

12. Factorize (a) 7ab- 4bc+ 3ba-2cb (b)

t2l t21

8 b x-l S a y-6 b y+2 0 a c

C'q?ab- 4\L+ 3ba-)ch = &ab - *flac,+ 3oJ0- Lbc, a Loa-b 6 bc

121

q,

r y -t ?

0 , * c =+ q

tll

- UbAf )D'axb) kbE,- rE""V

= kbv- -Lbrlt Loo'r-lSo"g ? )bt )x--7U, * rruLQr-3g)

: L+>3gJtrb+5a-)

ANSWER KEY

l. 3,13;-30,33; Ji, ,

7, (a)zx+ 4 (bxi)80 (iDr: 2C+80

2. (a)202 (bxi) 6 (ii) 1260

s.(")-# o);

3. (aXi)70 (ii) 30 (b) x, +

e. (a)-3e-t6dc) =f

a. @)r2.8(ii)2

10. (a) 24 r32 x5 ft) 22 x3xl k\ 23 x32x5

5. (a) 5

1 1 .( a )1 9 ( D1 7 ( i i )1 5 ( b )p = 5 , q = 2 p

6. (") -* 1u)3e

12. (a) 2b(5a-3c) (b) (x-3y)(2b+5a)

6