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1 Calculate the value of 33023 8 Calculate the value of )642(365
2 Calculate the value of 23612 9 Calculate the value of
2
13616
3 Calculate the value of )345(239 10 Calculate the value of )4(3667 +
4 Calculate the value of 124849 11 Calculate the value of )2(3647
5 Calculate the value of)]9(12[255 +
12 Calculate the value of )336(478
6 Calculate the value of 154534 13 Calculate the value of )5(683
7 Calculate the value of 92771 14 Calculate the value of 36327
2
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15 Calculate the value of21
2
2
13
2
11 + and
expre the an!er a a fract"on "n "t
lo!et ter#$
19 Calculate the value of15
2
4
11
6
1 + and
expre the an!er a a fract"on "n "t
lo!et ter#$
16 Calculate the value of16
3
7
11
5
1 + and
expre the an!er a a fract"on "n "t
lo!et ter#$
20 Calculate the value of14
3
3
12
5
2+ and
expre the an!er a a fract"on "n "t
lo!et ter#$
17 Calculate the value of15
4
2
12
2
11 and
expre the an!er a a fract"on "n "t
lo!et ter#$
21 Calculate the value of46
11)
3
13
2
1( + and
expre the an!er a a fract"on "n "t
lo!et ter#$
18 Calculate the value of
+
4
3
2
13
2
1 and
expre the an!er a a fract"on "n "t
lo!et ter#$
22 Calculate the value of14
3
6
5
3
21
and
expre the an!er a a fract"on "n "t
lo!et ter#$
3
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23 (a) %"nd the value of &
3 008$0
(') Calculate the value of &
3
525
4
27 (a) %"nd the value of &
3 000064$0
(c) Calculate the value of &
2
)2(16
1
24 (a) %"nd the value of &
3 027$0
(d) Calculate the value of &
2
38116
28 (a) %"nd the value of &
3 125$0
(e) Calculate the value of &
2
3 481
25 (a) %"nd the value of &
3 216$0
(f) Calculate the value of &
3
4
1
144
29 (a) %"nd the value of &
3
125
1
() Calculate the value of &
23
9
227
26 (a) %"nd the value of &
3
125
8
(h) Calculate the value of &
( )2
100025$0
30 (a) %"nd the value of &
3
8
33
(") Calculate the value of &
3
2)2(361
31 xpand each of the follo!"n expre"on&
(a) )5(3 hk
35 xpand each of the follo!"n expre"on&
(a) )3(2 yx
4
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(') 17p* 2(3 + 5p) (') 12n+ 2(3n* 5)
32 xpand each of the follo!"n expre"on&(a) )9(2 hg
(') 25y* 4(1 + 3y)
36 xpand each of the follo!"n expre"on&(a) )3(3 abb
(') 7h* 3(8 , 5h)
33 xpand each of the follo!"n expre"on&
(a) )3(2 vu
(') 13s* 2(5 * 3s)
37 xpand each of the follo!"n expre"on&
(a) )68(2
1kj
(') 27g* (,3 * 10g)
34 xpand each of the follo!"n expre"on&
(a) )912(3
1wu
(') 45m* 3(9 + 5m)
38 xpand each of the follo!"n expre"on&
(a) )7(3 wu
(') 15r* 2(3r, 7)
39 Diagram 1"n the an!er pace ho! -uadr"lateral STUVdra!n on a r"d of e-ual
-uare$ UT" the "#ae of UTunder a rotat"on 180.a'out the po"nt /$
n Diagram 1 co#plete the "#ae of -uadr"lateral STUV$
5
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n!er &
Diagram 1
40 Diagram 2"n the an!er pace ho! -uadr"lateralABCD dra!n on a r"d of e-ual
-uare$BC" the "#ae ofBCunder a rotat"on 180.a'out the po"ntX$
n Diagram 2 co#plete the "#ae of -uadr"lateralABCD$
6
UV
TS
T
U
Q
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n!er &
Diagram 2
41 Diagram 3"n the an!er pace ho! -uadr"lateralPQRSdra!n on a r"d of e-ual
-uare$ QR" the "#ae of QRunder a rotat"on 180.a'out the po"ntX$
n Diagram 3 co#plete the "#ae of -uadr"lateralPQRS$
7
C
D
B
A
X
C
B
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n!er &
Diagram 3
42 Diagram 4"n the an!er pace ho! -uadr"lateral STUVdra!n on a r"d of e-ual
-uare$
8
X
P
Q
R
S
Q
R
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n Diagram 4 dra! the "#ae of -uadr"lateral STUV under a reflect"on a'out the
l"nePQ$
n!er &
Diagram 4
43 Diagram 5 "n the an!er pace ho! pentaon ABCDEdra!n on a r"d of e-ual
-uare$
n Diagram 5 co#plete the "#ae of pentaonABCDE under a reflect"on a'out the
l"nePQ$
9
UV
T
S
P
Q
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n!er &
Diagram 5
44 Diagram 6 ho! t!o -uadr"lateral PQRS and PQRS dra!n on a Carte"an
plane$PQRS" the "#ae ofPQRSunder tranfor#at"on F$
10
A
B C
ED
P
Q
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y
x24 6420
2
4
6
4
2
Q
S
RP
Q
S
RP
ecr"'e "n full tranfor#at"on F
45 Diagram 7 ho! t!o -uadr"lateral PQRS and PQRS dra!n on a Carte"an
plane$PQRS" the "#ae ofPQRSunder tranfor#at"on F$
11
Diagram 6
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y
x24 6420
2
4
6
4
2
P
R S
Q
ecr"'e "n full tranfor#at"on F
46 Diagram 8 ho! t!o -uadr"lateral PQRS and PQRS dra!n on a Carte"an
plane$PQRS" the "#ae ofPQRSunder tranfor#at"on F$
12
Diagram 7
Q
R
P
S
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y
x642
ecr"'e "n full tranfor#at"on F
47 Diagram 9 ho! t!o -uadr"lateral PQRS and PQRS dra!n on a Carte"an
plane$PQRS" the "#ae ofPQRSunder tranfor#at"on F$
13
Diagram 8
2
4
6
P
Q
R
S
24 0
4
2
P
Q
R
S
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y
x24 6420
2
4
6
4
2
P
R
S
Q
ecr"'e "n full tranfor#at"on F
48 Diagram 10 ho! t!o -uadr"lateral PQRS and PQRS dra!n on a Carte"an
plane$PQRS" the "#ae ofPQRSunder tranfor#at"on F$
14
Diagram 9
P
Q
R
S
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y
x24 6420
2
4
6
4
2
P
R S
Q
ecr"'e "n full tranfor#at"on F
49 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 2x* 1 3 $
55 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"tx , 7 >,1$
50 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"tx + 7 >5$
56 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 3x , 1 >5$
15
Diagram 10
P
Q
R
S
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51 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 6 ,x >5$
57 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 622 x
52 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 41 x58 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 813 +x
53 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 752 >x59 "t all the "nteer value ofx!h"ch
at"f the "ne-ual"t 107 n
61 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 3x* 2 4 and
x + 6 5$
16
n & 0 1 2
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62 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 2x* 1 9 and
2,x 1$
63 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 3x+ 2 5 and
1,x 3$
64 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 4x* 1 7 and
3 *x 5$
65 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 2x+ 1 9 and
3 ,x 1$
17
n & 2 3 4 5
n & , 1 0 1
n & , 1 01 2
n & 2 3 4
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,67 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 2x+ 5 : 3 and
4 ,x 5$
68 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 3x+ 7 : 4 and
4 ,x >1$
69 "t all the "nteer value ofx!h"ch at"f 'oth the "ne-ual"t"e 2x+ 7 3 and
3 ,x >2$
70 ;n Diagram 11 C" the #"dpo"nt of the tra"ht l"neBD$
18
A
B DC
13 c#
7 c#
x.
n & , 1 0 1
n & , 1 0 1 2
n & , 2 , 1 0
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Diagram 11
%"nd the value tanx.
71 iagram 12ho! a r"ht anled tr"anleE!andDE" a tra"ht l"ne$
Diagram 12
%"nd the value cox.
72 ;n iagram 13,QTS" a tra"ht l"ne$
19
D E
20 c#
16 c#
x.
!
Q ST
8 c#
12 c#
x.
P
y.
R
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Diagram 13
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Diagram 15
75 Diagram 16 ho!a r"ht anled tr"anle PQR"
Diagram 16
76 Diagram 17 ho!t!o r"ht anled tr"anlePQT and CDB
21
5 c#
x.
S
15 c#
P
RQ
39 c#
y.
T
R
y.
;t " "ven that "nx.=13
5and coy
.=5
3
(a) f"nd the value tan x.
(') calculate the lenth "n c# ofPQR$
QP
;t " "ven that co y.=135
calculate the lenth "n c# ofPQ$
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Diagram 17
77 Diagram 18 ho!a r"ht anled tr"anle PQR"
Diagram 18
78 >he d"ara# ho! a parallelora#$ n the -uare r"d of "de 1 c# "n the an!er pace
dra! the parallelora# u"n the cale 1 & 200$
22
10 c#
x.
S
30 c#
P
RQ 48 c#
y.
14 #
8 #
6 #
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79 >he d"ara# ho! a trape?"u#$ n the -uare r"d of "de 1 c# "n the an!er pace
dra! the trape?"u# u"n the cale 1 & 200$
80 >he d"ara# 'elo! ho! polon @ dra!n on a r"d of e-ual -uare !"th "de of
1 un"t$
23
16 #
6 #
10 #
S
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n the r"d "n the an!er pace redra! polon @ u"n the cale $2
1&1
81 >he d"ara# 'elo! ho! a polon$
24
45 #
20 #
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n the r"d "n the an!er pace redra! the polon u"n the cale $500&1
82 >he d"ara# ho! a parallelora#$ n the -uare r"d of "de 1 c# "n the an!er pace
dra! the parallelora# u"n the cale $3
1&1
25
35 #
10 #
4 c#
2 c#
1 c#
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26