2
My
.
16
.
12
25
21
⑦
22
13.
It 2]
14, 2
24
Is
!↳
V
6
73
25, 4483
, 300
17
&
18 &
.
8
V 19.
10.
13
zo
+
15
S
2024
33/20
-
-
2011
~.
E
.
12
13
1983
.
21
⑭
.
22
23
.yo
360
.
24
07
.
25
.
42
16 , 3
.
8 .7
9 ~ 18 36 1255 1256
7
+
+
,
.
10/19 . V
19
20. to
7
.
7
.
s
6
.
-)
=
=
=-
- it -
-I
S
- -
-
5
- ++
=
-
=
-
+
T
+...
-
to
e
col~ 20063X
2023
-
2023
=
7x289
17 x119 High
.
153
↳
53
9979 ?
171449
lig
zo
-
'T 76
③ If is
s
a
real
fraction
n
,
&S
are
prime natural
numbery and find the Lun of possible values of b
,
,
flute
> 14b (2023
-
factor of 2023
=> 7 17 + 119 +289+
> b if a
-
+
2023
⑦ Let m
of
m
-
be I natural numbers find the number of solutions
in
n
,
! 2023.
=
Solution
Only
so
m=
D
45n 2
=
.
worky.
Find the value of
99
⑤
H
+... + 25
+
42 + 52 62
4 - 0016
57 0025
6 7 0036
77 0049
8- 0064
Formulas
>fur
-
of equares first h natural numbers
97 0081
D(2n 1)
-(n
+
10 -01 88
11-012/
12
·
:
6
>
-
first
44
3
52
> firsth
-
00
I
wos
2n(n + 1)(in)
-
3
i
,
223x24x47 ( 22
-
4324
=
+ 4/
Y
even
Da
190The
21f
old nos :
n
-)(2n+)
-(2n
1401 99
1770289
+
=
4318
-
+
14
+
3)
:
:
⑧ I -ty
x
=
+
-
+ 12) (2)2
4x (=
+
+
130x + 52
39x() 70([zx23) +26x +2023
+
-
-
2
x(gx 18x + 529) + 3(9x
=
-
-
128x+
3
52) + =(3x 23) 35(3x 2)
+
-
-
26x +2023
+
-
(43
=
-
I
138x+52x
+ 27x2
I
&
414x + 1587 + 17x
-
&
-
17 + 1054 897
-
&
I
+ 27
TT
=
60
(x3 111x x + 1
%
-
+
=
Ex +
it
567 + 148
Z
=
-
=
-
6
+
-
=
803
529
(x(() 111(xzy + G +
=
62
54
817
Z
I
2023
+-
+
↳
+26x +
529
-138
f
x
-
+x-+
i
609
540
5223
4529
4347
z
x
-
347
E( +
x
-
347242
- +-347
62
↓
+
-
23= 0
x
z
1825
=
↑
HX
+
Y
(E) 2
+ 3x
=
Fe
⑧
Given
that LE+x 23 find the
=
2x2+ 3x
-
23
,
=
0
Solution
-
4x5+ 12x4 34x3 70x +26x +202]
-
-
=
24(2x2 +3x 23) +6x4 + 72
-
-
70x2 +26x+2023
I
3x(2x+ 3x 27) + 2x+7x + 2023
=
2x2 + 7x 23 + 2046
-
-
-u
value of
4x3+ 12x4 34x3-70
-
+26x +
202]
⑦
J
Find the
remainder when
202
52 ,
521
-7
.
/ (mod7)
=
(521933xE52
,
202
(od 7)
(mod #)
=
521
=
- (modif
O
I
must be an
:
even
number
(2Ineson
Jun= 2 + 4 +6 +... + 2018 + 2010 +22
2 +4
+6 +... +2022
24681012141618 20 22
24681012
eme
- Sn = X(n l)
1
+
(2 2022)x1011 = 2
=
+
=
1023132
&-
⑱
air-ab-actbo
a(a b)
-
-
c(a b)
(a c)(a b)
-
,
3
2
&
=
-
-
8 Xn b0c
=
, ,
5
,
7
,
11
,
are
13 17
,
,
prime ros
23 29 31 37
19
,
,
,
,
,
85
=
:
:
85 5x17
:
(a b) = 15/#7
-
(a b) 11715
-
=
Va
-
va
-
c =
2
>
z -
=
-atb +c
=
-
7
~
2 + 7 += 28
...
⑪
-
Perimeter of a
-
Area
-
of
triangle
42
:
84
triangle
Area f circle Als
a
in
Find the value
I
give
of K
:
triangle 1 X
up this
=
Let a & b
⑫
↑
Yattb
=
be the yide length
172
a + 5 = +29.
J
+o
A Finda
~
433
i
I
=
(a +3)
2
=
Zab I
43
...
..
q
220v
9
(a b)= 9
-
ab = 3
↳
...
1849
a-Zab +5=
of 2 eq3 .
/
⑬
(x 1)4 6(x 1) y 4(x 1)
+
=
(x+ 1)4
=
=
A4
+
+
-
-
-
+
182x+1) + 9
10A y
(A) 1) (AT 1)
-
+
-
-
((x 1) = f)((x 1)
=
+
+
=
=
(n+2x
-
1)
8)(x + 2x)
"
-
x(x+ 2)(x 4)(x 2)
+
-
⑭
(x+y (x y)
-
=
2023
>20,n
-
174119
IXyy
x
-
=
201,
=
/
W
AND
T
OR
t
↓
⑫
⑮
-
JTEPJ2 500
S
+
=
+
JTH2
25 REJEFT
+
Ex
=
~
JIOESI 11 tzEt
-
-
+
-
44
J +57 +
=
+
3x117x1/
JHJFESTI
-
EE57
JTIJ (FTE)
+
=
+
E +
5+
=
77
T7(JE 2)
+
JIET)
J
-
=
F+E +j
⑯
Find
5xz
Y
-
3x0 +8 :
(x +
>x
-
y
18y + 6z
-
+67 24 -..
:
ytbz
3x
18y
8
2x :
-
-
90
=
12z = 0
+
+
62 = 45
5y
+
(x
y zz 6x 16y 12z
-
+
-
-
15 y
147
-
...
=
-
=
4
25
-
3x 5 :
15 y + 182 1 y + 14z
-
-
322
25
160
=
160
=
=
z = 5
Sub
5y
Sus
y
into
> & E = 5 into
+ 10 = 22
4
5x+
2y
+z =
-
5
+
=
x+ 18
..
=
30 + 5 + 5
Q
.
6
: -
⑰ 20m Im
225
50
On
are
This mult be
a
↓
n
e
m
X9042
x7307 6
35270
x243079
Y
24512
/35g
=15
In
must he
Let
=
35
379
560 2)T440
=
=
45560
Two = 7/25 =
·
On be natural hos Zom
Let m
,
no
n.
of
least possible
Solutorun
factor of
factor of 3
a
eJ
a
natur of
=
=
8550- 245
35 5T,
Gri, find
the
& A 55
,
C
,
-
* ABXNIDCX
LABXvINMX
e
MN
5NX
-
=
AX
NEAXN
MN
AXXMN
=
=
0
UN
x+ x +
AYXMN
MNDX
=
5
-
21
=
NX= DN-Ax
AX + NX
=
DN
...
0
Ex
⑭
How
may
no S
.
between
-
-
999099
1008
-
C449
-
(include a
S
172
im
⑳ f(x
+ 1 = 4x4+54+ 6
4x2( +n + (x + +5 74(x24)2
=
f(x -1)
2
=
=
Yx (x) 1) +
(x -1)+5
-
4x4
-
3x2 + 4
3(xy
-
+5
⑪
ai+=
-
ab
=
(a +b) la2- ab +b2)
Carb)
Can past by
=
·
+
)
)
1
The
-
②
Ttsja
+
aia
(38x77x34x3(x11x3)
2
Origin :
I
~
W
=
2 x 3 (1x/7x19x31x37
x
132417x19x3/x37
=
New
:
C
-
2x/9x37x2x17x31x11x3
=
34 73 32
.
.
W
-
31 30
.
·
29 28
.
.
27
--
8 7 6 5 4 3 2%
.
.
.
.
.
.
~
z
~
=
2X
=
17x5x11 31x29x2x3x3
+
2-x 3 x (1x17x29x31
dis
=
118x1x 2ex31
-
17
i
8
626876
30
-
1878228a
zig
156204
=
Total
:
g
CG = 56.
=
t
②
#
stops
4x6
t
4
(2 topt) bottom
E)
(2Erfbottom
2
8
23
-
·
83.
.
= 48
( )
Ap)
+
25