NGUYEN HAI CHAU

.

LE THONG NHAT. DANG VAN QUAN

r0 sncH vroLYMPrc

f$p

ruun

xuAr sAN GtAo ouc vtEr

heri

NAM

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h.
:r

HI./SNG DAN SU DUNG SACH

1

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C6c em cAn doc kT dO x6c dinh yeu cAu cia tung bdri thi, d6i vOi c6c hinh thuc
lhi'. "Chon dap an d1ng"; "Di6n k6t qud vdo ch6,,; ,,Vuot chvong ngai v6t,,;
"Tim dudng trong m€ cung" c6c em lam bdi truc ti6p tr6n d6.

oc ftruqn tiQn cho vi6c stlv dung s6ch vdr dp dung vdo bai thi tr6n website, & tQp
hai, hinh thOc trri loi c6c dqng bai thi "Chon cqp bang nhau',; ,,Sdp x6p,,;
"Tim dwong trong m6 cnng" c6 sqr thay d6i so vcyi tap mOt. cdch ldrm cdc dang
bai thi ndy duoc hudng d5n chi tiiSt nhu sau:
1. Tim dwong
YOu

trong m6 cung

ciu:

Em hdy gi1p th6 tim dwong trong mO cung dO d€n 6 co c0 cd r6t va gidi bai to6n
5n trong cdc 6 tr1n duong di dd chon.

Cdch ldm bdi:
BuOc 1: Tim duong di trong mO cung cho Thd
DUng b0t v6 mOt ducrng di qua di qua c5c 0, xu6t pnet
6 c6 cr] cd r5t.

Chrt

f:

Kh6ng dwEc v6 vdo c6c 6 co tuong

tu vi tri

da,* . . Vi du:

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O

c6 Thd d6n vi tri

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BwOc 2: Gi6i cEtc bititoan gQp phditr€n duong di dd chon

X6c dinh vi tri cdc 6 trong bdng ch0a c6c bdi to6n trOn ducrng di dd v6.
Vi dU: Trong mO cung & tr6n, c6c bdri to6rn Th6 gqp tr6n ducrng di ld:

4+

Bdrito6n !3 3; Baito6n

at

4

6; Bii toSn

A'

*

8 vd Bdrito6n

,t

*;11

Gidi c6c bdi to6n trong c6c 6 dd x6c dinh r6i di6n k6t qud hofc dap s6 vdo ch5
"....." sau baito6n d6.
Vi du:

a

Bdito6n 4 3
Gi6 tri c0a bi6u th0c

lx-

1l +

A.-9

x-2lai
B.

x = -3 ld:

c.-1

1

D.9
Ddp 6n: C

Bii to6n

6

t' 6

Thr,rc hiQn ph6p tinh i[(90

-2.5)

-

100] + 10 : (- 2)] : (- 5).

Ddp s6:5

4t

Biito6n G g
Tinh t6ng c5c gi6 tri nguy6n cira x th6a mdn -99 < x < 98.

Ddp s6: -197

,r
Bdrito6n

*

11

Tim gi5 tr! ldn nhdt crla bi6u th0c 15

-

(x

-

2)'.
Dap s6: 15

2. Chgn

cfp bing nhau

:

YOu cAu:

Hdy chgn trong bitng cdc cdp 6 chwa s6, ketqud phdp tinh bdng nhau'

Cdch ldm bdi:
BaOc 7; Tinh nhAm hoic ldrm tr6n giSy nh6p c6c phep tinh dC c6 kQt qud d m5i

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O.

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cqp g6m hai 0 ch0a s6,
cho c{p 6 do.

.=.--t. :

gl'

ilti

;r

-

625

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ili
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32+1

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tr
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{ (-2)':(-2)"

@

ng nhau. LAn luEt

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(2u + 6.24)

ll

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kCt

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if,
I

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",:'......==*.*"=

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3. S5p x6p
YOu

cdu:
,ia:,-

Hay sap xep cac o chua

s6, phdp

tinh trong bdng sau theo thu

ttX

gia tr! c6c s6,

k1t qud phep tinh trong 6 tdng dAn.
C6ch ldm bdi:

Buoc 7; Tinh nh6m hodc ldrm tr6n giSy nh6p c6c phep tinh de c6 k6t qud & m6i
S5p x6p c6c k6t qud theo gi6 tri tang dAn.

tnf

O.

duEc sip x6p theo c6c gi6 trl ph6p tinh trong 6
tdng dAn. 0 c6 gi6 tri nh6 nhdt trong bdng duEc dSnh s6 1; 6 c6 gid tri nh6 thr?
hai trong bdng duEc ddnh s6 2; ...
BuOc 2; Di6n s6

tqr cho c6c O

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2.(-3) + (-7)

l- 2l'. l-

t- 4l'

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o
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3.1

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+,.

...

-

' ,cAc.DETUruyEN"

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&*

*

5

*., =* hdy chgn d6p 6n dring cho m6i c6u du6i d6y bing
vio hinh
trdn

1.

"O" tru6c d6p 6n d6.

Trong cdc k6t qud sau, t6t qud ndro dring?
(1) (-5).6 > (-6).(_5)
1zy 1-21.22,

(4)2.F2)

(3) l-181 :6=-3
O n. 1zy

O a. (1) va (2) C c. (s)
2. Gi5 tri crla bi6u thrlc lx- 1l * x-.2taix =-3 ld:

On.-s

Oa.r

Oc.-r

3.

Gfd tri crja x th6a m6n 2x+ 25 =

4.

O n.t
Oa.-z
Cc.ra
clo a ld s6 nguy€n am. s6 nguy6n b phdi c6 nhong

-11

(a) lbl < lal
O n. lzy va

(3)

C

o. (2) va (3)

Op.g

ld:

di6u kiQn sau d6 a + b td s6 nguyen duong?
(1) b la s6 nguy6n duong
(2) b la s6 nguy6n dm
(3) lbl > lal

5.

c6ch t6 dfm

C

o.

-ra

di6u kiQn ndo trong cdc

O a. 1r) va (3) O c. lzy va (a) C

o. 1t) va (a)

qud ndo sau ddy d0ng?
(1) (4).25 > e.(-1 1)
KOt

(2) 12 - 3l = 13 -21
(3) (-2)3 < -32

O n.

1r1

O

O c. 1r) va (2) O o. lzy va (3)

e. (z)

8

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6.

Cho b

ldr

s6 nguy6n duong. KOt qud ndo sau ddy sai?

(1) b>-b
(2) -b<0
(3) -b = l-bl

Cn (s)

Ca.

Oc

1ty

C o. 1r)va (2)

1zy

Cho a la s6 nguy6n Am. H6i s5 nguy6n b phdi co nh0ng dieu kiQn ndo trong
cdrc di6u ki6n sau d6 a.b la mOt s6 nguy6n kh6ng 6m?

7.

(1) b la s6 nguy6n ducrng
(2) b la s6 nguyOn 6m
(3) b=0

O B.Q) va (3)
C o. 1t ) va (3)

C n. 1t)
C c. Q) hoac (3)
8.

Liet kC c6c phln tir cfra tQp hqp Q = {x e Z

l6 i x} ta duoc:

O n. O = {-6; -3; -2; -1; 0; 1;2;3;6}
OA.O={1;2;3;6)
o c. o = {_6; _3; _2; _1)

O p. O = i-6; -3;-2;-1;1;2;3;61
Ket qud cfra ph6p tinh {[(90

9.

On.s

-2.5)

C)n.+o

"i

Cc.-s

Oa.-r

10. Gi6 tri crla bi6u th0c x(x - 2)(x

Cs.o

- 100] + 10 : (-2)] : (-5) la:

-

3) tai x =

Co.r

-2la:

Cc.-e

O o. -+o

oi6n k6t qui thich hop vio ch6 ....... trong m6i cAu sau:

1. T?p hEp c6c gi6 tri c0a x th6a mdn (x -

1)(x + 2) = 0 (cac phAn tir duqc vi€t
.;') ld
theo thtr tv gia tr! tdng dAn, ngdn citch nhau bdi d1u
}

2. Gia tr! crla bi6u th0c-2a3b't ir= -1; b = -3 ld .......
3. 55 c6c udc s6 nguyOn cla 12la .. .....

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{.

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4. Ket qud cria ph6p tinh 15 - (3.52 - 5.32) Ia .....
5. Gia tri crla bi6u th0c lx + yl + lxl - lyl tai x = -2vdy = -3 la ......
6. T6ng c6c uoc nguy6n cia 4la .......
7. Gi5 trt c0a bi6u thuc -2.a.b'."u tgi a = -2;b = -3; c = -1 la .......
8. Ket qud c0a ph6p tinh (-7 + 113l)- (13 - l-71-25)- (25 + l-101- 9)ta .......
9. 56 phdn trly crlatQp hqpA= ix e Z l-610. Cho 10 diem thuOc ducrng th5ng a vd mot diem O nim ngodi ducrng thing
d6. 56 tam gi6c c6 c5c dinh ld 3 trong 1 1 diem tr6n ld .. . ....

,.'i$ffiE,Q
at

',',
^

hiy tim trong bing sau cdc c{p 6 ch&a s5, bi6u thr?c c6 gi6 tr!
bing nhau.
Em

32 +

e2)5

o

-..?

'7

oo

(-2)t
i

a.

:

(-2)3

\_-./

;

-35

i
,,'+,
.-.

2.5
()()
\-_-/

52 +

125

-"

+ 0.241: z2

/1
l-i

32.,

\--,/
2.24

\_-/

6.(-7) + (-31)

4

s2 -3.23

-1

o

+ (-1)

t----Q ;--a
10

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1.(-73)

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id
fu,t

-{r
{i

i.\*

VONG

20
Bai I

;t

..,82

Em hiy di6u khi6n xe vuqt qua c5c chw6ng ng4i
c6ch gi6i c5c bdi to6n o c6c chu6ng ng?i vft d6.

vft

tI6 ve dich bing

I
il

ffi

chuong ngqi

vQt 1:

Gia tri cia x th6a mdn 32.x= -27

ffi

Ex = .......

chweng ngqivQtl:

56 nguy6n xthoa mdn x > -3 vd x + 1 < 0 ld x

chueng ngqivQt3:
BiCt hai s5 nguy6n x, y th6a mdn lxl

+ lyl = 5. Khi d6 gi6 tri ldn nhdt crla tich xy

t4...^...

ffi

chuong nggivQt4:

Gi6 trl cira bi6u

th0cA = 1 + (-3) + 5 + (-7) + ... + 17 + (-19) la .......
11

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W

chuong ngqivdt

i:

T6ng c6c gia tri nguy6n cOa x th6a m6n -100 < x < 98 bang .......

ffi

chwong ngqivQtl:

Bi6t x th6a m6n Ix - 3l = 8. Khi do t6ng cttc gi6 tri crla x bang .......

ffi

chwong ngaivQtr:

Gia tri c0a bi6u thwc (20.2a

ffi

-

12.23

-

+8.2212 : (-8)3

chwong ngaivQtS:
a

^l
S0
cdc c{p so nguy6n (x; y) th6a m6n (x

Bei

2

-

1

XV + 2) = 7 ld

.......

LK
")

o^o Di€n k6t

1.

bing .......

qui thich hgp vio ch6 ....... trong m6i cdu sau:

56 phdn trl c0a tap hep X = {x e Zl-3 < x < 1} la .......

2. 56nguy6nxth6a mSnx- 1 <0vdx+ 1 >0 la.......
3. T6ng c6rc gi6 tri nguy6n c0a x th6a mdn -100 < x < '100 bang .......
4. Tflp hEp c6c gi6r tri nguy6n crla x th6a mdn lx + | - 5 = 0 la i. ......). (cac
1

.

phAn ttr duEc vi6t theo thu tar gi6 tr! tang dAn, ngdn cach nhau b1i dilu " i').

5.

Bi6t hai s6 nguy6n x, y th6a mdn lxl + lyl = 6. Khi do gia trt nh6 nh5t cOa tich
xy bdng .......

6.

Gia tri c0a bi6u thr?c.
C=1+

7.

(-2) *

3 + (- 4) + ... + 2A07 + (-2008) + 2009 + (-2010) ta .......

56 phAn tir crla t?p hqp citc gi(t tri crla x th6a mdn:
17

8.

-x+ lx- 4l=014.......

Tap hqp c6c gi6 tri nguy6n c0a xthda mdn lx + 1l+ lx + 2l= 1la {..........i
(cac phAn tir duEc viet theo thu trl gia tri tdng dAn, ngdn cdch nhau bdi
ddu ";").

9.

i..

Tap hep c6c s6 nguy6n n sao cho (n - 6)
..\ (cac
- 1)la
'(n ngdn
phan tir duEc vi6t theo thw tqr gia tr! tdng dAn,
cdch nhau bdi dilu ";").

10. 56 c6c

cip s6 nguyOn

(x; y) th6a mdn x(y

-

3) = -12ld .......

12

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W
?

;i

Hay s5p x6p c6c 6 chrla bi6u tht?c trong
.*' 'cria bi6u thr?c trong c6c 6 d6 ting din.
,

2.(-3) + (-7)

t4r

F2)3

o

-3.1-41

-

F3).2

1-t12

-

z4.l

-

(-,

11

o
o
o
o

o
o

(-6)

F3t1

(-2)3 : (-2)2

3 - 2.(4)2

- 12 - 3ll (-4)

-15

o

(,
(-1).(3

e2)3

l-213.F51

o

5).2

bing sau theo thri tqr gi6 tr!

(-13)

1el

(-5)2.( -3)3: 75

(4-8).5 *(-1)2

toO : 1s3 - zs;

o

z'(-z)

- 23.3

(-s)2

Fq)2

o
1s2

,i

-

- 251: 1-l'1
\.-,

(,

13

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hiy gi0p Th6 tim dudng trong mG cung O6 Oen dugc 6 c6 cti cd r6t
vi giii c6c bditoSn in trong c6c 6 tr6n dulng di dd chon.
Em

Duong di em chgn gilp Thd de vd d bdng tr1n.
Citc bditoan Th6 gdp trdn duong diva dap s6 la:
Bdi to6n

?,1,

Tim gi6 tri ldn nh6t c[ra bi6u th0c 15

-

(x

-

2)2

,

Dap s6:

Bdrito6n

? Z,

Tim s6 nguyOn x th6a m6n

x-

5 < 0 vd 3 -x < 0.

Bii toin & g'
Tim tQp hqp A c6c gi6 tri nguy6n crla x thda mdn lx + 3l + lx + 4l= 1 (cac phAn tir
dwEc vi6t theo thu tty gid tri tdng dAn, ngdn cdch nhau bhi ddu ";").
DaP s6: A = i.'....;..'.....'.)
14

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Bii to6n ?,4,
Tim gi6 tri nguy6n duong c0a x th6a m6n lx

Biito6n

?

- 1l = -(x - 1).

D6p

s6:

S'

Biet hai s6 nguyen x, y th6a mdn lxl + lyl = 8. Tim gi6 tr! nh6 nh6t cira tich xy.
Ddp s6:

Biitoin ?

O'

Tinh t6ng clc giA tri nguy6n c0a x th6a mdn -99 < x < 98'

BAi

to6n

^A

t (:

Tinh t6ng t5t cd clc gi6 tri c[ra x th6a mdn lx - 5l = MBdi to6n

Ddp s6:

Dap s5:

f, g'

Tinh gi6 tri c0a bieu thuc 54 - (-16)

- (-13) + 27.

Ddp s6:

-m,**ry
?
'^
1.

Em hiy chgn d6p 5rn dring cho m6i
vdo ht'nh trdn "O" tru6c d5P 5n d6.

Tren tQp hqp s6 nguy6n Z,t6ng c6c woc crla 6 bang:

C

2.

n.p

Oo.o

Gia tr! c0a bi6u thr?c {[14 1 (-2)] + 7] : (-14) bdng:

T6ng binh phucrng c6c s6 nguy6n

Oo.-z

Oc.o

Oe.-t
16

n th6a mdn

Oa.tg

On.o

4.

O c. -tz

Oa.o

On.t
3.

ciu duoi diy bing cach t6 dfm

-3 < n < 4 ld:

C o.t

O c. rr

TOp hEp c6c s6 nguy6n x th6a man x2 +

2x-7

chia h6t cho

x+ 2ld:

O a. {-g; -3; -1; 5; e}
O o. {-g; -3; -1; 5}

C n. i-g;-3; -1)
O c. {-3; -1; 5}
15

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5.

TOp hEp c6c gi6 tri

{s;-r}

C n. {-s; r}

6.

cia x th6a mdn -6lx - 2l = -19 td:
O e.
O c. {s; r}

Gia tr; c0a bi6u thwc (4)2.S4 b6ng:

C n. roooo

7.

Cn.ro

-5;

7) vd tQp hqp B =

ld:

Oa.n

>;n;

Oa.;a1

<;u;

C o. roo

{-2;4; -6;8i. 56 c6c tich ab, vdi a

Oc.rs

Cho hai s6 nguy6n avd b. Bi6ta <0; b >

On.;a;

9.

C e. -roooo O c. -roo

Cho tQp hqp A = i3;

eAvdbeB,

8.

O o. 1-s;-r1

0vda

Oc.

lal

Oo.g
+ b < 0. Khi

=lbl

Cfo:

Oo.;a;

<;o;

Cho a vd b ld hai s6 nguyOn khdc 0, tr6i d5u vd lal = b200e. Khi d6:
O R. a ducrng, b 6m
O a. a am, b ducrng

Oc.arb

Co.a>n

10. Gie tri l6n nh5t crla bi6u th0c -3

Ca.-s

On.s

:

Oc.-s

o
5-(2-7)
o
o
ls-tz-a)l
o
-lro
_22

t-zl

7ll 3

22.9

-3

(-z)t.s

3-92 -s)

3.22 -2.32

-2.(4)2

o

(l

-sl-a2l
llllz2 ,-1,

a)
\_-/

I

()

(3 -7).(3 +7)

- s3;.+

1s2

{)

\_-/

2.Q3

Oo.-r

cic cfp 6 choa bi6u thric c6 gii tr! bing

Em h6y tim trong bing sau
nhau.

lz3 -s1.1-sy

l,

- lx + 2l tir:

-3)

e43

ls-sl-la-sl
/\
I

l.

\_-/

-(-5).7

-32'

3.(3 - 5)

34

o

()

-(-3)2

()

(,

o

o

16

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r)

()

Download Ebook Tai: https://downloadsachmienphi.com

'

;i'. E, hiy chgn d6p 6n dring cho m5i c6u du6i diy bing cSch t6 dQm
^ '' vio hinh trdn "O" trD6c

1.

Chophdn s6 B=

+,neZ.DOgi6tri
n+5
o.e.z

O n,'rs

2.

D0 phAn s6

'b

d6p 6n d6.

3

c0a ph6ns6 B bang

O c. -rg

cO th6 viCIt ducvi dAng mQt

Oo.-z

s6 nguy6n thi di6u ki6n ld:

Oe.oeU(a) Cc.a>b

On.aet/(b)

II ,f in bing:

OD.a
3. Phan sO ndo sau day bang pnan s6 ]z
7

oc Z

14752 Oa.?9

O n. -:1

4.

Phdn s6 ndo sau dAy kh6ng bing ph0n sO

cn.
5.

oa. l9
45

-9
27

K6t qud r(t ggn c0a phdn

On.:!
2
6.

Cho phdn s6 B =

cp.-119

ta,

Oc.

Oa.rg

1
49

-12
9

oc.2*9

.6 8'5;8'2

oo.

3
2

Oo.ao

neZ. TQp hqp t6t cd c6c gi6 tri cia n d6 B nhan gi6
+,
n+7'

tri nguy6n ld:

O n. 1-to; -8; -6)
C c. {-8; -6;-a}
17

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7.

+=j=3,a,
x35z
5

CScgi6trix, y, z nguy6n th6a mdn'U =

On.x =45;y=4;z=-20
O C.x =45 y =4;z=-2

B.

-:u

Rtit sen phdn s6
'9999
1200-3

O O. x=45iy=14;z=-20
ta duEc k6t qud td:

Ce.ol3

Cn.e1
3

9.

B. x = 4; y =14; z= _20

oo.sf
-3

O c. t1
3

Cho hai s6 nguy6n duong c6 ti s6 cria ch0ng lit 2 : 5 vd tich cia ch0ng la 40.
r -, ,vay nat so oo
ta:

On.-+vd-10 Oa.+vd1o Oc.5vd8
10. Tap hEp c6c s6 nguy6n x th6a man

f .*.8

O n. 1-t; o; 1)
C c. {-1 o; 1;2)

1.

eict

1q=+
x4

C o. 2vit20

E

O B.{-2; -1; o; 1;2}
O o. {o;1;2}

Nhu vQyx = .......
.l?

56 nguyOn x nh6 nhdt ttr6a m6n x ,--:
7

56 gie tri nguy6n c0a n sao cho ph6n s5

Gi6 tri

cia x th6a mdn

--4=
6-24

ta .......

-3
(n

-

2)(1+ n)

kh6ng t6n tqi la .......

,a ... ....

5.

T6ng binh phuong crla cdc s6 nguy6n x th6a man

6.

56 cap phdn s6 bdng nhau duEc

lQp

15 ta ... ....

*22. * . 1 ta .......

tu b6n trong s5u s6 -5; -3; -2; O; 10;

18

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7.

Biet a, b la hai s6 trf nhi6n nguy6n t6 cirng nhau, tnOa man
Khi d6 t6ng

8.

a+b bdng .......

Bi6tx, y Ia hai s6 nguy6n th6a min

x

=1
3y

5a+7b
=
6a+5b

Khi d6x + ydQtgi6tri nh6 nh5t

ta .......

'=.. Khi d6t6ngx +y+2bang.......
#=
1= -u
y =-21
15 -9
10.
I. xr,i do t6ng binh phucrn g x2 +y' bang .. .. ..
- Bi6t yI =9:
x21

9.

eict

.

''8ff3.M
aI.

,t.,

^

Em hdy di6u khi6n xe vuot qua c6c chu6ng ngqi
c6ch giii c6c bii to6n o c6c chu6ng ngai vft d6.

vft

d6 vG dich bing

@ffi
ffi

chueng ngqivQtl:

56 nguy6n x ldn nhdt th6a mdn

x<--,1

3

?

|a.......

19

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&

chweng ngaivQt2:

T6ng binh phuong c5c gi6 tri nguyOn crla n ldm cho phAn s6

-5

(n+2)(2-n)

khOng

t6n tqi bing .......

ffi

chweng ngaiv1t3:

sr'
i

56 gi6 tri nguy6n crla n ldm cho ph6n

Chueng ngqi

-3
1rn

+=:=+.Khi
-65 3

' chuong ngqivdt i:
3
r t
-!Tong c6c so nguy6n c0a x th6a mdn
.

i

*.

do x + y = .......

5..

;

,a .......

chueng ngqivQt}:

56'cap s5 nguy6n (x; y) th6a man

ffi

]JY= I

ta . ... ...

chtwng ngqivQtr:

Bi6t x; y lii hai s6 nguy6n th6a mdn

2=y

x-3

. Khi d6 x - y c6 gia tri l0n

ta . ... ...

ffi.
ai6t

"'

vQt 4:

Cho x, y la hai s6 nguy6n th6a mdn

ffi

-*

kh6ns t6n tai la " "

,

chqong ngqivQt 8:

-l=*=

-gg = -14

618y2-

. rcr'i d6 t6ng x + y + z bang .......

20

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nhSt

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W
?^q

iEm hdy tim trong bing sau c6c cip 6 ch&a phdn sii c6 gi5'tri bing nhau.

1+4

3*5

\,

3-35

()
\--l

14

I
1+

tl

3

_7
1+5

\--l

2.4

r^)
\-/

12-2

8

-1-5 L'
1+3
1- 8
1+3

12

?"d

..E-#.:oian k6t

1.

2.

\--l

\'-,

28
-27

50

tt

\,

3+9

-14 ()

99

\--l

_q
e/\

\--/

10

-64
50

-

tl
30 \-/

3-18

ll

-22 \-/

-5J

o

qui thich hqp vdro ch6 ....... trong m5i cau sau:

Cho phAn s6 A
n

tl

ll

1-10 U

1-12 \,

1+1

=

H+,

vdi n ez. D6 sis tri cria phdn s6 n nans

)

tni

bing.......

56 phAn tr] c0a tQp hEp c5c s6 nguy6n
'22x th6a man

f .*.f

|a ... .. ..

3. PhAn s6 bdng phdn ,6 ]7-,, co tr}' bdng -4 thi co m5u bing .... ...
4.

Phdn s6 t6i gidn (vdi m6u duong) c0a phdn

,6

+

co t6ng crla trlr s6

m5u s6 bdng . ......

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vdr

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5.

56 phdn tr) crla tQp hqp c6c s6 nguy6n n de phdn

.6 n * 1 co gi6 tri nguyOn
n+1

ta .......

6.

cho ph6n s6 B =

2n+1'

voi

n

ez. T6ng c5c gidr tri c0a n sao cho B ldr s6

=,

nguyOn bdng...............

7.

Cho hai s6 nguyOn ducrng co ti s6 c0a chung ldtT
s6 be la 10. T6ng c0a hai s6 do ta .......

8.

Cho

9"

cho hai s6 nguyon duong c6 tis6 c0a ch0ng ldtT : 3vd tich
Hai.s6 d6 c6 t6ng binh phuong la .......

a va b la hai s5 tgr nhi6n,
5a+7b 29
6a+5b 28

10. Tich c6c s6 nguyen x th6a

'

Bai3

,n

,o.

:2 vd hi6u cfia s6 lcyn tru

nguy6n t6 cung nhau vd th6a mdn

cOa

ch[ng rd21.

,an -18
--'v""'
g . *.E4 bdns
.

JI<

Em h6y girip Th6 tim duo-ng di trong mG cung O6 OCn duqc 6 c6 c0

^ ci riit va gidi c6c bii to5n 6n trong c5c 6 tr6n duong di d6 ciign.

Duong di em chgn gilp ThO de vE d bdng trdn.
Cac bititoan Th6 gap tr,6n dwong divit d6p s5 /a:

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t,

Biito6n &

Ai6u thi 26 phrit dudi dqng phAn s6 t6i gian vcvi don vi gio.
Dap s5:

Bdito6n

?u.Z=

R0t gon bieu

thric

. .:.. :. qud
o
' fti6t
^2.011.162 +62.126.152
ket
duvi dqng phdn s5 tdi gian1.
2.012.104

-

e12.g603

Dap s6:
Biri to6n
Cho.

ft g'

o?

fi=

I. Tinh gia tri c.a x.
Ddp so:

Bii to6rn ?;4,

-- I.
-"-'-'- .6
19

Cho phdn

Tim s6

trnr

nhi6n phrii th6m d6ng thoi vdo

phdn s6 d6 d6 dugc phan s6 mcri beng

trir,

s6 vd m6u s6 cira

l.7
Dap s5:

Biito6n

Ar

*

C:

g1 gio ducri dqng s6 vcvi dcvn vi ph0t.
'3-

Bieu thi

Dap s6:
Bdi to6n

cno
Biri

&

O,

= +. Tinh gi6 tri coa x.
I824

to6n

A.

li [:

Cho ph6n sO

Ib-tOi giin. Bi6t reng n6u cQng trl s6 vfi 4, cQng mfiu s6 voi 10 thi

duEc phdn s6 mdi bdng phdn s6 dd cho. Tinh t6ng a +
Biri to6n

b.

Dap

s6:

?i g,

' " fl;
39co UCLN cOa tir s6 vd m6u s6 ldr 36.,

Tim phdn s6 c6 gi6 tri Oang

Dap sd:
23

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,u.', Em hdy chon dip 6n d(ng cho m6i c6u du0i d6y bing c6ch t6 dfm
^' vio hinh trdn "O" tru6c dilo 6n d6.

1.

56 cac gi6 tri nguy6n crla n ldm:cho ph6n s6
'

Cn.+

2.

O n.-z

4.

#=;=+

C 8.3.

Gi6 tri cia x th6a man

#

=

-

O c.z

Chox,ytdhai s6nguyOnth6hm6n

O e.zt

3.

Oe.s

- tai
-i td:
, -1)(1+2n)
,r? = . kh6ngr tOn

(n

*

O o.-1
Khi

d6x-ybing:

C c. -zt

Oo.-s

Oc.e

O

,.,

O a.z

56 c6c gi6 tri nguy6n crla n ldm cho ph6n s6

kh6ng t6n tai ld:

(2n -1)(1+ n2)

On.o
5.

Oe.r

On.o

Da.M

56 c6c cqp ph6n s6 Oang nhau
10; 15ld:

C x.q

7.

C c.z

T6ng binh phucrng crla c6c s6 nguyOn x th6a man

Bii5t a, b ld hai s6

Khi d6 t6ng a + b

O

n.t

Cc.rg
Clwoc lQp

Ce.s

o. m6t s6 mrec

Oo.s

l.42*.1

ta,

Oo.rs

tuib6n trong s6u s6 -S; -3; -2; 6;

O c.tz

Oo.ro

tu nhi6n, nguyen t6 cung- nhau vd th6a mdn 3a-?.b -11

a+Sb

bdng:
Oc.s

Oe.to
24

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Oo.t+

15

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8.

56 c6c cip s6 nguy6n (x; y) th6a man

C t. tz

1-0

-

r
Ca.-o

On.-s
15

=

]..

E,

Cc.+

Oe.o

9. Bi6t x, y lii hai s6 nguy6n ud ?x-J={.
10.
Biet
-6x21

{-ry=!
d6 x

O

Co.a

-

y dqt gi5 tri nh6 nn6t ta:

c.-t

Co.-g

rr'i d6 hiQu binh phucrn gy2 -x2

O e. tM+

O e. pzs

beng:

C c. tgso

O o. ozo

3-jgiiin k6t qui thich hgp vdo ch5 ....... trong.mSi ciu sau:
*:d

1.

cno

-!?

"no

*32= +.
96

2.

-36 . Gia tri c0a x bang . ... ...

=
22x

Gi6 tr! coa x bdng .......

3.

Bi6u thi 3,3 gio dudi dqng s6 voi don vi ph0t, ta c6: 3,3 gicv = ....... ph0t.

4.

phdn s6 t6i sidn c0a phan

5.

Cho phdn

'

.6

I18

,61.}]o

la .......

56 tu nhi6n phdi cQng th6m d6ng thcvi vdo trl s5 vd m6u s6

c0a phdn s6 oo d6 duEc phan s6 mdi bdng

Cho phAn 16

'47

+

Cho phdn so

'b

]

'a

56 nguy6n ph6i bot di d6ng thoi &

ph6n s6 d6 d6 du'Ec phan s6 mdi bSng
7.

n

tOi

*13

,^ . ..

trir

s6 vd m6u s6 crja

..

gidn. Bi6t rdng n6u cQng tir s6 vcvi 6, cQng m5u s6 voi 14

thl duEc phdn s6 mdi bang phAn s6

di

cho. Gi6 tri c0a t6ng a + b ld .......

25

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8.

Cho ph6n sO

'b

3

+ 0, t6i gian. Biet rang n6u cQng cd trl s6 vd m5u s6 voi ttlr

s6 cia phdn s5 d5 cho thi dugc phdn s6 m0i bdng mOt nCra phan s6 dd cho.
Khi d6 gia tri cia hiQu a - b ldr .......
9.

Ph6n s6 bdng phdn

.6

+
39

vd UCLN c0a

trJr

vd m5u bing 36 td ph6n s6 c6

m5u |dr.......

f
"264

10. Phdn s5 c6 gi6 tri' bang

vd co t6ng cria tu s6 vd m5u s6 bang 40

td

phan s6 co t& bang .......

Ern hdy diifu khi6n xe vuqt qua c6c chu6ng ngai vflt d6 v6 dich bing
c6ch giii c6c bii to6n & c5c chuOng ng?i vqt d6.

I
i

:

I
I
F:,r'

ffi
crro

cno

chuong nggivQt

1:

Gi6 tri crla x bdng.
{-21=-75.
x
- chweng nggi vQt 2:
. Gi6 tri cia x b6ng.
l=
14 +
98

26

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ffit

chueng ngqivQt 3:

Bi6u thi 3 gid 24 ph0t du0i dang phdn s5 t6i gian vdi don vi gio la . .. .. ..

ffih

chuortg ngqivQt 4:

Sl gicv duoi dqng s6 tnap ph6n vcri don vi phrit la .......
'3"

Bieu thi

Chuong ngqi vQt 5:

ffi

chueng ngqivQto:

Ti s6 ph6n trdm c0a 7 vd 8

ldr:

8.87,5o/o

A.780/0

C.

15%

D.

L800

Ddp an d1ng: ...................

ffi

chueng 4g1ivQtr:

K6t qu6 rut ggn c0a bi6u

,nr"

(52

611-1^62

+,62

2.612.104

ffi

-

12=6 152^)

lo

ra .......

912.9603

cht^wng ngqi vQt B:
BCNN c0a tir s6 vdr m5u s6 bdng 36Q ld:
" *,
20' "o
o
18
u._36
D.
B."20
40
80

PhAn s6 c6 gi6 tri bang

A.27
60

27

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Em hdy tim trong
nhau.

bing sau c6c c{p 6 chr}a bi6u thrlc c6 gi6.tr! bing

11
_+_
2.4 I
6+

::

d+*=&@:f

'.-.i.+:ii!ri=i

1

-+
2
'-'-

9

15

8

, -1-s L,

*,1

'-51 s

I

-7.5

-14.4 l,

1+3
_tr
v

20
10

-

30 (.-,

^ii ""_1*"^-^

/\
2.2 Z \-)

Di6n k6t qui thich hqp vdo ch6 ....... trong m6i cau sau:
Vdi

a

.. thi a2 + 4 vd ,2

-

4 d6u td s6 nguyGn t5.

56 b6 nh6t khi chia cho 3 dw 2, chia cho 4 du 3, chia cho 5 du 4, chia cho 6
du 5la s6.......
3.

VE n tia phAn biQt chung g6c. Bi6t rdng tr6n hinh vE co 36 g6c. Khi do gi6 tri
cOa n Ie ......

4.

Cho duong thing xy di qua di6m O. TrOn cing mOt n&a mqt phing bd xy, v6

c6cgoc

A&=2oo;@=600.

Khid6 A6B

=

28

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5.

Tim mQt s6 co b5n cho s6, biet ring t6ng c6c cho s6 crla no bdng 22 vit khi
chia s6 do cho 1996 thi dugc s6 du bang 199S. 56 cAn tim ta .......

6.

Tim s6 bi chia biCt s6 chia ld s0 tu nhi6n nh6 nh6t sao cho phep chia dy co
thuong ld 8, s6 du la 36. S6 Oi cfria cdn tim ta .......

7.

Khi chia mOt s6 ty nhi6n cho 52, mot hoc sinh dd ch6p nhAm chcr s6 hdng
trdm crla s6 b1 cfria ld 7 thdnh 3 vd chCv s5 nang don vi ld 3 thanh 7 nen dusc
thucrng ld 122 du 13. Thuong d[ng cr]a ph6p chia d6 la .......

8.

Cho g6cxOy kh6c goc bqt. TrOn tia Ox l5y h01ai di6m A, B kh6c O. TrOn tia
Oy l5y ba diem C, D, E kh6c O. 56 tam giSc co ba dinh la ba trong sdru di6m
A, B, C, D, E, O la .......

9.

Cho 7 di6m thuQc mOt ducrng thing a vd m6t di6m O nam
thing 5y. 56 tam gi6c c6 cAc dinh la ba trong 8 di6m tr6n td

I ,a
"85

10. s6 t5t cd c6c phdn s6 oang

ngoeri duong

tr) s6 va m5u s6 d6u rd c6c s5 tu nhi6n

co ba chtr s6 la .......

tt

u"; E.

^

hdy girip Th6 tim duong trong m6 cung A6 Oen duqc 6 c6
vd gidi c6c bdi to6n 5n trong c6c 6 tr6n dulng di di chgn.

29

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ci ci

r6t

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Dwong di em chgn giup Thd de vd d bdng tren.
Cac bditodn Thd gqp tr1n duong di va dap sd /a;

Bii to6n ?:1,
TrOn tia Ox, l5y b6n di6m A, B, C sao cho OA = 2cm; OB = 5cm; OC = 8cm. C6
.. t . . 3
tne Knang olnn:

A. A le trung di6m cira OB

B. B la trung di6m crla AC

C. B la trung di6m c0a OC

D. B nam gi[ra A vd O
Ddp 6n d1ng:

A^

Bii to6n !? Z:
nguoi di b0 dugc 40m trong mQt phtit vd mOt ngucri di xe dap di ducyc 12km
trong m6t gicr. Tinh ti s6 vqn t6c cia nguoi di bQ va ngucri di xe dqp Uiet du6i
dqng philn sO tli gidn).
MQt

Ddp s6:
Bdi to6n

?

g,

TrOn tia Ox, l5y ba di6m M, N, P sao cho OM
Khi d6:

A. NP = 6cm

B. OP = 1cm

C. NP = 4cm

D. MN = 2cm

= 4cm; ON = 5cm; MP = Scm.

Dap an d(tng:

Biitodn ?r+,
.. :.

a ,

Tim phdn s6 co gia tri bang

{

,.. J

pnan so mor oang

2 ..,.

i,5

"
khi cQng th6m 24 vdo trl s6 tfri thu Clu'oc
bi6t rdng

2

-.
3
D'6p'sdt

Bdri

to6n

A.

f:5:

Tim phdn s5 nh6 nhdt trons c6c phAn

t6

*'14',15',120
*, .3^
Ddp s6:

30

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Bdri

to6n 2. O'

tap hEp c5c s5 nguy6n {1;2; ...; 100} co tinh chSt sau: Kh6ng
c6 s6 hqng ndo g5p 3 lAn mOt s6 frqng khac. TQp hEp d6 c6 nhi6u nh6t bao nhi0u
phAn tu?
Dap s5:
MQt tap con crla

G,-

BititoAn

t,

[
=

Hd vi6t tu6i cr}a mlnh sau tu6i c0a b6, r6i l6y s6 c6 b6n ch0 s6 ndy tru di gi6 tri
tuyet d6i c0a hi6u s6 gioa tu6i c[ra b6 va con thi dugc s6 +zAg. Tinh t6ng s5 tu6i
crla hai b6 con Hdr.

Dap s6:

Bdito5n
Cho Sn

f; g,

=1-2+3-4+...

+ (-1)n.n, v0i n e N.. Tinh Srz + Soe + Sso.

Ddp s5:

31

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ffiVONG
L*t*#
\

,OlCn

t
qui thich hop vio ch6 ....... trong m5i cau sau:

cho 9 di6m trong do kh6ng co ba dicm

tning

hdrng. co qua hai diom ta
v6 dr-rcyc mOt ducrng thdng. Khi do s5 ducrng thdng v6 Clwoc la .......
ndro

2.

De 2n + I chia net cho n + 2 thi gia tri nguy6n duong cia n la .......

3.

Ph6n s6 co m6u s6 bang 10, nh6 f'crn

4.

V6 ba duong thing phdn biQt. s6 giao di6m nhi6u nhdt
d6 ta .... . ..

5.

TrOn tia Ox l5y ba di6m A, B, C sao cho OB = 2OA; OB = 70%OC. Bi6t
AB = 3,5cm. D0 dai doan OC bdng .......cm.

6.

V6 hai goc ke bir

62.

s6 do

G

G

vit

fi

,

co tr] s6 bdng .......
- I9-I9 vd ton fron

voi @z= 1000. Gqi ot

cia

ba ducrng thang

td tia phdn gi6c cria

ta .......o.

7.

vE n tia phan biQt chung g6c. Biet rang tron hinh vE coTB goc. Khi d6 gia tri
cira n bing .....

8.

Cho phdn s6 A

=

2n+7
. T6ng c6c gi6 tri c0a n dO
n+3

A la s5 nguy6n

bang.......

9.

s6 tdt cd

cAc

I
"35

phan s6 beng

md tr] s6 vdr m5u s5 deu ta c6c s6 ttr nhien

co ba chCt s6 la .......
f

0. vict th6m hai ch* s6 vdo bon phdi s6 378 ta ducvc s6
vdr 11. 56 d6 la'.......

mcvi

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chia h6t cho 2; 5

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it;.',

E, hiy chgn dip 5n d0ng cho rn6i cdu du6i ddy bing c6ch t6 dfm

^ " viro hinh trdn 'n0"

1"

ttrLp6c d6p 6n d6.

56 nguy6n n sao cho 6n + 5 chia fr6t cno n + 3 kh6ng th6 bdng:

Cc,ro

Ca.-o

C n.-z

Op.-+

TrOn tia Ox, chcl b5n di6m A, B, C, D thda m6n OA = 3cm; OB = 2cm; OC =

6cm; OD = 10cm. Ph6t bi6u ndo sau ddy kh6ng d0ng?

O A, pi6m C ldr trung di6m cia BD.
C n. Oi6m A ndm giCra B vd C,
O C. Di6m A ld trung di6m c0a BC. O O. Di6m C nim gi0a A vd D,
3.

TrEn tia Ox, ldy ba di6m M, N, P sao cho OM = 7cm; ON = 9cm; MP = 9cm.
Khi do:

On.up=oM Ce.Np=Gcm Oc.op=2cm C o, HrtN=op
TrOn tia Ox, l5y ba di6m A, B, C sao cho OA = 3cm; OB = 7cm; OC = 11cm.
C6 th6 khing dinh;

C n. n ld trung di6m c0a OB
C O. e ld trung di6m crla AC

C n" n ldr trung di6m c0a oC
CC.Bnimgi&aAvaO

5.

Trong c6c phdn s6 sau, phOn s6 ndo xen gi0a

On.

2

Ca.

7

Phdn s6 xen giira

On.
7.

3

Oc.

5

4 u^ f

xnons tnd

os.-a
10

o

-:5

Quy d6ng m5u s5 cOa ba phAn
r
,. ,,
0a pnan so mor la:

sO

va 1z

1

4

2

2

Oo.

I

2.5.7

5'6'g

TA

Oa.L,L,J24',24',24

9, 4,21

6 .15.21
o o. 24'24'.24

24',24'24

Oo. _,
1

vdi mdu s6 chung la 24 thi duqc

C n. 19, 2!,4
Oc

7

td:

oc.-1
10

24',24',24

6

33

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Cho doAn thing AB = 4cm, I lii trung di6m c0a AB. Tr6n tia Bl, t6y cii6m C
sao cho BC = 3cm. TrOn tia Al, l6y di6m D sao cho CD = 2cm. C6 th6 k6t luOn:
O n. O ld trung di6m c0a
O g. C td trung di6m c0a Dt

BC
O C. B ldr trung di6m crla lD

KGt qud c0a phep

tinh

O p. I td trung di6m crla CD

*32+1,2+l

ra,

oa.z:30

ca. r1
30

oc.s1
30

op.+1
30

10. Khing dinh ndo sau ddy sai?
(1) 56 nghich ddo crla

-943,. -1

(2) Ti s6 phAn trim c;la7 vd 8 ld 78%.

(3) -86 > -9

23

O

10

R. cni cau

(3) O a. chi c6u (2) O c. (2) va (3) O o. (1) va (2)

?

*-* E, hiy di6u khi6n xe vugt qua c5c chu6ng ngqi vqt d6 vd dich bing
^ "c6ch giii c6c bii to6n b cilc chu6ng nggi vft d6.

il:f i

i!il

irl;-i,

if$

i;i:i_:

34

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chuong ngqi vgt't:
63
aict 91=

20x35=J-.
chwutg

KOt

qud rrit ggn

rni d6 x = ......,; y = .......
nggi vgt 2:

"0u

15'7rr[9 ra ..'."' (vi6t kot qud dttoi
45

dang phdn so t6i gidnl'

Chu6ng ngqi vQt 3:
So s6nh hai h6n sO:

19
209 &

Chuong ngqi

vQt

4:

f

Tim phfin s6 c6 gi6 tr! Oang
-39 . BiCt khi cQng th6m 18 vdro mfiu s6 thi thu duEc

'
phdn s6 mfi bans j|.

ffi

enan s6 c5n tlm ld ...'...

chueng nggivfits:

Tim rnQt phin s6 c6 ttlp s6 nh6 hon m5u s5 vdr khi quay nguqc s6 d6 theo chi6u
kim ddng h6 hoac nEUEc lai, ta v5n cluqc phdn s5 ban dAu.
r -' r.
la .......
Pnan so oo
Chweng ngqi vfrt 6:
K6t qud ctia ph6p tinrr

f .(+.?.|)*t'

ra ...... $iet

kot qud duoi dqns

phan sd t5i gidnl.

ffi*

chwong ngqi vst r:

Do4n thEng AB dai 3cm, do4n thing CD dai 1,6cm. fi s6 OO ddri cia doan thing
AB vd Ooan tfring CD la ....... (vi6t klt qud dwoidqng phdn s6 t6igidnl'

ffi

chuong ngqivQtl:

Tinh gi6 tri crla bi6u thrlc 3a + 2b + c vdi s =

?;6 = ;-1 ;c=
J
3

la ..... .. (vi6t klt qud dv0i dang phdn s6 t6igidn).

35

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-1 ta duEc k6t qud
,

v

Download Ebook Tai: https://downloadsachmienphi.com

,;'* , Em h5y ...