Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
1
PHN 1: M U
I. L do chn ti.
Trong chng trnh gii tch cp ba, ni dung gii phng trnh, bt phng trnh
cha cn chim mt v tr khng nhiu, nhng n li l kin thc c bn cho vic gii cc
phng trnh bt phng m, phng trnh bt phng trnh lgarit, l mt trong nhng bi
ton trong cc thi tt nghip trung hc ph thng cng nh trong cc thi tuyn sinh
i hc, Cao ng.
u im ca phng php ny gip cho hc sinh c c mt s phng php
gii phng trnh cha cn.
Trong qu trnh ging dy ti nhn thy cc em hc sinh hay gp kh khn khi gii
cc bi ton c cha cn. Cc em thng khng bit bt u t u do trong qu trnh hc,
ni dung kin thc sch gio khoa cung cp qu t dng, trong khi thi tuyn sinh i hc
hay l thi hc sinh gii th c qu nhiu dng l, iu lm cho hc sinh gp nhiu kh
khn. Do ti chn ti ny nhm gip cc em hc sinh c thm t liu nghin cu.
Nhm gip hc sinh nm chc cc kin thc v gii phng trnh cha cn, c k nng
gii cc bi ton lin quan n phng trnh cha cn, ti chn ti Mt s phng php
gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
II. Mc ch nghin cu
- Ch ra cho hc sinh thy nhng phng php khc nhau gii mt phng trnh
c cha cn.
- Bi dng cho hc sinh v phng php, k nng gii ton. Qua hc sinh nng
cao kh nng t duy, sng to.
III. Nhim v nghin cu
- nh gi thc t qu trnh vn dng gii bi tp c lin quan n vic gii phng
trnh cha cn, cc bi ton lin quan c c bi gii ton hon chnh v chnh xc.
IV. i tng nghin cu
- Cc bi ton lin quan n phng trnh cha cn .
V. Phng php nghin cu
- Phng php nghin cu ti liu.
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
2
PHN 2: NI DUNG
CHNG I: C S L LUN V C S PHP L CA TI
I. C s l lun
Hc sinh cn nm c mt s vn sau y (lin quan n ni dung v phm vi
nghin cu ca ti)
1.1. Cc cng thc c bn ca phng trnh cha cn:
Cc cng thc c bn ca phng trnh:
a) DNG C BN:
1) {
2) {
3)
4) {
b) CC DNG KHC:
t iu kin cho
l A 0 nng c 2 v ln lu tha tng ng kh cn
thc.
Lu :
{
1.2. Tnh cht ca cc cn thc bc hai:
1) Nu a 0, b 0 th .
2) Nu a 0, b 0 th
3) Nu a 0, b > 0 th
.
4) Nu a 0, b < 0 th a a
b b.
II. C s php l
- Da trn nhng khi nim, nh ngha, nh l, cc cng thc c bn hc trong qu
trnh gii phng trnh cha cn.
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
3
- Da trn nhng kt qu ng n v nhng chn l hin nhin c chng minh,
tha nhn.
CHNG II: THC TRNG CA TI
Trong thc t, khi hc sinh hc gii phng trnh cha cn thng gp phi nhng kh
khn sau:
- Sch gio khoa ch gii thiu mt s dng c bn.
- Khi cn tm sch hng dn th cng khng c sch no bin son y cc dng.
CHNG III: BIN PHP THC HIN V KT QU
NGHIN CU CA TI
I. Bin php thc hin
khc phc nhng kh khn m hc sinh thng gp phi, khi nghin cu ti, ti
a ra cc bin php nh sau:
1. B sung, h thng nhng kin thc c bn m hc sinh thiu ht
- Phn tch, m x cc khi nim, nh ngha, nh l hc sinh nm c bn cht
ca cc khi nim, nh ngha, nh l .
- a ra cc v d, phn v d minh ha cho cc khi nim, nh ngha, nh l.
- So snh gia cc khi nim, cc quy tc hc sinh thy c s ging v khc nhau
gia chng.
- H thng li cc dng bi tp trong cng ch , cho cc bi tp tng t cho hc
sinh luyn tp.
2. Rn luyn cho hc sinh v mt t duy, k nng, phng php...
- Thao tc t duy: phn tch, so snh, ...
- K nng: lp lun vn , chn phng n ph hp gii quyt vn .
- Phng php: phng php gii ton.
3. i mi phng php dy hc ( ly hc sinh lm trung tm ).
- S dng phng php dy hc ph hp vi hon cnh thc t.
- To hng th, am m, yu thch mn hc cho hc sinh.
- S dng phng tin dy hc, thit b dy hc nhm lm cho bi ging sinh ng
hn, bt kh khan v hc sinh khng cm thy nhm chn. Chng hn s dng bng ph,
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
4
phiu hc tp, nu c iu kin th s dng gio n in t kt hp vi vic trnh chiu
th hm s, cc hnh v, hnh ng lin quan trc tip ti bi ging.
4. i mi vic kim tra, nh gi.
- T lun vi 6 mc nhn thc: nhn bit - thng hiu - vn dng - phn tch - tng
hp - nh gi.
- Gio vin nh gi hc sinh.
- Hc sinh nh gi hc sinh.
5. Phng php dy hc.
Gio vin c phng php dy hc, hnh thc dy hc sao cho ph hp vi tng loi i
tng hc sinh, ch ra cho hc sinh nhng sai lm thng mc phi khi gii cc bi ton v
phng trnh bt phng trnh cha cn. Hng dn cho hc sinh t hc, t lm bi tp.
6. Phn dng bi tp v phng php gii.
- H thng kin thc c bn.
- Phn dng bi tp v phng php gii.
- a ra cc bi tp tng t, bi tp nng cao.
- Sau mi li gii cn c nhn xt, cng c v pht trin bi ton, suy ra kt qu
mi, bi ton mi. Nhm lm cho hc sinh c t duy linh hot v sng to hn.
II. Nghin cu thc t.
1. DNG C BN:
1) 2)
3) 4)
2. CC DNG KHC:
t iu kin cho l A 0 nng c 2 v ln lu tha tng ng kh cn thc.
Lu : A = B A2n+1
=B2n+1
.
A = B
t n ph a v phng trnh hay h phng trnh n gin.
Dng 1) Dng c bn:
V d
1. 24 2 2x x x
Gii. 24 2 2x x x
0
2
BA B
A B
0 ( 0)A hay BA B
A B
33 A B A B
0
0
2( )
A
A B C B
C A B
2n A
. 0
2 2
A B
n nA B
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
5
2 2
2
2 0
4 2x 4x 4
2
2 6x=0
2
0 3
3
x
x x
x
x
x
x hay x
x
Khi gii phng trnh c bn ny ch cn hc sinh vn dng ng nhng cng thc hc.
gii tt cho dng ton ny hc sinh ch cn nhn cho c dng ca phng trnh ri
gii. Qua mi ln bin i tng ng hc sinh cn nhn li dng ton mi trc khi nng
ln ly tha ln tip theo trnh sai st.
Bi tp p dng:
2. s: x=5
3. s: x=-1 4. s: x=2
Dng 2) Bnh phng 2 v(c th t n s ph): dng ton ny i hi hc sinh phi cn thn hn trong qu trnh gii v y khng phi
dng ton c bn, m y l nhng bi ton c dng gn nh c bn. Do trong qu trnh
gii cn phi ch k iu kin bi ton, nu khng rt d dn n nhng sai st l khng
th trnh khi.
V d:
1.
2
2 2
2
1 2x 6 3
1
6
3
(x 1)(2x 6) (x 3)
1
2x 4x 6 6x 9
1
x 2x 15 0
1
x=5 v x=-3
5
x x
x
x
x
x
x
x
x
x
Bi tp p dng:
2. s: x=4,x=-4 3. s: x=0 4. s: x=5 5. s: x=6
7 1 2 4x x
24 6 4x x x
11 3 2 9 7 2x x x x
5 5 4x x
9 1 4x x x x
3 1 4 1x x
10 3 4 23x x x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
6
6. s: x=-1/2
7. s: x=5
8. s: x=1
9. s: x=1;-1/3
10. s: x=1;-2
11. s: x=
12. s: x =
13. s:x=0;9;x=
14. s: x =
15. Tm m phng trnh sau c hai nghim thc phn bit: (B-2006) s:m 9/2.
Dng 3) t n s ph a v phng trnh bc hai,ba,4: Khi gp mt s phng trnh phc tp th chng ta phi s dng phng php t n s ph
vi mc ch lm gim s phc tp ca bi ton, thng th chng ta t t l biu thc cha
cn bc hai, t l tng cc cn hay t l cn bc cao hn trong tng cn. T ta d nhn ra
c s quen thuc ca bi ton m c th tm ra c cch gii nhanh hn. Nhng dng
ton ny cc em hc sinh thng hay gp kh khn iu kin ca bi ton. trnh c
nhng kh khn ny i hi cc em phi c kinh nghim trong qu trnh gii ton.Trc
tin, cc em hy xem xt s cn thit ca iu kin cho tng bi ton c th, thng thng
th khi t n ph th ta ch quan tm n iu kin cho n ph, cho n khi no quay li n
chnh th ta mi quan tm n iu kin cho n chnh. Nu thy iu kin cho bi ton qu
phc tp th ta c th khoan xt n iu kin, tr nhng bi ton s dng tnh n iu ca
hm s, ta hy tip tc gii bi ton cho n khi no tht s cn iu kin th mi xt n
iu kin.
V d:
1. (x-3)(x+1)+4(x-3) = 5
t 21
(x 3) (x 3)(x 1)3
xt t
x
Phng trnh tr thnh 2 4 5 0t t 1 5t hay t
Vi t = 1 ta c 1
1 (x 3)3
x
x
3 4 1 2 3x x x
11 11 4x x x x
2 21 1 2x x x x
2 23 2 8 3 2 15 7x x x x
2 2 27 2 3 3 19x x x x x x
2 23 2 1x x x x 1 5
2
2( 1)(2 ) 1 2 2x x x x
1
2
29 9 9x x x x 9 65
2
21 0x x x x 2 2 1 5 4 2
2
2 2 2 1x mx x
1
3
x
x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
7
2
3 0
10
3
(x 1)(x 3) 1
3
x 2 x 4 0
3
x 1 5 1 5
1 5
x
x
x
x
x
hay x
x
Vi t = -5 ta c 1
5 (x 3)3
x
x
2
3 0
10
3
(x 1)(x 3) 25
1
x 2 x 28 0
1
x 1 29 1 29
1 29
x
x
x
x
x
hay x
x
Vy phng trnh c hai nhim l: x =
Bi tp p dng :
2. s: x=-7;2
3. (x+5)(2-x)=3 s: x=1;-4
4. s: x= 1
5. x2 + = 12 s: x=
6. s:x=1,x= 2 - .
7. x2 +x +12 = 36 s:x=3
8. s:x= 2
9. s:x=3
10. s: x= 3
11. s: x =
12. s:x=0;1
13. s: x= 9/16
14. s: x= 6/5 B2011
1 5, 1 29x
2( 4)( 1) 3 5 2 6x x x x
2 3x x
4 2 21 1 2x x x x
2 6x 10
22 1 3 1 0, ( )x x x x R 2
1x
23 2 1 4 9 2 3 5 2x x x x x
22 3 1 3 2 2 5 3 16x x x x x
32 2 5 1 12 0x x
34 2 217 2 1 1x x 1
2 21 13
x x x x
1212
x x x x x
23 2 6 2 4 4 10 3x x x x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
8
Dng 4) t n ph na vi: C mt s bi ton khi ta t n s ph th rt kh chuyn ht theo mt n s ph, v lm
nh vy th bc ca phng trnh s cao dn n vic gii kh khn. Nn i khi ta khng
th a ht theo mt n, khi chng ta coi nhng x cn li nh tham s v tin hnh gii
tm n ph theo x. T ta c phng trnh mi gii tip tm x v kt thc bi ton.
V d: 2 28x 11x 3 2x 2x 3x 1
t 2 2 22x 3x 1 2x 3x 1t t
Phng trnh tr thnh: 24 2x 1 0t t x (1) 2 2 24(x 1) x 4x 4 (x 2)x
(1) 2 1
4 2
x xt
hay
2 1
4 2
x x xt
Vi 1
2t ta c 2 2
1 3 3 32x 3x 1 2x 3x 0
2 4 8x
Vi 1
2
xt
ta c
2
2 2 2
1 112x 3x 1 1
2 8x 12x 4 2x 1 7x 10x 3 0
x xxx
x
Vy nghim ca phng trnh l: 3 3
18
x hay x
Bi tp p dng:
1. x2+3x+1=(x+3) s:x=
2. s: x =
Dng 5) ng dng hng ng thc: Trong qu trnh gii phng trnh cha cn, nhiu khi s dng cc hng ng thc quen
thuc li rt hu dng cho vic gii phng trnh. Trc ht ta nhc li cc hng ng thc
quen thuc: 2 2 2a 2a (a b)b b hay 2 2 2a 2a (a b)b b . nhn dng, th cc em hc
sinh nn ch n cc s hng cha cn bc hai thng thng l 2ab . Thng th ta a
phng trnh v mt trong hai dng sau:
Dng 1: 2 2 .A B A Bhay A B
Dng 2: 2 20
00
AA B
B
V d 1 Gii phng trnh sau: 22 3 9x 4x x
Phn tch: T s hng 2 3x gi cho ta ngh n 2ab trong hng ng thc. Do ta s
lm xut hin hng ng thc 23 2 3 1 ( 3 1)x x x .
Li gii. Phng trnh cho tng ng vi 23 2 3 1 9xx x
2 1x 2 2
2 22 1 2(1 ) 2 1x x x x x 1 6
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
9
2 2
2
2
2
2
( 3 1) 9x
3 1 3x
3 1 3x
3x 1
3 9x 6x 1
3x 1
3 9x 6x 1
1x
3
9x 7x-2=0
1x
3
9x -5x-2=0
x
x
x
x
x
5 971
18x hay x
Bi tp p dng:
1. s: x=2
2. s: y =5; y= 1
3. s:x= 3
4. s:x= 3; x = -1
5. s:
6. s: v nghim.
7. s:x= 25/4
Dng 6) on nghim chng minh nghim duy nht: Khi gii phng trnh ,khng phi khi no cng gii trc tip m i lc chng ta phi on
nghim, chng minh nghim on c l nghim duy nht ca phng trnh cho. on
nghim c th th vi cc s c bit hay s dng my tnh vi lnh shift solve tm
nghim c bit. Sau ta s dng cc phng php hc, phng php nh gi hay s
dng tnh n iu ca hm s m chng minh nghim duy nht.
V d:
1. Phn tch: bi ton ny khng c dng c bit nhng c mt nghim c bit rt d on l
x = 1. K thut d on nghim t bit thng l nhng s lm cho cn bc hai l s
nguyn.
22 1 ( 1) 0x x x x x x
32 1 2 1
2
yy y y y
2 2 2 1 1 4x x x
52 2 1 2 2 1
2
xx x x x
2 1 2 1 2x x x x 1
12
x
1 2 2 1 2 2 1x x x x
4 84
xx x
2 215 3 2 8x x x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
10
Li gii: 2 215 3x 2 8x x 2 2
2 2
2 2
8 3 15 4 3x 3 0
1 13(x 1) 0
8 3 15 4
x x
x x
x x
2 2
1 1(x 1)( 3) 0
8 3 15 4
x x
x x
2 2
1 11hay 3 0
8 3 15 4
x xx
x x
Ta chng minh rng 2 2
1 13 0
8 3 15 4
x x
x x
v nghim.
Ta c 2 2 22
11 2x 1 8 9 6 8
8 3
xx x x
x
25 3 8x x hin nhin.
Tng t2
11
15 4
x
x
. Suy ra VT 1 hay
2 2
1 13 0
8 3 15 4
x x
x x
v nghim.
Vy phng trnh c nghim duy nht l x = 1.
Bi tp p dng:
1. s:x = 1
2. (x+3) =x2-x-12 s:x = -3
2. s:x= -1/2
3. x-2 s:x = 2
4. s:x = 1
5. s:x = -3; x = 2
6. s:x = 4;x = 5.
7. B2010 s:x= 5
Dng 7) t n s ph a v h i xng loi I: Nhiu khi, vic gii mt phng trnh l kh khn, nhng nu ta a v vic gii mt h
phng trnh th bi ton tr nn n gin hn.Sau y, ti gii thiu mt cch gii phng
trnh nh vo vic a v h phng trnh i xng loi I. Nh vy cc em phi bit cch
gii h phng trnh i xng loi I.
H i xng loi I vi
Cch gii: t S= x+y v P =xy gii tm S,P iu kin S2 4P.
Suy ra x,y l nghim ca ptrnh t2 St +P=0.
V d :
1.
t 2 2 2 2 217 17 17y x y x hay x y
2
3 2 13 2
xx x
x
210 x
2 22 1 2 ( 1) 2 3 0x x x x x x
21 ( 1) 0x x x x x
2(1 ) 16 17 8 15 23x x x x
2( 1) 2 2 2x x x x
22 7 2 1 8 7 1x x x x x
23 1 6 3 14 8 0x x x x
( ; ) 0
( ; ) 0
f x y
g x y
( ; ) ( ; )
( ; ) ( ; )
f x y f y x
g x y g y x
2 217 17 9x x x x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
11
Ta c h phng trnh2 2 217 ( ) 2x 17
9 9
x y x y y
x y xy x y xy
t .
S x y
P x y
ta c h phng trnh
2 22 17 2(9 ) 17
9 9
S P S S
S P S P
2 5 7 5 72 35 0
9 4 169
S hay S S SS Shay
S P P PS P
loi
Vi 5
4
S
P
ta c
5 1 4
. 4 4 1
x y x xhay
x y y y
Vy phng trnh c hai nghim: x = 1; x = 4
Bi tp p dng:
2. s:x = -15; x =13
Dng 8) t n s ph a v h i xng loi II Tng t cch gii a v h i xng loi I th ta cng c th t n ph a v h i
xng loi II.
i vi phng trnh c dng: (vi p=a; b+ =b).
t t+ = , ta c h i xng loi 2:
V d :
1.
t 33 2x 1 2x 1y y
Ta c h phng trnh 3
3
1 2
1 2x
x y
y
3 3 3 2 2
3 3 3
1 2 2 2x ( )(x y xy 2) 0
1 2x 1 2x 1 2x
x y x y y x y
y y y
3
3 2 2
1 2x
2x 1 0 x y xy 2 0
x y yhay
x
v nghim
3
1 51
22x 1 0
x yx hay x
x
Vy nghim ca phng trnh l: x=1;x=
Bi tp p dng:
2. s:
3. s: ,
4.
Dng 9) Phng php a v cc biu thc ng dng cho cc phng trnh dng:
3 312 14 2x x
( )n nx p ax b
axn b( )
( )
n
n
x at b
t ax b
3 31 2 2 1x x
1 5
2
2 2 2 2 1x x x 2 2x
22 6 1 4 5x x x 2 2x 1 2x
2011 2011x x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
12
B1: Vit pt v dng
B2: ly (b2 +pa2) chia cho p,hc sinh t chn p, chn kt qu l s hu t p.
B3: Thay kt qu vo phng trnh (1) gii tm a nu ng th dng nu sai lm li B2.
B4: t n ph a ra phng trnh tch ri gii.
Phng trnh cha cn bc 3 lm tng t.
Phng php ny cng dng cho dng s dng tnh n iu gii phng trnh.
1. V d 1: Gii phng trnh: 22x 8 4x 16x 12
B1: Ta vit phng trnh v dng: 24 .0 4 .0
(2x 8) 2x 8 ( x a) ( x a)p p
p pp p
B2: Ta lp bng
P 1
4
p
2
B3: Thay vo B1 ta c 22x 8 2x 8 (2x ) 2xa a 2 22x 8 4x (4a 2 2) 8x a a ta ng nht phng trnh ny vi phng trnh
bi ta c a = 4. Khi phng trnh c vit li c dng ng dng nh sau: 22x 8 2x 8 (2x 4) 2x 4
22x 8 2x 8 (2x 4) 2x 4
(2x 4 2x 8)(2x 4 2x 8) (2x 4 2x 8) 0
(2x 4 2x 8)(2x 4 2x 8 1) 0
2x 5 2x 8 0hay2x 4 2x 8 0
Vi 2x 5 2x 8 0
2
2
2x 8 2x 5
2x 5 0
2x 8 4x 20x 25
5x
2
4x 18x 17 0
5x
2
9 13 9 13
4 4
9 13
4
x hay x
x
2 2
2 1 0 2 1 0a x a x a b x b x b
3 2 3 233 2 1 0 3 2 1 0a x a x a x a b x b x b x b
2 2 22 2 2 22 0 2 0p(a x ... ) a x ... ( ) ( )
b pa b paa a p x a x a
p p
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
13
Vi 2x 4 2x 8 0
2
2
2x 8 2x 4
2x 4 0
2x 8 4x 16x 16
x 2
4x 14x 8 0
7 17
4x
Vy : 9 13
4x
hay
7 17
4x
2. V d 2: Olympic 2011
B1: Ta vit phng trnh v dng 33 3 31 0. 1 0.
(2x 9) 5 2x 9 ( x a) 5( x a)p p
p pp p
B2: Ta lp bng
P 1
31
p
1
B3: Thay vo B1 ta c 33(2x 9) 5 2x 9 (x a) 5(x a) 3 2 2 335 2x 9 3a (3a 2 5) x 5a 9x x a ta ng nht phng trnh ny vi phng
trnh bi ta c a = -5. Khi phng trnh c vit li c dng ng dng nh sau:
33
3 33 3
2 23 3 3
2 23 3 3
(2x 9) 5 2x 9 (x 5) 5(x 5)
(x 5) ( 2x 9) 5[(x 5) 2x 9] 0
(x 5 2x 9)((x 5) (x 5) 2x 9+( 2x 9) +5] 0
x 5 2x 9 0hay(x 5) (x 5) 2x 9+( 2x 9) +5 0 vn
3x 5 2x 9 0
3 2
3 2
2
15x 75x 125 2x 9
15x 73x 116 0
( 4)(x 11x 29) 0
x
x
x
11 5 11 54
2 2x x x
Bi tp p dng:
1. s:x = -1; x = 2.
2. s:
3. s:x = 1;
3 2 315 78 141 5 2 9x x x x
3 33 2 3 2x x
25 5x x
1 21 1 17;
2 2x x
3 31 2 2 1x x 1 5
2x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
14
4. Olympic2009-LHP
5. Olympic2009-T
III. Kt qu nghin cu
Qua nghin cu, ng dng ti vo thc tin ging dy ti nhn thy kt qu t
c c kh quan hn. C th qua kt qu thu hoch c khi kho st tnh hnh gii bi tp
ton lp 10CV nh sau:
Lp 10 CV (s s 36) trc khi gii thiu phng php gii dng ton s 9
S lng Phn trm
Khng gii c 36 100 %
Gii sai phng php 00 00 %
Gii ng phng php 00 00 %
Lp 10 CV (s s 36) sau khi gii thiu phng php gii dng ton s 9
S lng Phn tram
Khng gii c 6 16,7 %
Gii sai phng php 2 5,5 %
Gii ng phng php 28 77,7 %
Nh vy, bc u ti gp phn nng cao cht lng hc tp ca hc sinh v
em li hiu qu r rt. Trong thi gian ti, ti ny s tip tc c p dng vo thc tin
ging dy trong nh trng v mong rng s t c hiu qu tt p nh tng t c
trong qu trnh thc nghim.
PHN 3: KT LUN - KIN NGH
I Kt lun
Trc ht, ti ny nhm cung cp cho cc em hc sinh nh mt ti liu tham kho.
Vi lng kin thc nht nh v gii cc phng trnh cha cn, vi nhng kin thc lin
quan, ngi hc s c ci nhn su sc hn v nhng cch gii ton. ng thi, t nhng
phng php , hc sinh rt ra cho mnh nhng kinh nghim v phng php gii ton
ring, c th quay li kim chng nhng l thuyt c trang b lm ton. T
thy c s lgic ca ton hc ni chung v ca chuyn gii cc phng trnh c cha
cn ni ring.
3 2 33 3 3 5 1 3x x x x
33 2 3 26 12 7 9 19 11x x x x x x
Sng kin kinh nghim Gio vin: Nguyn Php
Mt s phng php gii phng trnh cha cn trong chng trnh ton trng trung hc ph thng.
15
cp trng trung hc ph thng, ti c th p dng ci thin phn no cht
lng b mn, cng c phng php gii ton, gp phn nng cao cht lng dy v hc,
gip hc sinh hiu r hn bn cht ca cc khi nim, nh ngha, nh l cng nh nhng
kin thc lin quan c hc, gip cc em trnh khi lng tng trc mt bi ton t ra
v d dng tm ra mt cch gii hp l cho bi ton.
Trong khun kh bi vit ny, ti khng c tham vng s a ra y cc phng
php gii phng trnh cha cn. V vy, ti rt mong nhn c s ng gp kin ca
Hi ng s phm trng Trung hc ph thng Nguyn Hu Hun.
II Kin ngh
Vic gii cc phng trnh v bt phng trnh cha cn th khng c nhiu trong
chng trnh hin hnh nhng n li xut hin kh nhiu trong cc thi tuyn sinh i
hc,Cao ng. Hc sinh cn gp cc phng trnh v bt phng trnh cha cn khi hc gii
phng trnh, h phng trnh m lgarit.
Chnh v l , ti hi vng ti ny s ng gp mt phn nh b vo vic gii cc
dng ton nu trn, l ti liu tham kho cho cc em hc sinh trong qu trnh hc ton
cng nh n thi tt nghip v thi vo cc trng i hc, Cao ng v Trung hc chuyn
nghip.