ÔN THI GIỮA KÌ 1 LỚP 12
Năm học: 2020 – 2021.
Lưu hành nội bộ.
LOREM IPSUM
DOLOR SIT
AMET
1. Các dạng toán thường gặp.
2. Bộ 10 đề cơ bản.
3. Các bài toán vận dụng & vận dụng
cao thường gặp.
www.facebook.com/NhómToán-Thầy-Lê-Văn-Đoàn112798047209867/
0933.755.607 thầy Đoàn
0983.047.188 thầy Nam
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@gmail.com
MỤC LỤC
Trang
PHẦN 1. NHỮNG DẠNG TOÁN THƯỜNG GẶP .................................................................................... 1
PHẦN 2. BỘ 10 ĐỀ CƠ BẢN ......................................................................................................................... 17
ĐỀ SỐ 01 ........................................................................................................................................ 17
ĐỀ SỐ 02 ........................................................................................................................................ 24
ĐỀ SỐ 03 ........................................................................................................................................ 31
ĐỀ SỐ 04 ........................................................................................................................................ 38
ĐỀ SỐ 05 ........................................................................................................................................ 45
ĐỀ SỐ 06 ........................................................................................................................................ 52
ĐỀ SỐ 07 ........................................................................................................................................ 59
ĐỀ SỐ 08 ........................................................................................................................................ 66
ĐỀ SỐ 09 ........................................................................................................................................ 73
ĐỀ SỐ 10 ........................................................................................................................................ 81
PHẦN 3. NHÓM BÀI TOÁN VẬN DỤNG VÀ VẬN DỤNG CAO THƯỜNG GẶP .......................... 89
BẢNG ĐÁP ÁN .......................................................................................................................... 110
ĐỊA CHỈ GHI DANH
TRUNG TÂM THẾ VINH – 45A LÊ THÚC HOẠCH – Q. TÂN PHÚ (ĐỐI DIỆN TRƯỜNG TRẦN PHÚ).
TRUNG TÂM HOÀNG GIA – 56 PHỐ CHỢ – P. TÂN THÀNH – Q. TÂN PHÚ (SAU CHỢ TÂN PHÚ).
71/25/10 PHÚ THỌ HÒA – P. PHÚ THỌ HÒA – Q. TÂN PHÚ – TP. HỒ CHÍ MINH.
ĐIỆN THOẠI GHI DANH
0983.047.188 – Zalo (Thầy Nguyễn Đức Nam) – Face: /> 0933.755.607 – Zalo (Thầy Lê Văn Đoàn) – 0929.031.789 – Face: />NHÓM TOÁN THẦY LÊ VĂN ĐOÀN
Ths. Lê Văn Đoàn – Ths. Trương Huy Hoàng – Ths. Nguyễn Tiến Hà – Thầy Bùi Sỹ Khanh – Thầy Nguyễn
Đức Nam – Thầy Châu Văn An – Thầy Đỗ Minh Tiến – Thầy Nguyễn Duy Tùng – Thầy Trần Nguyễn Vĩnh
Nghi – Thầy Hoàng Minh Thiện – Thầy Trần Quốc Tuấn.
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
PHN 1. NHNG BI TON THNG GP
Bi mu s 01
Bi mu s 02
Cho th hm s y f (x ) nh hỡnh v sau:
Cho th ca hm s y f (x ) nh hỡnh v sau:
a) Tỡm cỏc khong ng bin v nghch bin ca
hm s y f (x ) ?
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b) Tỡm im cc i, im cc tiu ca hm s ?
Tỡm im cc i, im cc tiu ca th
hm s y f (x ) ?
a) Tỡm cỏc khong n iu ca hm s f (x ) :
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b) im cc i, im cc tiu ca th hm s
y f (x ) :
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Bi mu s 03
Bi mu s 04
Cho hm s y f (x ) xỏc nh v liờn tc trờn
Cho hm s y f (x ) xỏc nh v liờn tc trờn
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Cỏc khong ng bin ca hm s f (x ) l
Cỏc khong ng bin ca hm s f (x ) l
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Cỏc khong nghch bin ca hm s f (x ) l
Cỏc khong nghch bin ca hm s f (x ) l
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Hm s t cc i ti im: .............................
Hm s t cc i ti im: .............................
Hm s t cc tiu ti im: ............................
Hm s t cc tiu ti im: ............................
v cú f (x ) x (x 1)(x 2) , x .
2
3
v cú f (x ) x 3 (1 x )2 (2 x )3 (3 x )4 , x .
Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-1-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 05
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 06
Cho th hm s y f (x ) nh sau:
Cho th hm s y f (x ) nh sau:
a) Xột hm s g(x ) f (x ) 2x . Hóy tỡm:
a) Xột hm s g(x ) f (x ) 3x . Hóy tỡm:
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Cỏc khong ng bin ca hm s g(x ) l:
Cỏc khong ng bin ca g(x ) trờn (1; 2):
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Cỏc khong nghch bin ca hm s g(x ) l:
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Hm s g(x ) t cc i ti im: ....................
Hm s t cc tiu ti im: ............................
b) Tỡm tham s m hm s h(x ) f (x ) mx
Cỏc khong nghch bin g(x ) trờn (1; 2):
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Trờn [1; 2), hm s t cc i ti: ..............
Trờn [1; 2), hm s t cc tiu ti:..............
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b) Tỡm tham s m hm s h(x ) f (x ) mx
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Khụng cú im cc tr ?
Cú ỳng 1 im cc tr ?
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Cú 2 im cc tr ?
Cú ỳng 3 im cc tr ?
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1
c) Xột hm s k (x ) f (x ) x 3 2x 2 2x .
3
Tỡm khong n iu v cc tr ca k (x ) ?
Cú 3 im cc tr ?
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2
c) Xột hm s k (x ) f (x ) x 3 . Tỡm cỏc khong
3
n iu v cc tr ca k (x ) ?
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Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-2-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 07
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 08
Tỡm tt c cỏc giỏ tr ca tham s m sao cho hm Tỡm tt c cỏc giỏ tr thc ca tham s m sao cho
mx m 2
mx 5m 6
nghch bin trờn khong
s y
ng bin trờn tng khong hm s y
x m
x m
(3; ) ?
xỏc nh ca nú ?
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Bi mu s 09
Bi mu s 10
Tỡm tt c cỏc giỏ tr ca tham s m sao cho hm Tỡm tt c cỏc giỏ tr ca tham s m sao cho hm
s y
(m 1) x 1 2
x 1 m
nghch bin (17; 37) ?
s y
3x 2
3x m
ng bin trờn (13; 1) ?
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Bi mu s 11
Bi mu s 12
Tỡm tt c cỏc giỏ tr ca tham s m sao cho hm Tỡm tt c cỏc giỏ tr ca tham s m sao cho hm
3
cos x 2
(m 1)sin x 2
; ?
s y
nghch bin 0; ?
s
y
ng
bin
2
2
cos x m
sin x m
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Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-3-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 13
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 14
Tỡm tt c cỏc giỏ tr ca tham s m sao cho hm Tỡm tt c cỏc giỏ tr thc ca tham s m sao cho
1
1
s y x 3 mx 2 (m 2)x 1 ng bin trờn hm s y (m 1)x 3 (m 1)x 2 x nghch
3
3
khong (; ) ?
bin trờn khong (; ) ?
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Cn nh: nh lớ du tam thc bc hai:
................
ax 2 bx c 0, x
.
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Bi mu s 15
................
ax 2 bx c 0, x
.
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Bi mu s 16
Tỡm tt c cỏc giỏ tr thc ca tham s m sao cho Tỡm tt c cỏc giỏ tr thc ca tham s m sao cho
1
1
hm s y x 3 x 2 mx 2020 ng bin hm s y x 3 (m 1)x 2 (m 2 2m )x 30
3
3
trờn khong (1; ) ?
nghch bin trờn khong (0;1) ?
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Cn nh:
m g(x ), x D m.........................
m g(x ), x D m ...........................
Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-4-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 17
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 18
Tỡm cỏc khong n iu v cc tr ca hm s Tỡm cỏc khong n iu v cc tr ca hm s
g(x ) f (2x 1) 12x, bit hm s y f (x ) cú g(x ) f (1 2x ) 12x, bit hm s y f (x ) cú
o hm f (x ) x 2 x , x .
o hm f (x ) x x 2 , x .
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Bi mu s 19
Bi mu s 20
Cho hm s y f (x ) cú bng xột du o hm:
x
f (x )
0
2
1
0
Cho hm s y f (x ) cú bng xột du o hm:
x
f (x )
1
1
2
4
0 0 0 0
Tỡm cỏc khong n iu v cc tr ca hm s
g (x ) f (x 2 2) ?
Tỡm cỏc khong n iu v cc tr ca hm s
Li gii. .................................................................
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g(x ) f (1 2x ) ?
Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-5-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 21
Bi mu s 22
Cho th ca hm s y f (x ) nh hỡnh v:
y
y f (x )
1
O
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Cho th ca hm s y f (x ) nh hỡnh v:
4 x
1
Tỡm cỏc khong n iu v cc tr ca hm s Tỡm cỏc khong n iu v cc tr ca hm s
g(x ) f (2 x ) ?
g(x ) f (2x 4) ?
Li gii. .................................................................
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Bi mu s 23
Bi mu s 24
Cho th ca hm s y f (x ) nh hỡnh v:
y
Cho th ca hm s y f (x ) nh hỡnh v:
1
1
O
1
2
x
1
Tỡm cỏc khong n iu v cc tr ca hm s Tỡm cỏc khong n iu v cc tr ca hm s
g(x ) f (x ) x ?
g (x ) 2 f (x ) x 2 ?
Li gii. .................................................................
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Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-6-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 25
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 26
Cho th ca hm s y f (x ) nh hỡnh v:
Cho th ca hm s y f (x ) nh hỡnh v:
y
1
2
O
4
x
2
Tỡm cỏc khong n iu v cc tr ca hm s Tỡm cỏc khong n iu v cc tr ca hm s
g (x ) f (1 2x ) x 2 x ?
g (x ) 3 f (1 2x ) 8x 3 21x 2 6x ?
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Bi mu s 27
Bi mu s 28
Cho th ca hm s y f (2 x ) nh hỡnh v: Cho th ca hm s y f (3x 1) nh hỡnh:
Tỡm cỏc khong n iu v cc tr ca hm s Tỡm cỏc khong n iu v cc tr ca hm s
y f (x ) ?
y f (x ) ?
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Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-7-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 29
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 30
Cho hm f (x ) cú f (x ) x (x 1)2 (x 2 mx 9). Cho hm f (x ) cú f (x ) x 2 (x 1)(x 2 mx 5).
Tỡm m hm s g (x ) f (3 x ) ng bin trờn Tỡm m hm s g (x ) f (x 2 ) ng bin trờn
khong (3; ) ?
khong (1; ) ?
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Bi mu s 31
Bi mu s 32
Cho hm s f (x ) cú bng bin thiờn ca f (x ) :
Cho hm s f (x ) cú bng bin thiờn ca f (x ) :
S im cc tr ca hm s g (x ) f (4x 2 4x ) l S im cc tr ca hm s g (x ) f (x 2 2x ) l
bao nhiờu ?
bao nhiờu ?
Li gii. .................................................................
Li gii. .................................................................
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Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-8-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 33
Bi mu s 34
Cho hm s bc bn f (x ) cú bng bin thiờn:
S im cc tr ca hm s g(x) x
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
4
Cho hm s bc bn f (x ) cú bng bin thiờn:
f (x 1) l S im cc tr ca hm s g(x ) x 4 f (x 1) 2
2
l bao nhiờu ?
bao nhiờu ?
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Bi mu s 35
Bi mu s 36
Cho hm s y f (x ) cú bng bin thiờn:
Cho hm s y f (x ) cú bng bin thiờn:
Tỡm s im cc i v s im cc tiu ca hm Tỡm s im cc i v s im cc tiu ca hm
s y f 2(2x ) 6 f (2x ) 9 ?
s y f 2 (2x ) 2 f (2x ) 1 ?
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Ths. Lê Văn Đoàn - Ths. Trương Huy Hoàng - Ths. Nguyễn Tiến Hà - Bùi Sỹ Khanh - Châu Văn An - Nguyễn Đức Nam - Đỗ Minh Tiến
-9-
Điện thoại ghi danh: 0983.047.188 (Thầy Nam) 0933.755.607 (Thầy Đoàn)
Bi mu s 37
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 38
1 3
x3
x mx 2 (m 2 m 1)x 1. Cho hm y
(m 1)x 2 (m 2 3m 2)x .
3
3
Tỡm m hm s t cc tiu ti im x 1 ?
Tỡm m hm s t cc i ti im x 0 ?
Cho hm s y
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Cn nh: Cho hm s bc ba y ax 3 bx 2 cx d .
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Hm s t cc i ti x x 0
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Bi mu s 39
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Hm s t cc tiu ti x x 0
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Bi mu s 40
1 3
1
x mx 2 (m 6)x 1. Tỡm Cho hm y mx 3 (m 1)x 2 mx 7. Tỡm
3
3
tham s m sao cho hm s cú:
tham s m sao cho hm s cú:
Cho hm s y
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2 im cc tr ?
2 im cc tr ?
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0 im cc tr ?
0 im cc tr ?
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2 im cc tr nm hai bờn trc tung ?
2 im cc tr nm hai bờn trc tung ?
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Cn nh: Hm s cú n im cc tr y 0 cú n nghim phõn bit.
Cỏc bi toỏn thng liờn quan n Viột (hai nghim dng, hai nghim õm,)
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Bi mu s 41
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 42
1 3
1
x mx 2 x m 1. Tỡm Cho hm s y x 3 mx 2 x 1. Tỡm tham s
3
3
tham s m hm s cú 2 im cc tr x 1 v x 2 m sao cho hm s cú 2 im cc tr x 1 v x 2 tha
Cho hm s y
tha món x 12 x 22 2.
món x 12 x 22 x 1x 2 7.
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Bi mu s 43
Bi mu s 44
2 3
1
x (m 1)x 2 (m 2 4m 3)x . Cho hm s y x 3 mx 2 (m 2)x 1. Tỡm
3
3
Tỡm tham s m th hm s cú 2 im cc tham s m th hm s cú 2 im cc tr
tr nm bờn phi trc tung ?
nm bờn phi trc tung ?
Cho f (x )
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Bi mu s 45
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 46
Cho hm s y x 3 3x 2 m. Tỡm tham s m Cho hm s y x 3 3mx 2 2. Tỡm tham s m
hm s cú hai im cc tr A, B sao cho tam hm s cú hai im cc tr A, B sao cho ba
im A, B, M (1; 2) thng hng ?
giỏc OAB vuụng ti gc ta O ?
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Bi mu s 47
Bi mu s 48
Cho hm s y x 4 2mx 2 1. Tỡm tham s m
th hm s cú ba im cc tr A(0;1), B, C
tha món BC 4 ?
Cho hm s y x 4 2(m 1)x 2 m. Tỡm tham
s m th hm s cú ba im cc tr A(0; m ),
B, C tha món OA BC ?
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Bi mu s 49
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 50
Bit M (0;2) v N (2; 2) l cỏc im cc tr ca Bit th hm s y ax 4 bx 2 c cú hai im
th hm s y ax 3 bx 2 cx d . Tớnh giỏ tr cc tr l M (0;2) v N (2; 14). Tớnh giỏ tr ca
ca hm s ti x 2.
hm s ti x 3.
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f (x 0 ) 0
Cn nh: M (x 0 ; y 0 ) l im cc tr ca th hm s y f (x )
.
M
(
x
;
y
)
y
f
(
x
)
0
0
Bi mu s 51
Bi mu s 52
Cho hm s y 3x 4 4x 3 12x 2 m . Tỡm m
Cho hm y x (2m 1)x 2 (3 m ) x 2.
hm s ó cho cú 7 im cc tr ?
3
Tỡm m hm s ó cho cú 3 im cc tr ?
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Bi mu s 53
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Bi mu s 54
Tỡm giỏ tr ln nht v giỏ tr nh nht ca hm s Tỡm giỏ tr ln nht v giỏ tr nh nht ca hm s
1
1
x3
y 3 trờn khong (0; ) ?
y
2x 2 3x 4 trờn on [4; 0] ?
x
x
3
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Bi mu s 55
Bi mu s 56
mx 1
Cho hm s y x 3 3m 2x 6. Tỡm tham s m
Cho hm s y
Tỡm m hm s cú
x m
sao cho giỏ tr ln nht ca hm s trờn on [0; 3]
giỏ tr nh nht trờn on [1;2] bng m 2.
bng 42.
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f (x ) f (a )
min
[a ;b ]
y f (x ) ng bin [a;b ]
.
max f (x ) f (b )
[
a
;
b
]
Bi mu s 57
Cho th ca hm s y f (x ) nh hỡnh sau:
f (x ) f (b)
min
[a ;b ]
y f (x ) nghch bin [a;b ]
.
max f (x ) f (a )
[
a
;
b
]
Bi mu s 58
Cho th ca hm s y f (x ) nh hỡnh sau:
Hóy tỡm giỏ tr ln nht v nh nht ca hm s Hóy tỡm giỏ tr ln nht v nh nht ca hm s
y f ( f (x )) trờn on [1;1] ?
y f (3 sin2 x 2).
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Bi mu s 59
Bi mu s 60
Tỡm m sao cho giỏ tr ln nht ca ca hm s Cho hm s y (x 3 3x m)4 . Tỡm tham s m
y x 3 3x m trờn on [0; 3] bng 16.
sao cho min y 1.
[1;1]
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Bi toỏn: Xỏc nh GTLN & GTNN ca hm s y f (x ) trờn [; ] (hoc hm f 2n (x )).
Bc 1. Tỡm GTLN l A v GTNN l a ca hm s khụng cú tr tuyt i y f (x ).
Bc 2. Xột hm s tr tuyt i y f (x ) trờn on [; ] :
max
f (x ) max A ; a
;
A a A a
2
A a A a
khi Aa
. 0.
min
f
(
x
)
2
;
0
khi Aa
. 0
Bi mu s 61
Bi mu s 62
Cho hm s y f (x ) cú th nh hỡnh v:
Tỡm m giỏ tr ln nht ca y f (x ) m 1
trờn on [1;1] bng 9.
Cho hm s y f (x ) cú th nh hỡnh v:
2
Tỡm m giỏ tr nh nht ca y f (x ) m
trờn on [1;1] bng 9.
2
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Bi mu s 63
Bi mu s 64
Cho hm s y f (x ) cú bng bin thiờn:
x
y
y
1
0
0
1
1
Cho hm s y f (x ) cú bng bin thiờn:
5
2
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
3
Tỡm tim cn ng v ngang ca th hm s
ó cho ?
S ng tim cn ng ca y
bao nhiờu ?
1
l
f (x ) f (x )
2
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Cn nh:
Tỡm ng TCN: lim y (1 s c th) y l tim cn ngang.
x
Tỡm ng TC: lim y TC: x x 0 (thng x x 0 hoc trong BBT thỡ x 0 ti ).
x x 0
Bi mu s 65
Tỡm m th hm s y
ng tim cn ng ?
x 2
cú hai
2
x mx 1
Bi mu s 66
2x 2 3x m
Tỡm tham s m
x m
th hm s khụng cú tim cn ng ?
Cho hm s y
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Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
PHN 2. B 10 C BN
S 01
Cõu 1.
Cho hm s y f (x ) cú bng xột du o hm bờn di. Mnh no di õy ỳng ?
x
y
A.
B.
C.
D.
Cõu 2.
1
0
0
Hm s f (x ) ng bin trờn khong (2; 0).
Hm s f (x ) ng bin trờn khong (; 0).
Hm s f (x ) nghch bin trờn khong (0;2).
Hm s f (x ) ng bin trờn khong (;2).
2
0
Cho th hm s y f (x ) nh hỡnh v. Tỡm khng nh ỳng ?
A. Hm s nghch bin trờn khong (0;2).
B. Hm s ng bin trờn cỏc khong (1; 0), (2; 3).
C. Hm s ng bin trờn cỏc khong (; 0), (2; ).
D. Hm s nghch bin trờn cỏc khong (; 0), (2; ).
Cõu 3.
Cho hm s f (x ) xỏc nh trờn v cú th hm s y f (x ) l ng cong trong hỡnh v
bờn di. Mnh no di õy ỳng ?
A. Hm s f (x ) ng bin trờn khong (1;2).
B. Hm s f (x ) ng bin trờn khong (2;1).
C. Hm s f (x ) nghch bin trờn khong (1;1).
D. Hm s f (x ) nghch bin trờn khong (0;2).
Cõu 4.
Cho hm s y x 3 3x 2 4. Mnh no di õy ỳng ?
A. Hm s ó cho ng bin trờn khong (0;2).
B. Hm s ó cho nghch bin trờn khong (;2).
C. Hm s ó cho ng bin trờn khong (0; ).
D. Hm s ó cho nghch bin trờn khong (0;2).
Cõu 5.
Cho hm s f (x ) cú f (x ) (x 1)2 (x 1)3 (2 x ), x . Hm s f (x ) ng bin trờn khong
A. (2; ).
C. (1;2).
Cõu 6.
D. (; 1).
mx 2
Tỡm tt c cỏc giỏ tr ca tham s m hm s nghch bin trờn
x m 3
tng khong xỏc nh ca nú ?
Cho hm s y
A. 1 m 2.
C. 1 m 2.
Cõu 7.
B. (1;1).
B. m 1.
D. m 2.
Cú bao nhiờu giỏ tr nguyờn ca tham s m (10;10) hm s y
bin trờn khong (3; ).
A. 2.
C. 12.
mx 6m 5
ng
x m
B. 3.
D. 11.
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Cõu 8.
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Cú bao nhiờu giỏ tr nguyờn õm ca tham s m hm s y
bin trờn khong (; ) ?
A. 4.
Cõu 9.
1 3
x mx 2 4x m ng
3
B. 3.
C. 2.
D. Vụ s.
A. m 1.
B. m 1.
Tỡm tt c cỏc giỏ tr ca tham s m hm s y x 3 3x 2 3mx 201 nghch bin trờn
khong (0; ).
C. m 1.
D. m 1.
Cõu 10. Cho hm s f (x ) cú bng bin thiờn nh hỡnh di. Tỡm giỏ tr cc i yC v giỏ tr cc tiu
yCT ca hm s ó cho.
A. yC 3, yCT 2.
B. yC 2, yCT 0.
C. yC 2, yCT 2.
D. yC 3, yCT 0.
Cõu 11. im cc tiu ca th hm s y x 4 2x 2 5 l
A. A(1;6).
B. x 0.
C. 5.
D. B(0;5).
Cõu 12. Hm s f (x ) xỏc nh v liờn tc trờn v cú o hm f (x ) 2(x 1)2 (x 1). Hi khng
nh no sau õy ỳng ?
A. Hm s f (x ) t cc i ti im x 1.
B. Hm s f (x ) t cc tiu ti im x 1.
C. Hm s f (x ) t cc i ti im x 1.
D. Hm s f (x ) t cc tiu ti im x 1.
Cõu 13. th hm s y f (x ) cú th nh hỡnh v di õy. Hm s y f (x ) 3x 2020 cú bao
nhiờu im cc tr ?
A. 1.
B. 2.
C. 3.
D. 0.
Cõu 14. Hm s y x 3 3x 2 mx 2 t cc tiu ti im x 2 khi
A. m 0.
C. m 0.
B. m 0.
D. m 0.
Cõu 15. Cho hm s y x 3 3mx 2 3mx m 2 . Cú bao nhiờu giỏ tr nguyờn ca tham s m (5; 5)
hm s cú 2 im cc tr ?
A. 5.
C. 7.
B. 6.
D. 4.
Cõu 16. Gi A, B l hai im cc tr ca th hm s f (x ) x 3 3x 2 m vi m l tham s thc
khỏc 0. Tỡm tham s m trng tõm tam giỏc OAB thuc ng thng 3x 3y 8 0 ?
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Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
A. m 5.
B. m 2.
C. m 6.
D. m 4.
Cõu 17. Cho hm s f (x ) cú bng bin thiờn bờn di. Trờn khong ( 5, 5) thỡ hm s y f (x 2 )
t cc i ti im no sau õy ?
A. x 2.
B. x 2.
C. x 0.
D. x 2.
Cõu 18. Cho hm s y f (x ) xỏc nh v liờn tc trờn [2; 3] cú bng bin thiờn nh hỡnh bờn. Gi
M , m ln lt l giỏ tr ln nht v nh nht ca hm s trờn on [2; 3]. Tng M m bng
A. 1.
B. 3.
C. 1.
D. 4.
Cõu 19. Giỏ tr ln nht ca hm s f (x ) x 4 2x 2 3 trờn on [0; 3] bng
B. 8 3.
A. 9.
C. 6.
D. 1.
Cõu 20. Bit hm s f (x ) x 2020
P x o 2020 bng
A. 4036.
1
t giỏ tr ln nht trờn khong (0; 4) ti x o . Giỏ tr ca
x
B. 2020.
C. 2021.
D. 2019.
Cõu 21. Cho hm s y f (x ) xỏc nh v liờn tc trờn [2;2], cú th y f (x ) nh hỡnh v bờn
di. Tỡm giỏ tr x hm s y f (x ) t giỏ tr ln nht trờn [2;2].
A. x 2.
B. x 1.
C. x 2.
D. x 1.
y
x
2 1 O
1
2
Cõu 22. Cho hm s y x 3 3m 2x 6. Tỡm tt c cỏc giỏ tr thc ca tham s m sao cho giỏ tr ln
nht ca hm s trờn on [0; 3] bng 42.
A. m 1.
B. m 1.
C. m 1.
D. m 2.
m 2x 4
(m l tham s thc). Gi S l tp hp s nguyờn m tha món
x 1
3 max y 2 min y 4. S phn t ca S l
Cõu 23. Cho hm s y
[1;3]
[1;3]
A. 0.
B. 3.
C. 4.
D. 5.
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Cõu 24. Cho hm s y f (x ) xỏc nh trờn D \ {1}, liờn tc trờn mi khong xỏc nh v cú bng
bin thiờn:
x
f (x )
f (x )
0
0
1
5
2
0
3
Hi mnh no di õy ỳng ?
A. Hm s cú 2 ng tim cn.
B. Giỏ tr cc tiu ca hm s l yCT 3.
C. Giỏ tr cc i ca hm s l yCD 5.
D. th hm s cú hai tim cn ngang l y 0, y 5 v tim cn ng l x 1.
3 2x
x 1
D. x 2, y 1.
Cõu 25. Tỡm ng tim cn ng v ng tim cn ngang ca th hm s y
A. x 1, y 2. B. x 1, y 2.
C. x 1, y 2.
4 x2
Cõu 26. th hm s y 2
cú tt c bao nhiờu ng tim cn ?
x 3x 4
A. 0.
B. 3.
C. 1.
D. 2.
Cõu 27. Tỡm tham s m tim cn ng ca th hm s y
A. m 4.
C. m 6.
B. m 1.
x 3
i qua im A(5;2).
x m 1
D. m 4.
Cõu 28. Tp hp tt c cỏc giỏ tr thc ca tham s m th hm s y
tim cn ng l
A. (; 4] [4; ).
C. (; 4) (4; ) \ {5}.
x 4
cú hai ng
x mx 4
2
B. \ {5}.
D. (; 4) (4; ).
Cõu 29. ng cong hỡnh bờn l th ca hm s no ?
A. y x 4 2x 2 .
B. y x 4 2x 2 .
C. y x 4 2x 2 1.
D. y x 4 2x 2 .
Cõu 30. Cho hm s y ax 3 bx 2 cx d cú th nh hỡnh v. Mnh no ỳng ?
A. a 0, b 0, c 0, d 0.
B. a 0, b 0, c 0, d 0.
C. a 0, b 0, c 0, d 0.
D. a 0, b 0, c 0, d 0.
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Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Cõu 31. Cho hm s y f (x ) cú bng bin thiờn nh hỡnh v bờn di. S nghim ca phng trỡnh
2 f 2 (x ) 3 f (x ) 1 0 l
A. 6.
B. 0.
C. 3.
D. 2.
Cõu 32. Cho th hm s y x 3 3x 1. Tỡm tt c tham s m phng trỡnh x 3 3x m 0
cú ỳng 2 nghim phõn bit ?
A. m 1, m 5.
B. m 4, m 0.
C. 0 m 4.
D. m 4.
Cõu 33. th hm s y x 4 x 2 2 v th ca hm s y 4 cú tt c bao nhiờu im chung ?
A. 0.
B. 1.
C. 4.
D. 2.
Cõu 34. Cú bao nhiờu giỏ tr nguyờn ca tham s m (20;20) ng thng d : y m 3x ct
th hm s y
2x 1
ti hai im phõn bit ?
x 1
A. 12.
B. 28.
C. 9.
D. 18.
Cõu 35. Cho hỡnh chúp S .ABC cú SA (ABC ). Tam giỏc ABC vuụng ti C , AB a 3, AC a,
SC a 5. Th tớch ca khi chúp S .ABC bng
A.
6a 3
6
B.
6a 3
4
2a 3
10a 3
D.
3
6
Cõu 36. Cho hỡnh chúp S .ABCD cú ỏy ABCD l hỡnh ch nht cú AB a, AC 5a. Hai mt bờn
(SAB ) v (SAD ) cựng vuụng gúc vi ỏy, cnh bờn SB to vi ỏy mt gúc bng 60. Th
tớch ca khi chúp S .ABCD bng
C.
A. 2 2a 3 .
B.
4 2a 3
3
2 2a 3
C. 6 2a .
D.
3
Cõu 37. Cho hỡnh chúp S .ABC cú ỏy l tam giỏc u cnh a, mt phng (SAB ) vuụng gúc vi mt
phng (ABC ) v tam giỏc SAB vuụng cõn ti S . Th tớch khi chúp S .ABC bng
3
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A.
a3 3
12
B.
Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
a3 3
24
a3 3
a3 3
D.
3
4
Cõu 38. Cho khi chúp S .ABCD cú ỏy ABCD l hỡnh vuụng cnh bng 3a. Tam giỏc SAB vuụng
cõn ti S v nm trong mt phng vuụng vi ỏy. Th tớch hỡnh chúp ó cho bng
C.
A. 9a 3 3.
B.
9a 3 3
2
9a 3
2
Cõu 39. Khi t din u cú cnh l 3 thỡ th tớch bng
C. 9a 3 .
A.
2.
C.
4 2
9
D.
B. 2 2.
D.
9 2
4
Cõu 40. Cho khi chúp tam giỏc u S .ABC cú cnh ỏy bng a v cnh bờn bng a 3. Th tớch ca
khi chúp S .ABC bng
35a 3
24
A.
B.
3a 3
6
2a 3
2a 3
D.
6
2
Cõu 41. Cho hỡnh chúp t giỏc u S .ABCD cú cnh ỏy bng 2a, cnh bờn bng 3a. Th tớch ca
khi chúp ó cho bng
C.
A. 4 7a 3 .
B.
4 7a 3
9
4a 3
4 7a 3
D.
3
3
Cõu 42. Th tớch khi lp phng cnh 2 bng
C.
A. 6.
B. 8.
C. 4.
D. 2.
Cõu 43. Cho hỡnh hp ch nht ABCD.A B C D cú AB a, AD a 2, AB a 5. Th tớch ca
khi hp ó cho bng
A. a
3
10.
C. a 3 2.
2a 3 2
B.
3
D. 2a 3 2.
Cõu 44. Tớnh th tớch V ca vt th vi cỏc kớch thc c cho trong hỡnh v di õy ?
A. V 6600cm 3 .
B. V 5700cm 3 .
C. V 6400cm 3 .
D. V 7800cm 3 .
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Ôn thi giữa kỳ 1 lớp 12 năm 2020 2021
Cõu 45. Cho lng tr ng ABC .A B C cú ỏy ABC l tam giỏc vuụng ti B, BAC 60, AB a
v AA a 3. Th tớch khi lng tr bng
3a 3
A.
2
C.
a3 3
3
2a 3
B.
3
D.
a3 3
9
Cõu 46. Th tớch ca khi lng tr tam giỏc u ABC .A B C cú AC 5a v ỏy l tam giỏc u
cnh 4a bng
A. 12a 3 .
B. 20a 3 3.
C. 20a 3 .
D. 12a 3 3.
Cõu 47. Cho hỡnh lng tr ABC .A B C cú ỏy ABC l tam giỏc vuụng cõn ti B v AC 2a. Hỡnh
chiu vuụng gúc ca A trờn mt (ABC ) l trung im H ca cnh AB v A A a 2. Th
tớch ca khi lng tr ó cho bng
a3 6
6
B. 2a 3 2.
a3 6
C.
2
D. a 3 3.
A.
Cõu 48. Cho hỡnh chúp S .ABC cú A, B ln lt l trung im ca SA, SB. Gi V1, V2 ln lt l
th tớch ca khi chúp S .A B C v S .ABC . T s
1
8
B.
V
3
B.
A.
a3
6
B.
a3
2
C.
a3
4
D.
a3
3
A.
V1
V2
bng
1
4
1
1
D.
2
3
Cõu 49. Cho hỡnh chúp t giỏc S .ABCD cú th tớch bng V . Ly im A trờn cnh SA sao cho
SA 3SA. Mt phng qua A v song song vi ỏy ca hỡnh chúp ct cỏc cnh SB, SC , SD
ln lt ti B , C , D . Th tớch khi chúp S .A B C D bng
C.
A.
V
81
V
V
D.
9
27
Cõu 50. Cho hỡnh lp phng ABCD.A B C D cnh a. Gi E v E ln lt l trung im CD,
A B . Th tớch ca khi a din ABEDD A E bng
C.
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