Kỳ thi tốt nghiệp trung học phổ thông năm 2015 môn thi: Toán – Giáo dục trung học phổ thông

BỘ GIÁO DỤC VÀ ĐÀO TẠO KỲ THI TỐT NGHIỆP TRUNG HỌC PHỔ THÔNG NĂM 2015
Môn thi: TOÁN – Giáo dục trung học phổ thông
ĐỀ THI CHÍNH THỨC Thời gian làm bài: 120 phút, không kể thời gian giao đề
Câu 1 (1,0 điểm) Khảo sát sự biến thiên và vẽ đồ thị của hàm số 3y x 3x 
Câu 2 (1,0 điểm) Tìm giá trị lớn nhất và giá trị nhỏ nhất của hàm số 4f (x) x x  trên
đoạn [1;3]
Câu 3 (1,0 điểm)
a) Cho số phức z thỏa mãn 1 i z 1 5i 0( )    . Tìm phần thực và phần ảo của z
b) Giải phương trình : 22 x x 2 3log ( )  
Câu 4 (1,0 điểm)Tính tích phân xx 3 e
1
0
I = ( - ) dx
Câu 5(1,0 điểm) : Trong không gian với hệ trục Oxyz, cho các điểm A (1;-2;1), B(2;1;3)
và mặt phẳng (P) x y 2z 3 0    . Viết phương trình đường thẳng AB và tìm tọa độ
giao điểm của đường thẳng AB với mặt phẳng (P).
Câu 6 (1,0 điểm)
a) Tính giá trị của biểu thức P 1 3 2 2 3 2( cos )( cos )     biết 23sin 
b) Trong đợt phòng chống dịch MERS-CoV. Sở y tế thành phố đã chọn ngẫu nhiên
3 đội phòng chống dịch cơ động trong số 5 đội của Trung tâm y tế dự phòng
TPHCM và 20 đội của Trung tâm y tế cơ sở để kiểm tra công tác chuẩn bị. Tính
xác suất để có ít nhất 2 đội của các Trung tâm y tế cơ sở được chọn.
Câu 7(1,0 điểm): Cho hình chóp S.ABCD có đáy ACBD là hình vuông cạnh a, SA
vuông góc với mặt phẳmg (ABCD), góc giữa đường thẳng SC và mặt phẳng (ACBD)
bằng 450.. Tính theo a thể tích của khối chóp S.ABCD và khoảng cách giữa hai đường
thẳng SB,AC.
Câu 8 (1,0 điểm): Trong mặt phẳng hệ tọa độ Oxy, cho tam giác ABC vuông tại A. Gọi
H là hình chiếu của A trên cạnh BC; D là điểm đối xứng của B qua H; K là hình chiếu
của vuông góc C trên đường thẳng AD. Giả sử H (-5;-5), K (9;-3) và trung điểm của
cạnh AC thuộc đường thẳng : x - y + 10 = 0 . Tìm tọa độ điểm A
Câu 9(1,0 điểm) : Giải phương trình :
2
2
x 2x 8 x 1 x 2 2x 2x 3 ( )( )
       trên tập số thực
Câu 10 (1,0 điểm) Cho các số thực a,b,c thuộc đoạn [1,3] và thỏa mãn điều
kiện a b c 6  
Tìm giá trị lớn nhất của biểu thức
P =
2 2 2 2 2 2a b b c c a 12abc 72 1 abcab bc ca 2
     
BÀI GIẢI
Câu 1:
a) Tập xác định là R, y' = 3x2-3, y' = 0  x = -1 hay x = 1
Đồ thị hàm số đạt 2 cực trị tại: A (-1 ; 2) hay B (1 ; -2)
lim
x
y

  và lim
x
y

  .
Bảng biến thiên
x  -1 1 +
y’ + 0  0 +
y 2 +
 CĐ -2
CT
Hàm số đồng biến trên 2 khoảng (∞; -1) và (1; +∞)
Hàm số nghịch biến trên (-1;1)
y" = 6x; y” = 0 x = 0. Điểm uốn I (0; 0)
Đồ thị :
Câu 2: f’(x) = 2
41 x trên [1; 3] ta có : f’(x) = 0 2x 
f(1) = 5; f(2) = 4; f(3) = 133 . Vậy : [1;3]min ( ) 4f x  ; [1;3]max ( ) 5f x  .
Câu 3: a) (1 – i)z – 1 + 5i = 0  (1 – i)z = 1 – 5i

21 5 (1 5 )(1 ) 1 4 5 3 21 (1 )(1 ) 2
i i i i iz ii i i
          
Vậy phần thực của z là 3; phần ảo của z là -2.
b) 2 22 2log ( 2) 3 log 8 2 8 2 3x x x x x hay x           
Câu 4: 1
0
( 3) xI x e dx 
Đặt u = x – 3 du dx  . Đặt dv = exdx , chọn v = ex
I =
11 1
0 0
0
( 3) 2 3 4 3x x xx e e dx e e e       
Câu 5: a) AB đi qua A (1; -2; 1) và có 1 VTCP AB
uuur
=(1; 3; 2) nên có pt:
1 2 1
1 3 2
x y z   
b) Tọa độ giao điểm M của AB và (P) là nghiệm hệ phương trình:
1 2 1
1 3 2
2 3 0
x y z
x y z
        
(0; 5; 1)M  
Câu 6:
a) P = 2 21 3(1 2sin ) 2 3(1 2sin )           8 1 141 3(1 ) 2 3( )9 9 9P
              
y
0
-2
-1
2
x
1
b) Số phần tử của không gian mẫu là: 325( ) 2300n C  
A là biến cố có ít nhất 2 đội của các trung tâm y tế cơ sở.
Số phân tử của A là : n(A) = 2 1 320 5 20 2090C C C 
Xác suất thỏa ycbt là : P = ( ) 209( ) 230
n A
n 
Câu 7:
a) Do góc SCA = 45o nên tam giác
SAC vuông cân tại A
Ta có AS = AC =
=
3
21 22 . 23 3
aa V a a  
b) Gọi M sao cho ABMC là hình bình hành
Vẽ AH vuông góc với BM tại H, AK vuông góc SH tại K
Suy ra, AK vuông góc (SBM)
Ta có: 2 2 2 2 2 2
1 1 1 1 4 5
2 2 2AK SA AH a a a    
Vì AC song song (SBM) suy ra d(AC, SB) = d(A; (SBM)) = AK = 25
a
Câu 8:
Đường trung trực HK có phương trình y = -7x + 10
cắt phương trình (d): x – y + 10 = 0 tại điểm M (0; 10).
Vì ∆HAK cân tại H nên điểm A chính là điểm đối xứng
của K qua MH : y = 3x + 10, vậy tọa độ điểm A (-15; 5).
Câu 9: ĐK : x  -2
2
x 2 x 4 x 2x 1x 2x 3 x 2 2
( )( ) ( )      
2
x 2
x 4 x 1 1x 2x 3 x 2 2 ( )
       
 
2
2 2
1 x 4 x 2 2 x 1 x 2x 3
x 2 2 x 2 2 x 1 2 x 1 2 2
( ) ( )( ) ( )( )
( )( ) ( ) ( ) ( )
       
           
Đặt f(t) = 2t 2 t 2( )( )   3 2t 2t 2t 4   với t R 
2f t 3t 4t 2 0'( )      f(t) đồng biến
Vậy (2) x 1 x 2   
2
x 1 3 13x 2x 2x 1 x 2
       
. Vậy x = 2 hay x = 3 132

Câu 10: P =
2 2 2 2 2 2 12 72 1
2
a b b c c a abc abcab bc ca
     
Ta có : 2 2 2 2 2 2 2ab bc ca a b b c c a 2abc a b c( ) ( )       
= 2 2 2 2 2 2a b b c c a 12abc  
Đặt x = ab + bc + ca ≤
2a b c 123
( )  
Ta có : a, b, c 1 3[ ; ]
A
B CH
K
M
D
A
B C
D
H
K
S
M
a 1 b 1 c 1 0( )( )( )     abc ab bc ac a b c 1 0( )        
abc x 5 0    abc x 5  
Lại có : a 3 b 3 c 3 0( )( )( )    abc 3 ab bc ac 9 a b c 27 0( ) ( )        
abc 3x 27  
Vậy : 3x – 27 ≥ abc ≥ x – 5
3x – 27 ≥ x – 5  2x ≥ 22  x ≥ 11
P =
2 72 1
2
x abcx
  ≤
2 72 1 ( 5)2
x xx
   = 72 52 2
x
x  (x thuộc [11; 12])
 P’ = 21 722 x ≤ 0  P ≤
11 72 5 160
2 11 2 11  
P = 16011 khi a = 1, b = 2, c = 3. Vậy maxP =
160
11 .
BỘ GIÁO DỤC VÀ ĐÀO TẠO
ĐỀ THI CHÍNH THỨC
KỲ THI TRIUNG HỌC PHỔ THÔNG QUỐC GIA NĂM 2015
Môn: TIẾNG ANH
Thời gian làm bài: 90 phút, không kể thời
(Đề thi có 06 trang)
Mã đề thi 931
SECTION A (8 points)
Mark the letter A, B, C, or D on your answer sheet to indicate the word whose underlined part
differs from the other three in pronunciation in each of the following questions.
Question 1: A. supported B. finished C. noticed D. approached
Question 2: A. teach B. break C. deal D. clean
Mark the letter A, B, C or D on your answer sheet to to indicate the word that differs from the other
three in the position of primary stress in each of the following question.
Question 3: A. oceanic B. advantageous C. compulsory D. influential
Question 4: A. instrument B. recipe C commitment D. candidate
Question 5: A. contain B. conquer C conserve D. conceal
Mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the
following questions.
Question 6: The receptionist... answered the phone, told me that the director was out.
A. who B. whose C. that D. whom
Question 7: Students will not be allowed into the exam room if they......their student cards.
A. don’t produce B. didn’t produce C. produced D. hadn’t produced
Question 8:......the salesman promised to exchange the detective CD player for a new one, they
insisted on getting a refund.
A. And B. But C. Although D. Despite
Question 9: Changes have been made in our schooling program. As a result, young children......
do homework any more.
A. couldn’t B. needn’t C. oughtn’t D. haven’t
Question 10: Although MERS (Middle East Respiratory Syndrome) spreeds through close contact
with sick people, not through the air, many people still avoid.....to crowded places.
A. having gone B. going C. to go D. gone
Question 11: A large number of inventions and discoveries have been .....accident.
A. in B. by C. at D. on
Question 12: The headmaster has decided that three lecture halls......in our school next semester.
A. will be building B. will build C. are being built D. will be built
Question 13: After the new technique had been introduced, the factory produced ......cars in 2014 as
the year before.
A. twice as many B. twice many as C. as many twice D. as twice many
Question 14: It is.....of businessmen to shake hands in formal meetings.
A. familiar B. ordinary C. common D. typical
Question 15: John has finally found a new job after being.....for three months.
A.out of reach B. out of order C. out of work D. out of mind
Question 16: Nguyen Thi Anh Vien performed so well the 28th Sea Games Women’s 200m
butterfly that none of her rivals could.....her.
A. look up to B. come up to C. catch up with D. put up with
Question 18: Jane really loves the......, jewelry box that her parents gave her as a birthday present.
A. wooden brown nice B. nice wooden brown
C. brown wooden nice D. nice brown wooden
Question 19: When asked about their preference for movies, many young people say that they are in
favour......science fiction.
A. with B. of C. in D. for
Question 20: Global warming will result......crop failures and famine.
A. in B. from C. of D. to
Question 21:......at school yesterday when we were informed that there was no class due to a sudden
power cut.
A. We have hardly arrived B. We had arrived hardly
C. Hardly we had arrived D. Hardly had we arrived
Question 22: Such characters as fairies or witches in Walt Disney animated cartoons are purely.......
A. imaginary B. imaginative C. imagining D. imaginable
Question 23: Ken and Tom are high-school students. They are discussing where their study group will
meet. Select the most suitable response to fill in the blank.
Ken: "Where is our study group going to meet next weekend?" Tom: “..”
A. Studying in a group is great fun. B.We are too busy on weekdays.
C. Why don’t you look at the atlas? D. The library would be best.
Question 24: Mike and Lane are university students. They are talking about Lane's upcoming
high-school reunion. Select the most suitable response to fill in the blank.
Mike: "So, you have your fifth high-school reunion coming up?” Lane: “..”
A. Oh, the school reunion was wonderful. B. No. You're in no mood for the event
C. The food at the reunion was excellent. D. Yeah. I'm really looking forward to it.
Mark the letter A, B, C or D on your answer sheet to indicate the word(s)CLOSEST in meaning to
the underlined word(s) in each of the following questions.
Question 25: When Susan invited us to dinner, she really showed off her culinary talents. She
prepared a feast – a huge selection of dishes that were simply mouth-watering.
A. relating to medical knowledge B. involving hygienic conditions and diseases
C. concerning nutrition and health D. having to do with food and cooking
Question 26: “It’s no use talking to me about metaphysics. It’s a closed book to me.”
A. a book that is never opened B. an object that I really love
C. a subject that I don’t understand D. a theme that I like to discuss
Question 27: Suddenly, it began to rain heavily, so all the summer hikers got drenched all over.
A. very tired B. completely wet C. refreshed D. cleansed
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the
correct word or phrase that best fits each of the numbered blanks from 28 to 37.
Library is a collection of books and other informational materials made available to people for
reading, study, or reference. The word library comes (28)......liber, the Latin word for "book”. (29)......,
library collections have almost always contained a variety of materials. Contemporary libraries
maintain collections that include not only printed materials such as manuscripts, books, newspapers,
and magazines, (30)...... audio visual and online databases. In addition (31)......maintaining collections
within library buildings, modern libraries often feature tele-communications links that provide users
with access to information at remote sites.
The central mission of a library (32)......to collect, organise, preserve, and provide access to
knowledge and information. In fulfilling this mission, libraries preserve a valuable record of culture
that can be passed down to (33)......generations. Libraries are an essential link in this communication
between the past, present, and future. Whether the cultural record is contained in books or in electronic
formats, libraries ensure (34)......the record is preserved and made available for later use.
People use library resources to gain information about personal (35)......or to obtain recreational
materials such as films and novels. Students use libraries to supplement and enhance their classroom
experiences, to learn (36)..... in locating sources of information, and to develop good reading and
study habits. Public officials use libraries to research legislation and public policy issues. One of the
most valued of all cultural institutions, the library (37).....information and services that are essential to
learning and progress.
From “Library (institution)” by Richard S. Halsey et al.
Question 28: A. to B. in C. from D.out
Question 29: A. Therefore B. Instead C. However D. Despite
Question 30: A. but also B. as well C. only if D. or ebe
Question 31: A. in B. on C. from D. to
Question 32: A. has B. are C. is D. have
Question 33: A. success B. succeeding C. succeed D. successful
Question 34: A. that B. which C. what D. who
Question 35: A. appeals B. interests C. profits D. attractions
Question 36: A. skills B. talents C. capabilities D. abilities
Question 37: A. relates B. digests C. supplies D. apohes
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the
correct answer to each of the questions from 38 to 47.
Plants and animals will find it difficult to escape from or adjust to the effects of global warming.
Scientists have already observed shifts in the lifecycles of many plants and animats, such as flowers
blooming earlier and birds hatching earlier in the spring. Many species have begun shifting where they
live or their annual migration patterns due to warmer temperatures.
With further warming, animals will tend to migrate towards the poles and up mountainsides towards
higher elevations. Plants will also attempt to shift their ranges, seeking new areas as old habitats grew
too warm. In many places, however, human development will prevent these shifts. Species that find
cities or farmland blocking their way north or south may become extinct. Species living in unique
ecosystems, such as those found in polar and mountaintop regions, are especially at risk because
migration to new habitats is not possible. For example, polar bears and marine mammals in the Arctic
are already threatened by dwindling sea ice but have nowhere farther north to go.
Projecting species extinction due to global warming is extremely difficult. Some scientists have
estimated that 20 to 50 percent of species could be committed to extinction with 2 to 3 Celsius degrees
of further wanning. The rate of warming, not just the magnitude, is extremely important for plants and
animals. Some species and even entire ecosystems, such as certain types of forest, may not be able to
adjust quickly enough and may disappear.
Ocean ecosystems, especially fragile ones like coral reek, will also be affected by global warming,
warmer ocean temperatures can cause coral to "bleach", a state which if prolonged will lead to the
death of the coral. Scienists estimate that even 1 Celsius degree of additional warming could lead to
widespead bleaching and death of coral reefs around the world. Also, increasing carbon dioxide in the
atmosphere enters the ocean and increases the acidity of ocean waters. This acidification further
stresses ocean ecosystems.
From “Global Warming” by Michael Mastrandrea and Stephen H. Schneider
Question 38: Scientists have observed that warmer temperatures in the spring cause flowers to.....
A. bloom earlier B. lose color C. die instantly
D. become lighter
Question 39: According to paragraph 2, when their habitats grow warmer, animals tend to move.....
A. south-eastwards and down mountainsides towards tower elevations
B. north-westwards and up mountainsides towards higher elevations
C. towards the North Pole and down mountainsides towards tower etevattorts
D. towards the poles and up mountainsides towards higher elevations
Question 40: The pronoun “those” in paragraph 2 refers to.....
A. species B. ecosystems C. habitats D. areas
Question 41: The phrase "dwindling sea ice" in paragraph 2 refers to.....
A. the frozen water in the Arctic B. the cold ice in the Arctic
C. the violent Arctic Ocean D. the melting ice in the Arctic
Question 42: It is mentioned in the passage that if the global temperature rose by 2 or 3 Celsius
degrees.....
A. water supply would decrease by 50 percent B. the sea level would rise by 20 centimeters
C. 20 to 50 percent of species could become extinct D. half of the earth's surface would be flooded
Question 43: According to the passage, if some species are not able to adjust quickly to warmer
temperatures,......
A. they may be endangered B. they can begin to develop.
C. they will certainly need water D. they move to tropical forests.
Question 44: The word “fragile” in paragraph 4 most probably means ..........
A. very large B. easily damaged C rather strong D. pretty hard
Question 45: The bleaching of coral reefs as mentioned in paragraph 4 indicates ........
A. the water absorption of coral reefs B. the quick growth of marine mammals.
C. the blooming phase of sea weeds D. the slow death of coral reefs.
Question 46: The level of acidity in the ocean is increased by........
A. the rising amount of carbon dioxide entering the ocean
B. the decrease of acidity of the pole waters
C. the extinction of species in coastal areas.
D. the loss of acidity in the atmosphere around the earth
Question 47:What does the passage mainly discuss?
A. Influence of climate changes on human lifestyles.
B. Effects of global warming on animals and plants
C. Global warming and possible solutions
D. Global warming and species migration
Mark the letter A, B, C, or D on your answer sheet to indicate the underlined part that needs
correction in each of the following questions.
Question 48: The number of homeless people in Nepal have increased sharply due to the recent
A B C
severe earthquake.
D
Question 49: Since poaching is becoming more seriously, the government has imposed stricter laws
A B C
to prevent it.
D
Question 50: It is common knowledge that solar heating for a large office building is technically
A B C
different from a single-family home.
D
Question 51: All the candidates for the scholarship will be equally treated regarding of their age,
sex, or nationality. A B C
D
Question 52: Reminding not to miss the 15:20 train, the manager set out for the station in a hurry.
A B C D
Mark the letter A, B, C, or D on your answer sheet to indicate the word(s) OPPOSITE in meaning
to the underlined word(s) in each of the following questions.
Question 53: "Don't be such a pessimist. I'm sure you'll soon get over it. Cheer up!"
A. hobbyist B. optimist C. activist D. feminist
Question 54: "Be quick! We must speed up if we don’t want to miss the flight."
A. turn down B. slow down C. look up D. put forward
Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the
correct answer to each of the questions from 55 to 64.
Overpopulation, the situation of having large numbers of people with too few resources and too
little space, is closely associated with poverty. It can result from high population density, or from low
amounts of resources, or from both. Excessively high population densities put stress on available
resources. Only a certain number of people can be supported on a given area of land, and that
number depends on how much food and other resources the land can provide. In countries where
people live primarily by means of simple fanning, gardening, herding, hunting, and gathering, even
large areas of land can support only small numbers of people because these labour intensive
subsistence activities produce only small amounts of food.
In developed countries such as the United States, Japan,