Đề thi bằng Tiếng Anh môn Toán Lớp 11 - Mã đề: 305 - Năm học 2020-2021 - Sở GD&ĐT Nam Định (Có đáp án)

 NAM DINH DEPARTMENT OF CONTEST OF MATH AND SCIENCE IN 
EDUCATION AND TRAINING ENGLISH
 School year: 2020 -2021
 OFFICIAL Subject: MATH – Grade 11 
 Time allowed: 90 minutes
 CODE 305
I. PART 1. MULTIPLE CHOICE QUESTIONS (7.0 points)
Write the correct answer (A, B, C or D) for each of the following questions in the correspondingly numbered 
space on your answer sheet.
Question 1. Which of the following sequences is a geometric sequence?
 ùỡ u1 = 2021
 A. ớù B. 3, 33, 333,...,
 ù
 ợù un+ 1 = un + 2020
 ỡ u = 2021 ỡ =
 ù 1 ù u1 2021
 C. ớù D. ớ
 ù 2 ù u = 2020u
 ợù un+ 1 = un ợù n+ 1 n
Question 2. Rumor has it that an Indian King gave the chess inventor the right to ask for any prize he wished. 
The inventor then asked for an amount of rice that would cover 64 squares of a chessboard and satisisfied the 
following condition: there is one grain of rice on the first square, two grains on the second, four grains on the 
third and so on. In general, from the second square, each square had double the number of grains as the square 
before. Find the number of grains of rice on the twelveth square of the chessboard.
 A. 2048. B. 1024. C. 4096. D. 512.
Question 3. Find the sum of all positive solutions of the equation 
 ổ 2014p2 ử
 2 cos 2x ỗcos 2x - cos ữ= cos 4x - 1.
 ốỗ x ứữ
 A. 1080p. B. 1800p. C. 810p. D. 1008p.
Question 4. There are 14 teams in V- League 2021. How many matches will be arranged if two arbitrary 
teams meet each other exactly two times?
 A. 192. B. 180. C. 182. D. 140.
Question 5. In the three dimensional space, let two distinct lines a,b be parallel. How many planes contain 
line a but not parallel to lineb ?
 A. Infinite. B. Does not exist. C. Two. D. One.
Question 6. Given the tetrahedron ABCD. Let M and N be the centroids of triangles ABC and ABD, respectively. The 
line MN is parallel to which of the following planes?
 A. (ACD) B. (AMD) C. (ACB) D. (ABD)
Question 7. Given arithmetic sequence (un ) with u2 = 3,d = 4.Assume that un = 75, the value of n is
 A. 19. B. 23. C. 21. D. 20.
Question 8. In the Oxy coordinate plane, a rotation Q(O;a ) transforms the point M (1;0) into the 
point N (0;1).Which of the following points is the image of the point E(- 3;2) under the rotation Q(O;a ) ?
 A. F (3;- 2). B. F (- 2;- 3). C. F (2;- 3). D. F (3;2).
 x
Question 9. Let T be the period of function y = tan .The value of T is
 2
 p
 A. 2p. B. . C. p. D. 3p.
 2
 Page1/4 – Code 305 Question 10. Given that x, y, z in the same order is a geometric sequence and x,2y,3z in the same order is 
an arithmetic sequence ( x ạ 0 ). Find the common ratio q < 1 of the geometric squence.
 1 1
 A. q = . B. q = 1. C. q = 3. D. q = - .
 3 3
Question 11. Given three lines intersecting in pairs but there is no plane containing all of them. Which of the 
following statements is true?
 A. These three lines form a triangle. B. These three lines are concurrent.
 C. These three lines are overlap. D. These three lines are parallel to a plane.
Question 12. An box contains 4 green balls and 6 blue balls. Another box contains 16 green balls and N blue 
balls. From each box, a ball is drawn randomly. The probability of the event “both selected balls are the same 
color” is 0,584. The value of N is
 A. 144. B. 148. C. 184. D. 164.
Question 13. Let 10x - 3, x + 6, x (x > 0) in the same order be a geometric sequence. What is the value of 
 x ?
 A. x = 2. B. x = 3. C. x = - 2. D. x = 4.
Question 14. The first floor surface of a house is 0.5m higher than the yard surface. The staircase to the second 
floor consists 21 stairs, each of which is 18 cm in height. Calculate the heightd of the second floor as compared 
with the yard surface.
 A. d = 432(cm) B. d = 426(cm) C. d = 420(cm) D. d = 428(cm)
 12
 ổ 2 1ử
Question 15. Find the constant term in the expansion of the expression ỗx - ữ .
 ốỗ x ứữ
 A. - 498 . B. 495. C. 498 . D. - 495 .
Question 16. Three fair six-sided dice are rolled silmutaneously. What is the probability of the event “the 
numbers of dots on all three dice are the same”?
 1 1 3 1
 A. . B. . C. . D. .
 18 36 216 216
Question 17. In the three dimension space, given a cube. Using the vertices of a cube as vertices, how many 
tetrahedrons can be formed?
 A. 70. B. 58 C. 64. D. 60.
Question 18. Given the formula of general term un for each sequence as below. Which of the sequences is 
increasing?
 n+ 1 p n + 2021
 A. (- 2) .sin . B. .
 2021n n2
 2n+ 2020 10
 C. (- 1) (2020n + 2021). D. .
 n + 2021 + n
Question 19. Whichof the following statements is true ?
 A. Two distinct lines lying in the same plane are not diagonal.
 B. Two distinct linesin two different planes arediagonal.
 C. Two distinct non-parallel lines are diagonal.
 D. Two distinct non-intersecting lines are diagonal.
 1
Question 20. The domain of the function y = is
 1- cos x
 A. (k2p; +Ơ ). B. Ă \{k2p, k ẻ Â}.
 ùỡ p ùỹ
 C. Ă \ớù + kp, k ẻ Âýù . D. Ă \{kp, k ẻ Â}.
 ợù 2 ỵù
 Page2/4 – Code 305 Question 21. : In the three dimensional space, S.ABCD is a pyramid whose base is a parallelogram. Let F be 
the midpoint of side CD . Let plane (a) be parallel to the line AC and contain the line BF. Let E be the 
 EC
intersection of the plane (a) and the line SC. Determine the ratio .
 ES
 2 1 1 2
 A. . B. . C. . D. .
 3 3 2 5
Question 22. In the three dimensional space, given two distinct planes (P) and (Q) with intersection line d. Let 
 A,B be two points in (P) but do not belong to the line d;let S be a point which is not in (P). Two lines SA,SB 
cut (Q) at C, D, respectively (S,C, D are distinct). Let E be the intersection of AB and d, which of the 
following statements is true?
 A. AB,CD and d are not concurrent.
 B. E does not belong to the plane (SAB).
 C. The areas of two triangles SDA and ACE are equal.
 D. E belongs to CD.
Question 23. The maximum value of the function y = 2 cos(2x + 2021) + 3sin(2x + 2021) is
 A. 3 B. 1 C. 13. D. 13.
Question 24. The smallest positive solution of the equation sin x + sin 2x = cos x + 2 cos2 x is
 p p p 2p
 A. . B. . C. . D. .
 4 6 3 3
Question 25. In the three dimensional space, let A,B,C, D be four distinct and non-coplanar points. How 
many planes contain at least 3 points from these 4 points in total? (Recall that four points are coplanar if they 
belong to the same plane)
 A. 2. B. 3. C. 4. D. 1.
Question 26. Let S.ABCD be a pyramid, where the base ABCD is a parallelogram; let M ,N,P be the midpoints 
of AB, AD,SC,respectively. The cross-section created by the pyramid S.ABCD and the plane (MNP) is
 A. a triangle. B. a rectangle. C. a hexagon. D. a pentagon.
Question 27. Let W be the set of all positive integers less than 100 and all digits of these numbers are prime 
numbers. A teacher randomly selects a number inW. What is the probability of the event “the selected number 
is a prime number”?
 1 2 9 8
 A. B. . C. . D. .
 2 5 20 99
Question 28. Let a < b < c be three integers such that a,b,c in the same order is an arithmetic sequence and 
 a,c,b in the same order is a geometric sequence. Let c0 be the smallest possible value of c. Which of the 
following intervals contains c0 ?
 A. (8;12) B. (- 5;1) C. (- 18;- 12) D. (1;5).
Question 29. A box contains 3 white and 2 black balls. A teacher randomly choose 2 balls. What is the 
probability of getting 2 white balls?
 1 1 3 2
 A. . B. . C. . D. .
 5 3 10 5
Question 30. In the three dimensional space, let S.ABCD be a pyramid where the base ABCD is a
 parallelogram; let M ,N be two points on the sides SB,SD such that SM = MB, SN = 2ND. The plane
 SF
 (AMN ) cuts the line SC at F. Determine the ratio .
 SC
 Page3/4 – Code 305 2 2 1 1
 A. . B. . C. . D. .
 5 3 2 3
Question 31. Let a,b,c be three distinct lines in the three dimensional space. Assume that two lines a and b 
are parallel, which of the following statements is false?
 A. If c cuts a then c also cutsb.
 B. If a,c are parallel then b,c are also parallel.
 C. There exists exactly one plane containing both a and b.
 D. If A belongs to a and B belongs to b then three lines a,b, AB are on the same plane.
Question 32. Four fair six-sided dice are rolled silmutaneously. What is the probability that at least three of 
the four dice show the same face?
 1 1 7 1
 A. . B. . C. . D. .
 36 9 72 6
Question 33. The pyramid of Cheops, the oldest of the seven wonders of the Ancient world is modelled as a 
pyramid S.ABCD. Let I,J be the mid-points of SA,SB, respectively. Which of the following statements is 
false?
 A. Quadrilateral IJCD is a trapezoid.
 B. Line IB is the intersection of two planes (SAB) and (IBC).
 C.Line AO is the intersection of two planes (IAC) and (JBD), where O is the center of the square ABCD.
 D. Line JD is the intersection of two planes (SBD) and (JCD).
 2020 2 2020
Question 34. From the expansion of expression (2x - 1) = a0 + a1.x + a2.x + ...+ a2020.x , calculate
T = a1 + a2 + ...+ a2020 .
 A. T = 1. B. T = 0. C. T = 2. D. T = - 1.
Question 35. Given point A(- 4;3) in the Oxy coordinate plane. Find the image of point A under the 
symmetry about center O(O is origin).
 A. (4;- 3) B. (4;3) C. (3;4) D. (- 4;- 3)
II. PART II. PROBLEMS SOLVING (3,0 points)
Write the solutions to the following problems in the provided space on your answer sheet
Problem 1: Assume that 11,2x,4x in the same order is a geometric sequence and x is a prime number. Find the 
value of x.
Problem 2: Given a cube ABCD.A' B 'C ' D ' satisfying its faces are squares having the side a. Let M ,N be 
points on the segments AD ',BD, respectively such that AM = DN = x (0 < x < a 2).
Prove that when x is changed, the line MN is always parallel to a fixed plane.
Problem 3: In the final of a chess tournement, An and Tam play a BO9 series (best of 9 games). Every game 
has a win-lose result (no draw). The winner is the one who gets the 5 winning games first. After 6 games, An 
won 4 games and Tam won 2 games. The series has 3 games left. Assume that in any game, An and Tam have 
the same wining probability (50%). What is the probability of the event “An wins the series”?
 -THE END-
Student’s full name: ..Student’s ID: ...
First observer’s name and signature: ..
Second observer’s name and signature: ..
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