Đề thi bằng Tiếng Anh môn Toán Lớp 10 - Mã đề: 203 - Năm học 2020-2021 - Sở GD&ĐT Nam Định (Có đáp án)

 NAM DINH DEPARTMENT OF CONTEST OF MATH AND SCIENCE IN ENGLISH
 EDUCATION AND TRAINING School year: 2020 - 2021
 Subject: MATH - Grade 10 
 OFFICIAL Time allowed: 90 minutes
 CODE: 203
I. PART I. 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. In the Oxy coordinate plane, let M be the vertex of Parabol y ax2 bx c(a 0). The 
coordinates of M are
 b 4ac b2 b b2 4ac b 4ac b2 b 4ac b2 
A. ; . B. ; . C. ; . D. ; .
 2a 4a 2a 4a 2a 4a 4a 4a 
Question 2. Given two sets X A;1;2;4;6, Y 3;7;4;, the union of X and Y is
A. 1;2;3;4;5;6;7. B. 1;2;3;4;6;7. C. A;1;2;3;4;6;7;. D. A;1;2;3;4;6;7.
Question 3. In the Oxy coordinate plane, given A 2; 6 . Let B be the point which is symmetric to 
point A with respect to the origin O . Find the coordinates of point C satisfying that its horizontal 
coordinate equals 4 and ABC has the right angle at C. 
A. C 2 6; 4 or C 2 6; 4 . B. C 4; 24 or C 4; 24 . 
C. C 24; 4 or C 24; 4 . D. C 4; 2 6 or C 4; 2 6 . 
Question 4. Among the following propostions, whose inverse proposition is true? 
A. If a quadrilateral is an isosceles trapezoid then its two diagonals have the same length. 
B. If two triangles are congruent then their corresponding angles are equal.
C. If n is a natural number then n is a real number.
D. If a triangle is not regular then it has at least one interior angle less than 60 degrees. 
Question 5. Given two non-zero vectors a and b. Which of the following statements is false? 
A. Two vectors a and b with opposite direction to another nonzero vector are parallel.
B. Two vectors a and 3a have the same direction.
C. Two vectors a and ka are parallel.
D. Two vectors a and b with the same direction are parallel.
Question 6. Let a,b,c be three positive real numbers satisfying a b c 3. Determine the maximum 
value of T ab bc ca.
A. 3. B. 6.C. 4. D. 2.
Question 7. Given an isosceles triangle ABC with the right angle A , inscribed in a circle with center O 
and radius R . Let r be the radius of the incircle of triangle ABC. The ratio of R to r is
 R R 2 2 R 1 2 R 2 1
A. 1 2. B. . C. . D. .
 r r 2 r 2 r 2
Question 8. Given a right triangle ABC at A. Which of the following statements is false? 
                 
A. AC.BC BC.AB. B. AC.CB AC.BC. C. AB.BC CA.CB. D. AB.AC BA.BC.
Question 9. A ball is thrown straight up from 60 meters above the ground with a velocity of 20 meters 
per second (20 m/s). The height of the ball at second t after throwing can be computed by the quadratic 
function s t – 5t 2 20t 60,where s(t) is in meters. After how many seconds does the ball hit 
the ground?
A. t 1. B. t 4. C. t 6. D. t 2. 
 1/4 - Code 203 Question 10. Find all parameters m such that equation x2 (m 1)x m2 1 0 has two distinct roots 
and these roots have the same sign.
 5 5
A. –1 m 1. B. m –1. C. m –1or m 1. D. 1 m .
 3 3
Question 11. In the Oxy coordinate plane, let A( 3; 5); B(2;5). Determine the slope of line AB. 
A. -3. B. 5.C. 2. D. -5. 
 2
Question 12. The domain of the function y is
 6 2x
A. D 3; . B. D ;3 .C. D ¡ \ 3. D. D ;3. 
Question 13. Let a,b,c be real numbers and a 2021c b 2021c. Which of the following statements is true?
 1 1
A. a2 b2. B. 2021a 2021b. C. . D. 2020a 2020b.
 a b
Question 14. Which of the following two inequations are not equivalent?
 1 1
A. 5x 1 and 5x 1 0. B. 3x2 1 2x 1and 3x2 2x 2 0. 
 x 2 x 2
 1 1
C. 2x 1 0 and 2x 1 0. D. 2x 1 0 and 2x 1 .
 2x2 1 2x2 1
Question 15. Given rectangle ABCD with AD 2. Suppose that E is the point which lies on the side 
 1
AB such that AE 2BE and sin B· DE . Compute the length of the segment AB. 
 5
A. AB 3. B. AB 3 3. C. AB 2 2. D. AB 6.
Question 16. Given ABC with AB 13, BC 2 33, CA 17 . Compute the length of the median AM 
of ABC .
A. AM 194. B. AM 14. C. AM 15. D. AM 2 35.
Question 17. Given equation (x2 x 1)(x 1)(x 1) 0. Which of the following equations is equivalent 
to the given equation?
A. (x 1)(x 1) 0. B. x 1 0. C. x2 x 1 0. D. x 1 0.
  
Question 18. In the Oxy coordinate plane, given A 1; 3 and B 5; 4 . The coordinates of vector BA are
     
A. BA 6; 7 . B. BA 4; 1 . C. BA 6; 7 . D. BA 6; 7 
Question 19. Given ABC . Let M and N be the mid-points of sides AB and AC , respectively. Find 
    
the scalars m and n such that NM mAB nAC. 
 1 1 1 1 1 1 1 1
A. m , n . B. m , n . C. m , n . D. m , n .
 2 2 2 2 2 2 2 2
Question 20. Given an isosceles right triangle ABC with sides AB AC 42cm. Two medians BE and 
CF intersect at point G. The area of the triangle GEC is
A. 21 7 cm2. B. 147 cm2. C. 7 21 cm2. D. 174 cm2.
Question 21. The negation of the proposition “Fourteen is a composite number” is
A. Fourteen is a prime number.B. Fourteen has only two factors 1 and 14.
C. Fourteen is not a composite number. D. Fourteen has four positive factors.
Question 22. Find all values of m such that function y (m 1)x 2021 is decreasing on its domain.
A. m 1. B. m 1. C. m 1. D. m 1.
 2/4 - Code 203 Question 23. Given three distinct points A, B and C. Which of the following statements is true?
             
A. AB CA BC. B. BA AC CB. C. CA AB CB. D. BA BC AC.
Question 24. In the Oxy coordinate plane, given Parabol P : y x2 5x 2m. Let S be the set of all 
values of m such that the Parabol (P) cuts Ox at two distinct points A, B satisfying OA 4OB. 
Determine the sum of all elements of S.
 16 32 2
A. 2. B. . C. . D. .
 9 9 9
Question 25. Given ABC with the sides AC 3 3, side BC 3 2 , A 450 and B A C . 
Compute the degree measure of ·ABC.
A. ·ABC 600. B. ·ABC 1200. C. ·ABC 1500. D. ·ABC 300.
Question 26. Given two equations mx2 2(m 1)x m 2 0 and (m 2)x2 3x m2 15 0. How 
many values of m which make these above equations equivalent?
A. 0.B. 3.C. 1. D. 2. 
Question 27. A man travels from city X to city Y by train, then returns to city Y by his car. Given that the 
distance between these two cities is 200 km and the average speed of his car is 10 km/h faster than the 
train’s average speed. His journey takes 9 hours, find the sum of average speeds of the train and his car.
A. 60. B. 80. C. 100.D. 90. 
Question 28. Given A 1;2;3;4 . How many subsets does the set A have? 
A. 14. B. 18.C. 15. D. 16.
 x3 (2 3y) 8
Question 29. Given the fact that the system of equations has exactly two distinct 
 3
 (y 2)x 6
 4 4 4 4
solutions (x1, y1);(x2 , y2 ). The value of S x1 y1 x2 y2 is
A. 40. B. 28.C. 34. D. 36. 
Question 30. In the Oxy coordinate plane, given ABC . Points M 2; 3 , N 4; 1 , P 1; 1 are the 
mid-points of sides BC, CA and AB , respectively. The coordinates of vertex A are
A. A 10; 0 . B. A 10; 0 . C. A 7; 3 . D. A 7; 3 .
Question 31. In the Oxy coordinate plane, given ABC with A 1; 4 , B 6; 7 and C 2; 9 . Let G 
be the centroid of ABC . The coordinates of G are 
A. G 1; 4 . B. G 3; 12 . C. G 1; 4 . D. G 1; 4 .
   
Question 32. Given a right triangle ABC at B with AB 2a, AC 5a. Compute the dot product AB.CA. 
A. 5a2 B. 5a2 C. 4a2 D. 4a2.
Question 33. Which of the following sentences is not a proposition?
A. If “1+2 = 7” then “7 is an odd number”. B. If “ 3 x 4 ” then “ x 1”.
C. Five divides twenty. D. What a nice day!
Question 34. In the Oxy coordinate plane, let Parabol P : y ax2 bx 3and a point M ( 1;9) belongs 
to the graph of (P).The symmetric axis of (P) has equation x 2. Find the value of S a b. 
A. 16. B. 6. C. -6.D. -10. 
Question 35. In the Oxy coordinate plane, given two vectors a 6; 4 and b 10, 2 . Compute 
the angle between two vectors a and b .
A. 1350. B. 600. C. 450. D. 1200.
 3/4 - Code 203 II. PART II. PROBLEM SOLVING (3,0 points)
 Write the solutions to the following problems in the provided space on your answer sheet.
Problem 1. (1,0 point)
 To measure the height of the Cham temple tower Po Klong Garai in Ninh Thuan province (Figure 1), 
two points A and B which are chosen on the ground with the length AB 16m and the bottom C of the 
tower are collinear (Figure 2). Two total stations whose tripods have a height h 1,6m are put at point A 
and point B . Let D be the top of the tower and two points A1, B1 be collinear to C1 on height CD of the 
 · 0 · 0
tower. The measurements are DA1C1 54 and DB1C1 32 . Caculate the height CD of the tower then 
round the result to 3 decimal places. 
 D
 0 A 0
 54 1 32 
 C B1
 1 16 m
 1,6 m
 C A 16 m B
 Figure 1 Figure 2
Problem 2 (1,0 point). 
 Let f x ax3 bx2 cx d be a cubic function with f 0 k, f 1 2k, f 1 3k, where 
k is a given constant. What is the value of f 2 f 2 ? 
Problem 3 (1,0 point).
 The sum of 2025 consecutive positive integers is a perfect square. Find the minimum value of the 
largest of these integers? 
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Student’s full name: Student’s ID: 
First observer’s name and signature: Second observer’s name and signature: ..
 4/4 - Code 203