Đề thi Song ngữ môn Toán 7 năm học 2023-2024 (Có đáp án)

Nội dung text: Đề thi Song ngữ môn Toán 7 năm học 2023-2024 (Có đáp án)

1. PHềNG GD&ĐT VĨNH BẢO ENGLISH MATHEMATICS COMPETITION FOR GRADE 7 STUDENTS Number of pages:02 SCHOOL YEAR: 2023 – 2024 Time limit: 150 minutes PART I: OBJECTIVE TEST (100 mark) Choose the correct answerin 4 options (from Question 1 to Question 10) Question 1 : Number A 102025 4 has divisible by: A. 5 B. 3 C. 9 D. 18 Question 2. Find the unit digit of T = 23 + 37 + 411 + + 20048011 ? A. 6 B. 7 C. 8D. 9 Question 3. How many pairs interger (x,y) such that x y 4 A. 4 B. 8 C. 16 D. 20 Question 4 : Find x + y + z if x : y : z = 2 : 3 : 4 and 4x – 3y – 2z = 9 A. 6 B. -6 C. 9 D. -9 Question 5. If y = f(x ) = 2x2 -1 then f(-2) is: A. 7 B. - 9 C. 9 D. -7 Question 6. In a class, there are 48 students and the ratio of male students to female students is 1 : 2. How many female students are the in the class ? A. 12 B. 24 C. 32 D. 16 Question 7:Let ABCD be a rectangle with AB = 6cm and AD = 8cm. Let I be the midpoint of BC. What is the area of triangle AIC? A. 12 B. 48 C. 24 D. 28 Question 8: Given a triangle ABC with Bà 500 and àA Cà 100 . Find the measure of the greatest angle of The triangle ABC. Answer: The measure of the greatest angle of the triangle ABC is.......0 A. 40 B. 50 C. 60 D. 70 Question 9: According to the pattern of the following sequence, find the sum of the first eigth numbers: 1, 1, 2, 3, 5, 8, ... A. 21 B. 54 C. 44 D. 34 Question 10: Given D(x) = 1 + x3 + x5 + x7 + . + x2023 Find the value of D(- 1). Answer: D (-1) = .. A. 1010 B. -1010 C. 1009 D. -1009 2) Find x such that 2023 x 2024 x 2025 x 2 Question 12: Let ABC be a triangle with 3 acute angles (AB < AC). Draw outside triangle ABC the equilateral triangles ABD and ACE. Let I be the intersection of CD and BE; K be the intersection of AB and CD a) Calculate angle DIB b) Let M, N be the midpoints of CD and BE respectively, proving that triangle AMN is equilateral. Question 13: 1) Find the smallest natural number whose remainder is 5 when divided by 9, remainder 4 when divided by 7 and remainder 3 when divided by 5 2) Find pairs of integers such that: xy + 3x - y = 6 Question 14:
2. 1. For two real numbers x, y satisfy x + y = 2. Find the min value of 1 A = y2 + xy + x2 - x 2 2. Drop 257 small marbles onto the 64-square International chess board. Prove that there exists a box containing at least 5 marbles (even if the marbles lie on the edge of the square). ....... The end ...... UBND HUYỆN VĨNH BẢO ĐÁP ÁN, THANG ĐIỂM GIAO LƯU HSG CẤP HUYỆN ĐÁP ÁN ĐỀ THI ĐỀ XUẤT SCHOOL YEAR: 2023 – 2024 Number of pages:03 Mụn: Toỏn Tiếng Anh lớp 7 Time limit: 150 minutes I. Cõu 1 2 3 4 5 6 7 8 9 10 Đ.A B D C D A C A D B B Điểm 10 10 10 10 10 10 10 10 10 10
3. II. Điểm Tổng Bài Nội dung làm được chi tiết điểm 1)Given the number of students in classes 7A, 7B, 7C are 5 x, y, z respectively (x,y,z are positive integers) 7 x y We have: x + y + z = 105 and x y , 6 7 6 10 3 y z y z y z 4 3 4 6 8 x y z => 5 30 7 6 8 Applying the property of the series of equal ratios, we get x y z x y z 105 5 5 7 6 8 7 6 8 21 Bài 1 =>x = 5.7 = 35 (Satisfy the conditions) 5 (50 điểm) Hence, There are 35 students in class 7A. 2) 2023 x 2024 x 2025 x 2 We have: 2024 x 0 ; 10 => 2023 x 2025 x x 2023 2025 x 2 Because 20 2023 x 2024 x 2025 x 2 5 (x 2023)(2025 x) 0 => 2024 x 0 => x = 2024 5 Hỡnh vẽ Bài 2 (50 điểm) a) We have 10
4. AD AB;Dã AC Bã AE; AC AE ADC ABE(s.a.s) ã ã ã ã ABE ADC,but BKI AKD ( two opposite angles) 5 0 BIK and DAK => Bã IK Dã AK 60 5 ã ã b)Because ADC ABE CM EN, ACM AEN 10 50 ACM AEN(s.a.s) AM AN 10 andCã AM Eã AN ã ã 0 MAN CAE 60 . 10 => AMN is an equilateral triangle. 1. Let the natural number to be found is a We have: a divided by 9 remainder 5 5 a 9k 5 k Ơ 2a 9k1 1 2a 1 M9 We have a divided by 7 remainder 4 5 a 7m 4 m Ơ 2a 7m1 1 2a 1 M7 We have a divided by 5 remainder 3 20 a 5t 3 t Ơ 2a 5t1 1 2a 1 M5 Bài 3 5 (50 điểm) 2a 1 M9,7,5, mà 9;7;5 1and a is the smallest natural number 2a 1 BCNN(9,7,5) 315.So a 158 5 2. We have: xy + 3x - y = 6 => (x -1)( y + 3) = 3 10 x 1 1 x 1 3 ; 10 y 3 3 y 3 1 30 Hence, the pairs of integers (x,y) are : 10 ( 2;0), ( 0;-6), ( 4;-2), (-2;-4) 1. We have: x + y = 2ị y = 2 – x 1 A = (2- x)2 + x(2- x) + x2 - x 2 1 10 = .(4- 4x + x2) + 2x - x2 + x2 - x 2 1 1 = 2 - 2x + x2 + x = x2 - x + 2 2 2 1 1 30 = x2 - 2x + 4 = x2 - 2x + 1+ 3 Bài 4 ( ) ( ) 2 2 10 (50 điểm) 1 ộ 2 ự 1 3 = . ờ(x - 1) + 3ỳ= .(x - 1)2 + 2 ởờ ỷỳ 2 2 1 2 Because .(x - 1) ³ 0" x 10 2
5. 3 =>A ³ " x 2 3 So Amin = . The equality holds when (x – 1)2 = 0 2 => x=1 2. Think of 64 squares as 64 cages. 257 marbles are 257 5 rabbits We see 257 64.4 1 5 20 Put 257 rabbits into 64 cages, according to the Dirichle 10 principle, there exists a cage containing at least 5 rabbits. ---------------The end-------------------