Đề thi Violympic Toán Tiếng Anh lớp 8 vòng 8 năm 2016

Câu 1: If 𝑥 3 + 2𝑥 2 + 𝑘𝑥 + 2 is divisible by 𝑥 − 1 then 𝑘 = ⋯. 

Key: − 5 

Câu 2: Given a square with the length of one side is 8 cm and a isosceles triangle with the length of its base is 12 cm. If the area of the square is equal to the area of the isosceles triangle then what is the length of the height of the isosceles triangle, in cm? 

32/ 3 ; 23/ 3 ; 16 /3 ; 8 /3 

Câu 3: If 𝑥 = 2𝑦 then (1/𝑥 + 1/ 𝑦) / (1/ 𝑥 − 1 /𝑦) = ⋯. 

Key: − 3 

Câu 4: Given 𝐴 = 9𝑥 2 + 8 − 12𝑥 and 𝐵 = 2. 

To compare:𝐴 …𝐵. 

𝐴 > 𝐵;𝐴 < 𝐵; 𝐴 = 𝐵; not be compared

Câu 5: The triangle 𝐴𝐵𝐶 has three bisectors 𝐴𝑀,𝐵𝑁, 𝐶𝑃 

of the angles at 𝐴,𝐵,𝐶, respectively. Then the value of 𝐴𝑁/ 𝐶𝑁 × 𝐶𝑀/ 𝐵𝑀 × 𝐵𝑃/ 𝐴𝑃 𝑖𝑠 … 

Key: 1

Câu 6: Given the rectangle ABCD and the triangle BEC. Find the value of x such that the ratio of the area of the rectangle to the area of the triangle BEC is 7:3. 

Answer: x={} cm. 

Key: 6

Câu 7: A survey showed that of 120 secondary school students: 52 of them have a dog, 31 of them have a cat and 19 of them have both. 

How many of the 120 students have neither a dog nor a cat? Answer: {} students. 

Key: 56

Câu 8: The number of the solutions of 𝑥 4 + 𝑥 3 + 2𝑥 2 + 𝑥 + 1 = 0 is {}. 

Key: 0 

Câu 9: Three children: Mark, Tom, Andy ate 23 cookies altogether. Tom ate more cookies than Andy, Mark. What is the smallest possible number of cookies that Tom ate? 

Answer: The smallest possible number of cookies that Tom ate is {} cookies. 

Key: 9

Câu 10: The average of three numbers is 42. All three are whole positive number and are different from each other. 

If the least number is 20, what could be the greatest possible number of the remaining two numbers? 

Answer: {}.