Điều kiện xác định của phương trình $\frac{1}{\sqrt{x}}+\sqrt{{{x}^{2}}-1}=0$ là

The usual thermometer has two scales, Celsius measured in ⁰C and Fahrenheit measured in ⁰F. If m⁰C is the same temperature as n⁰F, the conversion formula is $m\times \frac{9}{5}+32=n$. What is the value of m if m⁰C is the same temperature as n⁰F and m + n = 60 ?

Điều kiện xác định của phương trình $\sqrt{x-2}+\frac{{{x}^{2}}+5}{\sqrt{7-x}}=0$ là

The diagram shows two intersecting circles of radius 10 cm. The four areas inside each circle have the same shape and equal length. Taking $\pi $ = 3.14, what is the area, in cm², of the shaded region which consists of 7 identical parts ?

The total number of players on three badminton teams is 29. No two players on the same team play against each other, while every two players on different teams play each other exactly once. What is the maximum number of games played ?

A class is putting up 40 rectangular posters of the same shape and size on a wall. Each poster must be held in place by one nail near each corner. Adjacent posters may overlap sligtly so that the same nail can serve to hold both of them. The diagram shows how 9 nails can hold four posters adjacent diagonally. What is the minimum number of nails required to hold all 40 posters ?

The diagram shows a sheep on a lawn, tied a string to a metal rod parallel to the ground. The length of the string is 10m, the length of the metal rod is 3m. The sheep is of negligible size and the height of the rod above the ground is also negligible. Taking $\pi $$\approx $ 3.14, what is the area, in m², of the part of the lawn from which the sheep can eat the grass ?

Leon uses a code to convert a letter string consisting only of As, Bs and Cs, into a number string consisting only of 0s and 1s, by replacing A with 101, B with 11 and C with 0. If the number string obtained is 111010101111100110101, what is the number of letters in the original letter string ?

The diagram shows a hexagon ABCDEF partitioned into four triangles by three diagonals AC, CF and FD, no two of which intersect expect at the vertices. What the total number of ways of partitioning ABCDEF into four triangles with three non-crossing diagonals ?

Điều kiện xác định của phương trình $\sqrt{x-1}+\sqrt{x-2}=\sqrt{x-3}$ là

Điều kiện xác định của phương trình $\frac{2x}{{{x}^{2}}+1}-5=\frac{3}{{{x}^{2}}+1}$ là

What is the value of 101010 – 10101 ?

The following figures are formed by idential squares. Which figures has the longest perimeter ?

Which of the following sets of fractions has sum greater than 1 ?

The diagram to the rightt shows two squares AMND and PQRS inside a rectangle ABCD. The areas of the two squares are 16 cm² and 4 cm² respectively. What is the sum of area of the shaded regions in cm² ?

Mike jogs at constant speed along a road with lamp pots which are evenly spaced. It takes him 2 minutes to go from the first lamp post to the fifth lamp post. He continues jogging to the n-th lamp post before turning back. If he has been jogging for 12 minutes when he returns to the first lamp post, what is the value of n ?

The smallest interior angle of a triangle is 50⁰. Which of the following statements about this triangle is correct ?

Each of A, B, C and D has a watch.

(1) A’s watch is 10 minutes faster than standard time but A believes that it is 5 minutes slower

(2) B’s watch is 5 minutes slower than standard time but B believes that it is 10 minutes faster.

(3) C’s watch is 5 minutes faster than standard time but C believes that it is 3 minutes faster

(4) D’s watch is 5 minutes slower than standard time but D believes that it is 10 minutes slower.

According to their watches and their beliefs, they go to school in order to be just in time. Who is late ?

The diagram below shows four squares with numbers which exhibit a certain pattern. What number should be inside the fourth box?

A piece of square paper is folded along a straight line, dividing it into two regions with the same area and the same shape. How many such straight lines are there?

The three figures in the diagram below have equal perimeters.     

What is a：b：c ?

A triangle is formed with 10 matchsticks of equal length connected end to end. No matchsticks are bent or broken. How many different triangles can be formed?

The total weight of 5 apples is equal to that of 6 bananas, and the total weight of 3 bananas is equal to that of 4 oranges. How many apples have the same total weight as 16 oranges?

Jane begins observing a hyacinth plant on last Friday, when some of its flowers bloom. Thereafter, the number of flowers which bloom on any day is equal to  the number of flowers which have already bloomed. No flowers wither. All the flowers have bloomed by the following Thursday. On which day of the week have exactly half of the flowers bloomed?

The side length of each square in the diagram below is 1 unit. An ant needs 5 seconds to crawl 1 unit horizontally, and 6 seconds to crawl 1 unit vertically. It requires 1 second to change direction. What is the minimum number of seconds for the ant to crawl from point A to point B?