A table has 3 rows and 3 columns. In each square, we put in the product of the row number and the column number of that square. For instance, the number in the third row and the second column is 3x2 = 6, as shown in the diagram. These nine numbers are then arranged in order of size, starting with the smallest. What is the fifth number in the arrangement ?

Oliver arranges his duck toy and turtle toy in a row as shown in the diagram. He desires that all duck toys to be on the left and all turtle toys on the right. He may switch the positions of any two adjacent toys. What is the minimum number of switches does he to achieve his desired arrangement ?

Max has a gray paper strip of width 5 cm. He cuts out some pieces and tapes them on the wall, to form a 50 cm by 35 cm window frame, as shown in the diagram, where each white area is 5 cm by 10 cm. What is the minimum length, in cm, of the paper strip required ?

The tap is leaking at the rate of one drop per second. The volume of each  drop is 0.05 mL. At 9 pm, Wendy puts an empty measuring cup under the tap. Some time during the night, she finds the cup partially filled, as shown in the diagram. No water is lost from the cup. At what time is the water level in the measuring cup closest to the time in the following ?

The upper part of a glass is a cylinder of height 8cm and diameter 20m. The middle part is a cone of height 8 cm and diameter 20 cm. The bottom part is a solid stem. Correct to one decimal place, what is the capacity, in cm³, of the cup ? Take $\pi =3.14$

A hall has four doors. Lea may enter the hall using any of them, and exit the hall using any of them. In how many different ways can she enter and exit the hall ?

ABCD is a square of side length 10cm. The segment BC is fixed. The segment AD moves in the plane to the segment A’D’ so that the lengths AB, DC and AD do not change. What is the area, in cm², of the shaded region in the diagram when the segment A’D’ intersects the segment CD at its midpoint G ?

On a table there is a ring, there are 12 equally spaced beads on the ring, 3 of which are black, as shown in the diagram. Which of the following five figures cannot be obtained from the given figure by rotating the ring on the table ?

The figure in the diagram is formed from 20 equilateral of equal sizes. How many equilateral triangles of any size does it contain ? The triangles may overlap.

The sectors MAB and MCD are inside the square ABCD of side length 10 cm, as shown in the diagram. What is the total area, in cm², of these two sectors, correct to 1 decimal place ? Take $\pi =3.14$

In the sequence 1, 1, 2, 3, 5, 8, 13, 21, ….., each term starting from the third one is the sum of the preceding two. How many among the first 2014 terms are divisible by 4 ?

The inside lane of a track has length 400m and the outside lane has length less than 500m. From the line, as shown in the diagram, Max and Lynn start running counterclockwise along the track at the same time. Max runs at constant speed on the inside lane. Lynn, whose constant speed is 3 times that of Max, runs on the outside lane. The first time both are back together at the marked line, Max has completed 3 laps. What is the length, to the nearest m, of the outside lane ?

How many pairs of unit squares in a 3 by 6 table are such that they have no common points ? The diagram shows one such pair.

Tính nhanh:

$\frac{1\times 3\times 5\times 7}{2\times 5\times 7\times 9}$ = .... ?

( Viết kết quả dưới dạng a/b)

Tính nhanh:

$\frac{3\times 16\times 5}{9\times 4\times 30}$ = .... ?

( Viết kết quả dưới dạng a/b)

Điền dấu thích hợp vào chỗ chấm:

$\frac{6}{11}...\frac{6}{15}$  ?

Điền dấu thích hợp vào chỗ chấm:

$\frac{40}{27}...\frac{40}{23}$  ?

Điền dấu thích hợp vào chỗ chấm:

$\frac{24}{27}...\frac{8}{9}$  ?

Hương ăn $\frac{3}{5}$ quả táo, Linh ăn $\frac{4}{7}$ quả táo đó. Ai ăn nhiều táo hơn ?

Với hai số tự nhiên 7 và 12, hãy viết phân số lớn hơn 1 ?

( Viết kết quả dưới dạng a/b)

Với hai số tự nhiên 7 và 12, hãy viết phân số bé hơn 1 ?

( Viết kết quả dưới dạng a/b)

Tính nhanh:

$\frac{9\times 4\times 5}{2\times 15\times 6}$ = .... ?

Tính nhanh:

$\frac{3\times 4\times 5\times 6}{4\times 5\times 6\times 7}$ = .... ?

( Viết kết quả dưới dạng a/b)

So sánh hai phân số sau:$\frac{18}{19}$ và $\frac{17}{18}$ ?

So sánh hai phân số sau:$\frac{9}{11}$ và $\frac{11}{9}$ ?