Level 3
The following is a sequence of numbers.

1. Find the 39^th number.
2. Find the 40^th number.

Level 3
Tina used stars and sticks to make the following patterns.

1. How many stars are there in Pattern 5?
2. If Tina counted 289 stars, which pattern number had she made?
3. How many stars are there in Pattern 120?

Level 3
Consider the pattern.

1. What is the sum of Row 9?
2. What is the sum of Row 50?
3. If the sum is 2702, what is the row number?

Level 2
The first three figures of a sequence are shown. The table records the number of shaded and unshaded rhombuses in each figure.

1. Find the number of unshaded rhombuses in Figure 10?
2. Find the number of shaded rhombuses in Figure 40?
3. Which figure number has 804 shaded rhombuses?

Level 3
The figure shows a tank made up of 3 sections. Cuboid A with a square base of side 4 cm and height 30 cm. Cube B with a side of 12 cm. Cuboid C that is 60 cm by 20 cm by 40 cm. Water from a tap above flows down at a rate of 1.2 litres per minute while water is drained out from the bottom at a rate of 1 litre per minute. How long did it take to fill up the tank to a height of 66 cm from the base? Give the answer in minutes correct to nearest whole number.

Level 3
The patterns show a sequence of shapes. Each shape has a number of small right-angled triangles. A dot is placed at each point where there is a vertex of one or more right-angled triangles. The total number of dots and the number of small right-angled triangles of each figure is shown in a table.

1. Find the total number of dots required to form Pattern 4.
2. Find the total number of dots required to form Pattern 20.
3. Find the number of small right-angled triangles in Pattern 50.

Level 3
The figure shows a cube with 3 painted parts A, B and C. These painted parts are of the same area and they are touching the midpoints of the sides of the cube. The total area of the painted parts is 96 cm². Find the volume of 3 such cubes.

Level 3
Some patterns of shaded and unshaded small triangles is given. The unshaded triangles are those which have at least one side on the edge of the big triangle. All of the other small triangles are shaded. The table below shows numbers of small triangles.

1. Find the total number of triangles in Pattern 80.
2. Find the number of shaded triangles in Pattern 40.
3. Find the number of unshaded triangles in Pattern 50.

Level 3
The figure is not drawn to scale. It is made up of a square and a rectangle. The ratio of the area of the square to that of the rectangle is 3 : 4. After the shaded part is cut out, the ratio of the area of unshaded part of the rectangle to that of the unshaded part of the square is 2 : 1. Given the length of the square is 9 cm, find the area of the shaded part.

Level 3
The figure is made up of identical cubes. The total area of the shaded faces is 338 cm². Find the volume of the solid figure when we add 1 more of such cubes to it.