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.
Find the total number of dots required to form Pattern 4.
Find the total number of dots required to form Pattern 20.
Find the number of small right-angled triangles in Pattern 50.
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.
Find the total number of dots required to form Pattern 4.
Find the total number of dots required to form Pattern 20.
Find the number of small right-angled triangles in Pattern 50.
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.
Find the total number of triangles in Pattern 80.
Find the number of shaded triangles in Pattern 40.
Find the number of unshaded triangles in Pattern 50.
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.
Find the total number of triangles in Pattern 80.
Find the number of shaded triangles in Pattern 40.
Find the number of unshaded triangles in Pattern 50.
Level 3
Darryl was drawing a pyramid-like structure as shown. It consists of shaded and unshaded rectangles. The rest of the structure follows the same pattern.
How many shaded rectangles are there in Row 9?
In which row would there be 37 rectangles?
Darryl had drawn a total of 144 rectangles. How many shaded rectangles were there in the drawing?
Level 3
Darryl was drawing a pyramid-like structure as shown. It consists of shaded and unshaded rectangles. The rest of the structure follows the same pattern.
How many shaded rectangles are there in Row 9?
In which row would there be 37 rectangles?
Darryl had drawn a total of 144 rectangles. How many shaded rectangles were there in the drawing?
Level 3
May added a certain number of white squares round a grey square and then a certain number of grey squares round the white squares and she continued adding more grey and white squares round the diagram in each pattern as shown.
How many grey squares did she need if the most outer layer had 11 squares on each side?
How many squares are there in the Figure 11?
Level 3
May added a certain number of white squares round a grey square and then a certain number of grey squares round the white squares and she continued adding more grey and white squares round the diagram in each pattern as shown.
How many grey squares did she need if the most outer layer had 11 squares on each side?