6 P6.PA.JC.17111301
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?
3 m
Equal intervals Square numbers
7 P6.PA.JC.17111306
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.
3 m
Repeated patterns Square numbers
8 P6.PA.JC.17111305
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.
3 m
Repeated patterns Square numbers
9 P6.PA.JC.17111316
Level 3
The figure shows a series of steps built using square cubes. The n number of steps is given by x -step.
  1. How many square cubes were used if n is 5?
  2. How many square cubes were used if n is 40?
  3. Find the number of steps if a total of 144 square cubes are used.
3 m
Square numbers Sum of odd consecutive
10 P6.PA.JC.17111303
Level 3
The diagram shows a sequence of patterns formed by square tiles. By considering the pattern information in the table, answer the questions.
  1. Find the number of tiles at the bottom layer in the 29th pattern
  2. Find the total number of tiles in Pattern 50.
3 m
Equal intervals Square numbers Sum of odd consecutive

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