1 P6.PA.JC.21022201
Level 3
The following is a sequence of numbers.
  1. Find the 39th number.
  2. Find the 40th number.
3 m
Equal intervals Square numbers
2 P6.PA.JM.18011208
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?
3 m
Square numbers
3 P6.PA.JC.17111315
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?
3 m
Square numbers
4 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
5 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
6 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
7 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
8 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
9 P6.PA.JC.17111318
Level 3
The diagram shows the pattern for the number of circles.
  1. How many circles will Pattern 4 contain?
  2. How many circles will Pattern 30 contain?
  3. Which pattern contains 421 circles?
3 m
Repeated patterns Square numbers Guess & check
10 P6.PA.JM.18011219
Level 3
Study the number pattern carefully.
  1. What is the missing number in the 5th pattern?
  2. What is the missing number in the 32th pattern?
  3. If this number pattern goes on, which pattern number will give you 445?
4 m
Square numbers
11 P6.PA.JM.18011220
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.
  1. How many grey squares did she need if the most outer layer had 11 squares on each side?
  2. How many squares are there in the Figure 11?
4 m
Square numbers
12 P6.PA.JC.17111323
Level 3
A pattern is made by putting shaded squares of unit length around a white square of similar unit length. He then continues to make patterns as shown in Figure 2 and Figure 3.
  1. Which figure uses 100 white squares?
  2. Find the number of shaded squares in Figure 30.
  3. Find the total number of squares in Figure 60.
4 m
Equal intervals Square numbers
13 P6.PA.JC.17111320
Level 3
At Richard's soap factory, a special soap bar 'Johnny's Bricks' is made by daily adding 1 cm3 soap bars around the previous day's region of soap bars.
  1. Find the number of 1-cm3 soap bars added on Day 5.
  2. Find the total number of soap bars on Day 9.
  3. Find the total number of soap bars on Day 30.
4 m
Repeated patterns Square numbers
14 P6.PA.JC.17111322
Level 3
The diagram shows the first four of a sequence of figures.
Figure 1 is made up of just 1 square.
Figure 2 is made up of one 2 x 2 and four 1 x 1 squares, so it has a total of 1 + 4 = 5 squares.
Figure 3 contains one 3 x 3 and some 2 x 2 squares and nine 1 x 1 squares.
The sequence continues as shown in Figure 4 and so on.
  1. How many squares are there in Figure 7?
  2. How many total number of squares will be there in sequence 7?
4 m
Repeated patterns Square numbers
15 P6.PA.JC.17111319
Level 3
Consider the following sequence:
  1. Find the sum of 2 + 6 + 10 + 14 + ... + 30.
  2. A given line of the sequence is as follows: 2 + 6 + 10 + 14 + ... + a = 648 = 2 x b2. Find the value of b.
  3. Calculate the sum of Line 40 if the pattern for the sum of the lines is as follows:- Line 1: 8 Line 2: 8 + 10 Line 3: 8 + 10 + 12
4 m
Equal intervals Repeated patterns Square numbers
16 P6.PA.JC.19091410
Level 3 PSLE
Study the pattern.
  1. Find the total number of white and grey triangles in Figure 100.
  2. Find the percentage of grey triangles in Figure 100. (Give the answer in decimals.)
4 m
Equal intervals Repeated pattern Square numbers Percent of a set
17 P6.PA.JM.18011221
Level 3
The graph shows 3 figures formed by shaded and white triangles.
  1. Complete the column for Figure 5. Give your answers for (i) and (ii) in numbers. (Eg 1, 2)
  2. What is the total number of triangles in Figure 16?
  3. How many shaded triangles are there in Figure 40?
4 m
Square numbers Sum of consecutive
18 P6.PA.JC.17111321
Level 3
Observe the following figures.
  1. Find the number of small triangles in Figure 4.
  2. Find the number of small triangles in Figure 50.
  3. Find the number of sticks in Figure 100.
4 m
Square numbers Times sum of consecutive
19 P6.PA.NK.21060305
Level 3 PSLE
Yasmin uses stars and circles to form figures that follow a pattern as shown.
  1. The table shows the number of stars and circles for the first four figures. Complete the table for Figure 5. List the answers in the following order using commas. (Eg i, ii, iii)
  2. A figure in the pattern has a total of 121 stars and circles. What is the figure number?
  3. Another figure in the pattern has 50 more stars than circles. What is the total number of stars and circles in the figure?
5 m
Square numbers More than or less than
20 P6.PA.JC.17111325
Level 3
A series of patterns of shaded and unshaded small triangles is shown.
  1. Which pattern has 141 shaded triangles?
  2. Find the number of unshaded triangles in Pattern 40.
  3. Find the total number of triangles in Pattern 90.
5 m
Equal intervals Square numbers

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