121 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
122 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
123 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
124 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
125 P6.VO.JC.22100305
Level 3 PSLE
Ann had some identitical cuboids with square base and height, h. She then stacked the cuboid to form the 2 towers. The figure shows the front view and the side views of the 2 towers.
  1. Find h.
  2. Find the volume of the cuboid.
4 m
Volume of cuboid Cube view Units & parts Elimination
126 P6.AP.NK.21060428
Level 3 PSLE
Figure 1 shows a square tile made up of 2 grey squares, A and B and 2 identical white rectangles C. The length of 1 side of square A is twice the length of 1 side of square B.
  1. What fraction of the square tile in Figure 1 is grey?
  2. Figure 2 shows a wall laid with square tiles. The wall is 9 m by 9 m and is completed covered with square tiles. Find the total area of the wall covered by grey squares.
3 m
Square Rectangle Cut & paste Tiling Fraction of a whole
127 P6.AN.NK.17051712
Level 3
In the figure, not drawn to scale, ABCD is a trapezium and PQCR is a square. AB//CQ. The size of ∠DCR is 54 of ∠DCQ . Find ∠ADC.
3 m
Square Trapezium Interior angles Fraction of a whole Units method
128 P6.AP.TL.17090772
Level 3
The figure is made up of 16 square tiles. What fraction of the figure is shaded? Give the answer in the simplest form.
3 m
Square Triangle Tiling Fraction of a whole F Simplest form
129 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
130 P6.VO.NK.17053018
Level 3
A rectangular block is sprayed grey on all the six faces before it is cut into 36 identical cubes as shown in the diagram. The total surface area of the 36 individual cubes is 576 cm2 more than the surface area of the original block that is sprayed grey. What is the volume of the rectangular block?
4 m
Volume of cube Square & square root Surface area More than or less than
131 P6.AP.NK.21060429
Level 3 PSLE
The pattern on the tile ABCD shows squares of different sizes. AF = FE and AE = ED.
  1. What fraction of the tile ABCD is shaded?
  2. Figure 2 is made up of four such tiles. The area of the unshaded part of Figure 2 is 80 cm2. What is the total area of the shaded parts in Figure 2?
3 m
Square Tiling Overlapping area Fraction of a whole
132 P6.PC.JC.19072701
Level 3 PSLE
There are some stickers in albums A and B. 50% of the stickers in album A and 20% of the stickers in album B are round stickers. There is an equal number of square stickers in both albums. If there are 51 more round stickers in album A than in album B, how many stickers are there in both albums altogether?
4 m
Percent to units More than or less than Equal stage Remainder concept Units table
133 P6.VO.NK.17053041
Level 3
The figure shows a tank 45 filled with water. The tank is made up of two cuboids. The top cuboid has a square base of length 10 m and a height of 16 m. The bottom cuboid has a square base of length 5 m and height 12 m. Find the height of the water level from the base of the container.
4 m
Volume of cuboid Height of cuboid Fraction of a whole
134 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
135 P6.VO.NK.17053017
Level 3
The figure is made up of identical cubes. If the volume of the solid is 702 cm3,
  1. Find the total surface area of the figure.
  2. How many more of such cubes is to be added to form a cube of side 54 cm?
4 m
Volume of cube Square & square root Cube & cube root Surface area Filling up with cubes
136 P6.VO.NK.17082401
Level 3
The figure is not drawn to scale. It shows the net of a solid. It is made up of 4 identical rectangles and 2 identical squares. Line A is 30 cm long and Line B is 15 cm long.
  1. Find the volume of the solid.
  2. This solid is a cardboard carton containing small boxes of sweets. Each box of sweets is 3 cm by 2 cm by 1 cm. If all these small boxes of sweets in the carton occupy more than 75% of the carton's volume, what is the minimum number of small boxes of sweets in the carton?
4 m
Volume of cuboid Filling up with cubes Nets Min-max D Place values D Round off Square Rectangle More than or less than
137 P6.PC.TL.16010119
Level 3
One minute ago, 80% of the students in a parade square were girls. 143 more students entered the parade square. As a result, the number of girls increased by 40% and the number of boys increased by 60%. How many students are in the parade square now?
4 m
Percent of a set Percent change by Percent to units Percent of different bases All change Units table
138 P6.VO.NK.21060407
Level 3 PSLE
A rectangular block A was cut along the dotted line into two smaller rectangular blocks of equal height, B and C, as shown. The volume of C is 1400 cm3 more than that of B.
  1. What is the height of each block?
  2. Pete packed 6 of block C such that they fit exactly into a box with a square base. The box has the same height as C. At most, how many of block B can be packed into such a box?
4 m
Volume of cuboid Base area x height Filling up with cubes Square W Remainder Min-max More than or less than
139 P6.AP.TL.17090782
Level 3
The figure shows 4 identical circles in a square, WXYZ. The area of the square is 16 cm2. Find the area of the shaded part. (Take π = 3.14)
3 m
Length Square & square root Circle area
140 P6.AN.NK.17052208
Level 3
Two corners of a square are folded as shown in the figure. Find ∠ABC.
3 m
Square Angles sum of triangle Overlapping angles Folded figure

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