421 P4.AN.NK.23041231
Level 3
The figure is made up of a square ABCD and a rectangle DEFG. ∠CDG = 69°. ∠x is twice of ∠y. Find ∠x.
3 m
Right angle Square Rectangle Overlapping angles Model Times-as-many Units method
422 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
423 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
424 P4.AN.JM.17092871
Level 3
The figure shows a piece of square paper ABCD folded at two of its corners B and D. Given that ∠CFD = 81° and ∠BEC = 78°, find ∠BCD.
3 m
Square Angles sum of triangle Overlapping angles Folded figure
425 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
426 P5.AP.NK.23022716
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Level 3
Peter had a square piece of paper. He cut it along the dotted lines as shown in Figure 1 to get one small square of side 2 cm and four identical right-angled triangles. One such triangle is shown in Figure 2. Find the perimeter of the square piece of paper in Figure 1 before it was cut.
3 m
Attempt
Square Square & square root Right-angled triangle
427 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
428 P6.AN.NK.21060913
Level 3 PSLE
The figure is made up of 3 squares. Find ∠a.
3 m
Square Angles on a straight line Angles sum of triangle Exterior angles of a triangle
429 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
430 P4.AP.NK.23050809
Level 3
Laura had 1 m of wire. She gave 0.64 m of the wire to Trevor and the remaining wire to Kathy. Trevor used the wire he received to form a square with no leftover. Kathy used the wire she received to form a triangle of equal sides, with no leftover. What was the difference in length between one side of the square and one side of the triangle?
3 m
Length Square Triangle More than or less than
431 P5.FR.JM.17083090
Level 2
The figure is made up of a square and a rectangle. The area of the square is 13 the area of the rectangle. Given that 12 of the square is shaded, what fraction of the whole figure is unshaded?
3 m
Fraction of a whole Fraction to units Area perimeter Overlapping area Combined repeated identity Units table
432 P5.AP.JM.17083153
Level 2
The figure shows a piece of square paper with two of the corners folded. Triangle A and Triangle B are identical and Triangle XYZ is an equilateral triangle. Find the area of the shaded part.
3 m
Square Equilateral triangle Folded figure
433 P6.AP.JC.17100101
Level 2 PSLE
Two figures R and S are shown in the square grid.
  1. Which figure has a bigger area?
  2. Which figure has a bigger perimeter?
  3. Which angle is bigger? ∠a or ∠b
3 m
Grid square Rhombus Estimation of an angle
434 P5.AP.JM.17083165
Level 3
PQRS is a square of area 64 cm2. X and Y are midpoints of PQ and PS respectively. Find the area of the shaded triangle.
3 m
Square Triangle common base
435 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
436 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
437 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
438 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
439 P4.AP.JM.17100195
Level 3
A rectangular floor, 18 m by 9.5 m, is laid with rubber tiles at a cost of $29 per square metre.
  1. Find the cost of tiling the floor.
  2. Round off the answer in (a) to the nearest thousand dollars.
3 m
Rectangle Tiling W Round off Money
440 P2.WN.ED.18011898
Level 2
If A + A + A = 18
What is A x A?
2 m
W 4 operations Square & square roots Units method

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