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 2 PSLE
At first, Logan had $90 and Polly had $60. Each bought a table at the same price. The amounts of money Logan and Polly had left were in the ratio 4 : 1. How much did the table cost?
Level 3
The figure is not drawn to scale. It is made up of a square and a rectangle. The ratio of the area of the square to that of the rectangle is 3 : 4. After the shaded part is cut out, the ratio of the area of unshaded part of the rectangle to that of the unshaded part of the square is 2 : 1. Given the length of the square is 9 cm, find the area of the shaded part.
Level 3
The figure is not drawn to scale. It is made up of a square and a rectangle. The ratio of the area of the square to that of the rectangle is 3 : 4. After the shaded part is cut out, the ratio of the area of unshaded part of the rectangle to that of the unshaded part of the square is 2 : 1. Given the length of the square is 9 cm, find the area of the shaded part.
Level 3
In a table-tennis competition, every player plays against every other player twice. Every player plays the same number of games. There are a total of 56 games played. How many players are there?
Level 3
In a jar, the ratio of the number of yellow balls to the number of purple balls was 1 : 3. Each time, 5 yellow and 7 purple balls were taken out of the jar. A while later, only 120 purple balls were left in the jar. What was the total number of balls in the jar at first?
Level 3
The ratio of the boys to the girls in school was 5 : 2. After 6 boys went home and 8 new girls came, there were 7 more boys than girls in the end. Find the number of children in the school at first.
Level 3
The ratio of Zoe's to Isabelle's incomes was 6 : 1 at first. After Zoe and Isabelle were given another $654 and $341 respectively, Zoe had 4 times as much money as Isabelle. How much did both of them have in the end?
Level 3
At a theme park, there were 60% as many boys as girls and 30% more adults than boys. Given that there were 90 more adults than boys at the theme park, how many children were there altogether?
