Sorting and classifying Knowledge-Based Download PDF

Questions

1. 1.

   A set of integers is given as $\{16, 21, 25, 27, 32, 49, 64\}$. When these numbers are sorted into categories of perfect squares and perfect cubes, which number belongs to both categories?

   • A) 16
   • B) 64
   • C) 27
   • D) 49
2. 2.

   A data set of polygons is sorted into two groups: Group 1 contains a square, a rectangle, a rhombus, and a parallelogram, while Group 2 contains a kite, an equilateral triangle, a regular pentagon, and a scalene triangle. Which classification rule correctly describes the criterion used to place the shapes into Group 1?

   • A) Polygons with at least two lines of symmetry
   • B) Polygons with two pairs of parallel sides
   • C) Polygons with all interior angles equal
   • D) Polygons with all sides of equal length
3. 3.

   A data set of geometric solids consists of a cube, a cylinder, a cone, a sphere, a triangular pyramid, and a rectangular prism. When sorting these solids by their surface properties, which group contains all the solids that have both at least one flat face and at least one curved surface?

   • A) Cone and sphere
   • B) Cylinder and cone
   • C) Cylinder, cone, and sphere
   • D) Cube, triangular pyramid, and rectangular prism
4. 4.

   A set of figures contains a regular pentagon, an isosceles triangle with side lengths 5 cm, 5 cm, and 6 cm, a scalene triangle with side lengths 4 cm, 5 cm, and 6 cm, and a square. When sorting these figures into categories, which figure has at least one line of symmetry but does not have all sides of equal length?

   • A) Regular pentagon
   • B) Isosceles triangle
   • C) Scalene triangle
   • D) Square
5. 5.

   A set of whole numbers is given as {12, 18, 25, 30, 36, 45, 50, 60}. How many of these numbers belong to both the category “divisible by 3” and the category “divisible by 5”?

   • A) 1
   • B) 2
   • C) 3
   • D) 5