Here are some competency-based mathematics questions that test problem-solving, reasoning, and application skills:

1. Logical Reasoning & Patterns

Q1. A sequence follows this pattern: 2, 6, 12, 20, ?, 42. Find the missing number.

2. Real-World Application

Q2. A farmer has a rectangular field of length 100 meters and width 60 meters. He wants to build a 2-meter-wide pathway around the field. What is the area of the remaining field after constructing the pathway?

3. Algebraic Thinking

Q3. The sum of the ages of a father and his son is 50 years. Five years ago, the father's age was three times the son’s age. Find their current ages.

4. Geometry & Measurement

Q4. A cylinder has a radius of 7 cm and a height of 10 cm. Find its total surface area and volume.

5. Probability & Statistics

Q5. A bag contains 5 red, 4 blue, and 3 green balls. One ball is drawn at random. What is the probability that it is not blue?