Grade 12 Problem Solving Worksheet

Grade 12 Problem Solving Challenge

Read each problem carefully and solve it using appropriate mathematical concepts and strategies. Show all your work for full credit. Good luck!

1. A rectangular garden has a perimeter of 80 meters. If the length of the garden is 4 meters more than twice its width, what are the dimensions of the garden?

2. In a group of 10 students, 6 are boys and 4 are girls. If a committee of 3 students is to be selected at random, what is the probability that the committee will consist of exactly 2 boys and 1 girl?

3. A cylindrical tank has a radius of 5 meters and a height of 10 meters. The volume of the tank is approximately   cubic meters. (Use π ≈ 3.14)

4. Two pipes are filling a large swimming pool. Pipe A can fill the pool in 6 hours, and Pipe B can fill it in 8 hours. If both pipes are opened simultaneously, how long will it take to fill the pool?

5. If all squares are rectangles, and all rectangles are quadrilaterals, then all quadrilaterals are squares.

6. The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 greater than the original number. Find the original number.