- In a triangle, one of the angle is same as the sum of two others, and those two angles are in the ratio of 4:5. What are three angles?
- In a rectangle, one side is more than the other side by 4 cms. If both the sides are increased by 3 cms each, the total area increases by 81 square-cms. What are the measurement of the sides of the original rectangle.
- A rectangular gallery has sides in the ratio of 5:2, and its total area is 100 square-mts. What are the side lengths?
- You need to find a two digit number, where sum of its digits is 12, and when the digits are reversed, the difference between the two numbers is 18.
- A very keen hockey player signed a contract, where he will get $20/per game which he plays, and -$5/per practice which he lands up missing. There is one practice and one game each day, and at the end of the 30 day season, the player was rewarded $450. How games this player played, and how many practices he missed.
- For her school project, Ms. Chrome, decided to make Kaleidoscope. She decided to make the one where the tube needs to have length of 30 cms, and its diameter to be 7cm. Of course, you roll a sheet of paper, to form this cylinder. What should be the dimensions of the sheet of the paper (assuming no wastage). Understand the relationship between the surface area of a cylinder and area of a rectangle via this problem.
- In our houses, we have a huge hot water tank in the basement. What is the surface area of this tank? How long the sheet of the metal must be rolled to make this tank? How do we find, how much volume it holds?
- Check the reasoning (a) a cow looks, at all the dogs in the barn, and sees that they have a tail. Cow looks at herself, and sees that she has a tail. She concludes that she is dog! (b) All humans are mammals, and all mammals are vertebrates. Are all humans vertebrates? (c) It rains on every Monday. It is raining today. Today is Monday. (d) It hasn't rain today at all, so it can't be Monday.
- Show that the product of any two consecutive even numbers is divisible by 4? Is it divisible by 8?
- What about the product of any three consecutive even numbers? Is it divisible by 16?
Sunday, October 17, 2010
Some more problems based on the NTSE Exam for Grade 8.