1. A certain rectangle is 3 inches by 5 inches. How many square inches bigger is a rectangle with dimensions 10% more compared to a rectangle with dimensions 10% less?


2. How many times bigger is the circle compared to the square formed with radii of the circle?



3. All triangles in the figure are equilateral, and their side lengths are whole numbers multiples of the smallest triangles. How many of the smallest triangles will it take to cover the entire figure?


4. A net for a cube is pictured. How many different (non-congruent) nets for a given cube are possible. [Warning: Not all possible arrangements of 6 squares form nets.]


5. The rectangle has an area of 108 square meters and a perimeter of 48 meters. How many meters is its longest dimension?

6. The over-crowded school puts all the students in one classroom that is 30 feet by 30 feet by 10 feet. Each student takes up 5 cubic feet, and there is no extra room for anyone else. How many students are in the school?

7. How many of the following symbols have rotation symmetry?

z v b a d f g h i [ N M J q W T Y $ \ % & ) _ ˆ

8. There are 5280 feet in a mile and 640 acres in a square mile. If acre is to be a rectangle whose dimensions are whole numbers of feet, how many different shapes are possible?

9. SQRD is a square. SBCA and RECT are rectangles. The diagonal of the largest rectangle goes through point R. If QR = 10 and RT = 4, what is the length of RE? [The figure is not drawn to scale.]



10. Two pieces of wire are of equal length. One wire is formed into the shape of a square, and the other is formed into the shape of a circle. What is the ratio of the area of the square to that of the circle?