1. A circle and a parabola are drawn in the plane. What is the largest number of regions they divide the plane into?

2. From a group of boys and girls, 15 girls leave. There are then two boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. What was the number of girls originally present?

3. What is the smallest positive integer x such that 750 x is a perfect square?

4. At 2:15, what is the angle between the hour hand and the minute hand of a clock?

5. The large square shown has area 1. The four interior lines each join a vertex of the square to the midpoint of a side as shown. What is the area of the small central square? D

6. Solve the equation x² + x - 8 = |x|.

7. What is the number of digits in 2003²⁰⁰³?

Here are the answers.