If the sum of the interior angles of a particular convex polygon is 9720˚, how many sides does the polygon have?

What is the area of a triangle with vertices at (-5, -1), (3, 5) and (1, 9) on the coordinate plane?  

Brenda gave Gail as many pieces of candy as Gail already had. Then Gail gave Brenda as many pieces of candy as Brenda needed to double her amount of candy. Now Brenda has three times as many pieces of candy as Gail. If Gail has at least one piece of candy, what is the minimum total number of pieces of candy needed for this to have occurred? 

The symbol * represents a sequence of mathematical operations. If 12 * 6 = 35, 4 * 2 = 3, 11 * 14 = 8, 5 * 7 = 3 and 10 * 7 = 8, what is the value of 8 * 4? 

A sequence of positive integers is formed by first selecting any positive two-digit integer as the first term of the sequence. Each term after the first term is the sum of twice the tens digit and twice the ones digit of the previous term. If the second term of the sequence is 16 and the third term is 14, how many values are possible for the first term?

Ten percent of the male students at James HS are over six feet tall. The number of female students who are taller than six feet is equal to 10% of the number of male students over six feet tall. At James HS there are 250 female students and 20% more male students than female students. How many female students are taller than six feet? 

What is the probability that in a group of three friends no two of them were born on the same day of the week? Express your answer as a common fraction

The radius of a particular circle inscribed in an equilateral triangle is 2 units. What is the perimeter of the triangle? Express your answer in simplest radical form.

A math field day’s budget consists of $432 to pay problem-writers and $x per Mathlete for food, drinks, copying costs and trophies. A math field day for 100 Mathletes costs exactly half what a math field day for 248 Mathletes costs. What is the value of x?

What is the area of the region enclosed by the graphs of the lines y = -2x – 3, y = 2x – 3 and the x-axis? Express your answer as a decimal to the nearest tenth.

What is the total perimeter of a sector of a circle with a radius of 3 cm and a central angle measuring 90°? Express your answer as a decimal to the nearest tenth. 

  A teacher usually divides his class into six groups of n students each. However, on Monday, three of the students were absent, so the teacher divided the remaining students into seven groups of m students each. On Tuesday, four students were absent, so he went back to n students per group, but there was one fewer group than he usually has. How many students are in the class?  

The 460 students and 20 staff at Bosney School are planning a bus trip. The bus company has large buses that can hold up to 64 passengers and small buses that can hold up to 40 passengers. The large buses cost $960 each and the small buses cost $680 each. What is the cost per passenger for the cheapest combination of buses?  

A square is inscribed in a circle that forms a dartboard. If a dart randomly hits the dartboard, what is the probability it will hit the region outside the square but inside the circle? Express your answer as a percent to the nearest tenth.   

A circle with a radius of 2.5 cm is inscribed in a square. What is the area within the square region but outside the circular region? Express your answer as a decimal to the nearest tenth.

A farmer’s field is in the shape of regular hexagon ABCDEF. The distance from point A to point B is 420 feet. A fence post is placed at each vertex of the hexagon, and each side has 16 evenly spaced fence posts (counting the posts at the vertices). What is the distance from the center of one fence post to the center of an adjacent fence post on a side of the hexagonal field? 

Kelly’s heart beats 60 times per minute when she is sleeping. If she sleeps 7 hours per day for all of 2009 and 2010, how many times will her heart beat while sleeping for those two years? Express your answer in scientific notation with five significant digits. 

The sum of a and 4, the difference of b and 4, the product of c and 4 and the quotient of d and 4 are all equal to the same integer value. If the sum of a, b, c and d is 100, what is the ratio of a to d ? Express your answer as a common fraction. 

The sides of a quadrilateral have lengths x, x + 1, x + 2 and x + 3 units. The value of the perimeter is less than 100 units and is a perfect cube. The mean of the side lengths is twice the square root of the perimeter. What is the value of x? Express your answer as a decimal to the nearest tenth

The mean of three numbers is 6 more than the least of the numbers, and it is 7 less than the greatest number. The median of the three numbers is 8. What is the sum of the three numbers?