The graphs of y = x\(^2\) – 8x – 35 and y = –2x\(^2\) + 16x + 3 intersect in two points. What is the sum of the x-coordinates of the two points of intersection?

When creating a particular pattern, the designer begins with a line segment 1 unit long. Each successive stage is created by using congruent segments that are half as long as those in the previous stage. If you trace the design at Stage 4, how many units longer is it than the length of the design at Stage 1? 

The mean of the squares of three non-zero numbers a, b and c is three times the square of their mean. If b = 2a, what is the value of c/a ? Express your answer as a common fraction.  

 The product of two consecutive, positive, odd integers is 783. What is the sum of the two integers?

 Point A has coordinates (-2, 5) and point B has coordinates (10, 8). Point P is on segment AB, with AP = 2PB. What are the coordinates of point P? Express your answer as an ordered pair.

The numerator of a fraction is 8 less than the denominator. If the numerator is doubled and the denominator is decreased by 1, the value of the resulting fraction is 1. What is the original fraction? Express your answer as a common fraction.

The perimeter of a rectangle is 62 meters. The length is 1 meter more than four times the width. What is the area of the rectangle, in square meters? 

 In basketball, a player can score via 3-point shots, 2-point shots and 1-point free throws. If Shakeel made eight 2-point shots and scored 30 points in all, what is the minimum number of free throws he could have made? 

 A square with a diagonal of length 7 units is inscribed in a circle. What is the positive difference between the area of the square and the area of the circle? Express your answer as a decimal to the nearest hundredth.

 When a dart hits within the center circular region of this circular target, the score is 50, and when a dart hits within the outer ring, the score is 7. If three darts randomly hit the target, what is the probability that the total score is 64? Express your answer as a common fraction. 

 A two-year study was just completed. The project began with 40 participants and ended with 90 participants. After the first year, P participants were in the study. If the percent increase of the number of participants was the same for both years, what is the value of P?

Assume a diamond’s value is directly proportional to the square of its weight in carats. A huge diamond weighing 10 carats is broken into a 4-carat piece and a 6-carat piece. The sum of the values of the two pieces is what percent of the original value?

What is the sum of the integer values of x, where x < 8, that produce an integer value for the expression \(\sqrt{2+4+6+x}\)?

 Three books and eight CDs cost twice as much as one book and five CDs. If one book and one CD cost $45, what is the cost of six books?

 What is the length of the side of the only equilateral triangle whose perimeter has the same numerical value in units as its area in square units? Express your answer as a decimal to the nearest tenth.  

A painter takes two days to paint a room (all four walls and the ceiling). If he works at the same pace, how many days will it take him to paint a room that is twice as wide, twice as long, and twice as high?

 The diagonals of a square intersect at the point (3, 2). The coordinates of one of the vertices of the square are (5, 4). What is the area of this square?

The mean, median and range are all the same for a particular set of four numbers. What is the largest number in the set if the smallest number is 17?

Two cubes, each with faces with 0 through 5, are to be rolled. What is the probability that the sum will be less than 6? Express your answer as a common fraction.

How many factors does 1800 have that are greater than 15?