1. Points B and C lie on segment AD as shown below. Segment AD is 32 units long, segment AC is 23 units long, and segment BD is 27 units long. How many units long, if it can be determined, is segment BC?
2. For all pairs of real numbers M and N where M = 6N + 5, N = ?
3. In the figure below, the perimeter of the triangle is inches. What is the value of x, in inches?
4. The angle of elevation from a point on the ground to the top of a building is 35°, as shown below. The point is 70 feet away from the building. Which of the following is closest to the height, in feet, of the building?(Note: sin 35° â 0.573; cos 35° â 0.819; tan 35° â 0.700)
5. The median of a set of data containing 11 items was found. Six data items were added to the set. Three of those items were greater than the original median, and the other three items were less than the original median. Which of the following statements must be true about the median of the new data set?
6. The product of two integers is between 137 and 149. Which of the following CANNOT be one of the integers?
7. When x is divided by 7, the remainder is 4. What is the remainder when 2x is divided by 7?
8. A circle is circumscribed within a square with sides of 12 feet, as shown below. What is the area of the circle, to the nearest square foot?
9. The average of 7 consecutive numbers is 16. What is the sum of the least and greatest of the 7 integers?
10. In the figure below, ABCD is a trapezoid. Point E lies on line AD, and angle measures are as marked. What is the measure of angle BDC?