Common Core Math IIMidterm Review Name: ______

Common Core Math IIMidterm Review Name: ______

Multiple Choice:

  1. The smaller of two similar barrels has a surface area of 6,200 square centimeters. The barrels are cylindrical and the height of the larger barrel is 112 times that of the smaller. Which expression gives the surface area of the larger barrel?
  1. A surveyor wants to be sure that a group of triangular lots have the same size angles at the corners. Since the lots are supposed to be congruent, she plans simply to measure each side of every lot. What postulates about congruent triangles does she plan to use?
  1. Which of the following statements about congruent figures is not true?

A)Congruent figures have the same shape.

B) The corresponding angles of congruent figures are congruent.

C) The ratios of the corresponding side lengths of congruent figures is not equal to 1.

D) The lengths of the corresponding side lengths of congruent figures are the same.

  1. Alison lets out 50 feet of twine on her kite. The angle of elevation is 55˚. How high above Alison’s hands is the kite?
  1. Which condition(s) will prove a||b?
  1. Use the figure below. What is the relation between ABD and DBC?
  1. Using the diagram below, which is a correct statement and reason?
  1. What additional information would you need to prove ∆ABC∆DEC by the ASA Postulate?
  1. What is the value of x in the triangle below?
  1. A stone pathway forms the diagonal of a square garden. A side of the garden is 40 feet. How long is the pathway?
  1. At the local bakery, a small chocolate chip cookie has a 2-inch diameter. How much more cookie do you get if you buy a “super” cookie with a diameter of 6 inches?
  1. Which statements could be true for this figure?

I. z=x+y

II. zy

III. z=x

Constructed Response:

  1. Find the equation of the circle with center (3, 3) and radius of 3.
  1. A circle is drawn on a coordinate plane so that the endpoints of a diameter are located at points (–1, 4) and (7, 2). What is the area of this circle?
  1. A surveyor measures the angle of elevation to the top of a building to be 60°. The surveyor then walks 100 feet farther from the base of the tower and measures the angle of elevation to be 45°. The surveyor’s angle-measuring device is 5 feet from the ground. How tall is the building to the nearest foot?
  1. The composite structure shown below consists of two parts, a rectangular prism and a dome. The dome, a hemisphere, sits directly on top of the prism. Find the volume of this solid to the nearest cubic meter.
  1. A 20-foot ladder leans against a vertical wall. The ladder makes a 65˚ angle with the ground. How far from the base of the wall is the foot of the ladder? Round your answer to the nearest tenth of a foot.
  1. A park has the shape of an isosceles triangle with vertices S, L, and E. The measure of S is 70˚. What is the measure of E?
  1. Maria looks straight up and sees an airplane 5 miles above her. The airport runway is exactly 7 miles away from her. What is the distance between the runway and the airplane?
  1. A home plate for baseball is shown below. What is the value of x, to the nearest inch?
  1. Find the volume of the sphere. Round your answer to the nearest tenth.
  1. A forest ranger spots a fire at an angle of depression of 36 degrees from the top of his 48-foot watch tower. How far is the fire from the base of the tower?
  1. A right circular cylinder has a volume of 321 cubic feet. What is the volume of a right cone with the same height and base area?
  1. A line segment is drawn from A(14, 10) to B(6, 4). Find the coordinates of point P so that P divides the segment into the ratio 1:4.