1.
What is the next term in the geometric sequence 16, - 4, 1, - 1/4, .....?
Correct Answer
C. 1/16
Explanation
We can see that each time, the term is being divided by - 4. Therefore, to find the next term, we need to divide the last term (-1/4) by 4. This should give us 1/16.
2.
A 24-inch diameter pizza is cut into eight slices. What is the area of one slice?
Correct Answer
A. 18π
Explanation
The area of a circle is A=πr2. Since the diameter is 24, the radius of the circle is 12. Plugging 12 in for r in our equation for area, we get 144π. However, we do not need to know the area of the whole pizza, we only want the area for one-eighth of the pizza, so we need to divide the total area by 8. This gives us 18π.
3.
A person had a rectangular-shaped garden with sides of lengths 16 feet and 9 feet. The garden was changed into a square design with the same area as the original rectangular-shaped garden. How many feet in length are each of the sides of the new square-shaped garden?
Correct Answer
C. 12
Explanation
The area of a rectangle is length times width. This means the area of the rectangular garden is 144 square feet. The new square garden need to have the same area. Remember that all of the sides are equal in a square, so what perfect square gives us an area of 144 square feet? We can see that this number is 12, so each side of the square garden is 12 feet long.
4.
In the figure, ∆ABC is a right triangle. The length of AB is 6 units and the length of CB is 3 units. What is the length, in units, of AC ?
Correct Answer
B. 3√3
Explanation
Remember that Pythagorean Theorem (a2+b2=c2 where c is the hypotenuse) tells us about the side lengths of a right triangle. Therefore, a2+32=62. Solving for a, one should get √27. However, we want this answer in simplest radical form, so the final answer is 3√3.
5.
In the figure below, the lengths of DE , EF , and FG are given, in units. What is the area, in square units, of ∆DEG ?
Correct Answer
B. 60
Explanation
Remember that the area of the triangle is base times height divided by 2. So the area of triangle DGF minus the area of triangle EGF should give us the area of triangle DEG. The area of the triangle DGF is (19*10)/2=95 and the area of triangle EGF is (7*10)/2=35. We know that 95-35=60, so the area of triangle DEG is 60 square units.
6.
In the figure below, the circle centered at B is internally tangent to the circle centered at A. The smaller circle passes through the center of the larger circle and the length of AB is 5 units. If the smaller circle is cut out of the larger circle, how much of the area, in square units, of the larger circle will remain?
Correct Answer
D. 75π
Explanation
We need to find the area of the larger circle and subtract out the area of the smaller circle. Remember that the area of a circle is A=πr2. We know the radius of the smaller circle is 5 and the area of the bigger circle is the diameter of the smaller circle, so the radius of the bigger circle is 10. This means the area of the bigger circle is 100π and the area of the smaller circle is 25π. So 100π - 25π = 75π, which is the area left over in square units.
7.
The diagram below shows a pasture which is fenced in. All but 1 section of fence run straight north-south or east-west. Consecutive fence posts are 10 feet apart except for the 1 diagonal section. Which of the following statements best describes P, the perimeter of the pasture, in feet?
Correct Answer
A. P > 210
Explanation
If we count the pieces of fencing that are completely horizontal and vertical, we see that there are 20 posts. Since each post is 10 feet, we know that the perimeter should be more than 200 feet, since we have not counted the length of that diagonal post. Since the post we haven't considered yet is a diagonal piece, we know the length of this piece should be more than 10 feet. Therefore, the perimeter should be greater than 210 feet.
8.
In the sketch below, the area of each circle is 4π. What is the perimeter of WXZY?
Correct Answer
B. 32
Explanation
In order to find the perimeter of WXZY, we need to know each side length. Note that each side length is equal to the diameter of two circles and each diameter is double the length of the radius. Therefore, each side is as long as four radii. We know that the area of one circle is 4π and the equation for the area of a circle is A=πr2. Therefore, 4π=πr2. Solving for r gives us r=2. Therefore, the length of one side is 8. Since there are four equal sides, the perimeter is 32.
9.
In the coordinate plane, a square has vertices (4, 3), (-3, 3), (-3, - 4), and
Correct Answer
E. (4, - 4)
Explanation
By sketching a plot of the points, we can see that each side has a length of 7 units. Therefore, we need to place another point 7 units below the point (3, 4). We can see that this point is (4, -4) and this point completes the square.
10.
M is the midpoint of line segment RS. If RM = 3x + 1 and RS = 38, what is the value of x?
Correct Answer
C. 6
Explanation
Since M is the midpoint, we know that RM and MS have to be equal and RM+MS=RS. Therefore, plugging in what we know, 3x+1+3x+1=38. Simplifying gives us, 6x+2=38. Solving for x gives us x=6.