Timed Mini Exam 25 — Timed Mini Exams

Questions in this quiz (10)

1. Below is an octagon, of which each side length is 8 cm. Which of the following is the area of the octagon, in cm^2?

   • $$128$$
   • $$128(1+\sqrt{2})$$
   • $$64\sqrt{2}$$
   • $$64$$

2. In shape ABCDEF below, AF is perpendicular to ED, FE is parallel to BC, AB is parallel to DC, and AF and ED have the same length. What is the measure of angle CAB?

   • $$45^\circ$$
   • $$60^\circ$$
   • $$75^\circ$$
   • $$40^\circ$$

3. Liam has a display rack that can hold three trophies, but he owns eight different trophies. How many different ways can he arrange any three of his eight trophies on the rack?

   • $$336$$
   • $$24$$
   • $$512$$
   • $$6561$$

4. If AC is a semicircle, what is the perimeter of the shape?

   • $$7+2.5\pi$$
   • $$14\pi$$
   • $$7\pi$$
   • $$7+5\pi$$

5. The graph of the trigonometric function $$y=2\cos(\frac{1}{2}x)$$ is shown. Determine whether the function is even, odd, neither even nor odd, the inverse of a cotangent function, or undefined at $$x=\pi$$.

   • Even ($$f(x)=f(-x)$$ for all x
   • Odd ($$f(x)=-f(-x)$$ for all x
   • Neither even nor odd
   • Undefined at $$x=\pi$$

6. In the figure below, line $$q$$ in the standard $$(x,y)$$ coordinate plane has equation $$-2x+y=1$$ and intersects line $$r$$, which is distinct from line $$q$$, at a point on the x-axis. The angles $$\angle a$$ and $$\angle b$$ formed by these lines and the x-axis are congruent. What is the slope of line $$r$$?

   • $$4$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2}$$
   • $$-2$$

7. In the right triangle below, $$0$$ <b< $$a$$. One of the angle measures in the triangle is $$\tan^{-1}\left(\frac{a}{b}\right)$$. What is $$\cos\left[\tan^{-1}\left(\frac{a}{b}\right)\right]$$?

   • $$\frac{b}{a}$$
   • $$\frac{b}{\sqrt{a^2+b^2}}$$
   • $$\frac{\sqrt{a^2+b^2}}{a}$$
   • $$\frac{a}{\sqrt{a+b}}$$

8. The radio signal from the transmitter site of radio station WGGW can be received only within a radius of 52 miles in all directions from the transmitter site. A map of the region of coverage of the radio signal is shown below in the standard (x,y) coordinate plane, with the transmitter site at the origin and 1 coordinate unit representing 1 mile. Which of the following is closest to the area, in square miles, of the region of coverage of the radio signal?

   • 8500
   • 2500
   • 4500
   • 16500

9. The graphs of the equations $$y=x-1$$ and $$y=(x-1)^4$$are shown in the standard $$(x,y)$$ coordinate plane below.What real values of $$x$$, if any, satisfy the inequality$$(x-1)^4$$ < $$(x-1)$$?

   • $$x=1$$
   • $$0$$ <x< $$1$$
   • $$x=2$$
   • $$1$$ <x< $$2$$

10. Marcia makes and sells handcrafted picture frames in 2 sizes: small and large. It takes her 2 hours to make a small frame and 3 hours to make a large frame. The shaded triangular region shown below is the graph of a system of inequalities representing weekly constraints Marcia has in making the frames. For making and selling s small frames and l large frames, Marcia makes a profit of $$30s+70l$$ dollars. Marcia sells all the frames she makes. The weekly constraint represented by the horizontal line segment containing $$(9,2)$$ means that each week Marcia makes a minimum of:

    • 9 large frames
    • 2 large frames
    • 9 small frames
    • 2 small frames