Timed Mini Exam 30 — Timed Mini Exams

Questions in this quiz (10)

1. A square is inscribed in a circle with radius $$r$$. What is the probability that a randomly selected point within the circle will not be within the square?

   • $$\frac{2}{\pi}$$
   • $$\frac{1}{2}$$
   • $$\frac{2}{3\pi}$$
   • $$\frac{\pi - 2}{\pi}$$

2. If $$(x+1)^2=4$$ and $$(x-1)^2=16$$, what is the value of $$x$$?

   • 1
   • 5
   • -1
   • -3

3. The perimeter of a particular equilateral triangle is numerically equal to the area of the triangle. What is the perimeter of the triangle?

   • $$18\sqrt{3}$$
   • $$12$$
   • $$12\sqrt{3}$$
   • $$4\sqrt{3}$$

4. The equation of a circle in the $$xy$$-plane is $$x^2 + 4x + y^2 - 10y = 20$$. If the line $$x = k$$ intersects the circle in exactly one point, what is the possible value of $$k$$?

   • 3
   • 5
   • 9
   • 12

5. In the shown figure, if line $$k$$ has a slope of $$-1$$, what is the $$y$$-intercept of $$k$$?

   • 5
   • 6
   • 7
   • 4

6. The table below shows values of the two functions $$f$$ and $$g$$.For what value of $$x$$ is $$g(f(x))=x$$?

   • -3
   • 4
   • 8
   • 0

7. If $$\sin x^\circ = a$$, which of the following must be true for all values of $$x$$?

   • $$\cos x^\circ = a$$
   • $$\sin(90^\circ - x^\circ) = a$$
   • $$\cos(90^\circ - x^\circ) = a$$
   • $$\sin((x^\circ)^2) = a^2$$

8. Find the x-intercepts of $$f(x) = x^4 - 5x^2 + 4$$.

   • $$-1, 0, 1, 2$$
   • $$-2, -1, 1, 2$$
   • $$-2, 0, \frac{1}{2}, 4$$
   • $$-1, 0, \frac{1}{2}, 2$$

9. Ravi had a rectangular block of wood 10 cm by 5 cm by 4 cm. He painted all the faces of the block. Ravi cut the block into 1-cm cubes. How many of these cubes have none of the faces painted?

   • 52
   • 48
   • 40
   • 50

10. What is the area of a circle that is inscribed in an equilateral triangle whose sides are 2?

    • $$\frac{\pi}{3}$$
    • $$\frac{\pi}{2}$$
    • $$\frac{2\pi}{3}$$
    • $$\frac{3\pi}{4}$$