Mini Exam 13 — Timed Mini Exams

Questions in this quiz (10)

1. A circle has equation $$(x+3)^2+(y-4)^2=16$$ and represents circle $$R$$. Circle $$S$$ is obtained by shifting circle $$R$$ right $$5$$ units in the $$xy$$-plane. Which of the following equations represents circle $$S$$?

   • $$(x+2)^2+(y-4)^2=16$$
   • $$(x-2)^2+(y-4)^2=16$$
   • $$(x-8)^2+(y-4)^2=16$$
   • $$(x-2)^2+(y+4)^2=16$$

2. The function $$g(x)=x^3+px^2+qx+r$$ is defined above, where $$p,q,$$ and $$r$$ are integer constants. If the zeros of the function are $$-2,4,$$ and $$7,$$ what is the value of $$r$$?

   • $$60$$
   • $$54$$
   • $$48$$
   • $$56$$

3. The number $$a$$ is $$30\%$$ greater than the positive number $$b$$. The number $$c$$ is $$20\%$$ less than $$a$$. The number $$c$$ is how many times $$b$$?

   • $$1.30$$
   • $$1.04$$
   • $$0.84$$
   • $$1.10$$

4. A right triangle is inscribed in a circle such that each vertex of the triangle lies on the circumference of the circle. The hypotenuse of the triangle is $$3$$ times the length of the shorter leg of the triangle. The area of the triangle is $$432\sqrt{2}$$ square units. What is the length, in units, of the diameter of the circle?

   • $$24\sqrt{3}$$
   • $$36\sqrt{3}$$
   • $$30\sqrt{3}$$$
   • $$42\sqrt{3}$$$

5. The functions $$f$$ and $$g$$ are defined by the given equations, where $$x\ge0$$. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where $$x\ge0$$?$$I.$$ $$f(x)=4(x-3)^2+6$$$$II.$$ $$g(x)=7(3)^{x+2}$$

   • Neither I nor II
   • I and II
   • II only
   • I only

6. A circle in the $$xy$$-plane has a diameter with endpoints $$(-6,-5)$$ and $$(-6,7)$$. An equation of this circle is$$(x+6)^2+(y-1)^2=r^2,$$where $$r$$ is a positive constant. What is the value of $$r$$?

   • $$7$$
   • $$6$$
   • $$4$$
   • $$5$$

7. The perimeter of an equilateral triangle is $$246$$ inches. The height of this triangle is $$m\sqrt3$$ inches, where $$m$$ is a constant. What is the value of $$m$$?

   • $$40$$
   • $$44$$
   • $$38$$
   • $$41$$

8. In the given system of equations, $$k$$ is a constant.$$3x-ky=6$$$$x-ky=-10$$In the $$xy$$-plane, the graphs of these equations intersect at the point $$(p,3)$$, where $$p$$ is a constant. What is the value of $$k$$?

   • $$9$$
   • $$6$$
   • $$3$$
   • $$4$$

9. A parabola in the $$xy$$-plane is defined by the equation $$y=-x^2+6x-5$$. The line $$y=k$$ intersects the parabola at exactly one point. What is the value of $$k$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$5$$

10. The mean score on a quiz for a class of $$15$$ students was $$72$$. After one student's score is removed, the mean score for the remaining students is $$70$$. What was the score of the student that was removed?

    • $$104$$
    • $$96$$
    • $$92$$
    • $$100$$