Mini Exam 29 — Timed Mini Exams

Questions in this quiz (10)

1. The table above shows the distribution of a board game's pieces categorized by type and color. Each piece represents a product, a building, or a site on which a building can be constructed. Each purple building piece is either large or small. All the other building pieces are small. If $$10\%$$ of all building pieces in the game are large, how many of the purple building pieces in the game are small?

   • 24

2. $$x^2-6x+y^2+4y=36$$The equation above defines a circle in the $$xy$$-plane. What is the radius of the circle?

   • 7

3. For the linear function $$f$$, the table above shows several values of $$x$$ and their corresponding values of $$f(x)$$. The function $$g$$ is defined by $$g(x)=x+b$$, where $$b$$ is a constant. If $$g(x)>f(x)$$ for all values of $$x$$, which of the following could be the value of $$b$$?

   • $$2$$
   • $$1$$
   • $$0$$
   • $$-1$$

4. $$\frac{2x}{4x-6}-\frac{x}{2x-3}=0$$How many solutions does the equation above have?

   • None
   • One
   • Two
   • Infinitely many

5. $$p=5(n-1)+20$$The equation above represents the total number $$p$$ of athletes inducted into a hall of fame by the end of its $$n$$th induction ceremony. If a total of $$85$$ athletes have been inducted, how many induction ceremonies have occurred?

   • 14

6. $$x^2+y^2=9$$$$y=3-x$$If $$(x_1,y_1)$$ is a solution to the system of equations above, what is a possible value for $$y_1$$?

   • $$-3$$
   • $$0$$
   • $$2$$
   • $$-2$$

7. $$f(x)=-3x^2+24x-36$$The function $$f$$ is defined by the equation above. In which of the following equivalent forms of the equation does the maximum value of $$f(x)$$ appear as a constant or coefficient?

   • $$f(x)=-3x^2+18x+6x-36$$
   • $$f(x)=-3x(x-6)+6(x-6)$$
   • $$f(x)=-3(x-4)^2+12$$
   • $$f(x)=-3(x-2)(x-6)$$

8. $$4x-3y=9$$$$y=ax+2$$In the system of equations below, $$a$$ is a constant. For which value of $$a$$ will the system of equations have no solution $$(x,y)$$?

   • $$-\frac{4}{3}$$
   • $$-\frac{3}{4}$$
   • $$\frac{3}{4}$$
   • $$\frac{4}{3}$$

9. What is the result when $$840$$ is increased $$25$$ percent?

   • 1050

10. On Arbor Day this year, a young dawn redwood tree was planted. A botanist predicts that the tree's height on Arbor Day next year will have increased $$125\%$$ of its height when it was planted. If $$h$$ represents the tree's height when planted, which of the following represents the botanist's predicted height of the tree on Arbor Day next year?

    • $$0.25h$$
    • $$1.25h$$
    • $$2.25h$$
    • $$12.25h$$