Mini Exam 26 — Timed Mini Exams

Questions in this quiz (10)

1. If $$x-2y=10$$, $$y=z+1$$, and $$z=2$$, what is the value of $$x$$?

   • $$10$$
   • $$12$$
   • $$14$$
   • $$16$$

2. In the figure above, $$\angle BAC=30^\circ$$, $$\angle BCD=60^\circ$$, and the length of $$AC$$ is $$4$$. What is the area of $$\triangle ABC$$?

   • $$4\sqrt3$$
   • $$8$$
   • $$8\sqrt3$$
   • $$16$$

3. A bag contains $$3$$ red marbles and $$6$$ black marbles. What is the probability that you select two red marbles if you reach in the bag and randomly grab two marbles without replacement?

   • $$\frac{2}{9}$$
   • $$\frac{1}{36}$$
   • $$\frac{1}{18}$$
   • $$\frac{1}{12}$$

4. In the figure above, a circle is tangent to the sides of equilateral triangle $$PQR$$, and the radius $$r$$ equals $$5$$. What is the perimeter of $$\triangle PQR$$?

   • $$30$$
   • $$30\sqrt3$$
   • $$35$$
   • $$40\sqrt2$$

5. If $$rs^2t^3u^3$$ > $$0$$ and $$u$$ < $$0$$, which of the following must be true?

   • $$rt$$ < $$0$$
   • $$urt$$ < $$0$$
   • $$r$$ > $$0$$
   • $$st$$ > $$0$$

6. To arrive on time, a ship needs $$5$$ hours to complete a voyage. If the ship must arrive in $$4$$ hours, by what percent must the speed of the ship be increased?

   • $$15\%$$
   • $$20\%$$
   • $$25\%$$
   • $$27\%$$

7. In the figure above, $$r_1$$ and $$r_2$$ are the radii of two circles with the same center. If the area of the shaded region is $$12$$ and the ratio of $$r_1$$ to $$r_2$$ is $$1:2$$, what is the area of the smaller circle?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

8. The table above shows some values for the function $$f$$. If $$f$$ is a linear function, what is the value of $$b$$ in terms of $$a$$?

   • $$b=\frac{7}{2}a$$
   • $$b=3a$$
   • $$b=a+6$$
   • $$b=2a+3$$

9. In the $$xy$$-plane, the equation of line $$\ell$$ is $$x+3y=5$$. If line $$m$$ is perpendicular to line $$\ell$$, what is a possible equation of line $$m$$?

   • $$y=-\frac{1}{3}x+2$$
   • $$y=\frac{1}{3}x-1$$
   • $$y=\frac{3}{2}x-3$$
   • $$y=3x+\frac{5}{2}$$

10. In a certain class, $$\frac{4}{7}$$ of the students are boys, and the ratio of the students older than or equal to $$10$$ years to the students less than $$10$$ years old is $$2:3$$. If $$\frac{2}{3}$$ of the girls are less than $$10$$ years old, what fraction of the boys are older than or equal to $$10$$ years?

    • $$\frac{9}{20}$$
    • $$\frac{11}{20}$$
    • $$\frac{14}{15}$$
    • $$\frac{9}{35}$$