Mini Exam 12 — Timed Mini Exams

Questions in this quiz (10)

1. The expression $$\frac{a^{-2}b^{\frac{5}{2}}}{a^{4}b^{-1}},$$ where $$a$$>$$1$$ and $$b$$>$$1$$, is equivalent to which of the following?

   • $$\frac{b^{\frac{7}{2}}}{a^6}$$
   • $$\frac{a^6}{b^{\frac{7}{2}}}$$
   • $$\frac{b^{\frac{7}{2}}}{a^5}$$
   • $$\frac{b^{\frac{5}{2}}}{a^6}$$

2. The graphs of the equations in the given system of equations intersect at the point $$(x,y)$$ in the $$xy$$-plane. What is a possible value of $$x$$?$$8x+y=20$$$$2x^2=y+32$$

   • $$2+\sqrt{30}$$
   • $$-2-\sqrt{30}$$
   • $$-2+\sqrt{28}$$
   • $$-2+\sqrt{30}$$

3. The first term of a sequence is $$5$$. Each term after the first is $$4$$ times the preceding term. If $$a$$ represents the $$n$$th term of the sequence, which equation gives $$a$$ in terms of $$n$$?

   • $$a=5+4(n-1)$$
   • $$a=4\cdot5^{n-1}$$
   • $$a=5\cdot4^n$$
   • $$a=5\cdot4^{n-1}$$

4. The table below provides the coordinates of two points on a line in the $$xy$$-plane:The $$y$$-intercept of the line is represented as $$(p-6,c)$$, where $$p$$ and $$c$$ are constants. Determine the value of $$c$$.

   • $$18$$
   • $$15$$
   • $$12$$
   • $$9$$

5. In the given system of equations, $$k$$ is a constant.$$\frac{7}{8}x-\frac{1}{4}y=\frac{3}{4}-\frac{1}{8}x$$$$\frac{3}{5}y+\frac{6}{5}=kx-\frac{2}{5}$$If the system has no solution, what is the value of $$k$$?

   • $$\frac{14}{5}$$
   • $$\frac{10}{5}$$
   • $$\frac{8}{5}$$
   • $$\frac{12}{5}$$

6. The table below shows the distribution of students in a school based on whether they play a sport and whether they are in a club.To the nearest tenth of a percent, what percent of students who play a sport are not in a club?

   • $$20.0\%$$
   • $$32.0\%$$
   • $$25.0\%$$
   • $$12.5\%$$

7. The table below shows the distribution of primary academic concentrations for sophomore and junior students at a university.A student whose concentration is in $$STEM$$ is chosen at random. The probability that the student is a sophomore is $$\frac{2}{9}$$. What is the value of $$x$$?

   • $$16$$
   • $$20$$
   • $$18$$
   • $$12$$

8. The equation $$x^2+y^2+10x-6y=q$$ represents a circle in the $$xy$$-plane. If the radius of the circle is $$8$$, what is the value of $$q$$?

   • $$26$$
   • $$28$$
   • $$30$$
   • $$34$$

9. Solve the equation:$$|5x-7|=18.$$What is the sum of the solutions to the given equation?

   • $$\frac{19}{5}$$
   • $$\frac{16}{5}$$
   • $$\frac{14}{5}$$
   • $$\frac{11}{5}$$

10. A scientist started an experiment with $$P$$ grams of a certain substance on January $$1,2012$$. The substance's amount doubled every year. By January $$1,2016$$, the amount of the substance had grown to $$320$$ grams. What was the initial amount $$P$$ of the substance?

    • $$25$$
    • $$20$$
    • $$15$$
    • $$10$$