Full Practice Exam 7 — Module 1

Questions in this quiz (22)

1. If $$6x-5=3(x+7)$$, what is the value of $$x$$?

   • $$\frac{3}{26}$$
   • $$\frac{23}{6}$$
   • $$\frac{26}{3}$$
   • $$\frac{13}{3}$$

2. If $$\frac{1}{4}(x+8)=y$$ and $$x=12$$, what is the value of $$y$$?

   • 5
   • Answer

3. If a line has a slope of $$4$$ and a $$y$$-intercept of $$b$$, what is the value of $$b$$ if the points $$(2,11)$$ and $$(5,23)$$ are on the line?

   • $$5$$
   • $$11$$
   • $$3$$
   • $$4$$

4. $$\frac{x^2-25}{x-5}$$Which of the following is equivalent to the expression below, in which $$x\ne5$$?

   • $$x+5$$
   • $$x^2-25$$
   • $$\frac{1}{x-5}$$
   • $$x-5$$

5. Gravitational potential energy, $$U$$, is calculated using the following formula, in which $$m$$ is mass, $$g$$ is gravitational acceleration, and $$h$$ is height:$$U=mgh$$What is the height in terms of the other variables?

   • $$h=\frac{mg}{U}$$
   • $$h=\frac{Um}{g}$$
   • $$h=\frac{Ug}{m}$$
   • $$h=\frac{U}{mg}$$

6. A data set of $$11$$ different numbers has a median of $$18$$ and a mean of $$20$$. If the smallest number in the set has $$4$$ subtracted from it and the largest number has $$12$$ added to it, while all the other elements remain the same, which of these is a correct statement?

   • The median increases and the mean increases.
   • The median decreases and the mean stays $$20$$.
   • The median stays $$18$$ and the mean decreases.
   • The median stays $$18$$ and the mean increases to $$20+\frac{8}{11}$$.

7. Consider the sum of the expressions $$-2x^2+7x-4$$ and $$3x^2-5x+9$$. If the sum is written in the form $$gx^2+hx+k$$, where $$g$$, $$h$$, and $$k$$ are constants, what is the value of $$k$$?

   • $$-5$$
   • $$2$$
   • $$5$$
   • $$1$$

8. In the $$xy$$-plane, a line passes through the points $$(6,0)$$ and $$(0,-4)$$. Another line is perpendicular to this line. What would be this perpendicular line's slope?

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

9. A particular protein bar provides $$18$$ g of protein, giving $$30\%$$ of the recommended daily value of protein for an adult. If another protein bar provides $$12$$ g of protein, approximately what percentage of the recommended daily value of protein for an adult would it provide, to the nearest whole percent?

   • $$20\%$$
   • $$15\%$$
   • $$25\%$$
   • $$40\%$$

10. The measure of an angle is $$\frac{5\pi}{12}$$ radians. How many angles of this measure would be equivalent to $$2\pi$$ radians?

    • $$\frac{10}{24}$$
    • $$\frac{12}{5}$$
    • $$\frac{24}{5}$$
    • $$\frac{5}{24}$$

11. For the system of inequalities $$y\le2x+1$$ and$$y\le-x+7$$, when $$y$$ is at its greatest possible value,what is the corresponding value of $$x$$?

    • $$1$$
    • $$3$$
    • $$2$$
    • $$4$$

12. What is the result when $$3x^2+5x-4$$is divided by $$x+2$$?

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

13. The volume $$V$$ in cubic inches of a right cylinder with a height of $$8$$ inches is $$128\pi$$ cubic inches. What is the circumference, in inches, of one of the bases of this cylinder?

    • $$16\pi$$
    • $$32\pi$$
    • $$8\pi$$
    • $$4\pi$$

14. What values of $$x$$ would make the product of $$\frac{5}{x+2}$$ and $$\frac{4}{x-3}$$ undefined?

    • $$x=-2$$ and $$x=3$$
    • $$x=3$$ only
    • $$x=-2$$ only
    • $$x=2$$ and $$x=-3$$

15. For a parabola with the equation $$y=4(x-6)(x+1)$$, what is the distance between the $$x$$-intercepts of the parabola?

    • $$2$$
    • $$4$$
    • $$7$$
    • $$8$$

16. If $$(x-7)(x+4)=ax^2+bx+c$$, in which $$a$$, $$b$$, and $$c$$ are all constants, what is the value of $$c$$?

    • $$-21$$
    • $$-11$$
    • $$28$$
    • $$-28$$

17. The given system of equations has solution(s) $$(x,y)$$.$$y=\sqrt{x+2}$$$$y=x-4$$What is the value of $$x$$ in the solution to the given system?

    • $$2$$
    • $$3$$
    • $$7$$
    • $$14$$

18. A population of rabbits in a wildlife reserve can be modeled by the function $$P(t)=P_0\cdot(b)^{t/k}$$, where $$P(t)$$ is the number of rabbits after $$t$$ months, $$P_0$$ is the initial population, and $$b$$ and $$k$$ are positive constants. If the rabbit population triples every $$6$$ months, and the initial population is $$200$$ rabbits, which of the following expressions represents the rabbit population after $$t$$ months?

    • $$P(t)=200\cdot(3)^{t/6}$$
    • $$P(t)=200\cdot(6)^{t/3}$$
    • $$P(t)=200\cdot(3)^{6t}$$
    • $$P(t)=200\cdot(9)^{t/6}$$

19. In the figure, point $$O$$ is the center of the circle. Tangent segments $$CA$$ and $$CB$$ are drawn from an external point $$C$$ to the circle, with points $$A$$ and $$B$$ on the circle. If the length of segment $$CA$$ is $$12$$ and the area of quadrilateral $$OACB$$ is $$96$$, what is the circumference of the circle?

    • $$12\pi$$
    • $$16\pi$$
    • $$24\pi$$
    • $$32\pi$$

20. A cubic polynomial $$P(x)$$ has roots at $$x=1$$, $$x=-2$$, and $$x=k$$. The y-intercept of the graph of $$y=P(x)$$ is $$(0,12)$$. The graph of $$y=P(x)$$ also passes through the point $$(3,-16)$$. What is the value of $$k$$?

    • $$\frac{45}{19}$$
    • $$\frac{45}{11}$$
    • $$-\frac{45}{11}$$
    • $$-\frac{45}{19}$$

21. For the quadratic equation $$mx^2-(12n)x+(36m)=0$$ suppose it has exactly one real solution and $$mn=100$$. What is the value of $$|m+n|$$?

    • 20

22. The bar graph shows the number of students who chose each type of pet as their favorite. How many students chose dogs as their favorite pet?

    • $$9$$
    • $$11$$
    • $$14$$
    • $$16$$