Full Practice Exam 18 — Module 2

Questions in this quiz (22)

1. Which of the following is the solution to the exponential equation $$25^{x/2}=5^{3x-1}$$?

   • $$\frac{1}{2}$$
   • $$\frac{2}{5}$$
   • $$\frac{2}{3}$$
   • $$\frac{4}{5}$$

2. A county in Nebraska has a shape that is approximately triangular and covers $$432$$ square miles. A map is produced using a scale of $$1:400{,}000$$. Which of the following must be true about the county on the map?

   • The map resembles the actual shape of the county, with an area of approximately $$69.9$$ square centimeters.
   • The map resembles a rectangle, with an area of approximately $$69.9$$ square centimeters.
   • The map resembles the actual shape of the county, with an area of approximately $$39.9$$ square centimeters.
   • The map resembles a rectangle, with an area of approximately $$39.9$$ square centimeters.

3. The function $$f$$ is defined by $$f(x)=x^2+4$$. In the $$xy$$-plane, which graph has no points of intersection with $$f(x)$$?

   • $$y=f(x-2)$$
   • $$y=f(x-2)+3$$
   • $$y=\frac{1}{2}f(x)-1$$
   • $$y=3f(x)-2$$

4. In the $$xy$$-plane, the graph of $$x^2-6x+y^2+8y-11=0$$ represents a circle. What is the circumference of the circle?

   • $$2\pi\sqrt{20}$$
   • $$2\pi\sqrt{15}$$
   • $$10\pi$$
   • $$12\pi$$

5. Which of the following expressions is equivalent to $$\left(\frac{3}{a^2-b^2}-\frac{1}{a^2+ab}\right)\div\frac{a}{a+b}$$?

   • $$\frac{2}{a^2}$$
   • $$\frac{1}{a+b}$$
   • $$\frac{2}{a(a-b)}$$
   • $$\frac{2a+b}{a^2(a-b)}$$

6. If the equation $$\frac{x^2+7x+10}{x-2}=ax+b+\frac{18}{x-2}$$ is true for all real values of $$x\ne2$$, what is the value of $$ab$$?

   • 9

7. For a set of resistors connected in parallel, $$\frac{1}{R_{\text{eff}}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$$. Which formula can be used to calculate $$R_{\text{eff}}$$?

   • $$\frac{R_1R_2+R_2R_3+R_3R_1}{R_1R_2R_3}$$
   • $$\frac{R_1R_2R_3}{R_1R_2+R_2R_3+R_3R_1}$$
   • $$R_1+R_2+R_3$$
   • $$\frac{R_1+R_2+R_3}{R_1R_2R_3}$$

8. The average monthly cost of a gym membership was $$40$$ dollars in $$2012$$ and $$85$$ dollars in $$2022$$. If the cost can be modeled by a linear function, which function best represents the membership cost $$C(t)$$, where $$t$$ is the year?

   • $$C(t)=4.5t-9014$$
   • $$C(t)=45t-9014$$
   • $$C(t)=4.5t+9014$$
   • $$C(t)=45t+9014$$

9. If the solutions to the quadratic equation $$9x^2-6x-8=0$$ are $$x_1$$ and $$x_2$$, what is the value of $$|x_1-x_2|$$?

   • 2

10. A rectangle is inscribed inside a circle of radius $$10$$ units. If the shorter side of the rectangle is $$x$$ and the longer side is $$2x$$, what is the area of the rectangle?

    • 160

11. If $$(x+2)^2$$ < $$9,$$ which of the following statements must be true?I. $$-3$$ < $$x+2$$ < $$3$$II. $$-5$$ < $$x$$ < $$1$$III. $$5$$ < $$x+10$$ < $$11$$

    • I only
    • II only
    • I and II only
    • I, II, and III

12. $$x^2+y^2=56$$$$y=\sqrt{x},$$According to the system of equations above, what is the value of $$x+y$$?

    • $$2\sqrt{7}$$
    • $$7$$
    • $$7+\sqrt{7}$$
    • $$8$$

13. Jay puts an initial deposit of $$400$$ into a bank account that earns $$5$$ percent interest each year, compounded semiannually. Which of the following equations gives the total dollar amount in the account after $$t$$ years, $$A$$?

    • $$A=400(1+0.05t)$$
    • $$A=400(1+0.1)^t$$
    • $$A=400(1.05)^t$$
    • $$A=400(1.025)^{2t}$$

14. A scientist counts $$80$$ cells in a petri dish and finds that each one splits into two new cells every hour. He uses the function $$N(t)=cr^t$$ to calculate the total number of cells in the petri dish after $$t$$ hours. Which of the following assumptions are correct values for $$c$$ and $$r$$?

    • $$c=40,\ r=2$$
    • $$c=80,\ r=0.5$$
    • $$c=80,\ r=1.5$$
    • $$c=80,\ r=2$$

15. At a math team competition, there are $$m$$ schools with $$n$$ students from each school. The host school wants to order enough pizza such that there are $$2$$ slices for each student. If there are $$8$$ slices in one pizza, which of the following gives the number of pizzas the host school must order?

    • $$\frac{mn}{8}$$
    • $$\frac{mn}{4}$$
    • $$\frac{m+2n}{8}$$
    • $$2mn$$

16. The table above shows the point $$(x,y)$$ represented on a straight line. If the point $$(16,m)$$ lies on the same line, what is the value of $$m$$?

    • 16

17. In the figure above, what is the value of $$a+b$$?

    • $$80$$
    • $$100$$
    • $$110$$
    • $$120$$

18. In the figure above, $$ABCD$$ is a square of side length $$3$$. If $$AW=AZ=CX=CY=1,$$ what is the perimeter of rectangle $$WXYZ$$?

    • $$3\sqrt{2}$$
    • $$4\sqrt{2}$$
    • $$6\sqrt{2}$$
    • $$8$$

19. The dotplot above shows the distribution of ages for $$24$$ winners of the Miss World beauty pageant at the time they were crowned. Based on the data, which of the following is closest to the average (arithmetic mean) age of the winning Miss World pageant contestant?

    • 20

20. The scatterplot above shows the relationship between heart rate and oxygen uptake at $$16$$ different points during Kyle's exercise routine. The line of best fit is also shown. Based on the line of best fit, what is Kyle's predicted oxygen uptake at a heart rate of $$110$$ beats per minute?

    • $$1$$
    • $$1.2$$
    • $$1.5$$
    • $$2$$

21. The manager of a large assembly line uses the table below to keep track of the number of vehicles that are produced during different shifts in the day.If a vehicle is selected at random at the end of the day, which of the following is closest to the probability that the vehicle will be either a car produced during the first shift or a truck produced during the third shift?

    • $$0.193$$
    • $$0.314$$
    • $$0.352$$
    • $$0.421$$

22. A data set $$S$$ contains $$n$$ distinct positive integers, where $$n\ge2$$. The mean of data set $$S$$ is $$M$$, and the standard deviation of data set $$S$$ is $$s$$. A new data set $$S'$$ is formed by adding one integer, $$X$$, to data set $$S$$. Which of the following statements must be true if $$X=M$$?

    • The mean of data set $$S'$$ is greater than $$M$$.
    • The median of data set $$S'$$ is equal to the median of data set $$S$$.
    • The standard deviation of data set $$S'$$ is less than $$s$$.
    • The range of data set $$S'$$ is greater than the range of data set $$S$$.