Full Practice Exam 12 — Module 1

Questions in this quiz (22)

1. A cylindrical tank initially contains $$4,800$$ liters of water. Water drains from the tank at a rate proportional to the amount of water remaining, such that every $$12$$ minutes the amount of water decreases by $$25\%$$. Which function best models the amount of water, in liters, remaining in the tank after $$t$$ minutes?

   • $$W(t)=4800(0.75)^{12t}$$
   • $$W(t)=4800(0.25)^{t/12}$$
   • $$W(t)=4800(0.75)^{t/12}$$
   • $$W(t)=4800-0.25t$$

2. The price of a computer was decreased by $$15\%$$ during a sale. One week later, the sale price was increased by $$20\%$$. After that, the new price was discounted by another $$10\%$$. What is the final price as a percentage of the original price?

   • $$91.8\%$$
   • $$92\%$$
   • $$95\%$$
   • $$102\%$$

3. In the $$xy$$-plane, the line defined by $$(2k-3)x+(k+4)y=30$$ has slope $$\frac{3}{2}$$. What is the $$x$$-intercept of the line?

   • $$3$$
   • $$5$$
   • $$6$$
   • $$-\frac{70}{11}$$

4. A company manufactures a specialized device. The company incurs a fixed monthly cost of $$24,000$$. For the first $$300$$ devices produced, the manufacturing cost is $$80$$ per device. For every device beyond the first $$300$$, the manufacturing cost decreases to $$60$$ per device. Each device sells for $$140$$. If the company wants a monthly profit of exactly $$54,000$$, how many devices must it sell?

   • $$900$$
   • $$950$$
   • $$1000$$
   • $$1050$$

5. Which expression is equivalent to $$\frac{x^2-9}{x-3}+\frac{x^2+7x+10}{x+5}$$ for all values of $$x$$ for which the expression is defined?

   • $$2x+2$$
   • $$2x+5$$
   • $$x^2+4x+1$$
   • $$x^2+7x+1$$

6. A random sample of $$800$$ voters is surveyed before an election. Of those surveyed, $$472$$ say they support Candidate A. The survey has a margin of error of $$3.5\%$$. Which statement is most plausible?

   • Exactly $$59\%$$ of all voters support Candidate A.
   • Between $$55.5\%$$ and $$62.5\%$$ of all voters support Candidate A.
   • Less than $$55.5\%$$ of all voters support Candidate A.
   • More than $$62.5\%$$ of all voters support Candidate A.

7. A factory uses Machine A and Machine B to manufacture computer chips. Machine A produces $$65\%$$ of all chips and has a defect rate of $$2\%$$. Machine B produces the remaining chips and has a defect rate of $$6\%$$. If a randomly selected chip is defective, what is the probability that it came from Machine B?

   • $$\frac{21}{34}$$
   • $$\frac{9}{17}$$
   • $$\frac{3}{10}$$
   • $$\frac{7}{20}$$

8. In the $$xy$$-plane, the graphs of $$y=x^2-8x+20$$ and $$y=4x+k$$ intersect at exactly one point. What is the value of $$k$$?

   • $$-16$$
   • $$0$$
   • $$4$$
   • $$8$$

9. The function $$f$$ is defined by $$f(x)=3x-7$$ The function $$g$$ is linear and satisfies $$g(x)=f(ax+b)$$ for constants $$a$$ and $$b$$. If $$g(2)=11$$ and $$g(5)=38$$, what is the value of $$a+b$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$5$$

10. The daily revenue, in dollars, for a company is modeled by $$R(p)=-8p^2+640p-3200$$ where $$p$$ is the price, in dollars, of the product. What is the maximum possible daily revenue?

    • $$9600$$
    • $$96000$$
    • $$12800$$
    • $$16000$$

11. In right triangle $$\triangle ABC$$, angle $$C$$ is a right angle. If $$\sin(A)=\frac{12}{13}$$ and the hypotenuse has length $$39$$, what is the area of the triangle?

    • $$270$$
    • $$378$$
    • $$420$$
    • $$486$$

12. For all real numbers $$x$$ satisfying $$\sqrt{2x+9}=x-3$$ what is the value of $$x$$?

    • $$5$$
    • $$8$$
    • $$9$$
    • $$11$$

13. A sphere is inscribed in a right circular cylinder. The total surface area of the cylinder is $$216\pi$$ square units. What is the volume of the sphere?

    • $$144\pi$$
    • $$192\pi$$
    • $$256\pi$$
    • $$288\pi$$

14. $$4x-3y=29$$$$7x+5y=1$$What is the value of $$43x-6y$$?

    • $$145$$
    • $$173$$
    • $$\frac{7558}{41}$$
    • $$203$$

15. $$y=x^2-8x+k$$$$y=4x-7$$The system has exactly one real solution. What is the value of $$k$$?

    • $$21$$
    • $$25$$
    • $$29$$
    • $$33$$

16. A line passes through the points $$(1,4)$$ and $$(5,16)$$. Another line is perpendicular to this line and passes through $$(0,10)$$. What is the $$y$$-coordinate of the intersection point of the two lines?

    • $$\frac{34}{5}$$
    • $$7$$
    • $$\frac{38}{5}$$
    • $$\frac{91}{10}$$

17. A company's revenue came from two divisions in $$2024$$:What was the approximate overall percent change in total revenue?

    • $$5\%$$ increase
    • $$7\%$$ increase
    • $$9\%$$ increase
    • $$12\%$$ increase

18. If $$(3m-x)$$ is a factor of $$(x^3-31pm^3)$$, where $$p$$ and $$m$$ are constants and $$m$$ > $$0$$, what is the value of $$p$$? Round your answer to the nearest hundredth.

    • 0.87

19. The dot plots show the distributions of two different data sets, Data Set A and Data Set B. Which of the following statements about the standard deviations of Data Set A and Data Set B is true?

    • The standard deviation of Data Set A is less than the standard deviation of Data Set B.
    • The standard deviation of Data Set A is greater than the standard deviation of Data Set B.
    • The standard deviation of Data Set A is equal to twice the standard deviation of Data Set B.
    • The standard deviation of Data Set A is less than the standard deviation of Data Set B.

20. In the figure, $$\triangle ABC$$ is shown. Point $$D$$ is on $$\overline{AB}$$ and point $$E$$ is on $$\overline{AC}$$ such that $$\overline{DE}\parallel\overline{BC}$$. Point $$F$$ is on $$\overline{AD}$$ and point $$G$$ is on $$\overline{AE}$$ such that $$\overline{FG}\parallel\overline{DE}$$. Suppose $$AB=3\cdot AD$$ and $$AF=\frac{2}{3}AD$$ If the area of trapezoid $$FGED$$ is $$56$$ square units, what is the area of trapezoid $$DECB$$?

    • $$98.3$$
    • $$112.7$$
    • $$126.8$$
    • $$806.4$$

21. A survey was conducted among $$140$$ pet owners to determine their primary pet type and their preference for indoor or outdoor pets. The results are summarized in the table below.Among the pet owners surveyed, if a pet owner is selected at random and it is found that they either own a cat or prefer outdoor pets, what is the probability that this selected owner is a dog owner?

    • $$\frac{5}{14}$$
    • $$\frac{3}{13}$$
    • $$\frac{5}{11}$$
    • $$\frac{8}{11}$$

22. A bakery produces two types of cakes: vanilla and chocolate. Each vanilla cake requires $$2$$ cups of flour and $$1$$ cup of sugar. Each chocolate cake requires $$3$$ cups of flour and $$2$$ cups of sugar. The bakery has a daily supply of no more than $$30$$ cups of flour and no more than $$20$$ cups of sugar. If $$v$$ represents the number of vanilla cakes and $$c$$ represents the number of chocolate cakes the bakery produces daily, which system of inequalities accurately describes the constraints on the number of cakes that can be produced?

    • $$2v+3c\le30,\ v+2c\le20,\ v\ge0,\ c\ge0$$
    • $$2v+3c\ge30,\ v+2c\ge20,\ v\ge0,\ c\ge0$$
    • $$3v+2c\le30,\ 2v+c\le20,\ v\ge0,\ c\ge0$$
    • $$2v+3c\le20,\ v+2c\le30,\ v\ge0,\ c\ge0$$