Full Practice Exam 9 — Module 2

Questions in this quiz (22)

1. The function $$f$$ is defined by:$$f(x)=-3(x-2)^2+11$$What is the maximum value of $$f$$?

   • $$-3$$
   • $$2$$
   • $$8$$
   • $$11$$

2. A population of bacteria quadruples every 6 hours. At the beginning of the observation, there are 150 bacteria. Which equation best models the population $$P$$ after $$t$$ hours?

   • $$P=150\cdot4^t$$
   • $$P=150\cdot4^{t/6}$$
   • $$P=150+t^4$$
   • $$P=150\cdot6^{t/4}$$

3. A laptop is discounted by 35% from its original price. After the discount, an 8.5% sales tax is applied. If the final price is $879.45, what was the original price of the laptop?

   • $$1247$$
   • $$1150$$
   • $$1400$$
   • $$1575$$

4. In the $$xy$$-plane, line $$m$$ passes through the points $$(-1,7)$$ and $$(5,-5)$$. Line $$n$$ is perpendicular to line $$m$$ and passes through the point $$(4,3)$$. Which equation represents line $$n$$?

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

5. The equation $$(k^2-9)x+4=(k+3)x+12$$ where $$k$$ is a constant, has no solution. What is a possible value of $$k$$?

   • $$-2$$
   • $$3$$
   • $$4$$
   • $$-4$$

6. Which expression is equivalent to $$\frac{5x^2-45}{x^2-6x+9}$$ for all $$x\ne3$$?

   • $$\frac{5(x+3)}{x-3}$$
   • $$\frac{5(x-3)}{x+3}$$
   • $$5(x+3)$$
   • $$\frac{5}{x-3}$$

7. A metal alloy contains 320 grams of copper and zinc combined. The alloy is 55% copper by mass. The alloy was created by combining two smaller alloys: Alloy A is 40% copper. Alloy B is 70% copper. If the mass of copper contributed by Alloy A is $$a$$ grams and the mass of copper contributed by Alloy B is $$b$$ grams, by what percent is $$a$$ less than $$b$$? Round to the nearest tenth.

   • 42.9

8. The table below summarizes the results of a survey of 300 students about whether they participate in sports or music programs.If a student selected at random participates in sports, what is the probability that the student also participates in music?

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

9. In the $$xy$$-plane, a parabola has vertex $$(-4,9)$$ and no $$x$$-intercepts. If the equation of the parabola is written in the form $$y=ax^2+bx+c$$ which of the following could be the value of $$a+b-c$$?

   • $$-25$$
   • $$7$$
   • $$18$$
   • $$31$$

10. The quadratic equation $$x^2-12x-13=0$$ has a solution that can be written in the form $$m.n$$, where $$m$$ and $$n$$ are positive constants and $$m$$ > $$n$$. What is the value of $$m+n$$?

    • 14

11. A right circular cylinder has radius 4 inches and height 9 inches. Water is poured into the cylinder at a constant rate of $$6\pi$$ cubic inches per minute. How many minutes will it take to completely fill the cylinder?

    • $$12$$
    • $$18$$
    • $$24$$
    • $$36$$

12. The profit $$P$$, in dollars, from selling $$x$$ units of a product is modeled by $$P(x)=-0.25x^2+180x-5000$$ What is the maximum profit, in dollars, that can be achieved?

    • $$18,000$$
    • $$22,400$$
    • $$27,400$$
    • $$32,400$$

13. In the $$xy$$-plane, the graph of $$9x^2-108x+9y^2+72y=1296$$ is a circle. If an equilateral triangle is inscribed in the circle, what is the area of the triangle?

    • $$81\sqrt{3}$$
    • $$108\sqrt{3}$$
    • $$147\sqrt{3}$$
    • $$243\sqrt{3}$$

14. A project requires between 480 and 720 total labor-hours, inclusive. A team consists of 6 senior workers and 4 junior workers. Each senior worker contributes between 30 and 45 hours per week. Each junior worker contributes between 18 and 28 hours per week. If the project is completed in exactly $$w$$ weeks, which inequality represents the possible values of $$w$$?

    • $$\frac{240}{191}\le w\le\frac{20}{7}$$
    • $$\frac{20}{37}\le w\le\frac{60}{29}$$
    • $$\frac{16}{29}\le w\le\frac{45}{22}$$
    • $$\frac{45}{22}\le w\le\frac{16}{29}$$

15. The system of linear equations below has no solution.$$(k+1)x+4y=12$$$$6x+(2k-1)y=-9$$What is a possible value of $$k$$?

    • $$\frac{-1+\sqrt{201}}{4}$$
    • $$\frac{1}{4}$$
    • $$\frac{20+\sqrt{5}}{4}$$
    • $$\frac{-20+\sqrt{5}}{4}$$

16. The system of equations below has exactly one real solution $$(x_0,y_0)$$.$$y=x^2-8x+c$$$$y=4x-7$$What is the value of $$x_0+y_0$$?

    • 23

17. For the function $$f$$, for each increase in the value of $$x$$ by $$\frac{1}{4}$$, the value of $$f(x)$$ increases by a factor of $$3$$. Which equivalent form displays the growth factor as a constant or coefficient?

    • $$f(x)=12(81)^x$$
    • $$f(x)=12(3)^x$$
    • $$f(x)=12(9)^{2x}$$
    • $$f(x)=12(27)^{\frac{4}{3}x}$$

18. Consider the system of equations:$$y=x^2-10x+30$$$$y=|x-5|+k$$where $$k$$ is a constant. For what value of $$k$$ does the system have exactly three distinct real solutions?

    • $$4$$
    • $$5$$
    • $$6$$
    • $$7$$

19. A right circular cone has a volume of $$V$$ cubic units. If the radius is doubled and the height is reduced to one-third of its original value, what is the new volume in terms of $$V$$?

    • $$\frac{2}{3}V$$
    • $$\frac{4}{3}V$$
    • $$2V$$
    • $$\frac{8}{3}V$$

20. In the system$$\frac{a}{4}x+\frac{5}{6}=\frac{b}{4}y-\frac{7}{6}$$$$-18x+7y=14-5y$$where $$a$$ and $$b$$ are constants, the system has no solution. The ratio $$a:b$$ is equivalent to $$14:k$$. What is the value of $$k$$?

    • $$\frac{28}{3}$$
    • $$\frac{3}{2}$$
    • $$\frac{18}{12}$$
    • $$\frac{2}{3}$$

21. A streaming service charges a fixed monthly fee for the first 8 GB of premium downloads. For any downloads exceeding 8 GB, an additional charge per GB is applied. If a customer downloads 14 GB and pays 92 dollars, and another customer downloads 26 GB and pays $164, which function $$C(d)$$ represents the total monthly cost, in dollars, for a customer who downloads $$d$$ GB, where $$d$$ > $$8$$?

    • $$C(d)=6d+8$$
    • $$C(d)=6d+20$$
    • $$C(d)=8d-20$$
    • $$C(d)=8d+12$$

22. The function $$f$$ is defined by $$f(x)=a(-x+b)^2$$, where $$a$$ and $$b$$ are constants. In the $$xy$$-plane, the graph of $$y=f(x)$$ passes through $$(4,0)$$, and $$f(-10)$$ > $$f(-1)$$. Which of the following must be true?

    • $$a$$ < $$f(b)$$
    • $$a$$ > $$b$$
    • $$f(2)$$ < $$f(-2b)$$
    • $$a$$ < $$b$$