Full Practice Exam 12 — Module 2

Questions in this quiz (22)

1. A vertical tower $$PQ$$ is supported by two cables, $$RQ$$ and $$SQ$$. The base of the tower, point $$P$$, lies on flat ground, and points $$R$$ and $$S$$ are on the same straight horizontal line as $$P$$. The distance from point $$R$$ to the base of the tower is $$12$$ meters. The angle of elevation from point $$R$$ to the top of the tower is $$30^\circ$$, and the angle of elevation from point $$S$$ to the top of the tower is $$60^\circ$$. What is the distance, in meters, between points $$R$$ and $$S$$?

   • $$12\sqrt{3}+4\sqrt{3}$$
   • $$12+4\sqrt{3}$$
   • $$4\sqrt{3}$$
   • $$16$$

2. The expression below is defined for all $$x\ne3$$.$$\frac{x^2-9}{x-3}-(x+5)$$Which of the following is equivalent to the expression above?

   • $$-5$$
   • $$x-5$$
   • $$-x+5$$
   • $$-2$$

3. A circle in the $$xy$$-plane has equation $$(x+4)^2+(y-1)^2=100$$ If a tangent line is drawn to the circle at the point $$(2,9)$$, what is the slope of the tangent line?

   • $$-\frac{3}{4}$$
   • $$-\frac{4}{3}$$
   • $$\frac{3}{4}$$
   • $$\frac{4}{3}$$

4. The function $$f$$ is defined by $$f(x)=-3x^2+18x-11$$ What is the maximum value of $$f$$?

   • $$11$$
   • $$16$$
   • $$27$$
   • $$45$$

5. A bacteria culture increases by $$30\%$$ during the first hour. During the second hour, the population increases by $$25\%$$ of the population at the end of the first hour. If the population after two hours is $$9750$$, what was the initial population?

   • $$5000$$
   • $$6000$$
   • $$6500$$
   • $$7500$$

6. A circle with center $$O$$ has radius $$8$$. Point $$P$$ lies outside the circle such that a tangent from $$P$$ touches the circle at point $$T$$. If $$OP=17$$, what is the length of $$PT$$?

   • $$8$$
   • $$15$$
   • $$17$$
   • $$19$$

7. The graph of the quadratic function $$y=x^2-6x+5$$ and the line $$y=kx-1$$ intersect at exactly one point. What is the value of $$k$$?

   • $$2$$
   • $$4$$
   • $$-6+2\sqrt{6}$$
   • $$8$$

8. A research company surveyed $$1,200$$ randomly selected adults. Of those surveyed, $$58\%$$ said they preferred online shopping over in-store shopping. The survey has a margin of error of $$3\%$$. Which of the following is the most reasonable conclusion?

   • Exactly $$58\%$$ of all adults prefer online shopping.
   • Between $$55\%$$ and $$61\%$$ of all adults likely prefer online shopping.
   • More than $$61\%$$ of all adults prefer online shopping.
   • Fewer than $$55\%$$ of all adults prefer online shopping.

9. The graph of $$y=g(x)$$ is shown above. If $$g(x)=f(3x+2)+4$$ for some linear function $$f$$, which equation defines $$f$$?

   • $$f(x)=x-3$$
   • $$f(x)=2x-4$$
   • $$f(x)=x-2$$
   • $$f(x)=2x-6$$

10. In triangle $$ABC$$, the measure of $$\angle BAC$$ is $$90^\circ$$. Point $$D$$ lies on side $$BC$$ such that $$AD$$ bisects $$\angle BAC$$. If $$AB=9$$ and $$AC=12$$, what is the length of $$AD$$?

    • $$36$$
    • $$\frac{2\sqrt{7}}{3}$$
    • $$\frac{36\sqrt{2}}{7}$$
    • $$\frac{7}{2}$$

11. In the equation $$(k^2-16)x+5k=(k-4)x+20$$, $$k$$ is a constant. If the equation has infinitely many solutions, what is the value of $$k$$?

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

12. A survey was conducted among $$240$$ students to determine their favorite school subject. The results are summarized below.If a randomly selected student prefers Science, what is the probability that the student is Female?

    • $$\frac{1}{3}$$
    • $$\frac{4}{13}$$
    • $$\frac{8}{13}$$
    • $$\frac{1}{2}$$

13. In the $$xy$$-plane, triangle $$ABC$$ has vertices at $$A=(0,15)$$, $$B=(-9,0)$$, and $$C=(9,0)$$. A horizontal line with equation $$y=k$$ intersects sides $$AB$$ and $$AC$$ at points $$D$$ and $$E$$, respectively, where $$0$$ < $$k$$ < $$15$$. If the area of $$\triangle ADE$$ is $$\frac{1}{9}$$ the area of $$\triangle ABC$$, what is the value of $$k$$?

    • 10

14. The population of a certain bacteria colony, in thousands, can be modeled by $$P(t)=40(1.08)^{t/2}$$ where $$t$$ is the time in hours. This function can be rewritten in the form $$P(t)=40\left(1+\frac{k}{100}\right)^t$$ where $$k$$ is a constant. What is the value of $$k$$, rounded to the nearest tenth?

    • 3.9

15. A manufacturing company produces two products, Product A and Product B. Each unit of Product A requires $$\frac{3}{4}$$ hour of cutting and $$\frac{1}{2}$$ hour of assembly. Each unit of Product B requires $$\frac{1}{2}$$ hour of cutting and $$\frac{3}{4}$$ hour of assembly. The company has at most $$180$$ cutting hours and $$180$$ assembly hours available each week. If the company produces at least $$120$$ units of Product A, what is the greatest possible number of Product B units that can be produced?

    • $$120$$
    • $$150$$
    • $$160$$
    • $$180$$

16. In the $$xy$$-plane, a parabola with equation $$y=a(x+2)^2+b$$ is tangent to the line $$y=-6x+1$$ where $$a$$ and $$b$$ are real constants and $$a\ne0$$. Which of the following equations must be true?

    • $$a(b-13)=-9$$
    • $$a(b+13)=-9$$
    • $$a(b-13)=9$$
    • $$a(b+1)=9$$

17. Line $$L$$ is defined by the equation $$Ax+4y=20$$ where $$A$$ is a constant. Line $$M$$ passes through the points $$(-3,8)$$ and $$(5,-4)$$. If line $$L$$ is perpendicular to line $$M$$, what is the value of $$A$$?

    • $$-\frac{8}{3}$$
    • $$-\frac{3}{2}$$
    • $$\frac{3}{2}$$
    • $$\frac{8}{3}$$

18. A rocket is launched from the top of a platform. The graph shows the height above the ground, $$h$$, in feet, of the rocket $$t$$ seconds after launch. What is the best interpretation of the point $$(4,25)$$ on the graph?

    • The rocket lands after $$25$$ seconds.
    • The rocket reaches a maximum height of $$25$$ feet after $$4$$ seconds.
    • The rocket is launched from an initial height of $$4$$ feet.
    • The rocket travels a total distance of $$25$$ feet.

19. $$y=x^2-6x+10$$$$y=|x-3|+2$$How many distinct $$(x,y)$$ solutions does the system have?

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

20. A streaming service charges a base monthly fee that includes the first $$15$$ GB of premium downloads. For every GB used beyond $$15$$ GB, an additional fee is charged. Customer A used $$25$$ GB and paid $$94$$. Customer B used $$40$$ GB and paid $$154$$. If Customer C used $$12$$ GB, what was the total charge?

    • $$46$$
    • $$50$$
    • $$54$$
    • $$58$$

21. The table below shows the distribution of a company's advertising budget across three platforms in $$2024$$, along with the projected increase in customer engagement for $$2025$$.Based on the information provided, what is the overall percentage increase in customer engagement from $$2024$$ to $$2025$$?

    • $$16.5\%$$
    • $$17.6\%$$
    • $$18.4\%$$
    • $$19.2\%$$

22. A circle has center $$O$$. Points $$A$$, $$B$$, and $$C$$ lie on the circle. The tangent line to the circle at point $$A$$ intersects the line containing chord $$BC$$ at point $$P$$. If $$\angle APB=40^\circ$$ and $$\angle ABC=60^\circ$$, what is the measure of $$\angle ACB$$?

    • $$50^\circ$$
    • $$60^\circ$$
    • $$70^\circ$$
    • $$80^\circ$$