Full Practice Exam 9 — Module 1

Questions in this quiz (22)

1. If $$6x-9=3x+18$$, what is the value of $$2x-5$$?

   • $$9$$
   • $$13$$
   • $$17$$
   • $$21$$

2. The function $$g$$ is defined by $$g(x)=3x^2-4x+7$$. What is the value of $$g(-2)$$?

   • $$11$$
   • $$19$$
   • $$27$$
   • $$31$$

3. The given equation relates the variables $$a$$, $$b$$, and $$c$$.$$\sqrt{a-2b}=c$$Which equation correctly expresses $$a$$ in terms of $$b$$ and $$c$$?

   • $$a=c^2-2b$$
   • $$a=c^2+2b$$
   • $$a=(c-2b)^2$$
   • $$a=\sqrt{c+2b}$$

4. In $$\triangle XYZ$$, the length of side $$\overline{XY}$$ is equal to the length of side $$\overline{YZ}$$. The measure of $$\angle X$$ is $$(4x-5)^\circ$$, and the measure of $$\angle Z$$ is $$(2x+25)^\circ$$. What is the measure of $$\angle Y$$?

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

5. A certain medicine decays such that the amount remaining after $$t$$ hours can be modeled by the function $$A(t)=A_0\left(\frac{1}{2}\right)^{t/h}$$, where $$A_0$$ is the initial amount and $$h$$ is the half-life in hours. If the initial amount is $$320$$ milligrams and after $$15$$ hours the amount remaining is $$40$$ milligrams, what is the half-life of the medicine, in hours?

   • $$3$$
   • $$5$$
   • $$6$$
   • $$10$$

6. The equation $$5x+3y=24$$ relates the variables $$x$$ and $$y$$. Which equation correctly expresses $$y$$ in terms of $$x$$?

   • $$y=-\frac{5}{3}x+8$$
   • $$y=\frac{5}{3}x-8$$
   • $$y=5x-24$$
   • $$y=-5x+8$$

7. The total cost $$C$$, in dollars, of joining a gym for $$m$$ months is modeled by the equation $$C=75+28m$$. What does the number $$28$$ represent in this context?

   • The one-time registration fee for the gym.
   • The total cost after $$28$$ months.
   • The monthly membership fee for the gym.
   • The maximum monthly cost of the gym.

8. The graphs of the equations $$y=x^2-6x+5$$ and $$y=5$$ intersect at the point $$(x,y)$$. What is a possible value of $$x$$?

   • $$-2$$
   • $$0$$
   • $$3$$
   • $$11$$

9. Which of the following expressions is equivalent to $$(2x+5)^2-(x-4)^2$$?

   • $$(x+1)(3x+9)$$
   • $$(x+9)(3x+1)$$
   • $$(3x+1)(x+9)$$
   • $$(4x+1)(x+9)$$

10. The height $$h$$, in feet, of a model rocket $$t$$ seconds after launch is modeled by the function $$h(t)=-16t^2+80t+12$$. What does the value $$h(0)=12$$ represent in this context?

    • The maximum height of the rocket is $$12$$ feet.
    • The rocket reaches the ground after $$12$$ seconds.
    • The initial height of the rocket when launched was $$12$$ feet.
    • The rocket rises $$12$$ feet every second.

11. A university researcher wants to estimate the percentage of all students on campus who support extending library hours. The researcher surveys $$40$$ students who are leaving the engineering building after a late-night study session, and $$34$$ students say they support extending library hours. Which of the following is the most appropriate conclusion?

    • About $$85\%$$ of all students at the university support extending library hours.
    • The results may not represent the entire university because the sample was not randomly selected.
    • Surveying $$40$$ students is always enough to generalize to the whole university.
    • All engineering students support extending library hours.

12. If the system of equations $$5x+2y=28$$ and $$2x+5y=31$$ has solution $$(x,y)$$, what is the value of $$x-y$$?

    • $$-1$$
    • $$1$$
    • $$3$$
    • $$5$$

13. The population of a species of fish in a lake is modeled by the function $$P(t)=1200(1.08)^t$$, where $$P(t)$$ is the population after $$t$$ years. What does the number $$1.08$$ represent in this function?

    • The initial population of fish in the lake.
    • The amount by which the population increases each year.
    • The factor by which the population is multiplied each year.
    • The percentage increase in the population over $$8$$ years.

14. A sector of a circle has a central angle of $$150^\circ$$ and an area of $$25\pi$$ square units. What is the circumference of the circle, in units?

    • $$2\pi\sqrt{10}$$
    • $$12\pi$$
    • $$4\pi\sqrt{15}$$
    • $$20\pi$$

15. A school district wanted to determine whether requiring students to complete daily online practice problems improves SAT math scores. Researchers randomly selected $$500$$ students from the district and randomly assigned half to complete daily online practice problems for $$4$$ months, while the other half did not complete the practice problems. At the end of the study, the students who completed the daily practice problems had significantly higher SAT math scores on average. Which of the following conclusions is most appropriate?

    • Completing daily online practice problems causes higher SAT math scores for students in this district.
    • Completing daily online practice problems guarantees higher SAT math scores for every student.
    • All students in the country will improve their SAT math scores by using daily online practice problems.
    • Students who naturally score higher are more likely to complete online practice problems.

16. A jacket was marked up by $$25\%$$. During a holiday sale, the store then offered a $$20\%$$ discount on the marked-up price. If the final sale price of the jacket was $$120$$, what was the original price of the jacket?

    • $$96$$
    • $$100$$
    • $$120$$
    • $$150$$

17. The graphs of the equations $$y=x^2-7x+10$$ and $$y=2x-5$$ intersect at two points in the $$xy$$-plane. What is the sum of the $$x$$-coordinates of these intersection points?

    • $$5$$
    • $$7$$
    • $$9$$
    • $$12$$

18. Let $$f$$ be a linear function. For every real number $$x$$, it is true that $$f(x+1)-f(x)=6$$. The graph of $$f$$ has an $$x$$-intercept of $$-2$$. What is the $$y$$-intercept of the graph of $$g(x)=f(x+3)$$?

    • 30

19. In right triangle $$RST$$, the measure of $$\angle T$$ is $$90^\circ$$. If $$\sin R=\frac{5}{13}$$, what is the value of $$\cos S$$?

    • $$\frac{5}{12}$$
    • $$\frac{12}{13}$$
    • $$\frac{5}{13}$$
    • $$\frac{13}{5}$$

20. In a circle with center $$O$$, $$\overline{AB}$$ is a diameter. Point $$C$$ is on the circle such that the measure of $$\angle CAB$$ is $$35^\circ$$. What is the measure, in degrees, of $$\angle COB$$?

    • $$35^\circ$$
    • $$55^\circ$$
    • $$70^\circ$$
    • $$110^\circ$$

21. A right triangle has a hypotenuse of length $$10$$ and an angle of $$60^\circ$$. What is the length of the leg opposite the $$60^\circ$$ angle?

    • $$5$$
    • $$5\sqrt{2}$$
    • $$5\sqrt{3}$$
    • $$10\sqrt{3}$$

22. The graph below represents a linear function. Which of the following equations represents the function shown?

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