Full Practice Exam 4 — Module 2

Questions in this quiz (22)

1. What are the values of $$y$$ that satisfy these conditions?$$x=y^2-4y-5$$$$3x=27$$

   • $$2$$, $$3$$
   • $$3\sqrt{2}$$, $$-3\sqrt{2}$$
   • $$2+3\sqrt{2}$$, $$2-3\sqrt{2}$$
   • $$2\sqrt{2}$$, $$-2\sqrt{2}$$

2. Whenever Sofia practices piano, she spends $$12$$ minutes arranging her sheet music and warming up before she begins. After warming up, she can fully practice one song every $$4$$ minutes. Assuming Sofia practices for more than $$12$$ minutes total, which expression gives the total number of songs s she can practice in $$t$$ minutes?

   • $$\frac{t-12}{4}$$
   • $$\frac{t+12}{14}$$
   • $$\frac{t-4}{12}$$
   • $$4t+12$$

3. How many solutions does the equation below have?$$7x-2y=41$$

   • Exactly 1
   • Exactly 2
   • None
   • Infinite

4. A museum will close an exhibit early if the number of visitors in attendance is fewer than $$25$$. Which expression represents the range of visitors $$V$$ needed for the exhibit to remain open, assuming $$V$$ is a whole integer?

   • $$V\le25$$
   • $$V$$ < $$25$$
   • $$V\ge25$$
   • $$V$$ > $$25$$

5. What is a possible value for x in the inequality below?$$-12$$ < $$\frac{5}{2} x$$ < $$3$$

   • $$-5$$
   • $$2$$
   • $$3$$
   • $$0$$

6. If the line given by the equation $$y=-3x+5$$ is reflected across the y-axis, which graph describes the resulting function?

   • A line with negative slope, passing through the point $$(0,5)$$ and going downward left-to-right.
   • A line with positive slope passing through $$(0,5)$$ and going upward left-to-right.
   • A line with positive slope, passing through the point $$(0,−5)$$ and going upward left-to-right.
   • A horizontal line crossing the y-axis at $$y=5$$.

7. What is the solution(s) for $$x$$ in this equation?$$\frac{20}{\sqrt[3]{x}}=5$$

   • $$64$$ only
   • $$-8$$ and $$8$$
   • $$-1$$ and $$125$$
   • $$125$$ only

8. How many solution(s) does this system of equations have$$3a-6b=12$$$$a-2b=4$$

   • $$1$$
   • $$2$$
   • No solutions
   • Infinitely many solutions

9. A computer randomly selects integers from $$1$$ to $$100$$ inclusive. Two experiments are conducted.Experiment $$A$$ selects $$20$$ numbers.Experiment $$B$$ selects $$200$$ numbers.After each experiment, the range of the selected numbers is recorded. Which statement best describes the expected relationship between the ranges of the two experiments?

   • The range from Experiment $$A$$ is expected to be larger.
   • The range from Experiment $$B$$ is expected to be larger.
   • The ranges are expected to be about the same.
   • It is impossible to predict which range will be larger.

10. Which of the following equations when combined with $$6x=3y+12$$ will result in a system of equations that has no solution?

    • $$y=2x-4$$
    • $$y=2x+10$$
    • $$y=-3x+12$$
    • $$y=2x-8$$

11. The amount of money $$A$$ in an investment account after a principal amount $$P$$ is invested for $$t$$ years at an annual interest rate $$r$$ compounded $$n$$ times per year is modeled by:$$A=P(1+\frac{r}{n})^{nt}$$A financial analyst wants to determine which variables if maximized would cause the account to earn the greatest amount of interest. Which of the variables $$P, r, n,$$ and $$t$$ if increased would cause the interest earned to increase?

    • $$P, r, n, t$$
    • $$P, r, n$$ only
    • $$P, r$$ only
    • $$P$$ only

12. In a certain right triangle the sine of angle $$B$$ is $$\frac{7}{25}$$ and the cosine of angle $$B$$ is $$\frac{24}{25}$$. What is the ratio of the shortest side of the triangle to the median to the hypotenuse?

    • $$\frac{25}{7}$$
    • $$\frac{7}{25}$$
    • $$\frac{14}{25}$$
    • $$\frac{18}{25}$$

13. If $$x$$ > $$0$$ and $$x^{2}-8x=9$$ what is the value of $$x-4$$?

    • $$-1$$
    • $$5$$
    • $$9$$
    • $$-5$$

14. If a set of $$30$$ different numbers has its five smallest and five largest values removed, how will that most likely affect the standard deviation of the remaining set?

    • It will increase.
    • It will decrease.
    • It will remain the same
    • Not known

15. What will happen to the graph of the function $$f(x)=3x^2+12,$$ if it is transformed into the function $$g(x)=3(x+4)^2-6?$$

    • The graph shifts right $$4$$ units and down $$18$$ units.
    • The graph shifts left $$18$$ units and down $$4$$ units.
    • The graph shifts left $$18$$ units and up $$4$$ units.
    • The graph shifts left $$4$$ units and down $$18$$ units.

16. Nina is buying supplies for her younger sibling's birthday party. She has a total budget of at most $$180$$ dollars. She buys a balloon pack for $$15$$ dollars, a decoration kit for $$30$$ dollars, and a custom cake topper for $$45$$ dollars. For the party favors, she wants to buy small toy bags that cost $$0.50$$ dollars each. If $$T$$ represents the number of toy bags she can buy, what inequality represents the possible number of toy bags Nina can purchase while staying within her budget?

    • $$0.50T\le180$$
    • $$0.50T+90\le180$$
    • $$90T+0.50\le180$$
    • $$90T+0.50\le18$$

17. What is the surface area, in square units, of a right rectangular prism with edges of $$3$$ units, $$5$$ units, and $$7$$ units?

    • $$15$$
    • $$21$$
    • $$35$$
    • $$142$$

18. Which of the following could be a value of $$x$$ in this equation?$$6x^2=-18x+3$$$$I$$. $$-1+\frac{\sqrt7}{2}$$$$II$$. $$\frac{-3-\sqrt{15}}{6}$$$$III$$. $$\frac{\sqrt7-1}{3}$$

    • $$I$$
    • $$I$$ and $$III$$
    • $$II$$
    • None of the above

19. A botanist is studying the growth of a rare vine. She records that $$3$$ months after planting, the vine is $$7$$ inches tall. At 9 months after planting, the vine is $$19$$ inches tall. She also observes that the vine has been growing at a constant rate since being planted. The vine's height is modeled by $$H(t)=mt+b.$$ According to this model, at approximately how many months after planting will the vine first reach a height of $$40$$ inches?

    • $$18$$
    • $$20$$
    • $$21$$
    • $$25$$

20. A landscape architect is designing a rectangular garden for a client. The client owns a fixed amount of edging material, which will be used to surround the garden. The edging is straight and can be joined only at right angles. All of the edging must be used. If the architect wants to maximize the area of the garden while using all of the available edging, what should be the relationship between the garden's length $$L$$ and width $$W$$?

    • $$L=W$$
    • $$L=2W$$
    • $$L=W^2$$
    • $$W=\frac{L}{3}$$

21. The table shows the number of international tourist arrivals, in millions, to the top nine tourist destinations in $$2016$$ and $$2017$$.Based on the information given in the table, how much greater, in millions, was the median number of international tourist arrivals in $$2017$$ than the median number in $$2016$$, to the nearest tenth of a million?

    • $$5.9$$
    • $$6.7$$
    • $$7.5$$
    • $$8.6$$

22. A city introduces a new local tax structure for single residents, based on the following brackets:If Amira earns $$11000$$ dollars in taxable income, what is the total amount of local tax she would pay under this system?

    • $$1100$$
    • $$1800$$
    • $$3080$$
    • $$3600$$