Full Practice Exam 3 — Module 1

Questions in this quiz (22)

1. What are the solutions for $$x$$ and $$y$$ in the equations below?$$\frac{5}{6}x-3\left(y+\frac{1}{3}\right)=4$$$$\frac{1}{2}x=7+y$$

   • $$(\frac{1}{2},5)$$
   • $$(\frac{1}{2},-\frac{4}{3})$$
   • $$(\frac{5}{3},2)$$
   • $$(24,5)$$

2. If $$n$$ percent of $$50$$ is $$15$$, what is n percent of $$300$$?

   • $$15$$
   • $$30$$
   • $$50$$
   • $$90$$

3. $$(9x^{4}-24x^{3}y+16x^{2}y^{2})\div(3x^{2}-4xy)=?$$

   • $$x^{2}(3x-4y)$$
   • $$x(3x-4y)^{2}$$
   • $$x(3x-4y)$$
   • $$x^{2}(3x-4y)^{2}$$

4. The wind chill $$W$$ in degrees Fahrenheit is approximated by the formula:$$W=35.74+0.6215T-35.75V^{0.16}+0.4275TV^{0.16}$$where $$T$$ is the air temperature and $$V$$ is the wind speed (mph). A researcher makes the following claims:$$I$$. For a fixed temperature, each $$5$$ mph increase in wind speed decreases wind chill less at high wind speeds than at low wind speeds.$$II$$. For a fixed wind speed, wind chill increases linearly as temperature increases.$$III$$. When temperature is below $$0°$$F, increasing wind speed decreases wind chill more drastically than when temperature is above $$0°$$F.

   • $$I$$
   • $$I$$ and $$II$$
   • $$I$$ and $$III$$
   • $$I$$, $$II$$, and $$III$$

5. $$\frac{a^3-b^3+a^2b-ab^2+3ab^2-3a^2b}{a^2-b^2}$$equals which of the following, given that $$a\neq \pm b$$?

   • $$a+b$$
   • $$a-b$$
   • $$ab(a-b)$$
   • $$a^2-b^2$$

6. What is the vertex of the parabola $$(x-3)^{2}=-12(y+1)$$?

   • $$(-3,1)$$
   • $$(1,-3)$$
   • $$(3,-1)$$
   • $$(-1,3)$$

7. A construction inspector measures the lengths of four wooden boards as $$72$$ inches, $$65$$ inches, $$80$$ inches, and $$58$$ inches. Each measurement has a possible error of plus or minus $$3$$ inches. What is the possible range of the sum of the boards’ actual lengths, in inches?

   • $$255 ≤$$ total length $$≤ 295$$
   • $$260 ≤$$ total length $$≤ 300$$
   • $$275 ≤$$ total length $$≤ 315$$
   • $$290 ≤$$ total length $$≤ 330$$

8. Given that neither $$x$$ nor $$y$$ is equal to $$0$$ and that $$\frac{2}{5}x=3y,$$ what is the value of $$\frac{1}{20}\left(\frac{4x+5y}{y}\right)?$$

   • $$\frac{1}{20}$$
   • $$\frac{4}{5}$$
   • $$\frac{7}{4}$$
   • $$\frac{15}{2}$$

9. A photographer's total charge for an event is given by the formula: $$40h+p+150$$where $$h$$ is the number of hours the photographer works and $$p$$ is the cost of printing photos. What is the best interpretation of the number $$40$$ in the formula?

   • The photographer earns $$40000$$ dollars per year.
   • The photographer charges $$40$$ dollars for each printed photo.
   • The photographer charges $$40$$ dollars for each hour of work.
   • The printing cost represents $$40$$ percent of the total charge.

10. A recipe that yields $$8$$ cakes uses $$6$$ eggs, $$4$$ cups of flour, and $$10$$ cups of sugar. A bakery plans to make a batch of cakes using exactly $$15$$ eggs, keeping the ingredient ratios the same. After scaling the recipe, the baker realizes that $$2$$ cups of flour were spilled and cannot be replaced, but the sugar amount remains unchanged. How many cakes can the bakery make?

    • $$20$$
    • $$16$$
    • $$12$$
    • $$8$$

11. The following equations each involve a constant $$k$$. For which equation does there exist at least one value of $$k$$ such that the equation has no solution for $$x$$?

    • $$x=k-5$$
    • $$kx+4=4$$
    • $$\frac{k}{x}=k$$
    • $$3x=kx+6$$

12. In the $$xy$$-plane, what is the $$y$$-coordinate of the point of intersection of the graphs $$y=(x+2)^2$$ and $$y=3x+1$$?

    • $$-11$$
    • $$0$$
    • $$1$$
    • Does not exist

13. The rational function $$f$$ is defined by an equation of the form $$f(x)=\frac{a}{x-b},$$ where $$a$$ and $$b$$ are constants. The graph of $$y=f(x)$$ shows a vertical asymptote at $$x=-3$$. If a new function is defined by $$h(x)=f(x-2),$$ which of the following equations could define $$h(x)$$?

    • $$h(x)=\frac{a}{x-1}$$
    • $$h(x)=\frac{a}{x+5}$$
    • $$h(x)=\frac{a}{x-5}$$
    • $$h(x)=\frac{a}{x+1}$$

14. For two acute angles, $$\angle A$$ and $$\angle B$$, $$\sin(A)=\cos(B)$$. The measures, in degrees, of $$\angle A$$ and $$\angle B$$ are $$2x+18$$ and $$x+42$$, respectively. What is the value of $$x$$?

    • $$10$$
    • $$30$$
    • $$45$$
    • $$60$$

15. An isosceles right triangle has legs of equal length, and its hypotenuse measures $$42$$ inches. What is the perimeter, in inches, of this triangle?

    • $$21\sqrt{2}$$
    • $$21$$
    • $$42$$
    • $$42\sqrt{2}+42$$

16. To investigate variations in material density, samples of granite were collected from several locations and cut into the shape of a cube. The length of the edge of one of these cubes is $$4.000$$ centimeters. This cube has a density of $$2.70$$ grams per cubic centimeter. What is the mass of this cube, in grams?

    • $$32.8$$
    • $$40$$
    • $$64$$
    • $$172.8$$

17. A data set of $$31$$ distinct numbers has a mean of $$50$$ and a median of $$50$$. A new data set is created by adding $$10$$ to each number in the original data set that is greater than the median and subtracting $$10$$ from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and the new data sets?

    • Median
    • Mean
    • Range
    • Number of data values

18. The graph represents a linear function $$f(x)$$.Which of the following equations could represent $$f(x)$$?

    • $$f(x)-3=\frac{2}{3}x$$
    • $$f(x)+2=\frac{1}{2}x$$
    • $$f(x)+3=\frac{1}{2}x$$
    • $$f(x)+1=\frac{2}{5}x$$

19. The three points shown define a circle. The area of this circle is given by $$k\pi$$, where $$k$$ is a constant. What is the value of $$k$$?

    • $$3$$
    • $$6$$
    • $$9$$
    • $$12$$

20. Three lines $$n$$, $$p$$, and $$m$$ are shown in the diagram. What is the value of angle $$a$$?

    • $$60$$
    • $$85$$
    • $$95$$
    • $$35$$

21. The scatterplot shows the average hourly cost of gasoline, in dollars, every $$10$$ years between $$1950$$ and $$2020$$. What does the line of best fit predict about the total increase in the average cost of gasoline over the $$70$$-year period?

    • $$3.75$$
    • $$4$$
    • $$4.74$$
    • $$5$$

22. The table shows the results of a poll of $$600$$ voters.A total of $$600$$ voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if $$9000$$ people vote in the election, by how many votes would Jordan Lee be expected to win?

    • $$225$$
    • $$375$$
    • $$600$$
    • $$2250$$