Full Practice Exam 3 — Module 2

Questions in this quiz (22)

1. A cubic function $$f(x)$$ has zeros at $$x=-\frac{1}{2}$$, $$x=\frac{4}{3}$$, and $$x=5$$. It can be written in factored form as $$f(x)=k(2x+1)(3x-4)(x-5),$$ where k is a nonzero constant. When $$f(x)$$ is written in standard form $$f(x)=ax^{3}+bx^{2}+cx+d,$$ the coefficient of $$x^{2}$$ is $$7$$. What is the value of $$k$$?

   • $$\frac{1}{35}$$
   • $$-\frac{1}{7}$$
   • $$-\frac{1}{5}$$
   • $$-\frac{4}{5}$$

2. The graph of the function $$f(x)=x^{2}$$ is transformed into the graph of $$g(x)=-3(x-5)^{2}+12$$. Which sequence of transformations maps the graph of $$f(x)$$ to the graph of $$g(x)$$?

   • Shift right $$5$$ units, stretch vertically by a factor of $$3$$, reflect across the $$x$$-axis, then shift up $$12$$ units.
   • Shift left $$5$$ units, reflect across the $$x$$-axis, stretch vertically by a factor of $$3$$, then shift up $$12$$ units.
   • Reflect across the $$x$$-axis, shift right $$5$$ units, shift up $$12$$ units, then stretch vertically by a factor of $$3$$.
   • Stretch vertically by a factor of $$3$$, shift right $$5$$ units, reflect across the $$y$$-axis, then shift down $$12$$ units.

3. The supply for a certain product at a varying price $$p$$ is given by $$s(p)=4p+5p^2.$$ The demand for the same product at price $$p$$ is $$d(p)=200-10p.$$ At what price are the supply and demand equal? (Round to the nearest whole number)

   • 3
   • 4
   • 5
   • 8

4. If $$x$$ and y are variables and $$k$$ is a nonzero constant, which of the following equations would not necessarily have a $$y$$ intercept when graphed?$$I$$. $$x=-k$$$$II$$. $$y=k$$$$III$$. $$y=kx+k$$

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

5. $$3x+2y=11$$$$3x-2y=7$$In the system of equations above, what is the value of $$6x$$?

   • $$6$$
   • $$12$$
   • $$18$$
   • $$24$$

6. What is the closest integer value of $$x$$ that satisfies the inequality $$\frac{3+2x}{4}+\frac{x+1}{2}\le-1$$?

   • $$-6$$
   • $$-5$$
   • $$-4$$
   • $$-3$$

7. A factory worker packages boxes and crates at a constant pace. The worker packages $$150$$ boxes per hour and $$30$$ crates per hour, simultaneously. If the worker works for a total of $$h$$ hours, which expression represents the total number of items, boxes and crates, packaged during that time?

   • $$180h$$
   • $$150h+30$$
   • $$180h+150$$
   • $$150h-30$$

8. For what value of $$k$$ does the equation below have no solution?$$3(2x-k)+4=2(x+5)+kx$$

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

9. Elena filled her car's $$16$$ gallon gas tank completely. The gas pump shows that she paid $$45$$ dollars for the gas, and the price was $$3$$ dollars per gallon. How many gallons of gas were already in Elena's tank before she started filling it?

   • $$1$$
   • $$3$$
   • $$5$$
   • $$10$$

10. Which of the following equations correctly represents the functional relationship described below?Take an input value, multiply it by $$3$$, then add $$7$$ to the result.

    • $$f(x)=3(x+7)$$
    • $$f(x)=10x$$
    • $$f(x)=3x+7$$
    • $$f(x)=\frac{3x}{7}$$

11. A line is given by the equation $$3x-2y=6$$. Which of the following equations represents a line that is parallel to the given line and passes through the point $$(4,-1)$$?

    • $$6x-2y=20$$
    • $$3x-2y=10$$
    • $$3x-2y=14$$
    • $$6x+3y=5$$

12. A certain radioactive substance has a half-life of $$12$$ years. The function $$m(t)=160(0.5)^{t/12},$$ gives the approximate mass of the substance, in grams, that remains $$t$$ years after a $$160$$-gram sample begins to decay. Which statement best interprets $$m(36)=20$$ in this context?

    • Approximately $$20$$ grams of the substance remains $$36$$ years after the sample begins to decay.
    • The mass of the substance has decreased by approximately $$20$$ grams $$36$$ years after the sample begins to decay.
    • Approximately $$36$$ grams of the substance remains $$20$$ years after the sample begins to decay.
    • The mass of the substance has decreased by approximately $$36$$ grams $$20$$ years after the sample begins to decay.

13. The function $$h$$ is defined by $$h(x)=4\left(x-\frac{3}{4}\right)^2+\frac{5}{2}.$$ What is the value of $$h\left(\frac{3}{4}\right)$$?

    • $$\frac{3}{2}$$
    • $$\frac{3}{4}$$
    • $$\frac{5}{2}$$
    • $$\frac{4}{3}$$

14. Triangles $$ABC$$ and $$DEF$$ are congruent, where $$A,B,C$$ correspond to $$D,E,F$$ respectively. The measure of angle $$A$$ is $$38$$ degrees, and the measure of angle $$B$$ is $$47$$ degrees. What is the measure, in degrees, of angle $$E$$?

    • $$38$$
    • $$47$$
    • $$65$$
    • $$95$$

15. In the right triangle shown, $$\angle C$$ is a right angle. The length of side $$BC$$ is $$21$$, and the length of the hypotenuse $$AB$$ is $$85$$. What is the value of $$\sin A$$?

    • $$21$$
    • $$\frac{21}{85}$$
    • $$\frac{8\sqrt{105}}{85}$$
    • $$85$$

16. The lengths of the legs of a right triangle are $$5$$ and $$12$$ units long. Which of the following is the length of the triangle’s hypotenuse?

    • $$49$$
    • $$25$$
    • $$16$$
    • $$13$$

17. The dimensions of a right rectangular prism are $$3$$ centimeters by $$7$$ centimeters by $$10$$ centimeters. What is the surface area, in square centimeters, of the prism?

    • $$21$$
    • $$30$$
    • $$70$$
    • $$242$$

18. At a science fair, the ratio of judges to participants is $$2$$ to $$15$$. If there are $$x$$ judges at the science fair, which of the following expressions represents the number of participants at the fair?

    • $$\frac{15}{2}x$$
    • $$2x+15$$
    • $$\frac{2}{15}x$$
    • $$15x$$

19. In a national election, four political parties received the following percentages of the total vote:A post-election survey showed the following:Women provided $$70\%$$ of the votes for the Green Alliance and Progressive Party combined. Men and women each made up $$50\%$$ of all voters. If the total number of voters was $$10$$ million, what is the number of men who voted for both the Green Alliance and Progressive Party?

    • $$1,050,000$$
    • $$2,450,000$$
    • $$3,500,000$$
    • $$5,000,000$$

20. The scatterplot shows ice cream sales, in dollars, at different temperatures, in degrees Celsius. A line of best fit is drawn through the data. Based on the line of best fit, which of the following is the best estimate of the increase in ice cream sales, in dollars, for each $$1^\circ C$$ increase in temperature?

    • $$34$$
    • $$40$$
    • $$42$$
    • $$45$$

21. The table summarizes the distribution of grade level and assigned team for $$72$$ students in a school program.One of these students will be selected at random. What is the probability of selecting a student from Team $$X$$, given that the student is in Grade $$7$$ or Grade $$8$$?

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

22. The graph shows the momentum, in newton-seconds, of an object as a function of time, in seconds. Which of the following statements is best supported by the graph?

    • The object’s momentum increases at a constant rate throughout the entire time interval.
    • The object’s momentum increases most rapidly between 0 and 2 seconds.
    • The object’s momentum decreases between 2 and 4 seconds and then increases.
    • The object’s momentum remains constant between 6 and 8 seconds.