Full Practice Exam 29 — Module 2

Questions in this quiz (22)

1. The table below shows three values of $$x$$ and their corresponding values of $$y$$. The linear relationship between $$x$$ and $$y$$ can be represented by an equation written in the form $$Ax+By=C,$$ where $$A,B,$$ and $$C$$ are constants. What is the value of $$\frac{A}{B}$$?

   • -2

2. A group loads money into an account to play arcade games. Each time they play a game, the same amount of money is deducted from the account. The function $$f(m)=25-4m$$ gives the amount of money, in dollars, left in the account after $$m$$ games have been played. Which of the following represents the amount of money, in dollars, deducted each time the group plays a game?

   • $$4m$$
   • $$4$$
   • $$25$$
   • $$25-4m$$

3. If $$\frac14y+7=10,$$ what is the value of $$4y$$?

   • $$16$$
   • $$24$$
   • $$36$$
   • $$48$$

4. A shopper has $$30$$ dollars to spend on pencils and notebooks. Each pencil costs $$1.50$$ dollars , and each notebook costs $$3.20$$ dollars . Let $$p$$ be the number of pencils and $$n$$ the number of notebooks. Which inequality shows how many items the shopper can buy?

   • $$1.5p+3.2n\le30$$
   • $$1.5p+3.2n\ge30$$
   • $$3.2p+1.5n\le30$$
   • $$3.2p+1.5n\ge30$$

5. In the equation $$25x^2+50x+c=0,$$ the graph of the parabola has exactly one real solution. What is the value of $$c$$?

   • $$15$$
   • $$20$$
   • $$25$$
   • $$30$$

6. Which of the following expressions is divisible by $$x+2$$?

   • $$4x^2+20x+24$$
   • $$4x^2+28x+24$$
   • $$4x^2+32x+24$$
   • $$4x^2+36x+24$$

7. The function $$f$$ is defined by the equation $$f(x)=(x-a)(x-b),$$ where $$a$$ and $$b$$ are integer constants. If $$f(2)$$ > $$0$$, $$f(5)$$ < $$0$$, and $$f(9)$$ > $$0$$, what is one possible value of $$a+b$$?

   • $$0$$
   • $$5$$
   • $$10$$
   • $$15$$

8. Which expression is equivalent to $$h(x)=\frac{3^{2x+1}}{9^{x-2}}$$ for $$x$$ > $$0$$?

   • $$3^5$$
   • $$3^{2x-1}$$
   • $$3^2$$
   • $$3^{2x+5}$$

9. Consider the exponential function $$f(x)=6^x$$. Let $$f(2)=k$$. Which of the following rewrites of $$f(x)$$ shows $$k$$ as a coefficient?

   • $$f(x)=(6^2)(6^x)$$
   • $$f(x)=36(6)^{x-2}$$
   • $$f(x)=(36)^x$$
   • $$f(x)=6^{x-2}$$

10. In the equation $$20|x-5|=m,$$ there is exactly one solution for $$x$$ if and only if which of the following is true about $$m$$?

    • $$m=-5$$
    • $$m=0$$
    • $$m=5$$
    • $$m=20$$

11. The equation $$x^2+y^2+2x+6y=-9$$ describes a circle in the $$xy$$-plane. What is the length of its radius?

    • $$0$$
    • $$1$$
    • $$2$$
    • $$3$$

12. The equation $$b^2+7c=12d$$ relates real numbers $$b,c,$$ and $$d$$. Which choice expresses $$b$$ in terms of $$c$$ and $$d$$?

    • $$b=\sqrt{12d-7c}$$
    • $$b=\frac{12d-7c}{b}$$
    • $$b=12d-7c$$
    • $$b=\frac{7c-12d}{b}$$

13. A real estate company offers a series of three webinars. $$5,000$$ people attended the first webinar. $$40\%$$ of the people who attended the first webinar attended the second webinar, and $$25\%$$ of the people who attended the first and second webinars attended the third webinar. How many people attended all three webinars?

    • 500

14. A science project tracked whether it rained on weekdays and weekend days for $$10$$ weeks, or $$70$$ days total. The results are summarized below. If one of the $$55$$ days on which there was no rain is selected at random, what is the probability that the day was a weekend day?

    • $$\frac2{11}$$
    • $$\frac3{11}$$
    • $$\frac17$$
    • $$\frac5{11}$$

15. The table shows the results of a poll. A total of $$900$$ voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if $$7,200$$ people vote in the election, by how many votes would Vanessa Cruz be expected to win?

    • $$176$$
    • $$956$$
    • $$1,248$$
    • $$2,816$$

16. The dot plots show data set A and data set B. Which of the following statements must be true? I. The median of data set A is equal to the median of data set B. II. The standard deviation of data set A is equal to the standard deviation of data set B.

    • I only
    • II only
    • I and II
    • Neither I nor II

17. A study was done on the weights of different types of fish in a lake. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained $$200$$ largemouth bass, of which $$25\%$$ weighed more than $$3$$ pounds. Which of the following conclusions is best supported by these sample data?

    • The majority of all fish in the lake weigh less than $$3$$ pounds.
    • The average weight of all fish in the lake is approximately $$3$$ pounds.
    • Approximately $$25\%$$ of all fish in the lake weigh more than $$3$$ pounds.
    • Approximately $$25\%$$ of all largemouth bass in the lake weigh more than $$3$$ pounds.

18. In the figure shown, line $$r$$ is parallel to line $$s$$, and both lines are intersected by line $$m$$. If $$x=3k+18$$, $$y=6k+30$$, and $$9k=a$$, where $$a$$ is a constant, what is the value of $$a$$?

    • 132

19. A rectangular circuit board is divided into $$270$$ square regions. Each of these regions has a length of $$L$$ units. The length of the circuit board is $$1.2$$ times its width. If the width of the circuit board is $$Lx$$ units, what is the value of $$x$$?

    • 15

20. In triangle $$QRS$$ and triangle $$TUV$$, the measures of angles $$R$$ and $$U$$ are each $$45^\circ$$. The lengths of $$RS$$ and $$UV$$ are each $$12$$ meters, and $$\frac{RS}{RQ}=\frac{UV}{TU}.$$ Which additional piece of information would be necessary to prove that triangle $$QRS$$ is congruent to triangle $$TUV$$?

    • The lengths of $$QR$$ and $$TV$$ are each $$9$$ meters.
    • The measures of angles $$S$$ and $$V$$ are each $$60^\circ$$.
    • The measures of angles $$Q$$ and $$T$$ are each $$90^\circ$$.
    • No additional information is necessary.

21. There are $$640$$ acres in $$1$$ square mile. The area of a forest is increasing at a rate of $$1$$ acre per decade. Which of the following is closest to the rate at which the area of the forest is increasing, in square kilometers per decade? Use $$1$$ kilometer $$=0.62$$ mile.

    • $$0.0006$$
    • $$0.0010$$
    • $$0.0025$$
    • $$0.0041$$

22. Rectangle $$ABCD$$ is similar to rectangle $$WXYZ$$. The area of rectangle $$ABCD$$ is $$486$$ square units, and the area of rectangle $$WXYZ$$ is $$54$$ square units. The length of the longest side of rectangle $$ABCD$$ is $$27$$ units. What is the length, in units, of the longest side of rectangle $$WXYZ$$?

    • $$6$$
    • $$9$$
    • $$12$$
    • $$18$$