Full Practice Exam 20 — Module 1

Questions in this quiz (22)

1. A line in the $$xy$$-plane has slope $$\frac{5}{3}$$ and passes through the point $$(6,4)$$. Which of the following equations defines the line?

   • $$5x-3y=18$$
   • $$3x-5y=2$$
   • $$y=\frac{5}{3}x+4$$
   • $$y=\frac{3}{5}x-2$$

2. The functions $$f$$ and $$g$$ are defined by $$f(x)=5x+12$$ and $$g(x)=3x-4$$, respectively. What is the value of $$f(g(x))$$ when $$x=4$$?

   • $$52$$
   • $$48$$
   • $$56$$
   • $$44$$

3. A fair coin is tossed once and a fair $$8$$-sided die numbered $$1$$ through $$8$$ is rolled once. What is the probability of obtaining tails and rolling a $$5$$?

   • $$\frac{1}{8}$$
   • $$\frac{1}{16}$$
   • $$\frac{1}{10}$$
   • $$\frac{1}{4}$$

4. In the equation $$7x+12=7nx+3m$$, $$m$$ and $$n$$ are constants. If the equation has infinitely many solutions, what is the value of $$m+n$$?

   • 5

5. A young tree grows at a rate of $$20$$ cm per year for the first two years. After that, the growth rate decreases by $$20\%$$ each year. What is the total growth of the tree at the end of the fourth year?

   • $$72.8\text{ cm}$$
   • $$64\text{ cm}$$
   • $$52.8\text{ cm}$$
   • $$68.8\text{ cm}$$

6. A train travels at a constant speed of $$180$$ yards per minute. How many kilometers does it travel in $$4$$ hours?$$1$$ meter $$=1.09361$$ yards

   • $$27.4$$
   • $$39.5$$
   • $$42.7$$
   • $$45.6$$

7. A bookstore sells notebooks for $$2$$ dollars each and pens for $$1$$ each. One day, the store sells a total of $$150$$ items and earns $$220$$. Which system of equations represents the situation if $$N$$ is the number of notebooks and $$P$$ is the number of pens?

   • $$N+P=150$$ $$2N+P=220$$
   • $$N-P=150$$ $$2N+P=220$$
   • $$N+P=220$$ $$2N+P=150$$
   • $$N+P=150$$$$N+2P=220$$

8. Given the system:$$3y=2x+8$$$$y=x-4$$If the solution is $$(a,b)$$, what is the value of $$b$$?

   • 16

9. The length of a side of a square is $$s$$. If the area of the square is $$A=s^2$$, which statement must be true?

   • The perimeter is $$2s$$.
   • The diagonal is $$s$$.
   • The perimeter is $$4s$$.
   • The area is $$4s^2$$.

10. The function $$P_N=500\cdot2^N$$ models the population of bacteria after $$N$$ doublings. According to the model, how many bacteria were present initially?

    • $$1000$$
    • $$500$$
    • $$250$$
    • $$2$$

11. A car gets $$30$$ miles per gallon on the highway and $$20$$ miles per gallon in the city. A driver begins with $$15$$ gallons of gas. After driving $$60$$ miles in the city, the driver continues on the highway. Which function represents the gallons of gas remaining after driving $$d$$ miles on the highway?

    • $$R(d)=12-\frac{d}{30}$$
    • $$R(d)=15-\frac{d}{20}$$
    • $$R(d)=12+\frac{d}{30}$$
    • $$R(d)=15-\frac{d}{30}$$

12. If the slope of the graph of $$y=\frac{1}{3}(6x+9)+kx$$ is $$\frac{11}{3}$$, what is the value of $$k$$?

    • $$\frac{1}{3}$$
    • $$\frac{2}{3}$$
    • $$\frac{5}{3}$$
    • $$\frac{7}{3}$$

13. The population of a town can be modeled linearly. In $$2000$$, the population was $$80$$ thousand. In $$2008$$, the population was $$64$$ thousand. Using the model, what is the estimated population, in thousands, in $$2020$$?

    • 40

14. Consider the system:$$y=x^2-4x+1$$$$y=x+b$$Where $$b\ne0$$. If the system has real solution(s), what is the minimum integer value of $$b$$?

    • -5

15. The function $$f(x)=(x-5)^2+9$$ is a quadratic function. How many points of intersection does its graph have with the $$x$$-axis?

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

16. The graph of $$(x-4)^2+(y+3)^2=81$$ is a circle. If $$(a,b)$$ is a point on the circle and $$a$$ can equal $$13$$, what is the value of the $$x$$-coordinate of the center?

    • $$-4$$
    • $$4$$
    • $$9$$
    • $$13$$

17. A school surveyed $$280$$ male students and $$320$$ female students. The results are shown below.Given that a selected student is female, what is the probability that she does not exercise regularly?

    • $$\frac{5}{16}$$
    • $$\frac{5}{8}$$
    • $$\frac{3}{8}$$
    • $$\frac{7}{16}$$

18. The function $$f(x)=4x^2+kx+2$$ has an $$x$$-coordinate of the vertex equal to $$2-k$$. What is the value of $$k$$?

    • $$-16$$
    • $$-\frac{10}{7}$$
    • $$0$$
    • $$\frac{16}{7}$$

19. If $$18-4x\ge-10$$, what is the maximum value of $$x$$?

    • 7

20. In the figure above, a circle is tangent to the sides of equilateral triangle $$PQR$$ and the radius $$r$$ equals $$5$$. What is the perimeter of $$\triangle PQR$$?

    • $$20$$
    • $$30\sqrt{3}$$
    • $$35$$
    • $$40\sqrt{2}$$

21. The circle graph above shows the results of a vote for favorite professors in JFK University. If $$800$$ votes were cast, how many possible numbers of votes did Professor Lee receive?

    • $$150$$
    • $$200$$
    • $$250$$
    • $$400$$

22. In the figure above, the area of $$\triangle ABD$$ is $$16$$ and the area of $$\triangle BCD$$ is $$9$$. What is the ratio of the length of $$AD$$ to the length of $$DC$$?

    • $$2:1$$
    • $$3:1$$
    • $$4:3$$
    • $$16:9$$