Full Practice Exam 20 — Module 2

Questions in this quiz (39)

1. Which of the following equations is equivalent to $$\frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-2}{9}=2$$?

   • $$6\left(\frac{x}{2}-\frac{1}{6}\right)-2(3x-2)=36$$
   • $$3(x-1)-(3x-2)=18$$
   • $$\frac{x}{6}-\frac{1}{18}-\frac{x}{3}+\frac{2}{9}=2$$
   • $$\frac{3x-1}{18}+\frac{3x-2}{9}=2$$

2. Which of the following equations is equivalent to $$\frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-2}{9}=2$$?

   • $$6\left(\frac{x}{2}-\frac{1}{6}\right)-2(3x-2)=36$$
   • $$3(x-1)-(3x-2)=18$$
   • $$\frac{x}{6}-\frac{1}{18}-\frac{x}{3}+\frac{2}{9}=2$$
   • $$\frac{3x-1}{18}+\frac{3x-2}{9}=2$$

3. Which of the following equations is equivalent to $$\frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-2}{9}=2$$?

   • $$6\left(\frac{x}{2}-\frac{1}{6}\right)-2(3x-2)=36$$
   • $$3(x-1)-(3x-2)=18$$
   • $$\frac{x}{6}-\frac{1}{18}-\frac{x}{3}+\frac{2}{9}=2$$
   • $$\frac{3x-1}{18}+\frac{3x-2}{9}=2$$

4. Emily needs to buy $$28$$ muffins for a school event. A single muffin costs $$0.75$$ dollars, a box of $$8$$ muffins costs $$5$$ dollars, and a box of $$15$$ muffins costs $$8$$ dollars. What is the least amount of money needed to purchase at least $$28$$ muffins?

   • $$14$$
   • $$15$$
   • $$16$$
   • $$17$$

5. Emily needs to buy $$28$$ muffins for a school event. A single muffin costs $$0.75$$ dollars, a box of $$8$$ muffins costs $$5$$ dollars, and a box of $$15$$ muffins costs $$8$$ dollars. What is the least amount of money needed to purchase at least $$28$$ muffins?

   • $$16$$
   • $$15$$
   • $$14$$
   • $$13$$

6. Emily needs to buy $$28$$ muffins for a school event. A single muffin costs $$0.75$$ dollars, a box of $$8$$ muffins costs $$5$$ dollars, and a box of $$15$$ muffins costs $$8$$ dollars. What is the least amount of money needed to purchase at least $$28$$ muffins?

   • $$16$$
   • $$15$$
   • $$14$$
   • $$13$$

7. $$4x+y=8$$$$ax+2y=c$$If the system has no solution, which of the following must be true?

   • $$a=8\text{ and }c=16$$
   • $$a=8\text{ and }c=10$$
   • $$a=-8\text{ and }c=16$$
   • $$a=4\text{ and }c=8$$

8. Given the system $$4x+y=8$$ $$ax+2y=c$$ If the system has no solution, which of the following must be true?

   • $$a=8\text{ and }c=16$$
   • $$a=8\text{ and }c=10$$
   • $$a=-8\text{ and }c=16$$
   • $$a=4\text{ and }c=8$$

9. There are $$x$$ boys and $$y$$ girls in a classroom. If three boys leave the classroom and two girls enter, what fraction of the students remaining are boys?

   • $$\frac{x-3}{x+y-1}$$
   • $$\frac{x+2}{x+y-1}$$
   • $$\frac{x-3}{y+x+2}$$
   • $$\frac{x+3}{x+y-1}$$

10. Given the system $$4x+y=8$$ $$ax+2y=c$$ If the system has no solution, which of the following must be true?

    • $$a=8\text{ and }c=16$$
    • $$a=8\text{ and }c=10$$
    • $$a=-8\text{ and }c=16$$
    • $$a=4\text{ and }c=8$$

11. There are $$x$$ boys and $$y$$ girls in a classroom. If three boys leave the classroom and two girls enter, what fraction of the students remaining are boys?

    • $$\frac{x-3}{x+y-1}$$
    • $$\frac{x+2}{x+y-1}$$
    • $$\frac{x-3}{y+x+2}$$
    • $$\frac{x+3}{x+y-1}$$

12. There are $$x$$ boys and $$y$$ girls in a classroom. If three boys leave the classroom and two girls enter, what fraction of the students remaining are boys?

    • $$\frac{x-3}{x+y-1}$$
    • $$\frac{x+2}{x+y-1}$$
    • $$\frac{x-3}{y+x+2}$$
    • $$\frac{x+3}{x+y-1}$$

13. Forty liters of a $$30\%$$ salt solution is mixed with another $$40$$ liters of a solution with concentration $$x\%$$. If the resulting $$80$$-liter mixture has a concentration between $$20\%$$ and $$25\%$$, which of the following could represent the possible values of $$x$$?

    • $$10\%\le x\le20\%$$
    • $$15\%\le x\le25\%$$
    • $$10\%\le x$$ < $$25\%$$
    • $$15\%\le x$$ < $$20\%$$

14. Forty liters of a $$30\%$$ salt solution is mixed with another $$40$$ liters of a solution with concentration $$x\%$$. If the resulting $$80$$-liter mixture has a concentration between $$20\%$$ and $$25\%$$, which of the following could represent the possible values of $$x$$?

    • $$10\%\le x\le20\%$$
    • $$15\%\le x\le25\%$$
    • $$10\%<x\le20\%$$
    • $$10\%\le x<20\%$$

15. There are $$2000$$ residents in a town. Among them, $$1100$$ like soccer, $$700$$ like basketball, and $$300$$ like both sports. How many residents like neither sport?

    • $$400$$
    • $$500$$
    • $$600$$
    • $$700$$

16. Forty liters of a $$30\%$$ salt solution is mixed with another $$40$$ liters of a solution with concentration $$x\%$$. If the resulting $$80$$-liter mixture has a concentration between $$20\%$$ and $$25\%$$, which of the following could represent the possible values of $$x$$?

    • $$10\%\le x\le20\%$$
    • $$15\%\le x\le25\%$$
    • $$10\%<x\le20\%$$
    • $$10\%\le x<20\%$$

17. There are $$2000$$ residents in a town. Among them, $$1100$$ like soccer, $$700$$ like basketball, and $$300$$ like both sports. How many residents like neither sport?

    • $$500$$
    • $$400$$
    • $$600$$
    • $$700$$

18. The remainder when $$x$$ is divided by $$5$$ is $$3$$. What is the remainder when $$x^2+2x+4$$ is divided by $$5$$?

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

19. There are $$2000$$ residents in a town. Among them, $$1100$$ like soccer, $$700$$ like basketball, and $$300$$ like both sports. How many residents like neither sport?

    • $$500$$
    • $$400$$
    • $$600$$
    • $$700$$

20. A chemist needs $$12$$ liters of a solution containing $$35\%$$ salt. She mixes a $$20\%$$ salt solution with a $$50\%$$ salt solution. How many liters of the $$20\%$$ solution are needed?

    • $$4$$
    • $$5$$
    • $$6$$
    • $$7$$

21. The remainder when $$x$$ is divided by $$5$$ is $$3$$. What is the remainder when $$x^2+2x+4$$ is divided by $$5$$?

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

22. The remainder when $$x$$ is divided by $$5$$ is $$3$$. What is the remainder when $$x^2+2x+4$$ is divided by $$5$$?

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

23. A chemist needs $$12$$ liters of a solution containing $$35\%$$ salt. She mixes a $$20\%$$ salt solution with a $$50\%$$ salt solution. How many liters of the $$20\%$$ solution are needed?

    • $$4$$
    • $$5$$
    • $$6$$
    • $$7$$

24. A chemist needs $$12$$ liters of a solution containing $$35\%$$ salt. She mixes a $$20\%$$ salt solution with a $$50\%$$ salt solution. How many liters of the $$20\%$$ solution are needed?

    • $$4$$
    • $$5$$
    • $$6$$
    • $$7$$

25. The center of a circle is $$(0,0)$$, and the point $$(5,-2)$$ lies on the circle. What are the coordinates of the point symmetric to $$(5,-2)$$ with respect to the $$x$$-axis?

    • $$(4,2)$$
    • $$(-5,2)$$
    • $$(-5,-2)$$
    • $$(5,2)$$

26. The graph of a parabola passes through $$(-2,0)$$, $$(4,0)$$, and $$(0,8)$$. Which of the following could be its equation?

    • $$f(x)=-x^2+2x+8$$ $$f(x)=x^2-2x+8$$
    • $$f(x)=-x^2+2x+8$$
    • $$f(x)=-x^2+4x+8$$
    • $$f(x)=x^2+2x-8$$

27. The center of a circle is $$(0,0)$$, and the point $$(5,-2)$$ lies on the circle. What are the coordinates of the point symmetric to $$(5,-2)$$ with respect to the $$x$$-axis?

    • $$(5,2)$$
    • $$(-5,2)$$
    • $$(-5,-2)$$
    • $$(2,5)$$

28. The center of a circle is $$(0,0)$$, and the point $$(5,-2)$$ lies on the circle. What are the coordinates of the point symmetric to $$(5,-2)$$ with respect to the $$x$$-axis?

    • $$(5,2)$$
    • $$(-5,2)$$
    • $$(-5,-2)$$
    • $$(2,5)$$

29. A rectangular prism has volume $$1536$$ cm$$^3$$. The ratio of its length, width, and height is $$3:4:4$$. What is the surface area of the prism?

    • $$704\sqrt{2}$$
    • $$74(\sqrt[3]{11})$$
    • $$780$$
    • $$80(\sqrt[3]{32})^2$$

30. The graph of a parabola passes through $$(-2,0)$$, $$(4,0)$$, and $$(0,8)$$. Which of the following could be its equation?

    • $$f(x)=-x^2+2x+8$$
    • $$f(x)=x^2-2x+8$$
    • $$f(x)=-x^2+4x+8$$
    • $$f(x)=x^2+2x-8$$

31. The graph of a parabola passes through $$(-2,0)$$, $$(4,0)$$, and $$(0,8)$$. Which of the following could be its equation?

    • $$f(x)=-x^2+2x+8$$
    • $$f(x)=x^2-2x+8$$
    • $$f(x)=-x^2+4x+8$$
    • $$f(x)=x^2+2x-8$$

32. A rectangular prism has volume $$1536$$ cm$$^3$$. The ratio of its length, width, and height is $$3:4:4$$. What is the surface area of the prism?

    • $$704$$
    • $$736$$
    • $$768$$
    • $$800$$
    • $$80(\sqrt[3]{32})^2$$

33. What is the value of $$t$$ in the equation $$t=\sqrt{t+12}$$?

    • 4

34. A rectangular prism has volume $$1536$$ cm$$^3$$. The ratio of its length, width, and height is $$3:4:4$$. What is the surface area of the prism?

    • $$704$$
    • $$736$$
    • $$768$$
    • $$800$$
    • $$80(\sqrt[3]{32})^2$$

35. What is the value of $$t$$ in the equation $$t=\sqrt{t+12}$$?

    • $$4$$
    • $$6$$
    • $$3$$
    • $$9$$

36. What is the value of $$t$$ in the equation $$t=\sqrt{t+12}$$?

    • $$4$$
    • $$6$$
    • $$3$$
    • $$9$$

37. If $$\angle ABC=30^\circ$$ in $$\triangle ABC$$, what is the value of $$p$$?

    • $$80^\circ$$

38. A linear function $$f$$ is defined by $$f(x)=ax+c,$$ where $$a$$ and $$c$$ are constants. The graph of $$f$$ passes through the point $$(k,2k)$$. If $$f(x+1)-f(x)=5$$ for all real numbers $$x$$, what is the value of $$c$$ when $$k=3$$?

    • -9

39. The graph above shows Bob's weekly salary in dollars for the first four weeks working at a public library. Bob's salary at week $$4$$ is what percent greater than his salary at week $$1$$?

    • $$33\frac{1}{3}\%$$
    • $$40\%$$
    • $$50\%$$
    • $$66\frac{2}{3}\%$$