Full Practice Exam 26 — Module 2

Questions in this quiz (22)

1. If $$7x-5=3(2x+9),$$ what is the value of $$x$$?

   • $$32$$
   • $$-32$$
   • $$16$$
   • $$-16$$

2. If $$\frac14(3x-8)=y$$ and $$x=12,$$ what is the value of $$y$$?

   • 7

3. A line has a slope of $$6$$ and passes through the point $$(4,29)$$. If the $$y$$-intercept of the line is $$k$$, what is the value of $$k$$?

   • $$3$$
   • $$5$$
   • $$7$$
   • $$9$$

4. Which of the following is equivalent to $$\frac{x^2-16}{x-4},$$ where $$x\ne4$$?

   • $$x-4$$
   • $$x+4$$
   • $$x^2+4$$
   • $$x+16$$

5. A delivery service charges a fee depending on the number of packages delivered.Which function could be used to determine the total cost, $$C$$, of delivering $$x$$ packages?

   • $$C(x)=3x+3.5$$
   • $$C(x)=2.5x+6$$
   • $$C(x)=3x+1$$
   • $$C(x)=2x+8.5$$

6. The gravitational potential energy $$U$$ of an object is modeled by $$U=mgh,$$ where $$m$$ is mass, $$g$$ is gravitational acceleration, and $$h$$ is height. What is $$h$$ in terms of the other variables?

   • $$h=\frac{U}{mg}$$
   • $$h=\frac{mg}{U}$$
   • $$h=\sqrt{\frac{U}{mg}}$$
   • $$h=\frac{U^2}{mg}$$

7. A data set of $$21$$ different numbers has a median of $$40$$ and a mean of $$48$$. The smallest value in the set is increased by $$12$$, and the largest value is decreased by $$8$$, while all other values remain unchanged. Which statement must be true?

   • The mean decreases.
   • The mean remains the same.
   • The range decreases.
   • The range remains the same.

8. Consider the sum of the expressions $$4x^2-7x+6$$ and $$-3x^2+5x-8.$$ If the sum is written in the form $$ax^2+bx+c,$$ what is the value of $$a+b+c$$?

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

9. In the $$xy$$-plane, a line passes through the points $$(8,2)$$ and $$(2,14)$$. What is the slope of a line perpendicular to this line?

   • $$-\frac18$$
   • $$-\frac47$$
   • $$\frac47$$
   • $$\frac12$$

10. Tyrese takes a walk around his neighborhood. The distance he is from his house, in miles, at a particular number of minutes after beginning his walk is represented in the graph. At what interval of time in his walk did the distance he is from his house decrease most rapidly?

    • $$0\text{-}5$$ minutes
    • $$15\text{-}20$$ minutes
    • $$25\text{-}30$$ minutes
    • $$30\text{-}35$$ minutes

11. A vitamin contains $$450$$ mg of magnesium, which is $$36\%$$ of the recommended daily value. If another vitamin contains $$300$$ mg of magnesium, approximately what percentage of the recommended daily value does it provide, to the nearest whole percent?

    • $$20\%$$
    • $$24\%$$
    • $$30\%$$
    • $$40\%$$

12. The measure of an angle is $$\frac{5\pi}{6}$$ radians. How many angles of this measure are equivalent to $$1050^\circ$$?

    • 7

13. For the system of inequalities $$y\le2x+5$$ and $$y\le-x+11,$$ when $$y$$ is at its greatest possible value, what is the corresponding value of $$x$$?

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

14. The trapezoid shown has bases of lengths $$10$$ and $$18$$ and height $$6$$. How many units is the perimeter of the trapezoid?

    • 44

15. The table below shows values of $$x$$ and $$y$$.Which function expresses the relationship between $$x$$ and $$y$$?

    • $$y=\frac{3}{x^2}$$
    • $$y=\frac{12}{x^2}$$
    • $$y=\frac{x^2}{12}$$
    • $$y=\frac{x}{12}$$

16. What is the result when $$6x^2-11x+4$$ is divided by $$x-2$$?

    • $$6x+1+\frac{6}{x-2}$$
    • $$6x+1+\frac{2}{x-2}$$
    • $$6x-1+\frac{2}{x-2}$$
    • $$6x-1+\frac{6}{x-2}$$

17. The volume $$V$$, in cubic centimeters, of a right cylinder with height $$12$$ centimeters is $$432\pi$$ cubic centimeters. What is the circumference, in centimeters, of one of the bases of this cylinder?

    • $$36\pi$$
    • $$18\pi$$
    • $$24\pi$$
    • $$12\pi$$

18. Triangle $$EFG$$ is equilateral. If $$EF$$ is $$10$$ units long, and $$\angle EFZ=30^\circ$$, what is the length of $$\overline{FZ}$$?

    • $$5\sqrt2$$
    • $$5\sqrt3$$
    • $$10$$
    • $$10\sqrt2$$

19. What values of $$x$$ would make the product of $$\frac4x$$ and $$\frac5{x+2}$$ undefined?

    • $$0$$ only
    • $$-2$$ only
    • $$-2$$ and $$0$$
    • $$2$$ and $$0$$

20. For the parabola $$y=4(x-7)(x+1),$$ what is the distance between the $$x$$-intercepts?

    • 8

21. If $$(x+7)(x-4)=ax^2+bx+c,$$ where $$a$$, $$b$$, and $$c$$ are constants, what is the value of $$a+b+c$$?

    • -24

22. Consider the information in the table below with the variables representing numerical values.There are twice as many elementary school students as there are middle school students, and $$60\%$$ of elementary school students take the bus. How many middle school students walk to school?

    • $$20$$
    • $$30$$
    • $$40$$
    • $$60$$