Full Practice Exam 4 — Module 2

Questions in this quiz (22)

1. Solve for $$x$$. $$5x+2=3x+12$$

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

2. If $$f(x)=x^2-4x+3$$, what is $$f(5)$$?

   • $$8$$
   • $$9$$
   • $$10$$
   • $$11$$

3. The function is defined by $$f(x)=2x+5$$. What is the inverse function?

   • $$f^{-1}(x)=\frac{x-5}{2}$$
   • $$f^{-1}(x)=2x-5$$
   • $$f^{-1}(x)=\frac{x+5}{2}$$
   • $$f^{-1}(x)=\frac{2}{x-5}$$

4. If $$g(x)=3x^2$$ and $$h(x)=2x-1$$, what is $$(g\circ h)(x)$$?

   • $$6x^2-3x+1$$
   • $$3(2x-1)^2$$
   • $$3x^2+2x-1$$
   • $$2(3x^2)-1$$

5. $$x^2-5x+6=0$$What are the solutions to the equation?

   • $$2,3$$
   • $$-2,-3$$
   • $$1,6$$
   • $$-1,6$$

6. Which function represents exponential growth?

   • $$y=2x+3$$
   • $$y=3^x$$
   • $$y=-x^2+2$$
   • $$y=\sqrt{x}$$

7. The graph of $$y=(x-2)^2+3$$ has its vertex at which point?

   • $$(0,3)$$
   • $$(2,3)$$
   • $$(2,-3)$$
   • $$(-2,3)$$

8. A quadratic function has roots at $$x=-1$$ and $$x=4$$. Which equation could represent the function?

   • $$y=(x+1)(x-4)$$
   • $$y=(x-1)(x+4)$$
   • $$y=(x-1)(x-4)$$
   • $$y=(x+1)(x+4)$$

9. Which equation represents a circle with center $$(0,0)$$ and radius $$5$$?

   • $$x^2+y^2=5$$
   • $$x^2+y^2=10$$
   • $$x^2+y^2=25$$
   • $$x^2+y^2=50$$

10. If $$y=2x^2-8x+6$$, what is the axis of symmetry?

    • $$x=2$$
    • $$x=-2$$
    • $$x=4$$
    • $$x=-4$$

11. The graph of $$y=-x^2+4$$ opens in which direction, and what is its vertex?

    • Upward with vertex $$(0,4)$$
    • Downward with vertex $$(0,4)$$
    • Upward with vertex $$(0,-4)$$
    • Downward with vertex $$(0,-4)$$

12. A cell phone plan costs $$\$40$$ per month plus $$\$0.10$$ per text message. If Jacob spends $$\$55$$ in one month, how many text messages did he send?

    • $$100$$
    • $$120$$
    • $$130$$
    • $$150$$

13. A train travels at 60 miles per hour for 2 hours and then at 40 miles per hour for 3 hours. What is the average speed for the entire trip?

    • $$46\text{ mph}$$
    • $$48\text{ mph}$$
    • $$50\text{ mph}$$
    • $$52\text{ mph}$$

14. A box contains 3 red balls and 5 blue balls. One ball is selected at random. What is the probability of selecting a red ball?

    • $$\frac35$$
    • $$\frac38$$
    • $$\frac25$$
    • $$\frac14$$

15. The cost of a concert ticket increased from $$\$40$$ to $$\$50$$. What was the percent increase?

    • $$20\%$$
    • $$22\%$$
    • $$25\%$$
    • $$30\%$$

16. A student scores 80, 85, 90, and 95 on four tests. What score is needed on the fifth test to have an average of 90?

    • $$95$$
    • $$96$$
    • $$100$$
    • $$105$$

17. The diagonals of a rectangle are always which of the following?

    • Congruent
    • Perpendicular
    • Equal in length only if the rectangle is a square
    • Shorter than the sides

18. The volume of a sphere is given by $$V=\frac43\pi r^3$$. If $$r=3$$, what is the volume?

    • $$18\pi$$
    • $$27\pi$$
    • $$36\pi$$
    • $$36\pi$$

19. The measure of one angle of a triangle is $$50^\circ$$, and another angle is $$60^\circ$$. What is the measure of the third angle?

    • $$60^\circ$$
    • $$70^\circ$$
    • $$80^\circ$$
    • $$90^\circ$$

20. A right triangle has legs of lengths 5 and 12. What is the length of the hypotenuse?

    • $$12$$
    • $$13$$
    • $$14$$
    • $$17$$

21. If $$\tan\theta=\frac34$$, what is $$\sin\theta$$?

    • $$\frac34$$
    • $$\frac45$$
    • $$\frac53$$
    • $$\frac35$$

22. A square has a diagonal of length 6. What is the length of one side?

    • $$3$$
    • $$3\sqrt2$$
    • $$6$$
    • $$6\sqrt2$$