Full Practice Exam 3 — Module 1

Questions in this quiz (22)

1. If $$\frac{3x+12}{2x-4}=5$$ what is the value of $$6x-8$$?

   • $$7$$
   • $$\frac{3}{4}$$
   • $$12$$
   • $$\frac{136}{7}$$

2. In the $$xy$$-plane, a shaded triangular region has vertices at $$(0,2)$$, $$(6,2)$$, and $$(0,-2)$$. Which of the following points lies within the shaded region (including the boundary)?

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

3. Eight cups of sugar are needed to make one batch of lemonade. How many cups of sugar are needed to make enough lemonade to fill $$15$$ pitchers, if each pitcher holds $$1.25$$ batches?

   • $$120$$
   • $$140$$
   • $$150$$
   • $$160$$

4. If $$k$$ is an odd integer, which of the following expressions must be an even integer?

   • $$2k+3$$
   • $$3k-1$$
   • $$4k+2$$
   • $$k^2+1$$

5. A travel agency uses the equation $$c=0.85p+12$$ to convert $$p$$ U.S. dollars into Canadian dollars, where $$c$$ is the Canadian dollar amount. Which of the following is the best interpretation of the $$12$$ in the equation?

   • The agency charges 12 U.S. dollars as a service fee.
   • The agency charges $$12$$ Canadian dollars as a service fee.
   • One U.S. dollar is worth 12 Canadian dollars.
   • One Canadian dollar is worth 12 U.S. dollars.

6. A box contains $$5$$ green pens, $$9$$ black pens, and $$8$$ red pens. If three pens are removed from the box at random and are not returned, what is the probability that all three pens will be black?

   • $$\frac{1}{8}$$
   • $$\frac{12}{95}$$
   • $$\frac{3}{55}$$
   • $$\frac{6}{95}$$

7. Liam and Nora live $$180$$ miles apart. Each drives toward the other's house along a straight road connecting the two, Liam at a constant rate of $$45$$ miles per hour and Nora at a constant rate of $$35$$ miles per hour. If Liam and Nora leave their houses at the same time, how many miles are they from Liam's house when they meet?

   • $$70$$
   • $$78\frac{3}{4}$$
   • $$81$$
   • $$101\frac{1}{4}$$

8. There are $$m$$ liters of juice in a container. After $$n$$ liters have been poured out, in terms of $$m$$ and $$n$$, what percent of the juice has been poured out?

   • $$\frac{100n}{m}\%$$
   • $$\frac{100m}{n}\%$$
   • $$\frac{n}{m}\%$$
   • $$\frac{n}{100m}\%$$

9. How many solutions exist to the equation $$|3x+2|=|x-4|$$?

   • $$0$$
   • $$2$$
   • $$1$$
   • More than $$2$$

10. The graph of which of the following equations is parallel to the line with equation $$y=4x-7$$?

    • $$2x-y=5$$
    • $$y=-4x+3$$
    • $$8x-2y=10$$
    • $$3x+y=9$$

11. If a circle with center $$O$$ has a diameter of $$14$$, what is the area of the circle?

    • $$49\pi$$
    • $$98\pi$$
    • $$196\pi$$
    • $$7\pi$$

12. For all real numbers $$x$$, let $$f(x)=3x^2-5x+7$$ and define $$g(x)=2f(x-1)-x$$. What is the value of $$g(4)$$?

    • $$19$$
    • $$7$$
    • $$34$$
    • $$15$$

13. If $$k$$ equals $$25$$ percent of $$m$$, then in terms of $$k$$, $$50$$ percent of $$4m$$ is equal to which of the following?

    • $$\frac{k}{2}$$
    • $$2k$$
    • $$4k$$
    • $$8k$$

14. If $$\frac{\sqrt{y}}{3}=4\sqrt{3}$$ what is the value of $$y$$?

    • $$36$$
    • $$48$$
    • $$144$$
    • $$432$$

15. In triangle $$DEF$$, angle $$E$$ is a right angle and angle $$F$$ measures $$30^\circ$$. If $$DF=10$$, what is the length of $$EF$$?

    • $$5$$
    • $$5\sqrt{3}$$
    • $$10\sqrt{3}$$
    • $$15$$

16. The chart above shows the number of green and yellow parrots Maria sold in June and the average weight of each type of bird sold. If Maria sold no other parrots, what was the average (arithmetic mean) weight, in pounds, of the parrots that Maria sold in June?

    • 3

17. Simplify:$$2y\sqrt{16}-2y\sqrt{25}$$

    • $$-18y$$
    • $$-6y$$
    • $$-2y$$
    • $$6y$$

18. In the coordinate plane, what is the midpoint of the line segment with endpoints at $$(-2,5)$$ and $$(4,-1)$$?

    • $$(-3,2)$$
    • $$(1,2)$$
    • $$(2,-3)$$
    • $$(1,-2)$$

19. In the figure, lines $$p$$ and $$q$$ are parallel. The angles are labeled $$x^\circ$$, $$y^\circ$$, and $$z^\circ$$ as shown. What is the value of $$x$$ in terms of $$y$$ and $$z$$?

    • $$x=90-y-z$$
    • $$x=180-y-z$$
    • $$x=y+z+90$$
    • $$x=90-y+z$$

20. In the figure, triangle $$ABC$$ is a right triangle with the right angle at $$B$$. A square is constructed outward on side $$AB$$, and a rectangle is constructed outward using sides $$AB$$ and $$BC$$ so that the rectangle has side lengths $$AB$$ and $$BC$$. By how much is the perimeter of the square smaller than the perimeter of the rectangle?

    • $$4$$
    • $$8$$
    • $$10$$
    • $$14$$

21. The bar chart shows the distribution of kayak weights (in pounds) for $$20$$ kayaks made by Company A and $$20$$ kayaks made by Company B. The possible weights are $$45$$, $$46$$, $$47$$, $$48$$, and $$49$$ pounds. Which of the following correctly compares the median weight of the kayaks made by each company?

    • The median weight of kayaks made by Company A is smaller.
    • The median weight of kayaks made by Company B is smaller
    • The median weight is the same for both companies.
    • The relationship cannot be determined from the information given

22. A lemonade stand tracks its daily profit $$y$$, in dollars, based on the number of cups of lemonade sold $$x$$. The relationship is shown in the graph.Which of the following is the best interpretation of the $$y$$-intercept in the context of this problem?

    • The price of each cup of lemonade
    • The cost of making each cup of lemonade
    • The total profit when 1 cup of lemonade is sold
    • The daily cost of operating the lemonade stand.