Full Practice Exam 4 — Module 2

Questions in this quiz (22)

1. If the median of a set of five consecutive integers is equal to $$18$$, then what is the value of the smallest of these five integers?

   • $$14$$
   • $$16$$
   • $$17$$
   • $$18$$

2. If $$5x-3(2x-4)+7=4x+18,$$ what is the value of $$x$$?

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

3. If the probability of selecting a green marble is $$\frac{1}{4}$$ and the probability of selecting a yellow marble is $$\frac{3}{4}$$, what is the ratio of yellow marbles to green marbles?

   • $$1:3$$
   • $$3:1$$
   • $$4:3$$
   • $$3:4$$

4. The ratio of a rectangle's width to the length of a square's side is $$2:5$$. If the area of the square is $$100$$, and the rectangle's length is $$15$$, what is the area of the rectangle?

   • $$40$$
   • $$60$$
   • $$120$$
   • $$150$$

5. Given that $$|p+4|=9$$ and $$|q+1|=5$$ where $$p$$ < $$0$$ and $$q$$ < $$0$$, what is the value of $$pq$$?

   • $$-45$$
   • $$-40$$
   • $$40$$
   • $$78$$

6. A furniture store determines the retail price of a sofa by marking up its wholesale price by $$50$$ percent. After a $$20$$ percent discount off the sofa's retail price, the sofa costs $$480$$. What is the wholesale price of the sofa?

   • $$256$$
   • $$300$$
   • $$320$$
   • $$400$$

7. The average of $$p,q,$$ and $$r$$ is $$18$$. If the value of $$s$$ is $$30$$, what is the average of $$p,q,r,$$ and $$s$$?

   • $$12$$
   • $$15$$
   • $$21$$
   • $$24$$

8. If $$\frac{x}{y}=5$$ and $$y=12$$, then what is the value of $$6xy$$?

   • $$180$$
   • $$300$$
   • $$450$$
   • $$4320$$

9. If a line segment with a slope of $$-3$$ passes through the points $$(4,-2)$$ and $$(-2,k)$$, what is the value of $$k^2$$?

   • $$36$$
   • $$45$$
   • $$90$$
   • $$256$$

10. Emma can paint $$4$$ walls per hour. Liam can paint $$5$$ walls per hour, and Noah can paint $$10$$ walls per hour. If Emma and Liam paint together for one hour, and then Noah joins them, how many minutes will it take them to paint a total of $$114$$ walls?

    • $$120$$
    • $$180$$
    • $$240$$
    • $$392$$

11. If $$|5x|+3y^{-1}=9z+2x$$, what is the value of $$x$$ in terms of $$y$$ and $$z$$?

    • $$x=-3z+y^{-1}$$
    • $$x=\frac{3y^{-1}-9z}{7}$$
    • $$x=3z+y^{-1}$$
    • $$x=9z+3y^{-1}$$

12. $$a$$, $$b$$, and $$c$$ are three consecutive positive odd integers such that $$a$$ < $$b$$ < $$c$$. If their sum is $$57$$, what is the value of $$ac$$?

    • $$209$$
    • $$221$$
    • $$357$$
    • $$423$$

13. If $$a$$ is inversely proportional to $$b^{-1}$$ and $$a=k$$ when $$b^{-1}=5m$$, then what is the value of $$b$$ in terms of $$m$$ when $$a=3k$$?

    • $$\frac{m}{15}$$
    • $$\frac{3}{5m}$$
    • $$\frac{5}{m}$$
    • $$15m$$

14. Lina drills a cylindrical hole straight through the center of a wooden cube. The cube has a side length of $$8$$ centimeters, and the cylinder has a radius of $$3$$ centimeters. What is the total surface area of the cube after the cylinder has been removed?

    • $$384+30\pi$$
    • $$384-36\pi$$
    • $$256+36\pi$$
    • $$256-36\pi$$

15. In the $$xy$$-plane, segment $$PQ$$ passes through points $$(5,-2)$$ and $$(-3,6)$$. What is the midpoint of segment $$PQ$$?

    • $$(1,2)$$
    • $$(-4,2)$$
    • $$(2,-4)$$
    • $$(4,2)$$

16. The function $$f(x)=x^2-5x-36$$ and $$g(t)=t^2$$. If $$4g(t)=f(3x)$$, what is the value of $$x$$ in terms of $$t$$?

    • $$x=\frac{9\pm\sqrt{1521t^2+169}}{18}$$
    • $$x=\frac{5\pm\sqrt{16t^2+169}}{6}$$
    • $$x=\frac{3\pm\sqrt{1521t^2+144}}{2}$$
    • $$x=\frac{3\pm\sqrt{169t^2+144}}{18}$$

17. In the sequence $$24,66,\ldots$$ each term after the first term is twenty six less than three times the preceding term. What is the sum of the units digits of the first $$12$$ terms?

    • $$12$$
    • $$24$$
    • $$36$$
    • $$48$$

18. A woman buys $$p$$ pears and $$b$$ bananas. Each pear costs $$70$$ cents and each banana costs $$50$$ cents. If the woman buys fewer than $$20$$ fruits total and spends less than $$10$$ dollars, which of the following systems of inequalities best represents this situation?

    • $$p+b=20$$ ; $$7p+5b=100$$
    • $$p+b$$ < $$20$$ ; $$7p+5b$$ < $$100$$
    • $$p+b\leq20$$; $$7p+5b\leq100$$
    • $$p+b\leq20$$; $$7p+5b=100$$

19. The number of stores in a shopping mall between 2010 and 2018 is modeled by the equation$$S=240-8t$$In the equation, $$S$$ is the number of stores and $$t$$ is the number of years since 2010 (so $$t=0$$ represents 2010). What does the $$8$$ represent in this equation?

    • The number of stores in the mall decreased by a total of 8 between 2010 and 2018.
    • The number of stores in the mall decreased by $$8$$ each year after 2010.
    • There were 8 stores in the mall in 2010.
    • There were 8 stores in the mall in 2018.

20. The perimeter of an equilateral triangle is $$540$$ centimeters. The height of this triangle is $$m\sqrt3$$ centimeters, where $$m$$ is a constant. What is the value of $$m$$?

    • $$36$$
    • $$45$$
    • $$54$$
    • $$90$$

21. The measure of angle $$A$$ is $$\frac{3\pi}{4}$$ radians. The measure of angle $$B$$ is $$\frac{\pi}{6}$$ radians greater than the measure of angle $$A$$. What is the measure of angle $$B$$ in degrees?

    • $$30^\circ$$
    • $$60\circ$$
    • $$165^\circ$$
    • $$180\circ$$

22. Rectangle $$ABCD$$ has an area of $$72$$ square units. Point $$E$$ lies on side $$CD$$. Segment $$BE$$ is drawn, and the angle between $$BE$$ and side $$ED$$ is $$60^\circ$$. If $$EC=3\sqrt3$$, what is the length of $$AB$$?

    • $$3$$
    • $$9\sqrt{3}$$
    • $$8$$
    • $$8\sqrt{3}$$