Full Practice Exam 28 — Module 2

Questions in this quiz (22)

1. $$-\frac{3}{19}px+\frac{q}{8}=10-\frac{6}{17}x$$In the given equation, $$p$$ and $$q$$ are constants. The equation has no solution. What is the value of $$p$$?

   • $$\frac{2}{5}$$
   • $$\frac{38}{17}$$
   • $$\frac{8}{19}$$
   • $$\frac{5}{2}$$

2. A line in the $$xy$$-plane passes through the point $$(2,6)$$ and crosses the $$x$$-axis at the point $$(8,0)$$. The line crosses the $$y$$-axis at the point $$(0,b)$$. What is the value of $$b$$?

   • 8

3. Matthew is roping off a rectangular corral for his goats. The corral has a length of $$a$$ feet and a width of $$b$$ feet. He uses a total of $$56$$ feet of rope to enclose the corral. Which equation represents this situation?

   • $$2ab=56$$
   • $$a+b=56$$
   • $$2a+2b=56$$
   • $$ab=56$$

4. $$\frac75x+3y=20$$$$\frac25x+3y=10$$The solution to the given system of equations is $$(x,y)$$. What is the value of $$\frac95x+9y$$?

   • $$6$$
   • $$9$$
   • $$25$$
   • $$36$$

5. A freelance graphic designer charges $$\$25$$ per hour for the first $$30$$ hours worked in a month. For every hour worked beyond $$30$$ hours, she charges $$\$40$$ per hour. What is the minimum number of hours she must work in a month to earn at least $$\$1,150$$?

   • $$39$$
   • $$40$$
   • $$41$$
   • $$42$$

6. The quadratic function $$ax^2+40x+c$$ has at least one real solution, where $$a$$ and $$c$$ are positive integers. What is the greatest possible value of $$ac$$?

   • $$361$$
   • $$380$$
   • $$400$$
   • $$420$$

7. In the given equation, $$x^2(x+4)(x-k)=0,$$ $$k$$ is a positive constant. The sum of all solutions of the equation is $$6$$. What is the value of $$k$$?

   • $$1$$
   • $$2$$
   • $$6$$
   • $$10$$

8. The function $$g(x)=2^x-5$$ passes through the point $$(3,3)$$. If $$g(k)=-1$$, what is the value of $$k$$?

   • $$1$$
   • $$2$$
   • $$4$$
   • $$6$$

9. A quantity $$Q$$ starts at $$50$$ and doubles every $$6$$ days. Which of the following models $$Q$$ after $$d$$ days?

   • $$Q(d)=50+2d$$
   • $$Q(d)=50\cdot6^d$$
   • $$Q(d)=50\cdot2^{\frac{d}{6}}$$
   • $$Q(d)=50\cdot\left(\frac12\right)^d$$

10. If $$|x-7|+80=100,$$ what is the sum of the solutions to the equation?

    • $$-13$$
    • $$14$$
    • $$20$$
    • $$27$$

11. A circle in the plane has center $$(2,-3)$$ and radius $$15$$. Which is the standard form of its equation?

    • $$(x-2)^2+(y+3)^2=225$$
    • $$(x+2)^2+(y-3)^2=225$$
    • $$(x+2)^2+(y-3)^2=15^2+2$$
    • $$(x-2)^2+(y-3)^2=15^2$$

12. The composition of an animal is defined as the muscles, bones, and fat of the animal. A scientist studied a large goat and determined that the goat had $$84$$ kilograms of muscle, which made up approximately $$60.5\%$$ of its composition. Of the remaining composition of this goat, approximately $$40.0\%$$ was bone, and the remainder was fat. Based on these approximations, to the nearest tenth, how many kilograms of this goat's composition was bone?

    • $$17.8$$ kilograms
    • $$19.7$$ kilograms
    • $$21.9$$ kilograms
    • $$27.8$$ kilograms

13. A movie theater has $$400$$ customers, each located in theater A, B, or C. If one customer is selected at random, the probability that the selected customer is in theater A is $$0.45$$ and the probability the selected customer is in theater B is $$0.30$$. How many customers are located in theater C?

    • $$25$$
    • $$40$$
    • $$100$$
    • $$120$$

14. A proposal for a new community center was included on an election ballot. A radio show stated that $$4$$ times as many people voted in favor of the proposal as people who voted against it. A social media post reported that $$24,000$$ more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

    • $$6,000$$
    • $$8,000$$
    • $$12,000$$
    • $$24,000$$

15. The scatterplot shows measurements of the body length, in centimeters, of a New Zealand fur seal from age $$2$$ years to $$7$$ years old. A line of best fit is also shown. For a New Zealand fur seal at an age of $$4$$ years old, what is the body length predicted by the line of best fit, to the nearest $$10$$ centimeters?

    • $$100$$ centimeters
    • $$90$$ centimeters
    • $$110$$ centimeters
    • $$115$$ centimeters

16. Two lines intersect at exactly one point, forming two acute angles and two obtuse angles. The measure of one of these angles is $$(7x-70)^\circ$$. Which of the following could NOT be the sum of the measures of any two of these angles?

    • $$180^\circ$$
    • $$(14x-140)^\circ$$
    • $$(-14x+140)^\circ$$
    • $$(-14x+500)^\circ$$

17. In the figure shown, $$\overline{WZ}$$ and $$\overline{XY}$$ intersect at point $$Q$$. The segments have the following lengths: $$YQ=20$$, $$WQ=50$$, $$WX=60$$, and $$XQ=90$$. What is the length of $$YZ$$?

    • $$24$$
    • $$30$$
    • $$45$$
    • $$60$$

18. In triangle $$FGH$$ and triangle $$JKL$$, $$FG$$ and $$JK$$ are each equal to $$9$$ yards, and angles $$F$$ and $$J$$ each have measure $$42^\circ$$. Which additional piece of information is sufficient to prove that triangle $$FGH$$ is congruent to triangle $$JKL$$?

    • The measures of angles $$G$$ and $$H$$ are equal.
    • The lengths of sides $$GH$$ and $$KL$$ are equal.
    • The lengths of sides $$FH$$ and $$JL$$ are equal.
    • No additional information is necessary to prove that the two triangles are congruent.

19. In the right triangle shown, the value of $$\tan x=\frac{d}{21}$$. What is the value of $$d$$?

    • $$21$$
    • $$28$$
    • $$35$$
    • $$42$$

20. A hemisphere is half of a sphere. If a hemisphere has a radius of $$12$$ centimeters, which of the following is closest to the volume, in cubic centimeters, of this hemisphere?

    • $$200$$
    • $$800$$
    • $$2700$$
    • $$3600$$

21. A certain population is modeled by $$P(t)=A(1+r)^t$$, where $$t$$ is measured in years. If $$P(0)=500$$ and $$P(2)=605$$, what is $$P(5)$$ rounded to the nearest integer?

    • $$720$$
    • $$805$$
    • $$818$$
    • $$890$$

22. Which of the following may represent the graphs of $$y=ax+b$$ and $$y=ax^2+bx+c$$?