Full Practice Exam 6 — Module 2

Questions in this quiz (22)

1. What is an equivalent form of $$(0.9a+0.6b)-(1.5a-0.2b)$$?

   • $$0.6a+0.4b$$
   • $$-0.6a+0.8b$$
   • $$−0.6a−0.4b$$
   • $$2.4a+0.4b$$

2. If $$15x-12=3$$, what is $$-8+5x$$?

   • $$3$$
   • $$-6$$
   • $$6$$
   • $$-3$$

3. The volume of a cone, $$V$$, is given by the equation $$V=\frac{1}{3}\pi r^{2}h$$, in which $$r$$ is the radius of the cone and $$h$$ is the height of the cone. What is the height in terms of the other variables?

   • $$h=\frac{V}{3\pi r^2}$$
   • $$h=\frac{\pi r^2}{3V}$$
   • $$h=\frac{3V}{\pi r^{2}}$$
   • $$h=3\pi r^2V$$

4. $$(3x^2-2x)-(x^2+5x)$$Which of these options is equivalent to the following expression?

   • $$2x^2-7x$$
   • $$2x^2+7x$$
   • $$4x^2-3x$$
   • $$3x^2-5x$$

5. $$(x-4)^3=125$$What positive value of $$x$$ would make the above equation true?

   • 9

6. $$y=3x+6$$What is the $$x$$-coordinate of the $$x$$-intercept of the line with the above equation?

   • $$6$$
   • $$2$$
   • $$-6$$
   • $$-2$$

7. The number of pages a student reads each day, $$P$$, in a week can be modeled by the function $$P(d)=5d+20$$, in which $$d$$ is the number of days after the beginning of the week. What does the number $$5$$ represent in this function?

   • The student reads $$20$$ more pages each day.
   • The student reads $$5$$ pages on the first day of the week.
   • The student reads $$5$$ more pages per day.
   • The student reads $$5$$ pages total in the week.

8. If $$6=\frac{3}{2}(6x-2y)$$ and $$y=3x$$, what is the value of $$y$$?

   • $$2$$
   • $$1$$
   • $$0$$
   • No solution

9. Which of the following would be points at which the function $$y=(x-3)(x+2)x$$ intersects the $$x$$-axis?I. $$(3,0)$$II. $$(-2,0)$$III. $$(0,0)$$

   • I and II only
   • II only
   • I only
   • I, II, and III

10. The growth of a population of cells is modeled by the function $$C(t)=500\cdot2^t$$, in which $$C(t)$$ represents the number of cells after $$t$$ hours have passed. After how many hours will the population of cells be $$16$$ times its initial number?

    • $$5$$ hours
    • $$2$$ hours
    • $$4$$ hours
    • $$6$$ hours

11. The population of the greater metropolitan area of Los Angeles was estimated to have been $$13,000,000$$ at the end of the year $$2021$$. If the Los Angeles area represented $$10\%$$ of all of California’s population at the end of $$2021$$, what would be the closest estimate of California’s total population?

    • $$26,000,000$$
    • $$1,300,000,000$$
    • $$130,000,000$$
    • $$13,000,000$$

12. $$g(x)=(x+2)(x-5)$$For the function $$g$$ as defined below, what is the value of $$g(4)$$?

    • $$-6$$
    • $$2$$
    • $$4$$
    • $$5$$

13. $$y$$ > $$x+2$$$$y$$ < $$-x-4$$The solutions to this set of inequalities are found in which quadrant(s) of the $$xy$$-coordinate plane?

    • Quadrants $$II$$ only
    • Quadrants $$II$$ and $$III$$
    • Quadrants $$III$$ only
    • Quadrants $$III$$ and $$IV$$ only

14. If a computer costs $$2,000$$ and depreciates (i.e., the value decreases) by the same amount each year, how much is the annual amount of depreciation if after $$6$$ years the computer is worth $$800$$?

    • $$100$$
    • $$200$$
    • $$80$$
    • $$400$$

15. If a circle graphed in the $$xy$$-coordinate plane has a center at $$(-2,5)$$ and intersects the origin, what is the equation of the circle?

    • $$(x+2)^2+(y-5)^2=25$$
    • $$(x-2)^2+(y+5)^2=29$$
    • $$(x-2)^2+(y+5)^2=25$$
    • $$(x+2)^2+(y-5)^2=29$$

16. A cyclist pedals an average of $$45$$ times per minute while riding. In the $$2$$ hours the cyclist rides in a day, about how many times will the cyclist pedal?

    • $$5400$$
    • $$540$$
    • $$800$$
    • $$10,800$$

17. In a right triangle, the cosine of one acute angle is $$\frac{\sqrt{7}}{4}$$. If the side opposite this angle has a length of $$3$$ units, what is the perimeter of the triangle?

    • $$7-\sqrt{7}$$
    • $$7+\sqrt{7}$$
    • $$3+4\sqrt{7}$$
    • $$4+3\sqrt{7}$$

18. A delivery company tracked the number of miles $$m$$ driven by one of its trucks and the total fuel cost $$C$$, in dollars, over several trips. A scatterplot of the data suggested a linear association, and the line of best fit was determined to be:$$C=0.18m+25$$The recorded trips ranged from $$50$$ miles to $$300$$ miles. On one particular trip, the truck traveled $$360$$ miles. Based on the line of best fit, what is the predicted fuel cost for the trip, and what can be said about the reliability of this prediction?

    • Predicted fuel cost: $$\$89.80$$. The prediction is reliable because the model shows a linear relationship.
    • Predicted fuel cost: $$\$89.80$$. The prediction is unreliable because $$360$$ miles is outside the observed range of the data.
    • Predicted fuel cost: $$\$64.80$$. The prediction is reliable because the model shows a linear relationship.
    • Predicted fuel cost: $$\$64.80$$. The prediction is unreliable because $$360$$ miles is outside the observed range of the data.

19. $$|x+2|+y=8$$$$y=x^2+4x+1$$If $$(x,y)$$ is a solution to the system, what is the value of $$y$$?

    • $$\frac{11-\sqrt{33}}{2}$$
    • $$\frac{11+\sqrt{33}}{2}$$
    • $$\frac{7-\sqrt{33}}{2}$$
    • $$\frac{17-3\sqrt{5}}{2}$$

20. A quadratic function models a basketball player's height, in meters, above the court after jumping for a rebound. The player reaches a maximum height of $$3.2$$ meters $$0.8$$ seconds after jumping. The player lands back on the court $$2$$ seconds after jumping. What was the player’s initial height, in meters, when the jump began?Round your answer to two decimal places.

    • 1.78

21. In $$\triangle XYZ$$, point $$M$$ is on side $$XY$$ and point $$N$$ is on side $$XZ$$ such that $$MN$$ is parallel to $$YZ$$. Point $$R$$ is on segment $$MN$$. Segment $$XR$$ is drawn and intersects side $$YZ$$ at point $$S$$. If $$XM=6$$, $$MY=4$$, $$YZ=15$$, and $$MR=3$$, what is the length of $$SZ$$?

    • $$5$$
    • $$6$$
    • $$\frac{15}{2}$$
    • $$10$$

22. In the figure described, line segment $$\overline{AE}$$ intersects line segment $$\overline{BD}$$ at point $$C$$. It is given that $$\overline{AB}\parallel\overline{DE}$$. The lengths of the segments are given as:$$AC=x-3$$, $$CE=x+3$$, $$BC=2$$, $$CD=x$$What is the length of segment $$\overline{AE}$$?

    • 12