Full Practice Exam 1 — Module 2

Questions in this quiz (22)

1. If $$h(x)=7x-5$$ what does $$h(3x)$$ equal?

   • $$21x-15$$
   • $$21x-5$$
   • $$21x^2-15x$$
   • $$6x$$

2. $$4+3r=kw$$$$3r-2w=8$$The system has no solution. What is the value of $$k$$?

   • $$\frac{3}{2}$$
   • $$2$$
   • $$\frac{9}{2}$$
   • $$3$$

3. The population density of Brookdale is $$375$$ people per square mile. Brookdale has a population of $$141000$$ people, and $$15%$$ of the town's land is covered by lakes and cannot be inhabited. What is the area, in square miles, of the habitable land in Brookdale?

   • $$500$$
   • $$400$$
   • $$450$$
   • $$376$$

4. What is the solution or solutions to this equation?$$x=\sqrt{20-x}$$

   • $$-5$$
   • $$4$$
   • $$-5$$ , $$4$$
   • $$-4$$ , $$5$$

5. The function $$g(x)=\frac{2x^2-7x+5}{x^2-4}$$ is undefined for which value(s) of $$x$$?

   • $$-4$$
   • $$4$$
   • $$2$$ , $$-2$$
   • $$4$$ , $$-4$$

6. A car travels the first $$120$$ miles of a trip at an average speed of 60 miles per hour. The car then travels the next $$150$$ miles at an average speed of $$50$$ miles per hour. What is the car's average speed for the entire trip?

   • $$50$$
   • $$54$$
   • $$55$$
   • $$60$$

7. Consider a set of $$31$$ different numbers. If two numbers are added to the set, one greater than the current median of the set and one less than the current median of the set, which quantity about the set MUST remain unchanged?

   • Mean
   • Median
   • Range
   • Mode

8. Solve the equation:$$4(2x - 3) - (5x + 7) = 3(x - 8) + 9$$

   • 0
   • 2
   • Infinite solutions
   • No solution

9. Electrical engineers use Ohm's law, $$V=IR$$, to describe the relationship among voltage $$V$$, current $$I$$, and resistance $$R$$. Which of the following statements is always true based on Ohm's law?I. If the voltage increases while the resistance remains the same, the current increases.II. If the current decreases while the voltage remains the same, the resistance must increase.III. If the resistance decreases while the current remains the same, the voltage must decrease.

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

10. A physician uses guidelines for maximum recommended heart rate in beats per minute based on age.For a patient who is age $$50$$, the maximum recommended heart rate is $$170$$ beats per minute. The physician recommends that during exercise the patient maintain a heart rate greater than $$60\%$$ and less than $$90\%$$ of this maximum recommended heart rate. Which inequality represents the appropriate range for the patient’s heart rate $$H$$ during exercise?

    • $$60$$ < $$H$$ < $$90$$
    • $$85$$ < $$H$$ < $$150$$
    • $$102$$ < $$H$$ < $$153$$
    • $$153$$ < $$H$$ < $$170$$

11. A hiking trail map is drawn to scale so that $$1$$ inch corresponds to $$3$$ miles. A hiker walks the trail at a constant average speed of $$4$$ miles per hour. How many minutes will the hike take if the trail distance on the map is $$5$$ inches?

    • $$150$$
    • $$180$$
    • $$225$$
    • $$250$$

12. Simplify the expression:$$3x^{4}y^{3}-2x^{3}y^{5}+5x^{2}y^{4}+7x^{3}y^{5}-x^{2}y^{4}$$

    • $$8x^{4}y^{3}-2x^{3}y^{5}+6x^{2}y^{4}$$
    • $$8x^{4}y^{3}+2x^{3}y^{5}-6x^{2}y^{4}$$
    • $$3x^{4}y^{3}+5x^{3}y^{5}+4x^{2}y^{4}$$
    • $$8x^{4}y^{3}-2x^{3}y^{5}+4x^{2}y^{4}$$

13. If a circle has a radius of $$5$$ units, what is the length of the arc on the circle that measures $$\frac{\pi}{3}$$ radians?

    • $$5\pi$$
    • $$10\pi$$
    • $$\frac{5\pi}{3}$$
    • $$\frac{10\pi}{3}$$

14. A rectangular prism has dimensions $$x,$$ $$2x,$$ and $$3x.$$ A new prism is created by tripling the first dimension, doubling the second, and quadrupling the third. If the volume of the original prism is $$V$$ cubic units, what is the volume of the new prism in terms of $$V$$?

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

15. The sides of a right triangle are $$8$$, $$8\sqrt{3}$$, and $$16$$. In a triangle similar to this triangle, what is the measure of the triangle's smallest interior angle?

    • $$25^{\circ}$$
    • $$30^{\circ}$$
    • $$45^{\circ}$$
    • $$60^{\circ}$$

16. A line $$l$$ passes through the points $$(2,3)$$ and $$(8,15)$$. A second line m is perpendicular to $$l$$ and passes through the point $$(5,4)$$. The lines $$l$$ and $$m$$ intersect at point $$P$$. The $$x$$-axis, line $$l$$, and line $$m$$ form a triangle whose vertices are $$P$$ and the $$x$$-intercepts of $$l$$ and $$m$$. What is the area of this triangle?

    • $$5$$
    • $$\frac{25}{2}$$
    • $$25$$
    • $$\frac{125}{4}$$

17. Light travels at approximately $$3.00\times10^8$$ meters per second. When Saturn is at its closest point to Earth, it is $$1.20$$ billion kilometers away. When Earth and Saturn are this close, approximately how many minutes does light reflected off Saturn take to reach Earth?

    • $$40$$
    • $$67$$
    • $$80$$
    • $$100$$

18. If $$4n^5-6n^3=2n^7,$$ what is the sum of all possible values of $$n^2$$?

    • $$-3$$
    • $$1$$
    • $$3$$
    • $$0$$

19. Consider the function $$g(x)=x^2+4.$$ What operation could be performed on the right-hand side of the equation to expand the range to include negative values?

    • Add $$3$$
    • Add $$−1$$
    • Subtract $$-9$$
    • Subtract $$6$$

20. The formula for the area of a trapezoid is $$A=\frac{B_1+B_2}{2}\cdot H,$$ where $$B_1$$ and $$B_2$$ are the lengths of the bases and $$H$$ is the height. If the mean of the bases of a trapezoid is three times the height, and the trapezoid's area is $$108$$ square inches, what is the height of the trapezoid in inches?

    • $$4$$
    • $$6$$
    • $$9$$
    • $$12$$

21. Which of the following expressions is equivalent to:$$6(2m-3)-4(m-5)+2$$?

    • $$8m-12$$
    • $$12m-28$$
    • $$8m+4$$
    • $$12m-18$$

22. Speed is calculated by dividing the change in distance by the change in time. Suppose a scientist graphs a line representing the constant speed of a cyclist on the coordinate plane, using time as the $$x$$-coordinate and distance as the $$y$$-coordinate. Which property of the line represents the cyclist’s speed?

    • Its $$y$$-intercept
    • Its slope
    • Its range
    • Its domain