Full Practice Exams — Exam 9

Questions in this quiz (45)

1. The function $$M(v)$$ represents the gas mileage of a car traveling at $$v$$ miles per hour: $$M(v)=-\frac{1}{25}v^2+5v-50$$. Determine the speed at which the car obtains its greatest gas mileage.

   • $$25$$
   • $$50$$
   • $$62.5$$
   • $$30.25$$

2. Point $$O$$ is the center of the circle in the diagram below. If $$\angle ABO = 25^\circ$$ and $$\angle ACO = 25^\circ$$, what is the measure of the central angle $$\angle BOC$$?

   • $$50^\circ$$
   • $$25^\circ$$
   • $$75^\circ$$
   • $$100^\circ$$

3. The height of a rock thrown off a ledge relative to the ground beneath the ledge is graphed below. At what time did the rock reach its maximum height?

   • At the time of the throw
   • 1 second after the throw
   • 2 seconds after the throw
   • 3.5 seconds after the throw

4. Question 4

   • Mean
   • Median
   • Standard deviation
   • Range

5. A cake recipe calls for 3/4 cup of flour to make one cake. According to this recipe, how many cups of flour are needed to make 4 cakes?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

6. One traffic light turns green every 6 seconds, and another traffic light turns green every 8 seconds. At a certain instant, the 2 lights turn green at the same time. How many seconds elapse until the 2 lights next turn green at the same time?

   • $$12$$
   • $$16$$
   • $$24$$
   • $$48$$

7. If Maria biked $$15$$ miles in $$3$$ hours and Tom biked three times as far in one-third the time, what was Tom's average speed, in miles per hour?

   • $$15$$
   • $$30$$
   • $$35$$
   • $$45$$

8. On a map $$2.5$$ inches represents $$75$$ miles. About how many miles do $$3.2$$ inches represent?

   • $$88$$
   • $$96$$
   • $$100$$
   • $$110$$

9. If $$-5$$ < $$xy$$ < $$0$$ then which of the following cannot be true?

   • $$x$$ > $$0$$ and $$y<0$$
   • $$x0$$
   • $$+0$$

10. In the figure $$P$$ and $$Q$$ are points on $$MN$$. $$PQRS$$ is a square inside parallelogram $$MNRU$$. Given $$PQ=4$$ cm and $$SU=6$$ cm, what is the ratio of the area of square PQRS to the area of parallelogram MNRU?

    • $$\frac{1}{3}$$
    • $$\frac{2}{5}$$
    • $$\frac{1}{4}$$
    • $$\frac{1}{2}$$

11. In the standard (x,y) coordinate plane, what is the distance on the x-axis in units from point $$C(-6,4)$$ to point $$D(2,-3)$$?

    • $$2$$
    • $$4$$
    • $$6$$
    • $$8$$

12. A walkway is represented on the standard $$(x,y)$$ coordinate plane. The line segment showing the walkway passes through the points $$(-4,3)$$ and $$(8,9)$$. What is the slope of the walkway?

    • $$-\frac{1}{2}$$
    • $$\frac{1}{2}$$
    • $$-\frac{2}{3}$$
    • $$\frac{1}{3}$$

13. In the figure below. What is the measure of $$x+y$$?

    • $$120$$
    • $$240$$
    • $$300$$
    • $$260$$

14. How many ordered pairs $$(x,y)$$ of real numbers will satisfy the equation $$4x+9y=20$$?

    • $$0$$
    • $$2$$
    • $$4$$
    • Infinitely many

15. How many different positive 3-digit integers can be formed if the three digits $$2$$, $$6$$, and $$7$$ must be used in each of the integers?

    • $$9$$
    • $$12$$
    • $$3$$
    • $$6$$

16. The polygon below was once a rectangle with sides 12 and 15, before a right triangle was cut off. What is the perimeter, in inches, of this polygon?

    • $$180$$
    • $$52$$
    • $$47$$
    • $$54$$

17. You have enough material to build a fence 160-feet long. If you use it all to enclose a square region, how many square feet will you enclose?

    • $$1,200$$
    • $$900$$
    • $$1,600$$
    • $$640$$

18. For what nonzero whole number m does the quadratic equation $$x^2+6x+9m=0$$ have exactly one real solution for x?

    • $$1$$
    • $$2$$
    • $$3$$
    • $$9$$

19. In triangle ABC, points B, D, and C are collinear. Segment AB is perpendicular to segment BC, and segment AD bisects $$\angle BAC$$. If the measure of $$\angle DCA$$ is $$60^\circ$$, what is the measure of $$\angle ADB$$?

    • $$60^\circ$$
    • $$45^\circ$$
    • $$30^\circ$$
    • $$75^\circ$$

20. If the function $$g$$ satisfies the equation $$g(x\cdot y)=g(x)+g(y)$$ for every pair of positive real numbers $$x$$ and $$y$$, what is the possible value of $$g(1)$$?

    • $$-1$$ only
    • $$0$$ only
    • $$1$$ only
    • Any nonnegative real number

21. If $$p$$, $$q$$, $$r$$ are consecutive positive integers and $$3^p\times3^q\times3^r=729$$, then $$3^p+3^q+3^r=?$$

    • $$9$$
    • $$13$$
    • $$39$$
    • $$81$$

22. If $$40\%$$ of a equals $$20\%$$ of $$b$$, which of the following expresses $$b$$ in terms of $$a$$?

    • $$b=50\%$$ of $$a$$
    • $$b=100\%$$ of $$a$$
    • $$b=150\%$$ of $$a$$
    • $$b=200\%$$ of $$a$$

23. The total weekly revenue, $$R$$, in dollars, from producing and selling y units of a certain product is given by the function $$R(y)=180y-(120y+k),$$ where $$k$$ is a constant. If $$60$$ units were produced and sold last week for a revenue of $$2,400$$, what is the value of $$k$$?

    • $$400$$
    • $$1200$$
    • $$600$$
    • $$2400$$

24. In the figure below, find $$\cos a$$.

    • $$\frac{4}{3}$$
    • $$\frac{\sqrt{3}}{4}$$
    • $$\frac{3}{4}$$
    • $$\frac{3}{5}$$

25. For any real number $$b$$, the equation $$|x+3b|=7.$$ On a number line, how far apart are the $$2$$ solutions for $$x$$?

    • $$2b$$
    • $$7+b$$
    • $$3b$$
    • $$14$$

26. A wheel $$18$$ inches in diameter rolls along a straight path. How many inches does the wheel travel along the line in $$25$$ revolutions?

    • $$25\pi$$
    • $$18\pi$$
    • $$450\pi$$
    • $$250\pi$$

27. The sides of a triangle are $$7$$, $$24$$, and $$25$$ centimeters long. What is the angle between the two shortest sides?

    • $$90°$$
    • $$30°$$
    • $$45°$$
    • $$60°$$

28. The Parks Department is planning to build a circular flower garden inside a rectangular lot that measures $$20$$ feet by $$26$$ feet. A fence must be placed around the lot, and the garden must be at least $$3$$ feet away from the fence on all sides. If the garden is to be as large as possible, what should the radius of the circular garden be?

    • $$10$$
    • $$7$$
    • $$11$$
    • $$12$$

29. Emma jogged to the park, which took her t minutes. On her way back, she jogged at an average speed three times her speed to the park. Which expression gives the total time Emma jogged on her round trip?

    • $$4t$$
    • $$\frac{4t}{3}$$
    • $$2t$$
    • $$t+\frac{1}{3}$$

30. Considering all values of $$a$$ and $$b$$ for which $$a+b\le9$$, $$a\ge2$$, and $$b\ge-2$$, what is the minimum value of $$b-a$$?

    • $$7$$
    • $$11$$
    • $$-13$$
    • $$-15$$

31. If the edges of a cube are doubled in length to produce a new, larger cube, then the larger cube's volume is how many times larger than the smaller cube's volume?

    • $$2$$
    • $$4$$
    • $$6$$
    • $$8$$

32. For all $$x≠0$$ and $$y≠0$$, evaluate $$\frac{x-y}{y(x-y)+3x(x-y)}.$$

    • $$\frac{1}{y-x}$$
    • $$\frac{1}{y+x}$$
    • $$\frac{1}{3x-y}$$
    • $$\frac{1}{y+3x}$$

33. In triangle $$PQR$$, $$QP=4$$ and $$QR=2\sqrt{13}$$. $$QS$$ bisects $$PR$$. What is the length of $$SR$$?

    • $$3$$
    • $$\sqrt{13}$$
    • $$\sqrt{5}$$
    • $$5$$

34. A total of s students signed up for a field trip. Each of the $$b$$ buses used for transportation can hold a maximum of $$k$$ students. If one bus had $$8$$ empty seats and the remaining buses were filled to capacity, which expression gives the relationship among $$s$$, $$b$$, and $$k$$?

    • $$b+k-8=s$$
    • $$bk-8=s$$
    • $$b-k+8=s$$
    • $$bk+8=s$$

35. Molarity $$M$$ represents the number of moles of solute dissolved in exactly $$1$$ liter of solution. It is given by $$M=\frac{s}{v}$$ where $$s$$ is the number of moles of solute and $$v$$ is the volume of the solution in liters. A solution has molarity $$0.5$$ and total volume $$8$$ liters. What is the number of moles of solute contained in the solution?

    • $$4$$
    • $$6$$
    • $$8$$
    • $$12$$

36. A tree casts a $$120$$-foot shadow on level ground. The angle of elevation from the tip of the shadow to the top of the tree is $$35^\circ$$. To the nearest tenth of a foot, what is the height of the tree?

    • $$110.5$$
    • $$84.0$$
    • $$105.5$$
    • $$95.5$$

37. The Lakeside Music Festival collected entry fees over $$4$$ days. The mean amount collected per day during the $$4$$-day period is what, to the nearest dollar?

    • $$550$$
    • $$600$$
    • $$580$$
    • $$480$$

38. The table below gives values of the quadratic function g for selected values of $$x$$. Which function defines $$g$$?

    • $$g(x)=x^2+2x-3$$
    • $$g(x)=3x^2-3$$
    • $$g(x)=2x^2-3$$
    • $$g(x)=x^2+2$$

39. Which of the following statements is NOT true about the geometric sequence $$81,27,9,\ldots$$?

    • The fourth term is $$3.$$
    • The sum of the first four terms is $$120.$$
    • Each consecutive term is $$\frac{1}{3}$$ of the previous term.
    • Each consecutive term is evenly divisible by $$9.$$

40. The ratio of $$a$$ to $$c$$ is $$4:7$$, and the ratio of $$b$$ to $$c$$ is $$2:7$$. What is the ratio of $$a$$ to $$b$$?

    • $$2:5$$
    • $$2:1$$
    • $$4:7$$
    • $$7:2$$

41. In the standard $$(x,y)$$ coordinate plane, the line $$4x+3y=12$$ intersects the $$y$$-axis at point $$A$$ and the $$x$$-axis at point $$B$$. What is the length of segment $$AB$$?

    • $$7$$
    • $$4$$
    • $$3$$
    • $$5$$

42. In a game, $$90$$ marbles numbered $$00$$ through $$89$$ are placed in a box. Dave first draws marble $$47$$. Without replacement, what is the probability that the next marble has the same units digit as $$47$$?

    • $$\frac{8}{9}$$
    • $$\frac{1}{89}$$
    • $$\frac{2}{9}$$
    • $$\frac{8}{89}$$

43. What is the smallest possible value for the product of $$2$$ real numbers that differ by $$8$$?

    • $$-12$$
    • $$0$$
    • $$8$$
    • $$-16$$

44. If $$f(x)=2x^2-5x+4$$, then $$f(x+y)=?$$

    • $$2x^2+4xy+2y^2-5x-5y+4$$
    • $$2x^2+2y^2-5x+4$$
    • $$2x^2+4xy+y^2-5x-y+4$$
    • $$2x^2+y^2-5x+4$$

45. What is the median of the following $$9$$ test scores?$$64, 72, 85, 80, 72, 89, 95, 100, 76$$

    • $$85$$
    • $$76$$
    • $$80$$
    • $$72$$