Full Practice Exams — Exam 8

Questions in this quiz (45)

1. What percent of 75 is 15?

   • $$30\%$$
   • $$15\%$$
   • $$25\%$$
   • $$20\%$$

2. For all non-zero $$x$$ and $$y$$, simplify the following expression:$$\frac{15x^8y^{-1}}{5x^2y^{-7}}-\frac{21x^7y^7}{7xy}$$

   • $$3x^6y^6$$
   • $$-3x^6y^6$$
   • $$-6x^6y^6$$
   • $$0$$

3. Alex verses a bottle of water in a steel cone. The height of the cone is 7 inches and the radius of its top is 1.5 inches. If the volume of the bottle is 10 ounces and it is half full, what is most nearly the empty volume ratio of the cone after versing the water from the bottle in it?Note:The volume of a cone is $$V = \frac{1}{12}\pi D^2 H$$.$$1$$ ounce = $$1.8$$ cubic inches.

   • $$0.52$$
   • $$0.63$$
   • $$0.81$$
   • $$0.45$$

4. A Chinese company produces black, white, and pink headphones in the ratio $$4:5:3$$ respectively. If the company produces $$100$$ more white headphones than the black ones, determine the number of pink headphones produced.

   • $$100$$
   • $$400$$
   • $$300$$
   • $$500$$

5. For all $$x$$ such that $$|x|$$ < $$4$$, simplify the following expression:$$|2x+9|-|\frac{1}{x-5}|.$$

   • $$-2x-9-\frac{1}{x-5}$$
   • $$2x+9+\frac{1}{x-5}$$
   • $$2x+9-\frac{1}{x-5}$$
   • $$-2x-9+\frac{1}{x-5}$$

6. Adel bought a bed frame in 5 payments plus a $$200$$ dollars down payment. If the price of the bed frame is $$1800$$ dollars and the first payment is double the others, determine the amount of the $$4^{th}$$ payment that Adel made.

   • $$\frac{800}{3}$$
   • $$1600$$
   • $$160$$
   • $$\frac{160}{3}$$

7. A construction company is building a rectangular concrete wall of $$10$$ ft high, $$20$$ ft long, and $$2$$ ft wide. After building it, the company decided to paint one face of the wall. If one square foot of wall area requires $$6$$ ounces of paint and the price of $$1$$ ounce of paint is $$0.25$$ dollar, determine the price of the paint used to cover one face of the wall.

   • $$1200$$
   • $$400$$
   • $$300$$
   • $$800$$

8. Determine the slope of the line perpendicular to the following line: $$3x+27y=17$$

   • $$3$$
   • $$-3$$
   • $$9$$
   • $$17$$

9. In the polygon $$MNPQRM$$ shown, find the value of x.

   • $$6$$
   • $$7$$
   • $$8$$
   • $$9$$

10. From the figure below, determine the value of:$$\frac{\tan A}{\sin A}$$

    • $$\frac{15}{8}$$
    • $$\frac{15}{17}$$
    • $$\frac{17}{15}$$
    • $$\frac{17}{8}$$

11. What is the product of the two solutions of the equation below? $$x^2-(3i)x+28=0$$

    • $$28$$
    • $$-6$$
    • $$8$$
    • $$-9$$

12. In the figure shown below, $$AC=6$$, $$CH=4$$, and $$BH=x$$.What is the value of $$x$$?

    • $$4$$
    • $$5$$
    • $$10$$
    • $$2$$

13. The ratio of $$u$$ to $$v$$ is $$3:7$$, and the ratio of $$v$$ to $$w$$ is $$21:11$$. Determine the value of:$$\frac{v^2-u^2}{v^2-w^2}+\frac{7}{8}$$.

    • $$1$$
    • $$5$$
    • $$3$$
    • $$2$$

14. The figure below shows a trapezoid $$ABCD$$ drawn in the standard $$(x,y)$$ coordinate plane:Determine the area of the trapezoid $$ABCD$$..

    • $$21$$
    • $$15$$
    • $$30$$
    • $$18$$

15. Mickel started his morning run from the point $$(0,0)$$ of the standard coordinate plane. He ran $$12$$ minutes horizontally in the positive $$x$$ direction, and then $$18$$ minutes vertically in the positive $$y$$ direction. If Mickel did his whole run at a speed of $$0.02$$ coordinate units per second, find the coordinates of Mickel's location at the end of the run.

    • $$(12.4,18.6)$$
    • $$(16.6,18.6)$$
    • $$(21.4,18.6)$$
    • $$(14.4,21.6)$$

16. Determine the unit digit of $$7^{501}$$.

    • $$7$$
    • $$9$$
    • $$3$$
    • $$1$$

17. Determine the value of $$x$$ if:$$\frac{(x+2)(x+1)}{3}+\frac{4x^2-20}{6}=-\frac{(3+x)(3-2x)}{2}$$.

    • $$\frac{6 \pm \sqrt{27}}{24}$$
    • $$\frac{11 \pm \sqrt{27}}{2}$$
    • $$\frac{33 \pm \sqrt{1617}}{24}$$
    • $$\frac{12 \pm \sqrt{27}}{2}$$

18. One air train arrives each $$6$$ minutes while the opposite one arrives each $$8$$ minutes. At a certain moment, the two air trains arrive at the same time. How much time is needed for the two air trains to arrive at the same time again?

    • $$24$$
    • $$8$$
    • $$6$$
    • $$18$$

19. Determine the value of $$x$$ from the figure below:Note: $$C$$ is the center of the circle, and $$A, B, D$$ are all points on the circumference of the circle.Given:- The angle at $$A$$ is $$x$$.- The angle at $$B$$ is $$1.2x$$.- The angle at $$D$$ is $$35^\circ$$.

    • $$36.40^\circ$$
    • $$35.00^\circ$$
    • $$14.50^\circ$$
    • $$42.00^\circ$$

20. The equation of the ellipse $$E$$ is: $$\frac{9}{4}x^2+y^2=144$$Determine the area of the circle that can be inscribed in the ellipse $$E$$.

    • $$20\pi$$
    • $$4\pi$$
    • $$16\pi$$
    • $$8\pi$$

21. The mean of 7 numbers is 83, and the mean of the smallest two numbers is 69. What is the mean of the five other numbers?

    • $$44.3$$
    • $$27.6$$
    • $$13.8$$
    • $$88.6$$

22. $$u_n$$ is an arithmetic sequence such that: $$u_6=112$$ and $$u_{14}=56$$Determine the common difference between terms.

    • $$112$$
    • $$56$$
    • $$-7$$
    • $$8$$

23. Last week, Ali bought 4 carrots and 6 potatoes for a total of 4 dollars. Two days ago, he bought 12 potatoes for 4 dollars. Tomorrow, he is planning to go and spend 10 dollars. What is the maximum number of carrots he can purchase?

    • $$10$$
    • $$20$$
    • $$15$$
    • $$17$$

24. In the figure shown below, ABC is a right triangle at A and AH is its height. The length of AB is 3 units, and angle B is 60°. Determine the measure of HC.

    • $$\frac{11\sqrt{3}}{2}$$
    • $$\frac{\sqrt{2}}{2}$$
    • $$\frac{3\sqrt{2}}{2}$$
    • $$\frac{2\sqrt{2}}{2}$$

25. For all $$x$$ > $$y$$ > $$0$$, $$x^2-y^2=4$$ and $$x^2-2xy+y^2=2$$.Find the value of $$x+y$$.

    • $$4\sqrt{2}$$
    • $$2\sqrt{3}$$
    • $$2\sqrt{2}$$
    • $$4\sqrt{3}$$

26. What is the amplitude of the function $$-9\cos(3x+1)$$?

    • $$3$$
    • $$9$$
    • $$-9$$
    • $$1$$

27. Pumping water from a depth of $$D$$ feet requires a pump that pumps a minimum of $$\frac{9}{49}D^2-5D-50$$ gallons per minute. If Alex wants to pump water from a 70 feet deep well, what is the required pumping rate in gallons per minute?

    • $$900$$
    • $$350$$
    • $$500$$
    • $$300$$

28. In the circle shown below, $$O$$ is the center, $$AB$$ is the diameter parallel to the chord $$CD$$. If the length of the chord $$CD$$ is half the diameter and the distance between $$AB$$ and $$CD$$ is $$\frac{4}{3}$$, determine the radius of the circle.

    • $$\frac{8\sqrt{3}}{9}$$
    • $$\frac{\sqrt{3}}{3}$$
    • $$\frac{2\sqrt{2}}{3}$$
    • $$\frac{8\sqrt{2}}{3}$$

29. A triangle $$ABC$$ has vertices $$A(1,2)$$, $$B(-4,-2)$$, and $$C(3,-2)$$. Determine the area of the triangle $$ABC$$.

    • $$10$$
    • $$14$$
    • $$12$$
    • $$28$$

30. Simplify $$\frac{4+2i}{4-2i}$$, where $$i=\sqrt{-1}$$.

    • $$\frac{2}{5} + \frac{3i}{5}$$
    • $$\frac{4}{5} + \frac{2i}{3}$$
    • $$\frac{4}{5} + \frac{2i}{5}$$
    • $$\frac{3}{5} + \frac{4i}{5}$$

31. In the standard (x,y) coordinate plane, point M has coordinates (2,4), and point N(5,7). Find the length of the segment MH if the ratio MN:MH is 1:4 and the points M, N, and H are collinear.

    • $$12\sqrt{2}$$
    • $$4\sqrt{2}$$
    • $$2\sqrt{2}$$
    • $$7\sqrt{2}$$

32. Determine the perimeter length of the figure shown below if the diameter of all the circles is 10 inches.

    • $$20\pi + 40$$
    • $$5\pi + 10$$
    • $$10\pi + 40$$
    • $$30\pi + 40$$

33. A cookies store has 6 chocolate chip cookies, 4 brownie fudge cookies, and 5 vanilla sugar cookies. If Sam is planning to buy 6 cookies, what is the probability that he gets two of each kind?

    • $$\frac{1}{12}$$
    • $$\frac{9}{100}$$
    • $$\frac{180}{1001}$$
    • $$\frac{3}{20}$$

34. In the triangle ABC, AB=9, AC=7, and the angle $$\angle A$$ is 22 degrees. Determine the length of BC.

    • $$3.63$$
    • $$7.20$$
    • $$4.55$$
    • $$5.26$$

35. Two sets of numbers have both 10 distinct numbers. The two sets contain similar numbers with the exception of the largest number in each set. Which one of the following statements is true?

    • Similar median only
    • Similar range and median
    • Similar range and mean
    • Similar median and mean

36. If 1lb=454g and 1in=2.5cm, what is the equivalent of $$4kg/cm^2$$ in $$lb/in^2$$?

    • $$14.1lb/in^2$$
    • $$0.141lb/in^2$$
    • $$0.0141lb/in^2$$
    • $$1.41lb/in^2$$

37. Given that $$x=2^p$$ and $$y=4^q$$, simplify $$\log_2(x^3y)$$.

    • $$4p+2q$$
    • $$4p+3q$$
    • $$3p+2q$$
    • $$3p+4q$$

38. What is the domain of the function $$f(x)=\frac{\sqrt{x+1}}{x^2+2x+1}$$?

    • $$(-\infty,1)$$
    • $$(1,\infty)$$
    • $$(-1,\infty)$$
    • $$(-\infty,-1)$$

39. Determine the value of $$a$$ if $$x+1$$ is a factor of $$x^3+ax^2-5x-3$$.

    • $$-3$$
    • $$-1$$
    • $$3$$
    • $$-5$$

40. Simplify the following expression:$$\frac{x^{\frac{1}{4}} \cdot x^{-\frac{1}{3}}}{\frac{x^2}{x^{\frac{1}{2}}}}$$

    • $$\frac{1}{x^{\frac{19}{12}}}$$
    • $$\frac{2}{x^{\frac{3}{2}}}$$
    • $$\frac{1}{x^{\frac{1}{4}}}$$
    • $$\frac{2}{x^{\frac{1}{3}}}$$

41. What is the probability of getting exactly two heads on three coin tosses?

    • $$\frac{1}{4}$$
    • $$\frac{2}{3}$$
    • $$\frac{3}{8}$$
    • $$\frac{1}{3}$$

42. Solve for $$x$$: $$27^{5x}=\sqrt[3]{3^{x-3}}$$

    • $$-\frac{5}{27}$$
    • $$\frac{1}{9}$$
    • $$-\frac{3}{44}$$
    • $$\frac{27}{5}$$

43. Given $$h(x)=x^2$$ and $$g(x)=x-b$$, the function $$g(h(x))$$ passes through the point $$(0,4)$$. Determine the value of $$b$$.

    • $$-4$$
    • $$0$$
    • $$1$$
    • $$-2$$

44. The graph below shows the percentage of bridges built in the last seven years in Germany. Using the graph, determine the total percentage of bridges built in 1996 and 1997.

    • $$1655$$
    • $$1650$$
    • $$1550$$
    • $$1750$$

45. In the xy-plane, a parabola has a vertex at the point $$(10,-15)$$ and intersects the x-axis twice. Determine the value of $$a+b+c$$ if the equation of the parabola is $$y=ax^2+bx+c$$.

    • $$75$$
    • $$85$$
    • $$66$$
    • $$100$$