Full Practice Exams — Exam 6

Questions in this quiz (45)

1. The top face of a circular table has an area of $$12.7$$ square-feet. The diameter of the table's top surface is most nearly:

   • $$2.70$$
   • $$2.02$$
   • $$4.02$$
   • $$3.14$$

2. A box contains $$2$$ black cards, $$9$$ red cards, and $$5$$ white cards. What is the probability of drawing one white card from the box?

   • $$\frac{5}{16}$$
   • $$\frac{1}{5}$$
   • $$\frac{11}{16}$$
   • $$\frac{2}{5}$$

3. The volume of a right circular cone is given by: $$V = \frac{1}{12}\pi D^2H$$, where: $$D$$ is the diameter of the base, and $$H$$ is the height of the cone. If the volume of the cone is 65.5 cubic feet and its height is 10 feet, determine the radius of the circular cone in (ft):

   • $$25$$
   • $$5$$
   • $$10$$
   • $$2.5$$

4. Determine the measure of the angle $$\angle EDC$$ in the figure shown below:

   • $$120^\circ$$
   • $$30^\circ$$
   • $$60^\circ$$
   • $$90^\circ$$

5. Determine the difference of the two following expressions for all $$x$$: $$\frac{5}{2}x^2 + 2x - 10$$ and $$1.5x^2 + x - 11$$.

   • $$1.5x^2 + x + 1$$
   • $$1.5x^2 - x - 1$$
   • $$0.5x^2 - x - 1$$
   • $$x^2 + x + 1$$

6. A ball rolling at a constant rate along a straight path gives the table below. $$D$$ represents the distance traveled by the ball in meters and $$t$$ the time at which the distance is traveled in seconds.Determine the equation that represents the relationship between $$D$$ and $$t$$.

   • $$t = D + 12$$
   • $$t = 2D + 12$$
   • $$t = D -12$$
   • $$t = -D + 12$$

7. The final price of a t-shirt after a 30% discount and 7% tax applied after the discount is 18.725 dollars. Determine the net original price of the t-shirt.

   • 25 dollars
   • 18 dollars
   • 30 dollars
   • 15 dollars

8. Simplify the following expression for all real $$x$$:$$|x^2+2x+1|-2x-|6-7|$$

   • $$x^2+4x+1$$
   • $$-x^2-4x-1$$
   • $$-x^2-4x-2$$
   • $$x^2$$

9. Alex, Sam, and Oscar all contributed in buying a 4000 dollars electric scooter. If Alex contributed with 30% of the whole price and Sam contributed with double of what Oscar paid, determine the amount in dollars that Oscar contributed with:

   • $$1200.00$$
   • $$1150.25$$
   • $$933.33$$
   • $$2400.25$$

10. In the figure shown below, $$BG$$ and $$CF$$ are parallel to $$DE$$. Determine the length of $$AF$$:Given:$$BG = 4, AG = 3, CF = 6, AC = 7$$

    • $$4.5$$
    • $$3$$
    • $$4$$
    • $$5.5$$

11. The ratio of Michelle's age to her son's is $$7:2$$, and the sum of their ages is $$45$$. How old is Michelle's son?

    • $$5$$
    • $$9$$
    • $$7$$
    • $$10$$

12. Simplify the following expression:$$\frac{\sqrt{60}}{\frac{\sqrt{3}\cdot\sqrt{5}}{2}}-1$$

    • $$8$$
    • $$4$$
    • $$15$$
    • $$3$$

13. Alex will use half of his salary in paying rent, $$\frac{1}{6}$$ in gasoline, and $$\frac{1}{9}$$ in groceries. What fraction of money is left for other uses?

    • $$\frac{2}{9}$$
    • $$\frac{13}{18}$$
    • $$\frac{5}{6}$$
    • $$\frac{8}{9}$$

14. What is the value of $$x$$ if:$$\frac{x^2+2x+1}{(x+1)(x-1)}-1=0$$

    • $$-2$$
    • $$1$$
    • $$-1$$
    • No solution

15. Determine the area of the shaded region in the figure shown below. The figure consists of a rectangle with dimensions 10 units by 6 units. Two semicircles with radii 5 units each are drawn along the shorter sides of the rectangle, and an equilateral triangle is inscribed in the rectangle such that its base is along the longer side and its vertices touch the two semicircles.

    • $$25\pi - 60\sqrt{3}$$
    • $$25\pi - 25\sqrt{3}$$
    • $$60 - 25\pi$$
    • $$60 - 25\pi - 25\sqrt{3}$$

16. Determine the pair $$ (x, y) $$ that satisfies the following inequalities:$$x$$ > $$3$$$$y$$ > $$1$$$$x + y$$ < $$7$$

    • $$(4, 2)$$
    • $$(3, 1)$$
    • $$(5, 2)$$
    • $$(4, 1)$$

17. Determine the range of the function $$F$$ shown in the graph below:

    • $$(-\infty,\infty)$$.
    • $$[0, 2]$$.
    • $$[-2, 2]$$.
    • $$[-3, 3]$$.

18. Determine the value of $$f(g(-2))$$ if: $$f(x)=x^2+1$$ and $$g(x)=-3x-4$$

    • $$5$$
    • $$2$$
    • $$-2$$
    • $$-5$$

19. A factory is making and selling two products, A and B. In one day, the factory sold 500 pieces and made 6300 dollars. If the prices of products A and B are respectively 14 and 12 dollars, determine the number of product B sold on that day.

    • $$150$$
    • $$500$$
    • $$350$$
    • $$700$$

20. The scores shown below are earned by 12 students on the final exam of their physics class. Find the median score.Scores: 64, 62, 95, 73, 84, 75, 91, 87, 76, 93, 80, 71.

    • $$78$$.
    • $$73$$.
    • $$75$$.
    • $$76$$.

21. The perimeter of a rectangle is 84, and one of its sides measures 16. Find the area of this rectangle.

    • $$316$$
    • $$416$$
    • $$624$$
    • $$336$$

22. The mass of flour extracted from wheat is considered to be 85% of the wheat mass. If the mass of flour is 20 pounds, determine the mass of wheat.

    • $$37.23$$
    • $$23.53$$
    • $$17$$
    • $$33.23$$

23. Simplify the following expression for all $$a$$ > $$0$$:$$\frac{(a^{-2})^2}{a^2}$$

    • $$\frac{1}{a^6}$$
    • $$a^-2$$
    • $$a^2$$
    • $$\frac{1}{a^4}$$

24. A bag contains 10 green balls, 6 blue balls, and 12 white balls. How many white balls should be added to the bag so that the probability of drawing a white ball is $$0.5$$?

    • $$2$$
    • $$3$$
    • $$4$$
    • $$5$$

25. The figure below shows a standard (x, y) coordinate plane. Determine the area of the trapezoid ABCD in square coordinate units.

    • 25.5
    • 70
    • 35
    • 30

26. From problem the figure below, determine the distance between the points B and D.

    • $$8$$
    • $$6$$
    • $$9$$
    • $$\sqrt{73}$$

27. The coordinates of the points A and B are respectively $$(-2,4)$$ and $$(7,1)$$. What is the slope of the line passing by A and B?

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

28. In a zoo, the ratio of baboons to lions is $$5:4$$ and the ratio of giraffes to lions is $$1:2$$. What is the ratio of baboons to giraffes?

    • $$2:3$$
    • $$4:5$$
    • $$5:2$$
    • $$3:2$$

29. Determine the value of $$\log_5\sqrt[3]{625}$$.

    • $$\frac{3}{5}$$
    • $$\frac{4}{3}$$
    • $$\frac{5}{3}$$
    • $$\frac{25}{4}$$

30. Determine which expression is not equal to $$\cos(t)$$ if $$0$$ < $$t$$ < $$90$$:

    • $$\sqrt{1-\sin^2(t)}$$
    • $$\cos(-t)$$
    • $$-\cos(-t)$$
    • $$\sin(90-t)$$

31. Determine the measure of the angle shown in the figure below if the lines EF and HG are parallel.

    • $$36.87^\circ$$
    • $$30.96^\circ$$
    • $$53.13^\circ$$
    • $$45^\circ$$

32. Determine the value of $$\cos(E)$$ from the figure shown below. ABCD is a rectangle.

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

33. The least common multiple of two numbers is $$91$$ and their greatest common factor is $$1$$. What are the two numbers?

    • $$7$$ and $$13$$
    • $$12$$ and $$15$$
    • $$12$$ and $$21$$
    • $$13$$ and $$21$$

34. A statistical study was conducted on 2400 people who watched TV on Saturday night.+ $$\frac{9}{20}$$ of the people watched Channel 1.+ 600 people watched Channel 2.+ The remaining people watched Channel 3.Determine the percentage of people who watched Channel 3.

    • $$20\%$$
    • $$25\%$$
    • $$30\%$$
    • $$35\%$$

35. The probability that Alex wins his first tennis game of the season is $$0.75$$. The probability of him losing his second game is $$0.55$$. What is the probability of Alex losing both games?

    • $$0.18$$
    • $$\frac{1}{4}$$
    • $$20\%$$
    • $$0.14$$

36. What is the domain of the function $$f(n)=\frac{n+3}{n^2-4n+2}$$?

    • $$(-\infty,2)$$
    • $$(-\infty,2-\sqrt{2})U(2-\sqrt{2,2+\sqrt{2}})U(2+\sqrt{2},\infty)$$
    • $$(-2,\infty)$$
    • $$(-\infty,\infty)$$

37. The math portion of the ACT test has 60 questions and each one has 5 different answer choices. Determine the number of all possible combinations available.

    • $$3600$$
    • $$60^{5}$$
    • $$5^{60}$$
    • $$600000$$

38. Determine the coordinates of the point of intersection of the functions shown below:$$y=\ln(x+1)$$$$y=\ln(2x-1)$$

    • $$(-2,3)$$.
    • $$(2,-3)$$.
    • $$(\ln(2),\ln(3))$$.
    • $$(2,\ln(3))$$.

39. Simplify: $$(a+7i)^3$$ where $$i=\sqrt{-1}$$

    • $$a^3+14a-i(7a^2-40)$$
    • $$a^3+147a+i(21a^2+40)$$
    • $$a^3-147a+i(21a^2+40)$$
    • $$a^3-147a+i(21a^2-343)$$

40. Determine the number of units $$x$$ required to be produced and sold in order to maximize the profit $$P$$. Below are the revenue $$R$$ and the cost $$C$$ as functions of $$x$$:$$R(x)=70x-\frac{1}{3}x^2$$$$C(x)=4x+7$$

    • $$99$$
    • $$66$$
    • $$77$$
    • $$88$$

41. If a computer is able to perform $$2 \times 10^7$$ calculations per second, how many milliseconds would the computer require to perform $$400$$ calculations?

    • $$0.20$$
    • $$0.40$$
    • $$0.02$$
    • $$04.0$$

42. The coordinates of the points $$A$$ and $$B$$ are respectively $$(-5,7)$$ and $$(4,-3)$$. Find the coordinates of the midpoint of the segment $$AB$$.

    • $$(1, 5)$$
    • $$(1, 5)$$
    • $$(-0.5, 2)$$
    • $$(0.5, 5)$$

43. If $$f(x)=\sqrt{x}$$ is shifted up by 3 and right by 5, what is the new function?

    • $$f(x)=\sqrt{x-5}+3$$
    • $$f(x)=\sqrt{x+5}-3$$
    • $$f(x)=\sqrt{x-3}+5$$
    • $$f(x)=\sqrt{x+3}+5$$

44. The trajectory of a rocket is shown in the figure below. Determine the height of point E from the base.Given:$$AB=10$$$$BC=2\sqrt{3}$$$$CD=4\sqrt{2}$$$$DE=10$$

    • $$14\sqrt{6}$$
    • $$6\sqrt{14}$$
    • $$6\sqrt{6}$$
    • $$22$$

45. An engineer has an initial salary of 70000 dollars per year. He will receive a 5% raise every year. Determine his salary after 5 years.

    • $$89339.71$$
    • $$87300.50$$
    • $$95045.68$$
    • $$75039.27$$