Full Practice Exams — Exam 7

Questions in this quiz (45)

1. A florist sells 4 types of roses. In one day, he sold 50 roses in which 23 were from the same type. The sold ratio of the other types is 1:1:1. Determine the measure of the angle, in the chart below, that represents the type of roses that was sold the least on that day.

   • $$23^\circ$$
   • $$46^\circ$$
   • $$56.7^\circ$$
   • $$64.8^\circ$$

2. Simplify: $$2+\frac{1}{3+\frac{1}{1+\frac{1}{x}}}$$

   • $$\frac{9x+7}{4x+3}$$
   • $$\frac{3x+1}{x-3}$$
   • $$\frac{3x+1}{4x-3}$$
   • $$\frac{3x-1}{x+3}$$

3. The diameters of two concentric circles are 5 and 8 inches. Determine the area inside the larger circle and outside the smaller one in square inches.

   • $$9.75\pi$$
   • $$16\pi$$
   • $$4\pi$$
   • $$2.5\pi$$

4. 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 $$x$$:$$R(x)=70x-\frac{1}{3}x^2$$$$C(x)=4x+7$$

   • $$99$$
   • $$66$$
   • $$70$$
   • $$77$$

5. If 40% more than a number is 280, what is 30% less than the number?

   • 200
   • 140
   • 300
   • 180

6. Determine the slope, x-intercept, and y-intercept of the line equation below: $$4x+7y=12$$

   • Slope: $$-\frac{1}{4}$$ ; X-intercept: $$4$$ ; Y-intercept: $$\frac{12}{7}$$
   • Slope: $$-\frac{7}{12}$$ ; X-intercept: $$12$$ ; Y-intercept: $$\frac{1}{3}$$
   • Slope: $$-\frac{4}{7}$$ ; X-intercept: $$3$$ ; Y-intercept: $$\frac{12}{7}$$
   • Slope: $$-\frac{3}{7}$$ ; X-intercept: $$7$$ ; Y-intercept: $$\frac{1}{4}$$

7. A poke bowls restaurant offers 3 bases, 5 proteins, and 6 toppings. Each bowl has 1 base, 1 protein, and 1 topping. How many types of bowls are available?

   • $$120$$
   • $$150$$
   • $$90$$
   • Answer

8. For all nonzero $$x$$ and $$y$$, what is the value of the following expression?$$\frac{(9x^2y^3)^2(3x^2y^4)}{3x^5y^9}$$

   • $$\frac{3x^3}{y^2}$$
   • $$\frac{x}{3y^2}$$
   • $$81xy$$
   • $$\frac{9x^2}{5y^2}$$

9. Determine the measure of the angle $$\angle F$$ shown in the figure below.Note: $$AB = AD$$ and $$AC = BC$$.

   • $$15^\circ$$
   • $$60^\circ$$
   • $$30^\circ$$
   • $$45^\circ$$

10. 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?

    • $$0.5$$
    • $$0.4$$
    • $$0.04$$
    • $$0.02$$

11. In the figure shown below, A is the center of the circle. B and C are two points on the same circle. If the shaded area is $$75\pi$$ square inches and the distance $$AB=10$$ inches, determine the measure of the angle $$A$$ shown in the figure.

    • $$270$$
    • $$90$$
    • $$300$$
    • $$120$$

12. What is the matrix product of: $$[2] \cdot [1 \ 2 \ 3]$$?

    • $$[0.5 \ 1 \ 1.5]$$
    • $$[1 \ 4 \ 6]$$
    • $$[6 \ 4 \ 2]$$
    • $$[2 \ 4 \ 6]$$

13. An architect is making a floor plan drawing. The floor plan is rectangular and has a length of 60 feet and a width of 45 feet. He is using a scale of $$\frac{1}{3}$$ inches = 1 foot. Determine the area (in square inches) of the floor plan in the scale drawing.

    • $$450$$
    • $$600$$
    • $$300$$
    • $$500$$

14. If the expression $$(2x-6)(x+5)$$ < $$0$$, which one of the following expressions is always negative?

    • $$x+5$$
    • $$2x-6$$
    • $$x-5$$
    • $$2x+6$$

15. The scores of a Math test are shown in the table below:Determine the mean score of the test.

    • $$75.45$$
    • $$79.82$$
    • $$80.67$$
    • $$83.42$$

16. Alex deposited 5000 dollars at 4% interest compounded annually for 12 years. How much money will Alex have after 12 years?

    • $$8005.16$$
    • $$6010.32$$
    • $$7058.75$$
    • $$8546.83$$

17. Find the inverse function of $$g(x) = Ax + B$$.

    • $$g^{-1}(x) = \frac{x + A}{B}$$
    • $$g^{-1}(x) = \frac{x - B}{A}$$
    • $$g^{-1}(x) = \frac{x - A}{B}$$
    • $$g^{-1}(x) = \frac{x}{B-A}$$

18. The diagram shows that lines $$AB$$ and $$CD$$ are parallel. Given: $$\angle BEG = 40^\circ$$ and $$\angle FGC = 30^\circ$$. Determine the measure of $$\angle GCF$$.

    • $$110^\circ$$
    • $$30^\circ$$
    • $$40^\circ$$
    • $$10^\circ$$

19. A positive integer $$a$$ is written as $$a = 3q + r$$ and $$a = 4k + r$$, where $$q, k, r$$ are whole numbers. Choose the correct possibilities of $$q$$ and $$k$$:

    • $$q = 4$$; $$k = 6$$
    • $$q = 3$$; $$k = 4$$
    • $$q = 6$$; $$k = 8$$
    • $$q = 8$$; $$k = 6$$

20. In an equilateral triangle ABC, if AD is perpendicular to BC, then:

    • $$2AB^2 = 3AD^2$$
    • $$4AB^2 = 3AD^2$$
    • $$3AB^2 = 2AD^2$$
    • $$3AB^2 = 4AD^2$$

21. If $$4\tan\theta=3$$, then find the value of $$\frac{4\sin\theta - \cos\theta}{4\sin\theta + \cos\theta}$$

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

22. Find the solution of the quadratic equation:$$\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}$$

    • $${-2,3}$$
    • $${-\frac{1}{2},\frac{7}{2}}$$
    • $${-\frac{5}{2},\frac{3}{2}}$$
    • $${-\frac{7}{2},\frac{5}{2}}$$

23. If a rubber ball consistently bounces back $$\frac{2}{3}$$ of the height from which it is dropped, what progression is it forming?

    • Geometric progression with first term $$a = 0$$ and common ratio $$r = \frac{2}{3}$$.
    • Arithmetic progression with first term $$a = 0$$ and common difference $$d = \frac{2}{3}$$.
    • Geometric progression with first term $$a = h$$ and common ratio $$r = \frac{2}{3}$$.
    • Arithmetic progression with first term $$a = h$$ and common difference $$d = \frac{2}{3}$$.

24. If the angle between two radii of a circle is $$120^\circ$$, then find the angle between the tangents drawn at the endpoints of the radii.

    • $$50^\circ$$
    • $$40^\circ$$
    • $$60^\circ$$
    • $$45^\circ$$

25. A balloon is hovering at a height of $$80$$ meters above the ground. The string holding the balloon makes an angle of $$45^\circ$$ with the ground. Assuming the string is fully taut, what is the length of the string?

    • $$141.14$$
    • $$113.12$$
    • $$80.12$$
    • $$180.15$$

26. What point on the y-axis is at a distance of 10 units from the point $$(6, 3)$$?

    • $$(1, -6)$$
    • $$(0, -5)$$
    • $$(5, 11)$$
    • $$(-1, 11)$$

27. In the trapezoid $$WXYZ$$, $$WX = YZ$$, $$XY = 15$$, and $$WZ = 25$$. If the height of the trapezoid is $$10$$ units, what is the perimeter of trapezoid $$WXYZ$$?

    • $$10\sqrt{5} + 40$$
    • $$40$$
    • $$5\sqrt{5}$$
    • $$25$$

28. After a heavy rainfall, city workers collected 9000 cubic meters of water from drainage systems. If this water were evenly spread over a rectangular park with dimensions 50 meters by 60 meters, about how many meters deep would the water layer be?

    • 3
    • 6
    • 9
    • 11

29. The ratio of the side lengths for a triangle is exactly $$5:8:10$$. In a second triangle similar to the first, the shortest side is 12 inches long. What is the length of the longest side of the second triangle?

    • 24
    • 12
    • 10
    • 30

30. In a class of 30 students, 18 students like math and 16 students like science. What is the minimum number of students who like both math and science?

    • 0
    • 4
    • 5
    • 6

31. A rectangle is drawn on the coordinate plane with vertices at $$(0,0)$$, $$(b,0)$$, $$(b,c)$$, and $$(0,c)$$. A line $$l$$ passes through the point $$(a,0)$$ and $$(b,c)$$, forming a triangle with area equal to $$\frac{2}{5}$$ the area of the rectangle. It is also given that $$2b=3c$$. What is the slope of line $$l$$?

    • $$\frac{b}{a}$$
    • $$\frac{2}{3}$$
    • $$\frac{5}{6}$$
    • $$\frac{b}{c}$$

32. Carla takes a quiz five times. Her scores for the first four quizzes are 14, 22, 10, and 18. How many points must Carla score on her fifth quiz so that the median and mode of all five scores are equal?

    • 10
    • 14
    • 22
    • 20

33. Which of the following has the greatest value when $$x=-\frac{1}{5}$$?

    • $$x^{-2}$$
    • $$-\frac{4}{10x}$$
    • $$5x+2$$
    • $$12x$$

34. Stickers are sold according to the chart:If Mia wants to buy 3000 stickers, how much money does she save by buying 1000 stickers at a time rather than 10 stickers at a time?

    • 3600
    • 3000
    • 1800
    • 5400

35. The graph of $$y = g(x)$$ is shown in the standard $$(x, y)$$ coordinate plane. One of the following graphs is that of $$y = g(x - 2) + 1$$. Which graph is it?

36. A drone is descending steadily towards a landing pad. The table below shows the height $$h$$ (in meters) of the drone at 1-second intervals from $$t = 0$$ seconds to $$t = 4$$ seconds.Which of the following equations represents this data?

    • $$h = -4t + 15$$
    • $$h = 4t + 15$$
    • $$h = 15t - 200$$
    • $$h = -15t + 200$$

37. In the standard$$(x,y)$$coordinate plane, the region bounded by the lines$$x=k$$,$$y=0$$, and$$y=3x$$has an area of 27. What is the value of$$k$$?

    • $$\frac{3}{2}$$
    • $$18$$
    • $$\frac{1}{2}$$
    • $$3\sqrt{2}$$

38. A parabola passes through the point $$(2,-10)$$ and has $$x$$-intercepts at $$-2$$ and $$6$$. What is the vertex of the parabola?

    • $$(-10,16)$$
    • $$(5,8)$$
    • $$(2,-10)$$
    • $$(6,12)$$

39. As shown below, two circular pulleys with centers $$10$$ inches apart are connected with a tight belt. The belt wraps $$\frac{3}{4}$$ of the way around the larger pulley, which has a radius of $$4$$ inches, and $$\frac{1}{4}$$ of the way around the smaller pulley, which has a radius $$2$$ inches. What is the exact length of the belt, in inches?

    • $$7\pi + 2\sqrt{104}$$
    • $$\frac{3}{2}\pi +10$$
    • $$\frac{3}{2}\pi +10\sqrt{3}$$
    • $$8\pi + 6$$

40. The graphs of $$y=-x+1$$, $$y=x-3$$, and $$x^2+y^2=9$$ are shown in the standard $$(x,y)$$ coordinate plane below. The shaded region is the solution set to one of the following systems of inequalities. Which system is it?

    • $$y\le x-3$$ ; $$x^2+y^2\le 9$$
    • $$y\le x+1$$ ; $$x^2+y^2\ge 9$$
    • $$y\le -x+1$$ ; $$x^2+y^2\le 9$$
    • $$y\ge x-3$$ ; $$x^2+y^2\le 9$$

41. The table below gives the cost of buying notebooks by the pack from a certain supplier. The cost per pack depends on the number of packs in the order.Which of the following graphs best illustrates this information?

42. A jar contains $$g$$ green marbles and $$y$$ yellow marbles. If the probability of randomly drawing a green marble from the jar is $$\frac{2}{5}$$, what is the value of $$\frac{g}{y}$$?

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

43. Question 43

44. Graphed in the standard $$(x, y)$$ coordinate plane below is an ellipse. The center of the ellipse is $$(0, 0)$$, and points $$(-6, 0), (0, 4), (6, 0), (0, -4), P(4, m),$$ and $$Q(4, n)$$ lie on the ellipse. What is the distance, in coordinate units, from point $$P$$ to point $$Q$$?

    • $$\frac{8\sqrt{5}}{3}$$
    • $$\frac{80}{9}$$
    • $$\frac{4\sqrt{5}}{3}$$
    • $$\frac{80}{9}$$

45. Which of the following is equivalent to the given expression?$$(5 + 2i)(7 - 3i) - \sqrt{9i \cdot 3i}$$Note: $$i^2 = -1$$

    • $$41 +3i$$
    • $$41 - 3i$$
    • $$41 - 3\sqrt{3})i$$
    • $$41 - (1 + 3\sqrt{3})i$$