Full Practice Exams — Exam 12

Questions in this quiz (45)

1. 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. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?

   • $$10$$
   • $$8$$
   • $$24$$
   • $$12$$

2. Sophia and Liam are assembling toy cars together. Sophia can assemble $$4$$ toy cars per hour, while Liam can assemble $$7$$ toy cars per hour. If Sophia starts assembling first and Liam joins her $$3$$ hours later, how many toy cars will Liam have assembled by the time they finish assembling $$88$$ toy cars?

   • $$49$$
   • $$11$$
   • $$76$$
   • $$12$$

3. If $$\left|\frac{x^2}{x-1}\right|=12,$$what are the possible values of $$x$$?

   • $$6-2\sqrt{6},6-2\sqrt{7},-6-4\sqrt{3},6-4\sqrt{3}$$
   • $$6+2\sqrt{6},6-2\sqrt{6},-6+4\sqrt{3},-6-4\sqrt{3}$$
   • $$6-2\sqrt{6},6-\sqrt{6},6+4\sqrt{3},6-4\sqrt{3}$$
   • $$6+2\sqrt{6},6-2\sqrt{6},-6+\sqrt{3},-6+4\sqrt{3}$$

4. A library has a set of bookshelves that hold a total of 180 books. The number of books on each shelf is 6 more than the number of shelves. How many shelves does the library have?

   • $$6$$
   • $$10$$
   • $$4$$
   • $$12$$

5. What is $$\frac{5 \pi}{d}$$ radians converted to degrees?

   • $$\frac{180}{d}$$
   • $$\frac{900}{d}$$
   • $$\frac{5}{d}$$
   • $$\frac{90}{d}$$

6. In the arithmetic sequence below, how many terms are there between -20 and -50, exclusive of -20 and -50?$$-4, -8, -12, -16, -20,...., -48$$

   • 4
   • 6
   • 7
   • 10

7. A spherical ball of gelatin with a radius of 3 feet is melted and poured into a container shaped like a cube with an edge length of 6 feet. If the gelatin spreads evenly throughout the container, approximately how high will the gelatin fill the container in feet?(Volume of a sphere = $$\frac{4}{3}\pi r^3$$)

   • 3.14
   • 6.20
   • 2.16
   • 1.13

8. Jasmine’s phone plan charges her 25 dollars per month for the first 150 minutes and then 0.12 cents per minute for each additional minute. If Jasmine paid exactly 85 dollars last month, how many minutes did she use?

   • 85
   • 500
   • 150
   • 650

9. If $$f(x)=x^2+5x+3$$, what is $$f(4x^2)$$?

   • $$16x^4+4x^2+3$$
   • $$16x^4$$
   • $$16x^4+20x^2+3$$
   • $$16x^4+20x^2+12$$

10. If $$b$$ > $$0$$, what is the area of the circle defined by the equation: $$x^2 + y^2 = b^2$$

    • $$\pi . b^2$$
    • $$\frac{b \pi}{2}$$
    • $$\pi\sqrt{b}$$
    • $$2b \pi$$

11. If Emily rolls two 10-sided dice, each numbered from 1 to 10, what is the probability that the sum of the numbers on the dice will be exactly 12?

    • $$6%$$
    • $$18%$$
    • $$9%$$
    • $$10%$$

12. A warehouse stores pallets, each pallet contains crates, and each crate holds 12 bottles. If there are 864 bottles in total and there are 5 fewer pallets than crates per pallet, how many pallets are there?

    • 8
    • 5
    • 9
    • 12

13. Ethan wants to spend no more than $$400$$ on concert tickets for his friends. What is the maximum number of additional whole tickets he could buy at $$40$$ each compared to tickets that cost $$65$$ each?

    • 10
    • 6
    • 4
    • 7

14. In the equation below, what is the value of the sum of $$x$$ and $$y$$?$$(x + y)^2 = 4(x + y) - 4$$

    • 2
    • 4
    • -4
    • 0

15. Evaluate the expression $$x - \frac{x^2}{x + 2}$$ at $$x = \sqrt{5} - 1.$$

    • $$8\sqrt{5} - 16$$
    • $$1 - 2\sqrt{5}$$
    • $${3 - \sqrt{5}}$$
    • $$2\sqrt{5} - 4$$

16. If the difference between the area of a circle and half its circumference is $$20\pi$$, how long is the radius of the circle?

    • 5
    • 4
    • -4
    • 8

17. If the LCM of any three numbers $$a$$, $$b$$, and $$c$$ is $$x$$, then $$x$$ cannot be

    • less than the sum of numbers
    • equal to any of the numbers
    • greater than any of the numbers
    • less than any of the numbers

18. The distance between points C(x,4) and D(9,-5) is 15 units. If C lies in the second quadrant, what is its x-coordinate?

    • -6
    • 3
    • -3
    • 8

19. If $$\log_x\left(\frac{1}{27}\right) = -\frac{3}{2}$$, then what is $$x$$?

    • 3
    • 9
    • 27
    • 18

20. The shaded region in the graph below represents the solution set of one of the following systems of linear inequalities. Which one?

    • $$y \leq \frac{2}{3}x + 2$$ and $$y \leq -x + 4$$
    • $$y \geq \frac{2}{3}x + 2$$ and $$y \leq -x + 4$$
    • $$y \geq \frac{2}{3}x + 2$$ and $$y \geq -x + 4$$
    • $$y \leq \frac{2}{3}x + 2$$ and $$y \geq -x + 4$$

21. Solve the given pair of equations:$$2^x + 3^y = 17$$$$2^{x+2} - 3^{y+1} = 5$$

    • $$x = 2$$ and $$y = 2$$
    • $$x = 3$$ and $$y = 1$$
    • $$x = 1$$ and $$y = 2$$
    • $$x = 3$$ and $$y = 2$$

22. If $$\triangle ABC$$ and $$\triangle DEF$$ are similar such that $$2AB = DE$$ and $$BC = 8$$ cm, then find the length of $$EF$$.

    • 10
    • 8
    • 4
    • 16

23. If $$\theta$$ is an acute angle and $$\sin\theta = \cos\theta$$, simplify $$3\tan^2\theta + 2\sin^2\theta - 1$$

    • 1
    • $$\sin\theta$$
    • $$\cos\theta$$
    • 3

24. During a storm, a vertical pole breaks and the broken part falls in such a way that the top touches the ground, forming an angle of $$45^\circ$$ with the horizontal. The point where the top touches the ground is $$10$$ meters from the foot of the pole. Find the original height of the pole.Hint:Total height of the pole = remaining vertical part + length of the broken part

    • $$20$$
    • $$10(1 + \sqrt{2})$$
    • $$15\sqrt{2}$$
    • $$15\sqrt{2}$$

25. Two complex numbers are represented as vectors on a coordinate plane. Vector $$u$$ terminates at the point $$(6,3)$$ and vector $$v$$ terminates at the point $$(-2,-5)$$. Express the sum $$u+v$$ in the form $$a+bi$$.

    • $$4 - 2i$$
    • $$2 + 2i$$
    • $$-2 + 2i$$
    • $$-2 - 2i$$

26. In the diagram below, sides $$OC$$ and $$OB$$ of triangle $$OBC$$ are congruent. If the measure of angle $$OBC$$ is $$71$$ degrees, what is the measure in degrees of arc $$AD$$?

    • $$50^\circ$$
    • $$60^\circ$$
    • $$55^\circ$$
    • $$70^\circ$$

27. Which of the following is the equation of a parabola whose vertex is at $$(-3,2)$$?

    • $$(3,-2)$$
    • $$(-2,3)$$
    • $$(-3,2)$$
    • $$(2,3)$$

28. If $$\left(\frac{\frac{\sqrt{n}}{n}}{n^2}\right)m=7$$, what is the value of $$m$$ in terms of $$n$$?

    • $$2n^{\frac{7}{2}}$$
    • $$7n^{\frac{5}{2}}$$
    • $$5n^{\frac{7}{2}}$$
    • $$5n^{\frac{5}{2}}$$

29. If $$f(x)=5-3x^2$$ and $$g(x)=\sqrt{x+1}$$, what is the value of $$f(g(x))$$?

    • $$2x-3$$
    • $$2x+3$$
    • $$3x+3$$
    • $$2-3x$$

30. If angle 1 measures 50° and angle 4 measures 67°, what is the measure of angle 6?

    • $$63^\circ$$
    • $$30^\circ$$
    • $$45^\circ$$
    • $$25^\circ$$

31. If angle $$KMH$$ is $$\frac{5}{2}$$ times the size of angle $$KML$$ and the length of side $$JK$$ is $$L\sqrt{7}$$ units, what is the length of side $$IK$$?

    • 6.1
    • $$7\sqrt{7}$$
    • 7
    • $$\frac{\sqrt{7}}{7}$$

32. Hexagons $$UVWXYZ$$ and $$ABCDEF$$ are similar. The ratio of each side of hexagon $$UVWXYZ$$ to its corresponding side of hexagon $$ABCDEF$$ is $$3:2$$. If $$UV$$ and $$AB$$ are corresponding sides, and the length of $$UV$$ is $$6x-3$$, what is the length of $$AB$$?

    • $$6x-2$$
    • $$4x-2$$
    • $$6x+2$$
    • $$6x+1$$

33. Quadrilaterals $$PQRS$$ and $$WXYZ$$ are similar. If the perimeter of quadrilateral $$PQRS$$ is equal to $$9x^2$$, and the ratio of similarity from $$PQRS$$ to $$WXYZ$$ is $$3:1$$, what is the perimeter of quadrilateral $$WXYZ$$?

    • $$x^2+3$$
    • $$6x^2+9$$
    • $$3x^2$$
    • $$6x^2$$

34. The volume of a cube is given as $$y^3$$ cubic units, and the surface area of the cube is $$y^3$$ square units. What is the length of one edge of the cube?

    • 1
    • 2
    • 3
    • 6

35. If the length of $$MP$$ in square $$MNOP$$ is $$s$$ ft., what is the size of the shaded area?

    • $$\frac{s^2}{2}-\frac{\pi s^2}{8}$$
    • $$s^2 -\frac{\pi s^2}{4}$$
    • $$s^2-\frac{\pi s^2}{2}$$
    • $$\frac{s^2}{4}-\frac{\pi s^2}{2}$$

36. Angle $$A$$ of rhombus $$ABCD$$ measures $$120^\circ$$. If one side of the rhombus is $$10$$ units, what is the length of the longer diagonal?

    • 10
    • $$3$$
    • $$3\sqrt{3}$$
    • $$10\sqrt{3}$$

37. What is the midpoint of a line with endpoints at $$(4a - 2, 5b + 3)$$ and $$(2a + 6, -b - 5)$$?

    • $$(2a + 2, b - 1)$$
    • $$(3a + 2, 2b - 1)$$
    • $$(a - 4, 6b + 8)$$
    • $$(-2a + 8, -6b - 8)$$

38. Line P is perpendicular to line Q. If the slope of line P is multiplied by 3, what must the slope of line Q be multiplied by for the lines to remain perpendicular?

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

39. Which of the following statements is true of the graph below?

    • There are no values greater than 4 in the domain of the function.
    • There are eight $$y$$-intercepts for the equation.
    • There are at least eight different values for which $$f(x) = 1$$.
    • The graphed equation is not a function.

40. The graph below shows two ellipses $$\frac{x^2}{4} + \frac{y^2}{2} = 1$$ and $$\frac{x^2}{9} + \frac{y^2}{2} = 1$$. Which ellipse represents $$\frac{x^2}{4} + \frac{y^2}{2} = 1$$?

    • Dashed Red Ellipse
    • The blue Ellipse
    • The sum of both
    • Not shown in the graph

41. Which of the following represents the graph of the solution set of $$|x| - 1 \leq 3$$?

42. Matrices C and D are shown below. Which of the following is $$C - 2D$$?

43. For a biology project, Sofia recorded the growth of a sunflower over several weeks. She noticed that the sunflower's height increased rapidly during the early weeks, then the growth slowed down as the sunflower matured. Which of the following graphs could represent the relationship between time $$t$$ (in weeks) and the sunflower's height $$h$$?

44. During a school fair, Rita's Smoothie Stand tracked the number of smoothies sold to each customer. A total of 2000 transactions were made during the event. The results are shown in the table below.

    • 300
    • 600
    • 240
    • 760

45. Data from a random sample of 250 students at a university were collected. The table shows the number of students in three class levels (Freshman, Sophomore, Junior) and the number of hours they studied for the final exams in December. Two students are selected at random (without replacement) from the table. What is the probability that both selected students are from the same class level?

    • $$\frac{69}{1415}$$
    • $$\frac{139}{415}$$
    • $$\frac{89}{1415}$$
    • $$\frac{276}{415}$$