Full Practice Exams — Exam 16

Questions in this quiz (45)

1. If $$DE \parallel BC$$, then find $$x$$ in the given figure.

   • $$\frac{5}{2}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{6}$$
   • $$\frac{10}{3}$$

2. Determine the value of $$k$$ for which the given $$x=-\frac{1}{2}$$ is a solution of the equation: $$3x^2+2kx-3=0$$

   • $$\frac{1}{4}$$
   • $$-\frac{9}{4}$$
   • $$-\frac{1}{2}$$
   • $$-\frac{3}{2}$$

3. Which term of the arithmetic progression $$3, 8, 13, 18, \dots$$ is $$78$$?

   • 14
   • 15
   • 16
   • 13

4. Three friends were born in the year 2004. What is the probability that all three have different birthdays?

   • $$0.1839$$
   • $$0.99183$$
   • $$0.9831$$
   • $$0.97813$$

5. In the circle below, $$AOB$$ is a central angle, and $$ARB$$ is an inscribed angle subtending the same arc $$AB$$. If $$\angle AOB = t + 50^\circ$$ and $$\angle ARB = t + 20^\circ$$, what is the measure of the angle $$AB$$?

   • $$45^\circ$$
   • $$50^\circ$$
   • $$60^\circ$$
   • $$65^\circ$$

6. In the figure below, line $$p$$ is parallel to line $$q$$, and the angles near the intersection points are labeled. One of the angles adjacent to $$z$$ measures $$70^\circ$$, and the other angle across from $$z$$ measures $$60^\circ$$. What is the measure of $$z$$?

   • $$210^\circ$$
   • $$230^\circ$$
   • $$270^\circ$$
   • $$250^\circ$$

7. In trapezoid $$PQRS$$, point $$U$$ is the midpoint of side $$PS$$ and point $$V$$ is the midpoint of side $$QR$$. If $$PQ = 12$$ units, $$RS = 20$$ units, and the height of trapezoid $$PQVU$$ is $$6$$ units, what is the area of trapezoid $$PQVU$$?

   • 96
   • 56
   • 75
   • 84

8. If $$x$$ is a positive number less than 1, then which of the following is true?I. $$x^2$$ < $$x$$II. $$x^3$$ > $$x$$III. $$x+1$$ > $$1$$

   • I, II
   • I, III
   • II,III
   • I, II, III

9. A square-shaped garden ABCD has an area of $$81\text{ cm}^2$$. The diagonals $$AC$$ and $$BD$$ intersect at point $$O$$, dividing the square into four congruent triangles. A line segment $$EF$$ is drawn parallel to side $$AD$$. If the length of segment $$DF$$ is $$2\sqrt{2}$$ cm, determine the area of the shaded region enclosed by $$ADFE$$.

   • $$18 + 2\sqrt{2}$$
   • $$22$$
   • $$18 - 2\sqrt{2}$$
   • $$9\sqrt{2}$$

10. We survey 150 students at random from each of two schools labeled X and Y, and separate them into groups based on how many hours of homework they do per week. The results are shown in the table below. Which measure of center is the same in both schools?

    • Range
    • Mode
    • Mean
    • Median

11. If $$f(x)=x^2+4x-1$$ and $$g(x)=2-x$$, what is the value of $$f(g(3))$$?

    • 1
    • -4
    • -1
    • 4

12. If $$-\frac{4}{5}x+3\geq 2-\frac{1}{5}x$$, what is the highest value of $$\frac{3}{2}x+4$$?

    • 6.5
    • 5.5
    • 4.5
    • 3.5

13. Humidity percentage vary according to the temperature. The scatterplot below compares the temperature, in degree Fahrenheit and relative humidity on a certain day, every hour from 12:00 P.M. to 8:00 P.M. The line of best fit is also shown. Based on the line of best fit, what is the predicted humidity percentage at a temperature of 74 degrees Fahrenheit?

    • $$75\%$$
    • $$70\%$$
    • $$80\%$$
    • $$60\%$$

14. On the real number line shown below, with labeled coordinates, an object follows these instructions: starting at point P, it moves to the right to reach Q, then moves left to point R, continues right to S, and finally moves left again to return to its starting point at P. What is the best estimate, in coordinate units, of the total distance the object travels during this entire journey?

    • 36
    • 32
    • 34
    • 35

15. If $$\frac{1}{x-1}-\frac{1}{x+1}=1$$ and $$x\ne\pm1$$, what is the value of $$11x^2$$?

    • 22
    • 11
    • 10
    • 33

16. In triangle $$ABC$$, $$\sin C = 0.5$$. What is the measure of angle $$A$$?

    • $$60^\circ$$
    • $$30^\circ$$
    • $$45^\circ$$
    • $$35^\circ$$

17. Which of the following is the equation of the line perpendicular to the line with equation $$2x - 3y = -1$$ and passing through the midpoint of segment $$AB$$ given $$A(2, 7)$$ and $$B(-1, 3)$$?

    • $$y = \frac{2}{3}x + \frac{14}{3}$$
    • $$y = -\frac{2}{3}x + \frac{14}{3}$$
    • $$y = -\frac{2}{3}x - \frac{16}{3}$$
    • $$y = -\frac{3}{2}x + \frac{23}{4}$$

18. The distance between Sacramento and St Luis Obispo is approximately 500 km. To travel that distance, Mike received offers from 4 different taxi companies:Taxi A: fixed amount = 160, amount per 25 km = 15 dollars.Taxi B: fixed amount = 210, amount per 25 km = 13 dollars.Taxi C: fixed amount = 185, amount per 25 km = 14 dollars.Taxi D: fixed amount = 150, amount per 25 km = 16 dollars.Which company gave Mike the cheapest offer?

    • Taxi A
    • Taxi B
    • Taxi C
    • Taxi D

19. Given $$f(x)=2x^2+ax-1$$. What is the value of $$a$$ if the axis of symmetry of the graph of $$f$$ is equal to $$-2.5$$?

    • 5
    • 10
    • -5
    • -10

20. Using the figure below, what is the value of $$3x-1$$ if $$\overline{AC}$$ is parallel to $$\overline{FD}$$?

    • $$\frac{2}{3}$$
    • $$\frac{8}{3}$$
    • 10
    • $$\frac{20}{3}$$

21. If $$f$$ is a linear function with $$f(0)=\frac{1}{2}$$ and $$f(-3)=-\frac{3}{2}$$, what is the value of $$f(3)$$?

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

22. Which of the following is equivalent to $$\frac{4m\sqrt{3a}-2m^2\sqrt{27a}+m\sqrt{12a}}{\sqrt{243a^5}}$$ for all positive values of a and m?

    • $$\frac{6m}{9a^2}$$
    • $$\frac{2m(1-m)}{3a^2}$$
    • $$\frac{-m}{9a^2}$$
    • $$\frac{m}{9a^2}$$

23. The resistance $$R$$ of a resistor is expressed by $$R=\frac{U}{I}$$ with $$U$$ as the voltage in volts $$V$$ and $$I$$ as the current in amperes $$A$$. The linear graph below represents the characteristic current-voltage $$U-I$$ of a resistor.

    • $$U=0.4I$$
    • $$U=\frac{I}{400}$$
    • $$U=\frac{I}{4}$$
    • $$U=400I$$

24. The scatterplot below shows how many boys there are in two different villages and the changes in numbers since year 2011. The cubic curve of best fit, representing the number of boys in village A, has the following equation: $$y=-0.83x^3+51.43x^2+0.12x+2149.86$$. The line of best fit, representing the number of boys in village B, has the following equation: $$y=194.3x+2020.4$$What is the closest difference between the actual number of boys in village B and the number which can be predicted from the line of best fit in 2014?

    • 100
    • 53
    • 13
    • 26

25. Given that the points $$A(2,5)$$, $$B(9,-2)$$ and $$J(4,h)$$ lie on the same line, what is the value of $$h$$?

    • 4
    • 3
    • 2
    • 1

26. A school conducted a survey on the brand of the phone its employees are using. The survey data is shown in the table below:What is the percentage of staff members using iPhone out of all the employees?

    • $$11.11\%$$
    • $$9\%$$
    • $$10.25\%$$
    • $$39.25\%$$

27. If $$\frac{a+2i}{3-i}=2-5i$$ with $$i=\sqrt{-1}$$, what is the value of $$a^2$$?

    • $$19i+180$$
    • $$-2(19i+180)$$
    • $$-19i+180$$
    • $$-19i-180$$

28. Given the points $$A(1,4)$$, $$C(-4,-1)$$, $$B(4,1)$$, and $$R(-1,-4)$$, what is the value of the area of quadrilateral $$ABRC$$?

    • 30
    • 16
    • 32
    • 15

29. If then $$x+y+z=?$$

    • $$\frac{31}{6}$$
    • $$\frac{20}{3}$$
    • $$\frac{4}{3}$$
    • $$\frac{15}{2}$$

30. The function $$f$$ is defined by $$f(x)=\frac{2x+1}{x-3}$$ where $$x\ne3$$. The inverse of the function $$f$$ is $$f^{-1}(x)=\frac{3x+1}{x-k+1}$$. What is the value of $$k$$?

    • 1
    • 2
    • -1
    • 3

31. The vertex of a parabola is $$(4,2)$$. A second point on the parabola is $$(2,7)$$. Which point is also on the parabola?

    • $$(-2,7)$$
    • $$(4,7)$$
    • $$(6,7)$$
    • $$(4,-7)$$

32. The table below gives some statistics based on the scores Donia earned on her first three math exams.If it can be determined, what is the mean of her three scores?

    • 82
    • 84
    • 87
    • 79

33. In the figure below, ABCD is a square. If the shaded region is bounded by arcs of circles with centers at A, B, C, and D, then the area of the shaded region is:

    • $$16-4\pi$$
    • $$16-2\pi$$
    • $$16$$
    • $$64-16\pi$$

34. In a village, 80% of the people have been vaccinated. For some people, the vaccine didn't work out perfectly where 5% of the vaccinated persons will still catch the virus easily and get infected. On the other hand, 30% of the persons who didn't take the vaccine will not be infected. A person is chosen randomly and interviewed. What is the probability that this person is infected?

    • 0.18
    • 0.44
    • 0.35
    • 0.22

35. The component forms of vectors a and b are given by $$a = \langle 4, -2 \rangle$$ and $$b = \langle -1, 6 \rangle$$. Given that $$3a + (-2b) + c = 0$$ what is the component form of c?

    • $$\langle -4, 27 \rangle$$
    • $$\langle -14, 18 \rangle$$
    • $$\langle 4, 27 \rangle$$
    • $$\langle 16, -18 \rangle$$

36. Which of the following statements is NOT true about the arithmetic sequence $$17, 12, 7, 2, \ldots$$

    • The sum of the first 5 terms is $$35$$
    • The eighth term is $$-18$$
    • The common difference of consecutive terms is $$-5$$
    • The common ratio of consecutive terms is $$-5$$

37. In the figure shown below, each pair of intersecting line segments meets at a right angle, and all the lengths given are in inches. What is the perimeter, in inches, of the figure?

    • 64
    • 56
    • 80
    • 66

38. If $$0$$ < $$x$$ < $$\frac{\pi}{2}$$ and $$\frac{\cos x}{1-\sin^2 x}=\frac{3}{2}$$, what is the value of $$\cos x$$?

    • $$\frac{2}{3}$$
    • $$\frac{1}{3}$$
    • $$\frac{1}{9}$$
    • $$\frac{2}{9}$$

39. In the given figure, A is the center of the circle. C, D, E, and F are points on the circle. If segments AE and EF have the same length, what is the measure of angle $$\angle CAD$$?

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

40. Two curves with respective equations $$y=|x|-2$$ and $$y=10-|x|$$ intersect at the points A and B. What is the length of segment AB?

    • 6
    • 9
    • 12
    • 15

41. ABC is a right angled triangle at B such that $$AB=3BC$$. What is the value of $$\cos^2(A)$$ rounded to the nearest hundredth?

    • 0.1
    • 0.9
    • 0.5
    • 0.3

42. In the figure above, ABCD is a square and points A, B and O lie on the parabola of equation $$y=\frac{1}{k}x^2$$, where k is a constant number. If the area of ABCD is $$16\text{ cm}^2$$, what is the value of k?Note: Figure not to scale.

    • 1
    • 2
    • 3
    • 4

43. Alice surveyed all the students in the secondary department at her school to see their most important concern through the pandemic situation of corona virus. The results are shown in the figure. If the ratio of students who answered Vaccinations to those who answered Economic crisis was 3 to 2, what percentage of the students answered Vaccinations?

    • $$12\%$$
    • $$15\%$$
    • $$10\%$$
    • $$18\%$$

44. How many hours a day, on average, is the washer used on weekdays?

    • 5
    • 8
    • 7
    • 15

45. The polygon line above represents the grades distribution of a class on a history exam. What is the mode of the above distribution?

    • 20
    • 30
    • 35
    • 50