Full Practice Exams — Exam 11

Questions in this quiz (45)

1. Alex leaves point A in his car traveling to point B at an average speed of $$65 \, \text{mph}$$. At the same time, Sam leaves point B in his car traveling towards point A at an average speed of $$70 \, \text{mph}$$. If they both started their travel at 6:00 am and the distance between the points A and B is $$270 \, \text{miles}$$, determine the time, to the nearest minute, they will drive past each other.

   • $$9:00$$ am
   • $$8:00$$ am
   • $$10:00$$ am
   • $$11:00$$ am

2. Determine the coefficient of $$x^2$$ when expanding $$(x+1)^4$$.

   • $$1$$
   • $$4$$
   • $$6$$
   • $$2$$

3. 20 students selected a random number from the ones shown in the table below. Determine the median number selected for the 20 students.

   • 7
   • 5
   • 8
   • 9

4. Determine the volume in cubic yards of an 18 feet diameter sphere.

   • $$270.00$$
   • $$291.60$$
   • $$972.00$$
   • $$113.04$$

5. What is the smallest integer greater than $$\sqrt{120}$$?

   • $$\frac{549}{50}$$
   • $$13$$
   • $$12$$
   • $$11$$

6. A, B, and C are 3 points on a circle whose center is O. BC is the diameter of the circle, AB and AC are perpendicular at A, the length of AB is 5 centimeters, and the length of AC is 12 centimeters. Determine the length of AH in centimeters.

   • $$11.08$$
   • $$\frac{60}{13}$$
   • $$10$$
   • $$\frac{50}{13}$$

7. A parallelogram has consecutive angles with measures of 25 and $$x$$ degrees. Determine the value of $$x$$.

   • $$180$$
   • $$125$$
   • $$185$$
   • $$155$$

8. ABC is a right triangle at A. Determine the measure of the side AC if $$BC=10$$ and $$\sin C=\frac{\sqrt{3}}{2}$$.

   • $$10$$
   • $$5\sqrt{3}$$
   • $$5\sqrt{3}$$
   • $$5\frac{\sqrt{3}}{2}$$

9. Using the figure shown below, determine which inequality correctly relates to the sides of the triangle ABC.

   • $$c$$ > $$a$$ > $$b$$.
   • $$b$$ > $$a$$ > $$c$$.
   • $$c$$ > $$b$$ > $$a$$.
   • $$a$$ > $$b$$ > $$c$$.

10. The function $$f$$ is defined by $$f(x,y)=\log\left(\frac{10(x+8)^3}{\sqrt[3]{(y+5)^2}}\right)$$. Determine the value of $$f(2,5)$$.

    • $$4.45$$
    • $$2.25$$
    • $$2.50$$
    • $$3.33$$

11. The cost to rent a car is 50 dollars per day plus 0.5 dollar for every mile the car is driven. If Alex wants to rent the car for a whole week and plans to drive 500 miles, what is the total cost he will need to pay?

    • $$600$$
    • $$350$$
    • $$500$$
    • $$250$$

12. A pre-calculus class has 8 seniors and 4 juniors. The professor will randomly select 2 students to solve the problems written on the board. If the first student selected is a senior, what is the probability that the second student will be a junior?

    • $$\frac{2}{11}$$
    • $$\frac{4}{11}$$
    • $$\frac{8}{11}$$
    • $$\frac{9}{11}$$

13. What is 25% of $$1.6 \times 10^5$$?

    • $$1.6 \times 10^4$$
    • $$2.5\times 10^5$$
    • $$400000$$
    • $$4\times 10^4$$

14. In the standard $$(x,y)$$ coordinate plane, the graph of the function $$y = 10 \cdot \sin(x+1)-3$$ undergoes a double translation such that the equation of its image is $$y = 10 \cdot \sin(x-1)$$. Which of the following describes this translation?

    • The graph is translated $$2$$ units to the right and $$1$$ unit upward.
    • The graph is translated $$1$$ unit to the right and $$1$$ unit upward.
    • The graph is translated $$3$$ units to the right and $$1$$ unit upward.
    • The graph is translated $$2$$ units to the right and $$3$$ units upward.

15. A right circular cylinder has a height of 10 meters and a radius of 3 meters. The cylinder is fully filled with water. If the density of water is $$1 \times 10^3 kg/m^3$$, determine the weight of water in kg.

    • $$90000$$
    • $$9 \times 10^4 \pi$$
    • $$9 \times 10^5$$
    • $$90\pi$$

16. A sphere has a surface area of $$64\pi$$. What is its volume?

    • $$\frac{4}{3}\pi$$
    • $$\frac{2}{3}\pi$$
    • $$\frac{64}{3}\pi$$
    • $$\frac{256}{3}\pi$$

17. The vertex angle of an isosceles triangle is $$40^\circ$$, and the side opposite the vertex has a length of 12. What is the area of the triangle?

    • 98.89
    • 102.56
    • 87.76
    • 76.52

18. If $$3a + b = 10$$ and $$3a - b = 4$$ what is the value of $$9a^2 - b^2$$?

    • 40
    • 10
    • 49
    • 3

19. If a parabola has the equation $$y = (x + 4)^2 + 3$$ what is its vertex?

    • $$(-3, 4)$$
    • $$(4, -3)$$
    • $$(3, 4)$$
    • $$(-4, 3)$$

20. If $$0^\circ \leq x \leq 90^\circ$$ and $$\sin x = \frac{5}{13}$$, then what is $$\tan x$$?

    • $$\frac{144}{5}$$
    • $$\frac{8}{13}$$
    • $$\frac{5}{12}$$
    • $$\frac{12}{13}$$

21. If $$2 - \frac{3}{b} = 5 - \frac{7}{b}$$, then what is the value of $$2 - \frac{3}{b}$$?

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

22. One end of a wire is attached to the top of a 60-foot-high pole, and the other end is attached to a stake in the ground. If the wire makes a 45° angle with the ground, how long is the wire?

    • $$30\sqrt{2}$$
    • $$60\sqrt{2}$$
    • $$2\sqrt{3}$$
    • $$60\sqrt{3}$$

23. If the base of a triangle decreases by 10% and its corresponding altitude increases by 10%, by what percent does the area of the triangle change?

    • The area of the triangle decreases by $$1\%$$.
    • The area of the triangle stays the same.
    • The area of the triangle increases by $$10\%$$.
    • The area of the triangle decreases by $$10\%$$.

24. A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr, it would have taken 6 hours more than the scheduled time. Find the length of the journey.

    • 240
    • 480
    • 300
    • 720

25. The $$17$$th term of an arithmetic progression exceeds its $$10$$th term by $$7$$. What is the common difference?

    • 7
    • 9
    • 6
    • 1

26. A person standing on the bank of a canal observes that the top of a tower on the opposite bank subtends an angle of $$45^\circ$$. After walking $$15$$ meters backward from the canal, the angle reduces to $$30^\circ$$. Find the height of the tower and the width of the canal.

    • Height of tower: $$20.49$$ meters Width of canal: $$20.49$$ meters
    • Height of tower: $$25.50$$ meters Width of canal: $$26.70$$ meters
    • Height of tower: $$30.55$$ meters Width of canal: $$22.69$$ meters
    • Height of tower: $$27.56$$ meters Width of canal: $$27.32$$ meters

27. Each of the letters in the word BALLOON is written on separate cards and placed face down on the table. If you pick a card at random, what is the probability that its letter will be L or O?

    • $$\frac{2}{7}$$
    • $$\frac{4}{7}$$
    • $$\frac{5}{7}$$
    • $$\frac{1}{2}$$

28. Find all values of x:$$\sqrt{x - 1} = x - 7$$

    • 5
    • 10
    • 7

29. A linear equation in the xy-plane intercepts the y-axis at 4. For every 5 units the y-coordinate of the line increases, the x-coordinate decreases by 2 units. Which of the following is the correct equation for this line?

    • $$y = 2x + \frac{5}{2}$$
    • $$y = 4x - \frac{5}{2}$$
    • $$y = 2x + 4$$
    • $$y = -\frac{5}{2}x + 4$$

30. A circle graph shows the votes of 600 students regarding a proposed school policy.The votes are divided into two categories: FOR and AGAINST.If the central angle for the AGAINST section is $$60^\circ$$, how manystudents voted AGAINST the policy?

    • 100
    • 120
    • 180
    • 360

31. The graph below represents the price of gold per ounce in dollars between 1920 and 2020. Which of the following is closest to the price in dollars of an ounce of gold in the year 1980?

    • $$2500$$
    • $$1950$$
    • $$2200$$
    • $$2400$$

32. In the year 2005, approximately 5 million people subscribed to a streaming service. In the year 2015, approximately 160 million people were subscribers. Assuming the number of subscribers grew at a steady geometric rate, which function could be used to model the number of subscribers, $$S$$, in millions, $$T$$ years after 2005?

    • $$S(T) = 4 \cdot(0.5)^T$$
    • $$S(T) = 5 \cdot (-4)^T$$
    • $$S(T) = 5 \cdot (4)^T$$
    • $$S(T) = 5 \cdot (2)^T$$

33. The table below shows how many texts 20 students send daily.Twenty students were surveyed about how many texts they send daily. The results are shown in the table above. If two more students are added to this group — one who sends 5 texts and one who sends 45 texts per day — how would the median number of texts per student be affected?

    • Increases
    • Decreases
    • Remains the same
    • Cannot determine from the given information

34. Which of the following represents the function shown below in the graph?

    • $$f(x)=x^3$$
    • $$f(x)=x^2-1$$
    • $$f(x)=3^x-1$$
    • $$f(x)=2^x$$

35. If $$f(x)=x^2+2$$ and $$f(x+n)=x^2-4x+10$$, what is the value of the constant $$n$$?

    • -2
    • 4
    • -4
    • 2

36. Phobos, a moon of Mars, completes one orbit around Mars every 11 hours. Deimos, another moon of Mars, completes one orbit every 30 hours. For every full orbit Phobos makes, let that be represented by P. How many orbits (or fractions of an orbit) will Deimos complete, represented by D, in the same amount of time?

    • $$D=\frac{11}{15}P$$
    • $$D=\frac{5}{2}P$$
    • $$D=\frac{11}{30}P$$
    • $$D=\frac{30}{11}P$$

37. A company's revenue, $$R$$, for selling $$x$$ items is modeled by the following function:$$R = -5x^2 + 200x - 800$$How many items should the company sell to achieve its maximum revenue?

    • 20
    • 80
    • 50
    • 800

38. A graphic designer earns $$40$$ per hour plus a $$3000$$ project bonus at the end of the year. Which inequality represents the number of hours, $$h$$, she must work in order to earn at least $$35000$$ in total compensation for the year?

    • $$35,000 \ge 40h + 3,000$$
    • $$\frac{h}{40} \le 3000$$
    • $$35,000 \le 40h + 3,000$$
    • $$\frac{h}{40} \ge 3000$$

39. A certain investment account earns no interest in the first year and then earns 5 percent annual compounded interest on the original deposit for each year after. If $$y$$ dollars are deposited initially, which of the following equations expresses the total value $$V(n)$$ of the account $$n$$ years later, where $$n$$ is an integer greater than 1?

    • $$V(n) = y(1.05)^{n-1}$$
    • $$V(n) = y(0.05)^{n}$$
    • $$V(n) = y(0.05)^{n+1}$$
    • $$V(n) = y(0.05)^{n-1}$$

40. The growth of a colony of fungi is modeled by the function $$F(t) = 500 \cdot 3^t$$ where $$F(t)$$ represents the number of fungi after $$t$$ hours. After how many hours will the population of fungi be 27 times its initial number?

    • 3
    • 4
    • 5
    • 2

41. In the xy-coordinate system, the distance between the point (0,0) and point Q is $$\sqrt{52}$$. Which of the following could be the coordinates of point Q?

    • $$(4,6)$$
    • $$(5,5)$$
    • $$(6,5)$$
    • $$(7,3)$$

42. At what point will a circle with the equation $$(x+2)^2+(y-3)^2=16$$ and the line $$y=1$$ intersect?

    • $$(-2,\ 1)$$ and $$(\sqrt{3},\ 1)$$
    • $$(-1,\ 1)$$ and $$(2,\ 1)$$
    • $$(-2,\ 1)$$ and $$(\sqrt{3},\ 2)$$
    • $$(-2+2\sqrt{3},\ 1)$$ and $$(-2-2\sqrt{3},\ 1)$$

43. The function $$f$$ is defined as: $$f(n) = \frac{2}{\sqrt[4]{n} - 300}$$If both $$f(n)$$ and $$n$$ are integers, what is the largest possible value that $$n$$ can be?

    • 300
    • 301
    • 302
    • 303

44. If $$\frac{5x^2+65x+60}{x^2+10x-24}=\frac{5x+5}{x-2}$$ then which of the following are possible values of $$x$$?

    • 2
    • -12
    • 2, 12
    • All real numbers except $$-12$$ and $$2$$.

45. Which of the following is equal to $$\frac{1}{i}+\frac{1}{i^2}+\frac{1}{i^3}$$Note: $$i=\sqrt{-1}$$

    • 1
    • -1
    • $$i$$
    • $$-i$$