Full Practice Exams — Exam 1

Questions in this quiz (45)

1. If $$f(x)=5-2x$$ and $$g(x)=\frac{x^2}{4}$$, which of the following cannot be a value of $$f(g(x))$$?

   • -3
   • 0
   • 5
   • 6

2. A circle in the $$xy$$-plane has center $$(-2,-5)$$. A line $$k$$ is tangent to the circle at the point $$(-4,1)$$. What is the slope of line $$k$$?

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

3. If $$x^2 + bx + c = 0$$ has solutions $$r$$ and $$s$$, what is the value of $$(r - s)^2$$?

   • $$b^2 - 4ac$$
   • $$b^2 - 4c$$
   • $$b^2 - 2ac$$
   • $$\frac{b^2 - 4ac}{2}$$

4. If $$2^x = 5$$, what is $$2^{2x} - 3 \cdot 2^x + 1$$?

   • 111
   • 23
   • 25
   • 11

5. If $$\log_b{16} = 4$$, what is the value of $$b$$?

   • 2
   • 4
   • 8
   • 10

6. If $$\sin(\theta) = \frac{3}{5}$$ and $$\theta$$ is in quadrant II, what is $$\cos(\theta)$$?

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

7. The area of a sector is $$25\pi$$ and the radius is $$10$$. Find the central angle in radians.

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

8. Find the sum of the infinite geometric series $$9 + 3 + 1 + \ldots$$.

   • $$9$$
   • $$15$$
   • $$13.5$$
   • $$27$$

9. At first, Tank A was empty and one third of Tank B was filled with water. Both taps were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute. How long did it take for the height of the water to be the same in both tanks?

   • 15
   • 20
   • 25
   • 30

10. Pupils in a school are put into two groups for a learning journey. $$\frac{2}{5}$$ of the pupils are in Group A and the rest are in Group B. $$\frac{1}{4}$$ of the pupils in Group A are girls. In the school, $$\frac{3}{10}$$ of the pupils are girls. What fraction of the pupils in Group B are girls?

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

11. If $$f(x) = x^2 - 11$$, for what values of x is $$f(x)$$ < $$25$$?

    • $$x$$ < $$-6$$
    • $$x$$ > $$6$$
    • $$x$$ < $$5$$
    • $$-6$$ < $$x$$ < $$6$$

12. Rhombus ABCD is shown. If AD=10 meters and AC=12 meters, what is the length in meters of BD?

    • 4
    • 6
    • 8
    • 10

13. Carmen builds stacks of blocks so that each level has exactly one fewer block than the level directly beneath it, with the top level containing just 1 block. For example, a stack with 3 levels is shown. If Carmen builds a stack with 15 levels following this pattern, how many blocks will she need in total?

    • 225
    • 88
    • 144
    • 120

14. Find the measure of the angle x.

    • $$50^\circ$$
    • $$130^\circ$$
    • $$100^\circ$$
    • $$75^\circ$$

15. In the figure, the lines AD and BE intersect at C. In triangle ABC, the angle at A is 20° and the angle at B is x°. In triangle CDE, the angle at E is 40° and the angle at D is y°. If x=100, find y.

    • $$60^\circ$$
    • $$40^\circ$$
    • $$30^\circ$$
    • $$80^\circ$$

16. In the circle with center D, the radius CD is 4 centimeters. The segment BC has length 1 centimeter and is perpendicular to the radius AD at B. When the central angle ∠ADC is measured in degrees, what expression gives the length, in centimeters, of arc AC?

    • $$\frac{2\pi}{45}(\sin^{-1}(\left(\frac{1}{4}\right))$$
    • $$\frac{\pi}{45}(\cos^{-1}(\left(\frac{1}{4}\right))$$
    • $$\frac{\pi}{45}(\sin^{-1}((\frac{1}{4}))$$
    • $$\frac{2\pi}{45}(\cos^{-1}(\left(\frac{1}{4}\right))$$

17. Let x and y be positive numbers such that x<y. Which of the following expressions has the greatest value?

    • $$(x+y)/x$$
    • $$(x+y)/y$$
    • $$x/(x+y)$$
    • $$(x+y)/(y+x)$$

18. In the standard (x,y) coordinate plane, find the equation of the largest circle that can be inscribed in the ellipse$$9x^2+25y^2=225$$

    • $$(x-3)^2+(y-25)^2=225$$
    • $$(x+3)^2+(y+5)^2=225$$
    • $$x^2+y^2=9$$
    • $$(x-3)^2+(y-5)^2=25$$

19. What is the 415th digit after the decimal point in the repeating decimal $$7.\overline{3581}$$?

    • 3
    • 5
    • 8
    • 1

20. For whole numbers p and q, the list below has 5 as its mean, median, and mode. What is the value of pq?3, 7, 5, 2, p, q

    • $$5$$
    • $$8$$
    • $$40$$
    • $$16$$

21. In the standard (x,y) coordinate plane, point M(3,-2) is the midpoint of segment PQ. Point P lies on the line y=2x+1 and has an x-coordinate of 5 What are the coordinates of point Q?

    • $$(5,11)$$
    • $$(1,-15)$$
    • $$(8,-13)$$
    • $$(4,-\frac{13}{2})$$

22. Question 22

23. Given that $$2\le a\le 5$$, $$3\le b\le 6$$, and $$7\le c\le 9$$, what is the greatest possible value of $$(\frac{a}{b})\cdot(\frac{1}{c})$$?

    • $$\frac{5}{21}$$
    • $$\frac{2}{27}$$
    • $$\frac{2}{21}$$
    • $$\frac{1}{27}$$

24. The polynomial function defined by $$q(x)=x^{3}-2x^{2}-5x+6$$ has $$(x-1)$$ as one of its linear factors. What are all the zeros of $$q(x)$$?

    • $$x=1, x=3, x=-2$$
    • $$x=1, x=6, x=-3$$
    • $$x=1, x=-4, x=2$$
    • $$x=1, x=-2, x=4$$

25. Each time Coin D is tossed, it lands heads or tails. The probability of landing heads is twice the probability of landing tails. In a certain game, the player wins 1.50 dollars when Coin D lands heads and the player wins 3.00 dollars when Coin D lands tails. To the nearest cent, what is the expected value of each toss of Coin D in this game?

    • 2.50 dollars
    • 2.10 dollars
    • 2.20 dollars
    • 2.00 dollars

26. For all positive values of m, n, p, and q, when $$\frac{1}{3}mn^{2}+p=q$$ which of the following expressions is equal to n?

    • $$\sqrt{\frac{3(p-q)}{m^2}}$$
    • $$\sqrt{\frac{3(m)}{p-q}}$$
    • $$\sqrt{\frac{3(q-p)}{m}}$$
    • $$\frac{3(m)}{\sqrt{p-q}}$$

27. A motel manager charges 40 dollars per night for a room. The manager raises the room rate by 22 percent. Then a discount of 15 percent on the new rate is offered for guests who stay more than 3 nights. What is the nightly rate for those guests and what is the net percent change from the original price?

    • $$48.8\%$$
    • $$41.48\%$$
    • $$31.2\%$$
    • $$3.7\%$$

28. What is the slope of any line parallel to the line $$6x-4y=12$$ in the standard $$(x,y)$$ coordinate plane?

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

29. The vertices of a rectangle are $$(-3,-4)$$, $$(2,-4)$$, $$(2,2)$$, $$(-3,2)$$. When this rectangle is graphed in the standard $$(x,y)$$ coordinate plane, what percent of its total area lies in Quadrant III?

    • $$40\%$$
    • $$25\%$$
    • $$20\%$$
    • $$30\%$$

30. In 2000, the cost of groceries for a certain household was 480 dollars. In 2010, 10 years later, the cost of groceries for this household was 840 dollars. Assuming the cost increased linearly, what was the cost of groceries for this household in 2006?

    • $$708$$
    • $$712$$
    • $$696$$
    • $$698$$

31. Emily is planning to install a 150-foot-long driveway. The QuickPave Company charges a flat fee of 300 dollars, plus a set cost per foot of driveway. If Emily receives a total estimate of 1650 dollars for the project, what is the set cost per foot of driveway in dollars?

    • 9
    • 10
    • 100
    • 150

32. One sprinkler sprays water every 6 seconds, and another sprinkler sprays every 8 seconds. At a certain instant, both sprinklers spray at the same time. How many seconds will pass before the two sprinklers next

    • $$12$$
    • $$18$$
    • $$24$$
    • $$36$$

33. What is the amplitude of the function $$g(x)=3\sin(2x-\frac{\pi}{4})$$?

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

34. In the complex numbers, where $$i^2=-1$$, evaluate $$\frac{1+i}{1-i}\cdot\frac{1+i}{1+i}$$

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

35. In a survey, 1800 people are asked to select a number from 1 to 50. Most people selected a number between 1 and 15, and only a small portion selected a number greater than 35. Which descriptor best characterizes the distribution of the numbers the 1800 people selected?

    • Bimodal
    • Skewed right
    • Uniform
    • Skewed left

36. If the ratio of 3x to 4y is $$\frac{2}{25}$$, what is the ratio of x to y?

    • $$3:4$$
    • $$3:2$$
    • $$2:3$$
    • $$8:75$$

37. A survey asked 30 critics to rate a novel with 0 to 5 stars. The histogram shows counts for each rating. What should be the central angle in degrees of the pie-chart sector for the one-star reviews?

    • $$30^\circ$$
    • $$35^\circ$$
    • $$48^\circ$$
    • $$45^\circ$$

38. Let the segments AB and CD intersect at M with the following lengths: MA=3, MB=8, MC=2, MD=12. Find BD in terms of AC.

    • $$BD=2\cdot AC$$
    • $$BD=4\cdot AC$$
    • $$BD=\frac{1}{2}\cdot AC$$
    • $$BD=\frac{1}{4}\cdot AC$$

39. In the figure below, determine the measure of angle x if $$QS = QT = PV = PU$$.$$\angle MSV = 50^\circ$$, $$\angle TNR = 70^\circ$$, $$\angle UOR = 40^\circ$$, $$\angle TRN = x^\circ$$

    • $$50^\circ$$
    • $$70^\circ$$
    • $$60^\circ$$
    • $$80^\circ$$

40. Sofia biked along a hilly trail. The graph shows her speed in miles per hour from 0 to 60 minutes. Which statement about the ride is not true?

    • Sofia’s speed was increasing for 20 minutes straight in the middle of the race.
    • Sofia’s speed steadily decreased during the last 20 minutes of the ride.
    • Sofia’s maximum speed occurred sometime between minutes 30 and 60.
    • Sofia’s speed was higher at the end of the ride than at the beginning.

41. A team of biologists models the deer population by $$P(t)=P_0\cdot2^{0.25t}$$ where $$P_0$$ is the initial population and $$t$$ is time in years. If $$P(12)=200$$, what is $$P(20)$$?

    • $$200$$
    • $$400$$
    • $$600$$
    • $$800$$

42. The graph below shows an upward-opening parabola. Which equation matches the graph among the following choices?

    • $$y=x^2+2x-3$$
    • $$y=x^2-2x+3$$
    • $$y=x^2-2x-3$$
    • $$y=x^2+x+2$$

43. A circle graph shows a monthly budget for an income of 3500 dollars. How much more money is budgeted for rent than for food and clothing combined?

    • 60
    • 120
    • 210
    • 600

44. In a certain year, the population of the state of Florida was estimated to be 21,538,187. Which of the following values is closest to this estimate?

    • $$2.2\times10^7$$
    • $$2.2\times10^8$$
    • $$2.1\times10^8$$
    • $$2.2\times10^6$$

45. Alex claims, If a quadrilateral is in Set B, then it must be a rectangle. Later, Alex discovers that quadrilateral PQRS is a counterexample proving this claim false. Which statement must be true about PQRS?

    • It is a rectangle and in Set B.
    • It is not a rectangle and in Set B.
    • It is not a rectangle and not in Set B.
    • It is a rectangle and not in Set B.