Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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Simplify the radical expression.
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1.
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2.
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3.
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4.
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 factor 1: 1 factpr 2: 11 common
factor: 2
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5.
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6.
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7.
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8.
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9.
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A student visiting the Sears Tower Skydeck is 1353 feet above the ground. Find
the distance the student can see to the horizon. Use the formula  to approximate the
distance d in miles to the horizon when h is the height of the viewer’s eyes
above the ground in feet. Round to the nearest mile. a. | 45 miles | b. | 601 miles | c. | 36 miles | d. | 1010
miles |
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Simplify the radical expression by rationalizing the denominator.
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10.
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11.
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12.
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A square garden plot has an area of 24 ft2.
a. Find the
length of each side in simplest radical form.
b. Calculate the length of each side to the
nearest tenth of a foot.
a. |  ; 2.45 ft | c. |  ; 6
ft | b. |  ; 4.9 ft | d. |  ; 5 ft |
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Find the length of the missing side. If necessary, round to the nearest
tenth.
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13.
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14.
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15.
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A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean
floor. The rope is 140 feet long and the water is 40 feet deep. To the nearest tenth of a foot, how
far is the anchor from a point directly below the boat?
a. | 145.6 ft | b. | 9,000 ft | c. | 18,000 ft | d. | 134.2
ft |
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Determine whether the given lengths can be sides of a right
triangle.
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16.
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18 m, 24 m, 30 m
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17.
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7 cm, 40 cm, 41 cm
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Determine whether the forces in the pair are pulling at right angles to each
other.
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18.
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13 lb, 35 lb, resultant force 30 lb
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19.
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20 lb, 15 lb, resultant force 25 lb
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20.
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Find the distance from H(2, 3) to K(4, –3). If necessary,
round to the nearest tenth. 
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21.
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Find the perimeter of the triangle. Round to the nearest tenth. 
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22.
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Find the value of y if the points (–7, y) and (4, –3)
are  units apart. a. | –1 or –9 | b. | 2 or –9 | c. | 2 or –3 | d. | 0 or
–6 |
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Find the midpoint of each segment with the given endpoints.
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23.
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C(1, –5) and D(–5, 1)
a. | ( ,  ) | b. | (–2, –2) | c. | ( ,
–2) | d. | ( ,  ) |
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24.
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T(4, 16) and V(–7, –11)
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25.
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 is the diameter of a circle. The coordinates of C
are (–4, 7) and the coordinates of D are (5, –3). Find the center of the
circle.
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26.
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The King and Taylor families are hiking in a national park. The Kings leave the
visitor center and hike 2 km east and 2 km south. The Taylors leave the visitor center and hike 3 km
west and 3 km north. How far apart are the families?
a. | 7.1 km | b. | 7.2 km | c. | 1.4 km | d. | 50
km |
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Simplify the expression.
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27.
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28.
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29.
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(6 –  )(6 +  ) a. |  | c. | –85 | b. |  | d. | 25 |
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30.
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31.
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32.
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33.
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Find an exact solution for  . Then find the approximate solution to
the nearest tenth.
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34.
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The formula  gives the interest rate r that will allow
principal P to grow into amount A in two years, if the interest is compounded annually.
Suppose you have $425 to deposit into an account. Find the interest rate you would need to have $470
in the account at the end of the second year. a. | 5.2% | b. | 105% | c. | 0.052% | d. | 5.4% |
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35.
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Find the exact perimeter of the triangle. 
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36.
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Determine whether  is sometimes, always, or never
true. a. | never | b. | sometimes | c. | always |
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Solve the equation. Check your solution.
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37.
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a. | 6 | b. | 144 | c. |  | d. | 12 |
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38.
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39.
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a. | –3 | b. | 5 | c. | –5 | d. |  |
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40.
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The velocity of sound in air is given by the equation  where
v is the velocity in meters per second and t is the temperature in degrees Celsius.
Find the temperature when the velocity of sound in air is 369 meters per second. Round to the nearest
degree. a. | 507º | b. | 6,535º | c. | 7,081º | d. | 67º |
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Solve the equation. Identify any extraneous solutions.
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41.
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a. | 8 is a solution to the original equation. The value –5 is an extraneous
solution. | b. | 5 and 8 are both extraneous solutions. | c. | 5 is a solution to the original equation. The
value –8 is an extraneous solution. | d. | 5 and –8 are
solutions. |
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42.
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a. | 0 and 7 are solutions of the original equation. | b. | 0 is a solution of
the original equation. 7 is an extraneous solution. | c. | 7 is a solution of the original equation. 0 is
an extraneous solution. | d. | –7 is a solution of the original
equation. 0 is an extraneous solution. |
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43.
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The formula  can be used to find the velocity v in feet per
second of an object that has fallen h feet. Find the velocity of an object that has fallen 25
feet. Round your answer to the nearest hundredth. a. | 800 feet per second | c. | 200 feet per second | b. | 320 feet per second | d. | 40 feet per
second |
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44.
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Find the domain of  .
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45.
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Graph the function  .
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Match the function with its graph.
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46.
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47.
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48.
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49.
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Find the value of sin 66°. Round to the nearest ten-thousandth.
a. | 0.4067 | b. | 2.246 | c. | 0.9135 | d. | –0.0266 |
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Find the value of x to the nearest tenth.
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50.
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51.
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52.
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Suppose you live 4.4 miles from a hill. From your home you see a plane directly
above the hill. Your angle of elevation to the plane is 30°. What is the plane’s
altitude?
a. | –28.2 miles | b. | 3.8 miles | c. | 2.2 miles | d. | 2.5
miles |
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53.
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A ranger spots a forest fire while on a 45-meter observation tower. The angle of
depression from the tower to the fire is 12°. To the nearest meter, how far is the fire from the
base of the tower?
a. | 212 meters | b. | 10 meters | c. | 216 meters | d. | 71
meters |
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54.
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An airplane over the Pacific Ocean sights an atoll at an 13° angle of
depression. If the plane is 648 m above the water, how many kilometers is it from a point 648 m
directly above the atoll?
a. | 2806.8 km | b. | 2.81 km | c. | 1399.5 km | d. | 149.6
km |
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55.
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a. Find the value of each variable to the nearest tenth. b.
Find the perimeter of the triangle to the nearest tenth. 
a. | a = 30, c = 36.6, perimeter = 87.6 | c. | a = 36.6, c = 17.2,
perimeter = 74.8 | b. | a = 36.6, c = 30, perimeter = 87.6 | d. | a = 17.2, c = 36.6, perimeter =
74.8 |
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Determine whether the following statement is sometimes, always,
or never true.
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56.
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Two consecutive positive integers form part of a Pythagorean triple.
a. | never | b. | always | c. | sometimes |
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57.
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Two legs of a right triangle are equal and have length a, which is an
integer. The hypotenuse of that triangle has length c, which is also an integer.
a. | never | b. | sometimes | c. | always |
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58.
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The point P is  of the distance between M and
N. Find the coordinates of P. 
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59.
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Use  to find the value of cos A.
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Short Answer
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60.
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Simplify  by rationalizing the denominator. Show your work.
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61.
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A circle has a diameter  with endpoints (–1, 7) and (5,
6). a. Find the radius of the circle. Leave your answer in simplest radical
form. b. Find the area of the circle. Round to the nearest tenth.
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62.
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The sales of a certain product after an initial release can be found by the
equation  , where s represents the total sales (in
thousands) and t represents the time in weeks after release. a. Make a table of
values. b. Graph the function. c. Use the graph to estimate the sales 7 weeks
after release.
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63.
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Make a table of values and graph the function. 
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64.
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Use a trigonometric ratio to show that c = 2 a in the triangle
below.
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Essay
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65.
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In the diagram  . Use the Pythagorean Theorem to find x. Express
x as a radical expression in simplest form. Show your work. 
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66.
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Simplify  . Show your work. Justify each step
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67.
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Solve  . Check your solution. If there is no solution, write
no solution. Show your work.
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Other
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68.
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State the hypothesis and the conclusion of the conditional. Then write the
converse. Tell whether the converse is true or false.
If you are on the Georgia coast, then
you are at the Atlantic Ocean.
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69.
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Given:  and  are in simplest radical form. 
and  is in simplest radical form. Explain how c and d relate to a and
b. Give an example.
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70.
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Describe how to translate the graph of  to obtain the graph of
 .
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71.
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A student simplifies  as shown below. What error did the
student make? 
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72.
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Explain why you do not need the distance formula to find the distance from
(1, 10) to (1, –1).
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