Secondary 2 Honors Final Review (* means calculator allowed)

Simplify:

1. 2. 3. Find the perimeter of the shape. Lengths are given in cm.

4. 5.

6.

Evaluate:

7. g(x) = find: g(-3), g(

g(x-5)

8. f(x) = 2x + 1, g(x) = 1 – x find: (f+g)(x)

9. g(x) = h(x) = find (gh)(x)

10. f(x) = , h(x) = 3x + 2

find: (f – h)(x),

and the domain of

, (f + h)(3), (fh)(-2)

Simplify:

11.

12.

13. 14.

15. 16.

17.

Simplify:

18.

19.

20.

21.

22.

23.

24. 25.

26. 27.

Simplify – do not evaluate

28.

29.

30.

Simplify if possible, then state whether each answer is rational or irrational:

31.

32.

Simplify:

33.

34.

35. 36.

37. 38. Find the complex conjugate of the number, and then find the product of the number and its conjugate.

39.

Factor completely:

40. 41.

42. 43.

44. 45.

46. – – 47. – –

48. 49.

50.

51. Determine the midpoint of the segment with endpoints (–10, –11) and (8, –17).

52. A segment has an endpoint at (-10, 3) and a midpoint at (

, 4). Find the other endpoint.

53. Determine whether the following transformation represents a dilation. Justify your answer and determine the scale factor if possible.

54*. Determine the scale factor and whether the dilation is an enlargement, a reduction, or a congruency transformation.

55*. MNO has the following vertices: – , – , and – . What are the vertices under a dilation with a center at (0, 0) and a scale factor of 75%?

56*. Find all angles and side lengths given

57. Decide whether the pair of triangles is similar. Explain your answer.

58*. Identify the similar triangles. Find x and the measure of the indicated sides.

59*. At a certain time of day, a tree that is 12 feet tall casts a shadow that is 8 feet long. Find the length of the shadow that is created by a 10-foot-tall basketball hoop at the same time of day.

60*. Prove the triangles are similar.

61*. Find x.

Use the Triangle Proportionality Theorem and the Triangle Angle Bisector Theorem to find the

unknown lengths of the given segments.

62.

63*.

64*. Is ?

65. Find the value of x.

66. Find the value of a, b and x.

67*. To measure , the distance across a lake, a surveyor stands at point A and locates points B, C, D, and E. What is the distance across the lake?

68*. The height of a ramp at a point 2.5 meters from its bottom edge is 1.2 meters. If the ramp runs for 6.7 meters along the ground, what is its height at its highest point, to the nearest tenth of a meter?

69. List a pair of complementary angles. Write a statement about those angles using the

Complement Theorem.

Complementary Angles:

Statement:

In the diagram that follows, and intersect.

70*. Find m∠ if m∠ and m∠

71. Find m∠ if m∠ and m∠

Use the following diagram to solve problems 72, 73, given that and line is the

transversal. Justify your answers using angle relationships in parallel lines intersected by a

transversal.

72. Find m∠ if m∠ and m∠

73*. Find m∠ if m∠1 and m∠4

Find the value of the variables:

74.

75.

10.

76.

77.

78.

79. Identify the quadrilateral in as many ways as possible. Then identify the most precise name.

Find the values of the variables. Then find the length of the sides.

80. Kite

81. Rhombus HKJI

82. Graph and label the quadrilateral with the given vertices. Then determine and justify the most

precise name.

83. Find a

84. Find the value of the variables and the measure of each angle for the following parallelogram

Find the values of x and y for which ABCD must be a parallelogram. 85. 86.

87. Use the given information to find the lengths of all four sides of parallelogram ABCD

The perimeter is 92 cm. AD is 7 cm more than twice AB

88. Find the measures of the numbered angles in the rhombus.

89. Find the measures of the numbered angles in the rhombus.

90. Find the values of the variables for the parallelogram.

91. LMNP is a rectangle. Find the value of x and the length of each diagonal.

92. A carpenter is building a bookcase. How can they use a tape measure to check that the bookshelf is rectangular? Justify your answer and name any theorems used.

93*. Find the measure of each angle in the isosceles trapezoid.

94. Find the value of the variable for the isosceles trapezoid.

95*. Find the value of the variables in the kite

96*. Find the measures of the numbered angles in the kite.

97. The perimeter of a kite is 66 cm. The length of one of its sides is 3 cm less than twice the length of another. Find the length of each side of the kite.

98. Identify the terms, coefficients, and constant of

99. Simplify the expression and classify it as a monomial, binomial, or trinomial.

100. Write an algebraic expression, and simplify if possible a. twice the sum of a number and 11

b. The product of 7 and the square of , increased by the difference of 5 and 101. Simplify and determine if the expression is quadratic.

102. Write the quadratic expression in standard form and identify a, b and c

Without your calculator state whether the graph opens up or down and find the y-intercept. Then use your calculator to list the vertex and state whether it is a maximum or minimum, give the x-intercepts and state where the graph is increasing or decreasing.

103*.

104*.

Without the calculator state whether the graph has a maximum or minimum and find the y-intercept. Then use your calculator to find the max or min and the x-intercepts. 105*. The path of a snowboarder performing stunts is given by the equation

, where t is the time in seconds and y is the duration of the stunt.

106*. Find the domain of

107*. A bird is descending toward a lake to catch a fish. The bird’s flight can be modeled by the

equation , where h(t) is the bird’s height above the water in feet and t is the time in seconds since you saw the bird. What is the vertex? What does the minimum value mean in the context of the problem?

108*. The path of a snowboarder performing stunts is given by the equation Where t is time in seconds and y is the duration of the stunt. What are the t-intercepts? Explain the meaning of the t-intercepts in the context of the problem. How long does the stunt last?

109*. The senior class is putting on a talent show to raise money for their senior trip. In the past, the profit from the talent show could be modeled by the function

, where represents the ticket price in dollars. What is the reasonable domain for this function? For what domain value will the profits be maximized?

Solve by factoring:

110. 111.

112. 113.

114. Write a quadratic equation that has the zeros x =

115. The altitude of a triangle is 3 inches longer than its base. The area of the triangle is 20 square inches. Find the length of the base of the triangle. Solve:

116. 117.

118. 119.

120. The surface area of a cube with sides of length is given by . If the surface area of a cube is 200 square inches, what is the length of one side of the cube?

Find so that the expression is a perfect square trinomial.

121. Solve by completing the square.

122.

123.

124.

Solve using the quadratic formula.

125.

126.

127.

128. Identify the vertex and state whether the function has a minimum or maximum.

129. Find the equation of a quadratic in vertex form with a maximum at (2, 10) and it passes through the point (1, 8)

Convert each equation to vertex form and list the vertex.

130.

131.

On all problems list the vertex, direction of opening, x-intercepts, y-intercept and draw the graph. On the graph label the vertex, intercepts, and another point symmetrical to the y-intercept. 132.

133.

Solve the quadratic inequalities. All problems must include number lines.

134.

135. CALCULATOR PROBLEMS (Round to two decimals.):

136*.

137*.

138. Tell what changes are made to the graph of to obtain the graph .

139. Tell what changes are made to the graph of to obtain the graph .

x y

–2 –1

–1.5 –1.75

–1 –4

–0.5 –7.75

0 –13

0.5 –19.75

1 28

1.5 –37.75

140. Let . Write a new function that translates as described:

Vertical compression by

, reflect x-axis and down 2 units

141. Graph 142. Graph –

143. Calculate the average rate of change for between

144. Calculate the average rate of change using the table below between

Find the average rate of change between the given x values: 145.

146.

Find the inverse of each function. Restrict the domain of the function if needed.

147.

149.

150.

State a reasonable domain for the function. Then find the inverse function .

151. A rock band is selling tickets to a concert at a theater. The band earns money for each ticket

sold, but has to pay some of the earnings to the theater. The total money earned by the band can be

estimated using the function , where is the number of tickets sold.

Graph each of the following piecewise functions

152.

153.

154.

155.

156. Estimate the solution to the system that is represented by the circle shown and the line with the given equation by graphing.

157*. Graph the system and determine the real solutions (if any).

158. Solve the system algebraically.

159. Solve the system algebraically.

160. Solve the equation for . 161*. A pizza has a circumference of 40 inches. What is the area of the pizza?

162*. A company makes candles in the shape of cones. Their best-selling candle has a height of 6 inches and a circumference of 12 inches. What volume of wax is needed to make 1 candle?

163*. A pyramid in Giza, Egypt has a square base with side lengths of 230 meters. Its height is 146.5 meters. What is its volume?

164*. Find the volume. Round to 2 decimals

165*. A car loses value each year. The value of the car years from today can be modeled using the

function . If Elizabeth wants to sell her car in

years, what will the car’s

value be when she sells it?

166*. Mia is tracking her savings account balance. She knows the equation can be used to find her balance in any year , but she can’t remember what represents. Her balance

today,

years after opening her account, is . What is the value of ?

Problems 167 and 168: Find the percent rate of change of f(t) for each unit of t. State whether the

function shows exponential growth or decay.

167.

168*.

169. Neal opens a savings account that earns interest monthly. He can estimate the total dollars in his account, d(t), t years after opening the account by using .

a. How much money did Neal initially put into the account?

b*. What is the yearly rate of change of the account? Is it growing or decaying?

170*. Natalie is considering which method of travel- car, train or plane—would be best to travel the flight distance of 747 miles from Atlanta to New York City. Use this distance for each problem. The car travels a constant speed of 60 mph. The train can be modeled by the equation , where x represents the number of hours and T(x) represents the number of miles traveled. The table below represents the time and distance traveled during the plane trip.

Hours 0 0.5 1 1.5 2 2.5

Miles 0 149 300 455 612 747

If the car and train both leave Atlanta at 7 A.M. and the plane leaves Atlanta at 4:30 P.M., determine which would arrive in New York City First.

171. Which function has a greater y-intercept?

172. You are considering investing $100 into a fund. The first fund will pay $1,000 each year. The second fund is modeled by the equation . The third fund is represented by the table.

x (year) 0 1 2 3

h(x) ($) 100 600 2,100 4,600

Which fund would you choose if you withdraw your money after 3 years?

Solve the following problems. Be sure to show how you set them up!

173*. Ashley has 7 places she wants to visit on her trip, but she only has one day free. If she can visit 1

place in the morning, 1 in the afternoon, and 1 in the evening, how many different ways can she plan

her trip?

174*. A pizzeria is offering a special on a large two-topping pizza. They offer 5 vegetable toppings and

4 meat toppings. How many different ways can the two-topping pizza be ordered, if each topping is

different?

175*. The table below lists items in Bryan’s closet.

Bryan randomly selects 2 items. What is the probability that both selected items are black?

176*. You are dealt a hand of three cards from a standard deck of 52 cards. What is the probability

that you will draw three hearts?

177*. A bag of marbles contains 5 blue, 3 white, and 7 red marbles. What is the probability that you

will draw a white marble, keep it, then draw another white marble?

178*. Jessica takes her 4-year old nephew into an antique shop. There are 4 statues, 3 picture frames,

and 3 vases on a shelf. The 4-year old accidentally knocks two items off of the shelf and breaks them.

What is the probability that he broke both a statue and a vase?

179. The following Venn diagram shows a relationship between favorite sport and gender.

What is the probability that a randomly chosen person will choose soccer as their favorite sport?

180. Nasir tosses a coin 3 times. What is the probability that he gets at least 2 tails?

181. Consuela is playing a card game with a standard 52-card deck. She wants a king or a diamond on

her first draw. What is the probability that she will get a king or a diamond on the first draw?

182*. Middletown High School has 240 students in the tenth grade. The only tenth grade math courses

are algebra and geometry. All of the tenth grade students are taking at least one math course. There

are 142 students taking algebra and 120 students taking geometry. What is the probability that a

randomly chosen student is taking both algebra and geometry?

183. A car dealership is having a contest. The first 10 customers to enter the contest are each given 2 raffle tickets. The remaining 20 customers are each given 1 raffle ticket. There is 1 contest winner, selected by randomly choosing one of the raffle tickets.

a) Spencer is one of the first 10 customers to enter the contest. What is the probability that he will win the raffle?

b) Hope is one of the remaining 20 customers to enter the contest. What is the probability that she will win the raffle?

c) Is the game fair? Explain.

184*. The buses at the Zoomy Express Bus Company depart as scheduled 80% of the time. The buses depart and arrive as scheduled 68% of the time. What is the probability that a Zoomy Express bus arrives as scheduled if it departs as scheduled?

185*. Jane rolls a pair of dice. What is the probability that the sum is even if the product is even?

What is the probability that the product is even given that the sum is even? Compare the probabilities

and interpret your answer in the context of the problem.

186. The following Venn diagram shows a relationship between favorite sport and gender. Use it to

answer the following questions.

What is the probability that a person is female if they say soccer is their favorite sport?

187. Fill in the two-way table, then answer the following probability questions

a. What is the probability that a student works at Taco Bell if they are in 11th grade?

b. What is the probability that a student is in 11th grade if they work at Taco Bell?

c. Compare P(Taco Bell|11th grade) and P(11th grade|Taco Bell). Interpret your answer in

context

188. Given the Tree diagram below, what is the probability that a person will test positive for TB

(tuberculosis) if they don’t have it? (They get a false positive.)

189*. For a statistics project, Tamara surveys a well-chosen sample that represents all the students at

her school. She finds that 72% have at least one sibling (brother or sister) and 27% have at least one

sibling and at least one pet in their home. Assume that having a sibling and having a pet are

independent events. Based on the survey, what is the probability that a randomly chosen student at

Tamara’s school has at least one pet at home?

190*. The Coolest Deal is a daily special sold at Ike’s Ice Cream Parlor. One day, the Coolest Deal is a large cone with one topping. The following table shows the sales data for the Coolest Deal that day. Using the data in the table, determine if the events stated in the problem seem to be independent. Show the work that supports your answer.

A random customer at Ike’s orders caramel and cookie dough for the Coolest Deal.

191*. Eastern High School’s highest academic award category is Highest Honors. The next highest

award is Academic Excellence. The table shows data about the awards by grade.

Are TEN and HH independent? Explain your reasoning and your answer.

192*. A car dealership offers a warranty on used cars purchased at the dealership. One five-year warranty completely covers three major components: air conditioning, power sunroof, and transmission. The warranty costs $1,000, and if any of the covered components require repair, the car owner pays nothing in repair costs. Karen researches the costs of these repairs for the car she would like to purchase, and finds the following:

Repair type Average cost

Air conditioning $1,200

Power sunroof $600

Transmission $3,000

She also finds information about the probability that each component will require a repair within five years, according to different consumer review websites. The probability that the air conditioning will need repairing is 0.64, the probability that the power sunroof will require repairing is 0.15, and the probability that the transmission will require repairing is 0.20.

Should Karen purchase the warranty? Explain.

193. Find the values of the six trig functions of for the right triangle:

TEN: a student is in the tenth grade

TWELVE: a student is in the twelfth grade

HH: a student received the Highest Honors award

AE: a student received the Academic Excellence award

194. Given the value of 1 trig function, find the values of the other 5 trig functions of .

cot 2

195. Find the complement of angle x = 41

196. Find the sine of the complementary angle.

197. Find a value of for which is true.

198*. Find the value of x. Round to the nearest degree:

Find the missing angle. Round to the nearest whole number.

199*.

Solve each right triangle. Assume that C represents the right angle and c is the hypotenuse. Round the measures of sides to the nearest tenth and measures of angles to the nearest degree. 200*. b = 6, c = 13

201*. B = 30 , b = 11

202*. One section of a ski run is 650 feet long and falls 260 feet in elevation at a constant slope. To the

nearest degree, what angle (θ) does the ski run form with the horizontal?

203*. A ladder manufacturer recommends that its ladders be used on level ground at an angle of 72.50

to the horizontal. At that angle, how far up on the side of a building will the top of a 14-foot ladder

reach?

204*. Brianna is hiking on a mountain trail. She hikes 345 feet uphill but a horizontal distance of 295

feet. To the nearest degree, what is the angle of elevation of the trail?

205*. A blimp provides aerial footage of a football game at an altitude of 400 meters. The TV crew

estimates the distance of their line of sight to the stadium to be 3282.2 meters. What is the television

crew’s angle of depression from inside the blimp?

206*. A slide at a water park sends riders traveling a distance of 45 feet to the pool at the bottom of

the slide. If the depth of the pool is 12 feet and the angle of depression from the top of the slide is 45 ,

what is the vertical distance from the top of the slide to the bottom of the pool?

Find the value of the following trig functions using the Pythagorean identities.

207. Find

208. Find

Simplify:

209.

210.

211.

212. Change 135 to radian measure. 213. Convert

radians to degrees.

214. Find the length of the arc: 215. Find the central angle, :

radius = 24 ft., arc length = 16 ft

216. Find the area of the shaded sector of the circle.

217. A circle has a radius of 11 units. Find the length of an arc intercepted by a central angle measuring 72

218. A circle has a radius of 2 units. Find the arc length of a sector with an area of 12 square units.

219. Find the values of x and y.

220. Find the value of x and the measure of .

221. Find ∠ and ∠ .

222. Find and .

223. Given that all circles are similar, determine the scale factor necessary to map .

has a diameter of 50 units and has a diameter of 12 units.

224. What is the value of w?

225. . What is the value of y?

226. In , . What is ∠ ?

227. Find the value of b.

228. The circumference of the trunk of a tree to be decorated is 12 inches. You have 7 inches of garland to wrap partially around the tree trunk. What is the arc angle of the trunk that you will decorate?

229. The slope of radius in circle Q is

. A student wants to draw a tangent to circle Q at point P.

What will be the slope of this tangent line? 230. Is tangent to circle F in the diagram below?

231. The sides of quadrilateral PQRS are tangent to the circle at the points as pictured below. What is

the length of ?

232. is tangent to at point B in the diagram below. What is the measure of ∠ACB?

233. and are tangent to in the diagram below. What is the value of x?

234. Construct the inscribed circle for the triangle.

235. Find the length of . Assume that I is the incenter.

236. Construct the circumscribed circle for the triangle.

237. The producers of a cooking show on the Snackers Network are designing a new set. A food

preparation station needs to be located between the refrigerator, sink, and stove. Which point of

concurrency, the circumcenter or the incenter, will result in the preparation station being located in a

place that is equidistant from the refrigerator, sink, and stove?

Write the standard equation of the circle described.

238. The center is (-5, 1) and the radius is

239. The center is (5, -2) and the circle passes through (0, -6)

240. Find the center and radius of the circle described by the equation .

241. Find the center and radius of the circle described by the equation

242. A particular cell phone tower is designed to service a 12-mile radius. The tower is located at (–3,

5) on a coordinate plane whose units represent miles. What is the standard equation of the outer

boundary of the region serviced by the tower? Is a cell phone user at (8, 0) within the service range?

Explain.