Name _______________________________________ Period _______

Secondary 2 Honors Final Review – Part 2 (* means calculator allowed)

Evaluate:

7. g(x) = 𝑥2 + 2𝑥 − 7 find: g(-3), g(2

3), g(x-5)

10. f(x) = 𝑥2 − 25, h(x) = 3x + 2

find: (f – h)(x), 𝑓

ℎ(𝑥) and the domain of

𝑓

ℎ(𝑥), (f + h)(3), (fh)(-2)

Simplify:

13. √−27𝑎9𝑏12 3 16. √98 − √72 + √32

17. 2

3√11 30.

(𝑦−34 𝑥

−23 )12

(𝑦14𝑥

73)24

Simplify:

35. (15 + 3𝑖) + (14 + 8𝑖) 36. (−5 + 2𝑖) − (5 + 2𝑖18)

Factor completely:

40. 10𝑎3𝑏 − 12𝑎2𝑏2 41. 81𝑦2 − 49

44. 3𝑛2 + 21𝑛 − 24 45. 𝑦4 − 16

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.

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

unknown lengths of the given segments.

62. 𝐸𝐶̅̅̅̅

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.

102. Write the quadratic expression in standard form and identify a, b and c (𝑥 − 2)(𝑥 + 3) − (𝑥 − 4)(2𝑥 + 5)

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. 𝑔(𝑥) = (𝑥 − 3)2 − 16 CALCULATOR PROBLEMS (Round to two decimals.):

137*. 𝑥2 + 10𝑥 − 3 < 7𝑥

141. Graph 𝑓(𝑥) = 2𝑥2 + 1 142. Graph 𝑓(𝑥) = − | 𝑥 – 1 | + 3

Find the average rate of change between the given x values: 145. 𝑔(𝑥) = 1 − 2𝑥, 𝑓𝑟𝑜𝑚 𝑥 = 2 𝑡𝑜 𝑥 = 7 146. 𝑓(𝑥) = 𝑥2 + 2𝑥, 𝑓𝑟𝑜𝑚 𝑥 = −1 𝑡𝑜 𝑥 = 4

Graph each of the following piecewise functions

152. 𝑦 = { −6, 𝑖𝑓1 ≤ 𝑥 ≤ 8

𝑥 − 10, 𝑖𝑓 𝑥 > 8 153. 𝑦 = {

7𝑥, 𝑖𝑓 𝑥 < 3

𝑥2, 𝑖𝑓 𝑥 ≥ 3

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

{𝑦 = 𝑥2 − 12𝑥 − 45𝑦 = 3𝑥 − 45

160. Solve the equation for 𝒙. 2(𝑥 + 1)2 − 90 = 𝑦

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

164*. Find the volume. Round to 2 decimals

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 𝑑(𝑡) = 4000(1.0008)12𝑡.

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 𝑇(𝑥) = −2.4𝑥2 +90.8𝑥 + 1.59, 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.

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?

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?

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

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.

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

199*.

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

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

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?

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 cos 𝜃 𝑖𝑓 sin 𝜃 = √3

2

208. Find cot 𝜃 𝑖𝑓 csc 𝜃 = 7

3

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

𝐹𝐺�̂� radius = 24 ft., arc length = 16 ft

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

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

221. Find 𝑚∠𝐵 and 𝑚∠𝐶.

225. ⊙ 𝐺 ≅⊙ 𝐸. What is the value of y?

226. In ⊙ 𝐴, 𝐵𝐷�̂� = 238°. What is 𝑚∠𝐵𝐴𝐶?

227. Find the value of b.

230. Is 𝐺𝐻̅̅ ̅̅ tangent to circle F in the diagram below?

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

234. Construct the inscribed circle for the triangle.

Write the standard equation of the circle described.

238. The center is (-5, 1) and the radius is 4.

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 𝑥2 + 𝑦2 + 6𝑥 − 4𝑦 − 27 = 0.

241. Find the center and radius of the circle described by the equation 𝑥2 + 𝑦2 − 8𝑥 + 10𝑦 − 67 = 0.

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.