# Semester Exam Practice Materials

**ALGEBRA II Honors/Algebra II**

**SEMESTER EXAM PRACTICE MATERIALS**

SEMESTER 2

2014–2015

______

- (6.1) What is an equation for the translation of that has asymptotes at and ?

(A)

(B)

(C)

(D)

- (6.1) What is the equation of the vertical asymptote of ?

(A)

(B)

(C)

(D)

- (6.1) Sketch the asymptotes and graph of . Identify the domain and range.
- (6.3) A board of length cm was cut into two pieces. If one piece is cm, express the length of the other board as a rational expression.

(A)

(B)

(C)

(D)

- (6.3, 6.4)Use the following expressions to answer the questions.

(a)Explain how to add two rational expressions. Simplify as an example. Be sure to give reasons for each step. Simplify completely.

(b)Explain how subtracting (such as simplifying) would be different from adding.

(c)Explain how to multiply rational expressions, simplifying as an example.

(d)Show how to divide by .

(e)Explain how you would solve a rational equation like . Then describe, in detail, the strategy for solving an equation like . Do not completely solve the equations. Instead, concentrate on the first two or three steps in solving; show what to do and explain why.

- (6.6) The rate of heat loss from a metal object is proportional to the ratio of its surface area to its volume.

(a)What is the ratio of a steel sphere’s surface area to volume?

(b)Compare the rate of heat loss for two steel spheres of radius 2 meters and 3 meters, respectively.

- (6.3) Multiply. Simplify your answer.

(A)

(B)

(C)

(D)

- (6.2) Which expression represents the quotient?

(A)

(B)

(C)

(D)

- (6.6) Last week, Wendy jogged for a total of 10 miles and biked for a total of 10 miles. She biked at a rate that was twice as fast as her jogging rate.

(a)Suppose Wendy jogs at a rate of miles per hour. Write an expression that represents the amount of time she jogged last week and an expression that represents the amount to time she biked last week. (hint:)

(b)Write and simplify an expression for the total amount of time Wendy jogged and biked last week.

(c)Wendy jogged at a rate of 5 miles per hour. What was the total amount of time Wendy jogged and biked last week?

- (6.2) Which expression is equivalent to for all ?

(A)

(B)

(C)

(D)

- (6.2) Which set contains all the real numbers that are not part of the domain of

?

(A){8}

(B){-4}

(C){-4, 8}

(D){-8, 4}

- (6.4) Solve the equation .

(A)-8

(B)7

(C)8

(D)No solution

- (6.6) A sight-seeing boat travels at an average speed of 20 miles per hour in the calm water of a large lake. The same boat is also used for sight-seeing in a nearby river. In the river, the boat travels 2.9 miles downstream (with the current) in the same amount of time it takes to travel 1.8 miles upstream (against the current). Find the current of the river.
- (6.6) A baseball player’s batting average is found by dividing the number of hits the player has by the number of at-bats the player has. Suppose a baseball player has 45 hits and 130 at-bats. Write and solve an equation to model the number of consecutive hits the player needs in order to raise his batting average to 0.400. Explain now you found your answer.

- (6.1) Which intervals correctly define the domain of

(A)

(B)

(C)

(D)

- (6.1) Which statement is true for the function ?

(A)4 is not in the range of the function.

(B)4 is not in the domain of the function.

(C)-4 is not in the range of the function.

(D)-4 is not in the domain of the function.

- (7.1) What is the value of?

(A)-42

(B)-17

(C)88

(D)363

- (7.2) Given the sequence 1, 2, 4, 8, ….

Find the sum of the infinite series.

(A)15

(B)18

(C)30

(D)

- (7.2) During a flu outbreak, a hospital recorded 12 cases the first week, 54 cases the second week, and 243 cases the third week.

a)Write a geometric sequence to model the flu outbreak.

b)How many cases will occur in the sixth week if the hospital cannot stop the outbreak?

- (7.2) Given the geometric sequence with common ratio , write a rule for the nth term of the sequence 4, -28, 196, -1372…

(A)

(B)

(C)

(D)

- (7.1, 7.2) In a classic math problem a king wants to reward a knight who has rescued him from an attack. The king gives the knight a chessboard and plans to place money on each square. He gives the knight two options. Potion 1 is to place a thousand dollars on the first square, two thousand on the second square, three thousand on the third square, and so on. Option 2 is to place one penny on the first square, two pennies on the second, four on the third, and so on.

Think about which offer sounds better and then answer these questions.

a) List the first five terms in the sequences formed by the given options. Identify each sequence as arithmetic, geometric, or neither.

Option 1

Option 2

b)For each option, write a rule that tells how much money is placed on the nth square of the chessboard and a rule that tells the total amount of money placed on squares one through .

Option 1

Option 2

c)Find the amount of money placed on the 20th square of the chessboard and the total amount placed on squares 1 through 20 for each option.

Option 1

Option 2

d)There are 64 squares on a chessboard. Find the total amount of money placed on the chessboard for each option.

Option 1

Option 2

e)Which gives the better reward, Option 1 or Option 2? Explain why.

- (7.4) If, then which of the following is ?

(A)

(B)7

(C)

(D)

- (7.4) Which is the inverse of ?

(A)

(B)

(C)

(D)

- (7.5) Find the value of.

(A)5

(B)1024

(C)16

(D)4

- (7.5) Consider the function.

a)Identify the transformation applied to to create.

b)Identify the transformation applied to to create.

c)Compare the graphs of and. What do you notice?

d)Use the properties of logarithms to explain your answer to part c.

- (7.6) Which is the same function as?

(A)

(B)

(C)

(D)

- (7.6) Rewrite in exponential form.

(A)

(B)

(C)

(D)

- (7.6) Psychologists try to predict the activation of memory when a person is tested on a list of words they learned. The following model is used to make this prediction: where A is the number of words learned, n is the number of exercises, T is the amount of time between learning and testing and L is the length of the list that was tested.

a)Write the formula as the ln of a single expression.

b)Discuss the influence on A (going up or down) when increasing n, T, and L, according to the formula. Do these results make sense?

c)If you want A to be bigger than 0, what conditions must be placed on L, T, and n?

- (7.8) If, then what is?

(A)81

(B)48

(C)27

(D)9

- (7.8) Which equation has the same solution as?

(A)

(B)

(C)

(D)

- (7.8) A biologist studying the relationship between the brain weight and body weight in mammals uses the formula:

Where =body weight in grams and=brain weight in grams. What is the formula for the body weight?

(A)

(B)

(C)

(D)

- (7.9) Choose the function that describes the graph below:

(A)

(B)

(C)

(D)

- (7.9) What function is represented by the following graph?

(A)

(B)

(C)

(D)

- (7.9) The graph of the equation is translated right 3 units and down 3.5 units to form a new graph. Which equation bestrepresents the new graph?

(A)

(B)

(C)

(D)

- (7.9) John graphs the equation. Lana graphs the equation. How does Lana’s graph compare to John’s graph?

(A)Lana’s graph shifts 2 units downward

(B)Lana’s graph shifts 2 units upward

(C)Lana’s graph shifts 2 units to the left

(D)Lana’s graph shifts 2 units to the left

- (7.10) In 1950, the city of San Jose had a population of 95,000. Since then, on average, it grows 4% per year. What is the best formula to model San Jose’s growth?

(A)95,000(1.04)t

(B)95,000(0.96)t

(C)-.04t + 95,000

(D).04t + 95,000

- (7.10) Sarai bought $400 of Las Vegas Cellular stock in January 2005. The value of the stock is expected to increase by 6.5% per year.

a)Write a model to describe Sarai’s investment.

b)Use the graph to show when Sarai’s investment will reach $1100?

- (7.10) The loudness of sound is measured on a logarithmic scale according to the formula, where is the loudness of sound in decibels (), is the intensity of sound, and is the intensity of the softest audible sound.

a)Find the loudness in decibels of each sound listed in the table.

b)The sound at a rock concert is found to have a loudness of 110 decibels. Where should this sound be placed in the table in order to keep the sound intensities in order from least to greatest?

c)A decibel is of a bel. Is a jet plane louder than a sound that measures 20bels? Explain.

- (7.10) Aaron invested $4000 in an account that paid an interest rate compounded continuously. After 10 years he has $5809.81. The compound interest formula is, where is the principal (the initial investment), is the total amount of money (principal plus interest), is the annual interest rate, and is the time in years.

a)Divide both sides of the formula by and then use logarithms to rewrite the formula without an exponent. Show your work.

b)Using your answer for part (a) as a starting point, solve the compound interest formula for the interest rate .

c)Use your equation from part (a) to determine the interest rate.

- (7.10) Denise is reviewing the change in the value of an investment.

Which statement can Denise use to model the data? Why is this type of function a good model for the data?

(A); an exponential function is a good model because the value of the investment changes by a constant amount in each time period.

(B); an exponential function is a good model because the value of the investment changes by a constant factor in each time period.

(C); a linear function is a good model because the value of the investment changes by a constant amount in each time period.

(D); a linear function is a good model because the value of the investment changes by a constant factor in each time period.

- (7.10) Amy recorded the total number of ladybugs observed in a garden over a 7-day period. The scatterplot below represents the data she collected.

Which type of function do these data points best fit?

(A)Cubic

(B)Exponential

(C)Linear

(D)Quadratic

- (7.10) Public Service Utilities uses the equation to determine the cost of electricity where represents the time in hours and represents the cost. The first hour of use costs $6.66 and three hours cost $18.11.

a)Determine the value of and in the model.

b)What is the of the graph of the model? What is the real world meaning of the ?

c)Use the model to find the cost for 65 hours of electricity use.

d)If a customer can afford $40 per month for electricity, how long can he or she have the electricity turned on?

- (7.10) On an the earth is located at (2, -1) and an asteroid is traveling on the path of .

a)Write an equation representing the distance from the earth to the asteroid.

b)If the asteroid is currently located at , what is the distance from the earth to the asteroid?

c)Sketch a graph of.

d)Find the point when the asteroid is closest to the earth.

- (7.10) Rashid is in Biology class and has gathered data on fruit flies. The table below shows the number of fruit flies in his sample at the end of each day for a week.

If the population continues to grow in this manner, which function will Rashid use to predict the population of fruit flies on any given day?

(A)

(B)

(C)

(D)

- (7.10) Which function best fits the data shown in this scatter plot?

(A)

(B)

(C)

(D)

- (7.10) The graph below shows the change in temperature of a burning house over time.

a)Describe the graph.

b)This graph was found in an old math

book and next to it was written:

Rise of temperature = t0.25

Show that this function does not

describe the graph correctly.

c)Assume that the power function

is a good description of the

graph. Find a reasonable value for .

Graph the new function.

d)Compare the graph in part (c) to the original one.

Do you think that a different power of might result in a better model? Would a larger or smaller power produce a better fit? Explain.

e)Use the original graph to find data. Carry out a power regression on the data to find a function that would produce a better fit.

Use for questions 47 and 48.

- (8.1) Which of the following is equal to?

(A)

(B)

(C)

(D)

- (8.1) Which expression represents the length of ?

(A)

(B)

(C)

- (8.1) If , what is ?

(A)

(B)

(C)

(D)

- (8.1) Find when and is in Quadrant I.

(A)

(B)

(C)

(D)

- (8.2) Convert to radians.

(A)radians

(B)radians

(C)radians

(D)radians

- (8.3) An analog watch had been running fast and needed to be set back. In resetting the watch, the minute hand on the watch subtended an arc of radians.

Part A: Suppose the radius of the watch is 1 unit. What is the length of the arc on the outside of the watch that the angle subtends?

Part B: If the watch was at 10:55 before being reset, what is the new time on the watch?

(A)Part A: units

Part B: 9:05

(B)Part A: units

Part B: 10:05

(C)Part A: units

Part B: 9:20

(D)Part A: units

Part B: 8:40

- (8.2) Convert radians to degrees.
- (8.2) Convert radians to degrees.
- (8.3) Suppose each paddle on the wall of a clothes dryer makes 80 revolutions per minute.

Part A: What angle does one paddle subtend in 10 seconds? Give your answer in radians.

Part B: Write an algebraic expression to determine the measure in radians of the subtended angle after x seconds. Show how the units simplify in your expression.

Part C: You are interested in determining the total distance a point on the drum travels in a 20-minute drying cycle. Can you use your expression from Part B? What other information, if any, is needed? Explain.

- (8.3) What is the exact value of ?

(A)

(B)

(C)

(D)

- (8.3) Which expression has the same value as ?

(A)

(B)

(C)

(D)

- (8.3) What is the reference angle corresponding to ?

(A)

(B)

(C)

(D)

- (8.3) A regular hexagon is inscribed in the unit circle. One vertex of the hexagon is at the point . A diameter of the circle starts from that vertex and ends on another vertex of the hexagon. What are the coordinates of the other vertex?

(A)

(B)

(C)

(D)

- (8.3) For what angles x in does the have the same value as ?

(A)and

(B)and

(C)and

(D)and

- (8.3) For which radian measures x will tan x be negative?

(A)

(B)

(C)

(D)

- (8.3) The diameter of a bicycle tire is 20 in. A point on the outer edge of the tire is marked with a white dot. The tire is positioned so that the white dot is on the ground, then the bike is rolled so that the dot rotates clockwise through an angle of radians.

Part A: To the nearest tenth of an inch, how high off the ground is the dot when the wheel stops? Show your work.

Part B: What distance was the bicycle pushed? Round your answer to the nearest foot.

Part C: Would changing the size of the tire (value of r) change either of the answers found in Parts A or B? Explain your reasoning.

- (8.3) A ribbon is tied around a bicycle tire at the standard position . The diameter of the wheel is 26 inches. The bike is then pushed forward 20 feet from the starting point. In what quadrant is the ribbon? Explain how you obtained your answer.
- (8.3) Find when and is in Quadrant IV.

(A)

(B)

(C)1

(D)

- (8.3) Two friends counted 24 evenly spaced seats on a Ferris wheel. As they boarded one of the seats, they noticed the edge of the wheel was 1 meter off the ground. They learned from the operator that the diameter of the wheel was 28 meters. After they got seated and started moving, in a counter-clockwise direction, they counted 13 chairs pass the operator, and then the Ferris wheel was stopped on the fourteenth chair to load another passenger.

Part A: Design a representation of the Ferris wheel and locate where the friends were when the wheel stopped to load the next passenger.

Part B: How many radians had they rotated through in the time before they stopped?

Part C: To the nearest tenth of a meter, how far above the ground were they? Show your work.

- (8.4) If and , then what is the value of ?

(A)

(B)

(C)

(D)

- (8.5) In , , , , and . Which expression can be used to find the length of side t?

(A)

(B)

(C)

(D)

- (8.5) Solve , given that , and .
- (8.5) Given with , and , find c. Round your answer to two decimal places.
- (8.5) Solve with , , and .
- (8.5) A 50 foot ramp makes an angle of with the horizontal. To meet new accessibility guidelines, a new ramp must be built so it makes an angle of with the horizontal. What will be the length of the new ramp?

- (8.6) Which equation would you use to find ?

(A)

(B)

- (8.6) Which expression can be used to find ?

(A)

(B)

(C)

(D)

- (8.7) Give an expression for the height hof , and use the expression to write a formula for the height of the triangle in terms of the variables shown by replacing h in the formula .

(A)

(B)

(C)

(D)

- (8.7) is an isosceles right triangle.

Part A: Determine the exact value of t. Use radical notation if necessary, and do not approximate. Show your work.

Part B:Use to determine the exact value of . Use radical notation if necessary, and do not approximate. Show your work.

Refer to to answer Parts C and D.

Part C:Use your answer to Part B to determine the exact value for the area of .

Part D:Using a calculator, determine the area of to the nearest tenth of a cm2.

- (8.7) Which expression represents the area of the triangle in square feet?

(A)

(B)

(C)

(D)

- (8.9) Which is the equation of the graph shown below?

(A)

(B)

(C)

(D)

- (8.9) The graph of which function has a period of and an amplitude of ?

(A)

(B)

(C)

(D)

- (8.9) Which function has an amplitude of 2 and a period of ?

(A)

(B)

(C)

(D)

- (8.9) Which function has an amplitude of and a period of ?

(A)

(B)

(C)

(D)

- (8.9) Which of the following is a vertical asymptote of the graph of ?

(A)

(B)

(C)

(D)

(E)

- (8.9) What is the equation for the graph shown?

(A)

(B)

(C)

(D)

(E)

- (8.9) Which function has an amplitude of 3 and a period of ?

(A)

(B)

(C)

(D)

- (8.9) Which function is represented by the graph shown?

(A)

(B)

(C)

(D)

- (8.9) Write an equation of the form, where and , with amplitude and period 12.

- (8.9) Write a function for the sinusoid.