Algebra 2 Segment Two Exam Review Solve by substitution...

Algebra 2 – Segment Two Exam Review

1. Solve by substitution

–y + z = -9

y– 5z = 29


y=x2−7x+10

3x+y=7

3. Solve by elimination

–2x – 5y = 18

5x– 5y = 60


5x – 4z = –23

2x – 2z = –12

5. Solve by graphing

–x + z = 4

–4x – 2z = –20


y=x2−7x+10

3x+y=7

7. Solve the exponential equation.

102a+3=10a−4

8. Solve the exponential growth problem.

If $75 is invested at an interest rate of 8% per year and is compounded

monthly, how much will the investment be worth in 15 years?

9. Solve the exponential decay problem.

A sofa depreciates at 20% of its original value each year. If the sofa was

$349 at its time of purchase, what is the value of the sofa after 4 years?

Round your answer to the nearest cent.

10. Solve the logarithmic equation.

logb1000 = 3


ln x = 2


log5x+log52=1

13. Simplify log2x+log23+log211.

14. Solve the exponential function.

5x=20

15. An isotope decays at a rate of 40 percent every decade. Find the

adjusted rate of decay if it is going to be calculated annually.

16. Graph and write a description of the exponential function.

f(x) = 4x


f(x) = (1/5)x

18. Graph using graphing technology.

f(x) = log 15 x


f(x) = log 0.5 (x - 3)

20. Identify the 34th term of the arithmetic sequence 2, 7, 12 ...

21. Identify the twenty-third term of an arithmetic sequence where a1

equals 3 and a7 equals 6.

22. What is the sum of a 44-term arithmatic sequence where the first

term is -9 and the last term is 120?

23. What is the first term of a 14-term arithmetic sequence where the

last term is -12 and the sum is 42?

24. Identify the 10th term of the geometric sequence 2, 8, 32 ...

25. Identify the sixth term of a geometric sequence where a 1 equals 18

and a3 equals 4.5 .

26. What is the sum of the geometric sequence -4, 24, -144 ... if there

are 10 terms?

27. What is the sum of an 8-term geometric series if the first term is

negative 9, the last term is 703,125, and the common ratio is -5?

28. Evaluate

5

1

1)4(3n

n

29. Evaluate

9

5

1)3(2n

n

30. find the 9th partial sum of

1

)36(i

i

31. Find

1

1 4

37

i

i

32. There are 185 students in the senior class. 98 seniors will be

attending graduation ceremonies. 143 seniors will be attending a

graduation party. A total of 62 seniors will be attending both the ceremony

and a party.

Construct a two-way table summarizing the data.

33. There are 250 students in the senior class at Stats High School.

Some are involved in clubs and some have part-time jobs. 130 students

have a part-time job (some of these students may be in a club). 110

students are involved in a club (some of these students may have a job).

100 students are NOT involved in a club and do NOT have a part-time job

Draw a Venn diagram to illustrate the data.

34. You are playing a game with your friend where you flip a coin and

roll a number cube.

Let Event A = (coin lands heads up, rolling an even number)

Let Event B = (coin lands heads up, rolling an odd number)

List all elements of the sample space and both subsets.

35. Determine if the set of events is dependent or independent, and

why:

Roll a number cube, then flip a coin


why:

Pick a Jack from a deck of cards, don’t put it back, then pick a King from

the same deck

37. In a population of 100,000 females, the probability that a woman

lives to age 60 is 88.7% and the probability that she lives to age 80 is

56.9%. If a woman is 60 years old, what is the probability she will live to

age 80?

38. Jeremy is rolling a number cube labeled one through six. Let E be

event that he rolls a six, and let F be the event that he rolls a number

greater than 4. If Jeremy is certain that event F has occurred, what is

P(E)?

39. Flight times for a certain airline are normally distributed with a

mean of 3.25 hours and s standard deviation of 0.15 hours. Approximately

what percentage of the flights last between 2.95 and 3.55 hours?

40. For a certain camera, the length of time needed to charge the

battery is normally distributed with a mean of 5 hours and a standard

deviation of 0.65 hours. John owns one of these cameras and wants to

know the probability that the length of time needed to charge the battery

is between 4.5 and 5 hours.

41. Melanie thinks her parents are more strict than most of her friends’

parents. She decides to present them with evidence that they are too

strict by conducting a study at her school.

Her goal is to estimate the proportion of students in the school who think

their parents are strict. She doesn’t have time to interview all 2000

students in the school, so she will use a sample of students.

What is her parameter of interest?

What statistic should Melanie use to estimate that parameter?

42. A fast food restaurant wants to make sure that customers receive

their order within one minute of arriving at the final window. A random

sample of 175 completed orders found that 91% were delivered within one

minute.

What is the 95% confidence interval for the population proportion?

43. A medical study of a random sample of 1,000 patients found the

mean cholesterol to be 212.4 mg/dL. The population standard deviation is

known to be 7.4 mg/dL.

What is the 90% confidence interval for the population mean?

44. Ada is conducting an experiment to determine the boiling point of

salt water. She fills two identical pots of water with equal amounts of

water. In one pot, she adds salt. She then puts the pots of water over a

flame and records the the temperature for each pot of water to boil when

it begins to boil.

What is the treatment?

45. Christine is testing different types of fertilizer to determine which

brand is most effective in making grass greener. She purchased 2

different brands of fertilizer from the local store.

She applied brand A to the grass in her front yard and brand B to the

grass in her back yard. She watered the front yard every day for one

week. At the end of the study, she concluded that Brand A caused the

grass to get greener.

Why is her conclusion not valid?

46. Convert 48° into radians.

47. Find the radian measure for 240° and its associated coordinate

point on the unit circle. Then, find the sine, cosine, and tangent.

48. What are the exact values of sine, cosine, and tangent of angle Θ if

(4, –3) is a point on the angle’s terminal side?

49. Find the arc length when the radius is 5cm and theta is pi/6 radians.

50. In which quadrants are each trigonometric function positive?

Describe the signs of the coordinate points in each quadrant.

51. Graph the function f(x)=2sin(3x – pi)

52. The temperature of a chemical reaction oscillates between a low of

20° Celsius and a high of 120° Celsius. The temperature is at its lowest

point when the elapsed time is zero (t = 0) and completes one cycle over a

six-hour period.

How long does it take for the chemical to reach its maximum temperature?

53. If sinΘ=3/4, what are the values of cos Θ and tan Θ?

54. If sinΘ=√(3) / 2, and π/2 < Θ < π, what are the values of cosΘ and

tanΘ?

55.

56.

Algebra 2 – Segment Two Exam Review Answer Key


–y + z = -9

y– 5z = 29

First equation: Solve for z.

z = -9 + y

Substitute into the second equation.

y – 5(-9 + y) = 29

Solve for y.

y + 45 – 5y = 29

-4y + 45 = 29

-4y = -16

y = 4

Substitute this answer into either equation, and solve.

z = -9 + (4)

z = -5

Final Answer: (4, -5)


y=x2−7x+10

3x+y=7


–2x – 5y = 18

5x– 5y = 60

Multiply the first equation by -1:

-1(-2x - 5y = 18)

So we have

2x + 5y = -18

5x– 5y = 60

Add the equations:

7x = 42

x = 6

Substitute x into equation 1:

-2(6) – 5y = 18

Solve for y.

-12 – 5y = 18

-5y = 30

y = -6

Answer: (6, -6).


5x – 4z = –23

2x – 2z = –12

Multiply the second equation by -2:

-2(2x – 2z = -12)

So we have

5x – 4z = -23

-4x + 4z = 24

Add the equations:

x = 1

Substitute x into equation 2:

2(1) – 2z = -12

2 – 2z = -12

-2z = -14

z = 7

Answer: (1, 7)


–x + y = 4

–4x – 2y = –20


y=x2−7x+10

3x+y=7

7. Solve the exponential equation.

102a+3=10a−4

8. Solve the exponential growth problem.

If $75 is invested at an interest rate of 8% per year and is compounded

monthly, how much will the investment be worth in 15 years?

9. Solve the exponential decay problem.

A sofa depreciates at 20% of its original value each year. If the sofa was

$349 at its time of purchase, what is the value of the sofa after 4 years?

Round your answer to the nearest cent.


logb1000 = 3


ln x = 2


log5x+log52=1

13. Simplify log2x+log23+log211.

14. Solve the exponential function.

5x=20

15. An isotope decays at a rate of 40 percent every decade. Find the

adjusted rate of decay if it is going to be calculated annually.


f(x) = 4x


f(x) = (1/5)x


f(x) = log 15 x


f(x) = log 0.5 (x - 3)

20. Identify the 34th term of the arithmetic sequence 2, 7, 12 ...

21. Identify the twenty-third term of an arithmetic sequence where a1

equals 3 and a7 equals 6.

22. What is the sum of a 44-term arithmatic sequence where the first

term is -9 and the last term is 120?

23. What is the first term of a 14-term arithmetic sequence where the

last term is -12 and the sum is 42?

24. Identify the 10th term of the geometric sequence 2, 8, 32 ...

r = 4

an = a1rn-1

a10 = 2*410-1

a10 = 524,288

25. Identify the sixth term of a geometric sequence where a 1 equals 18

and a3 equals 4.5 .

4.5 = 18r3-1

4.5 = 18r2

0.25 = r2

+/- 0.5 = r

If r = 5, then

a6 = 4.5*(0.5)6-1

a6 = 0.5625

If r = -0.5, then

a6 = 4.5*(-0.5)6-1

a6 = 0.5625

26. What is the sum of the geometric sequence -4, 24, -144 ... if there

are 10 terms?

27. What is the sum of an 8-term geometric series if the first term is -9,

the last term is 703,125, and the common ratio is -5?

28. Evaluate

5

1

1)4(3n

n

29. Evaluate

9

5

1)3(2n

n

30. Find the 9th partial sum of

1

)36(i

i

31. Find

1

1 4

37

i

i

32. There are 185 students in the senior class. 98 seniors will be

attending graduation ceremonies. 143 seniors will be attending a

graduation party. A total of 62 seniors will be attending both the ceremony

and a party.

Construct a two-way table summarizing the data.

33. There are 250 students in the senior class at Stats High School.

Some are involved in clubs and some have part-time jobs. 130 students

have a part-time job (some of these students may be in a club). 110

students are involved in a club (some of these students may have a job).

100 students are NOT involved in a club and do NOT have a part-time job

Draw a Venn diagram to illustrate the data.

34. You are playing a game with your friend where you flip a coin and

roll a number cube.

Let Event A = (coin lands heads up, rolling an even number)

Let Event B = (coin lands heads up, rolling an odd number)

List all elements of the sample space and both subsets.


why:

Roll a number cube, then flip a coin

Independent, because the outcome of the first event has no effect

on the outcome of the second event.


why:

Pick a Jack from a deck of cards, don’t put it back, then pick a King from

the same deck

Dependent, because a Jack is missing from the deck, so the

probability of getting a King on the second try is affected.

37. In a population of 100,000 females, the probability that a woman

lives to age 60 is 88.7% and the probability that she lives to age 80 is

56.9%. If a woman is 60 years old, what is the probability she will live to

age 80?

38. Jeremy is rolling a number cube labeled one through six. Let E be

event that he rolls a six, and let F be the event that he rolls a number

greater than 4. If Jeremy is certain that event F has occurred, what is

P(E)?

39. Flight times for a certain airline are normally distributed with a

mean of 3.25 hours and s standard deviation of 0.15 hours. Approximately

what percentage of the flights last between 2.95 and 3.55 hours?

40. For a certain camera, the length of time needed to charge the

battery is normally distributed with a mean of 5 hours and a standard

deviation of 0.65 hours. John owns one of these cameras and wants to

know the probability that the length of time needed to charge the battery

is between 4.5 and 5 hours.

41. Melanie thinks her parents are more strict than most of her friends’

parents. She decides to present them with evidence that they are too

strict by conducting a study at her school.

Her goal is to estimate the proportion of students in the school who think

their parents are strict. She doesn’t have time to interview all 2000

students in the school, so she will use a sample of students.

What is her parameter of interest?

What statistic should Melanie use to estimate that parameter?

42. A fast food restaurant wants to make sure that customers receive

their order within one minute of arriving at the final window. A random

sample of 175 completed orders found that 91% were delivered within one

minute.

What is the 95% confidence interval for the population proportion?

43. A medical study of a random sample of 1,000 patients found the

mean cholesterol to be 212.4 mg/dL. The population standard deviation is

known to be 7.4 mg/dL.

What is the 90% confidence interval for the population mean?

44. Ada is conducting an experiment to determine the boiling point of

salt water. She fills two identical pots of water with equal amounts of

water. In one pot, she adds salt. She then puts the pots of water over a

flame and records the the temperature for each pot of water to boil when

it begins to boil.

What is the treatment?

45. Christine is testing different types of fertilizer to determine which

brand is most effective in making grass greener. She purchased 2

different brands of fertilizer from the local store.

She applied brand A to the grass in her front yard and brand B to the

grass in her back yard. She watered the front yard every day for one

week. At the end of the study, she concluded that Brand A caused the

grass to get greener.

Why is her conclusion not valid?

46. Convert 48° into radians.

47. Find the radian measure for 240° and its associated coordinate

point on the unit circle. Then, find the sine, cosine, and tangent.

48. What are the exact values of sine, cosine, and tangent of angle Θ if

(4, –3) is a point on the angle’s terminal side?

49. Find the arc length when the radius is 5cm and theta is pi/6 radians.

s = r*theta, but theta must be in radians.

s = 5cm * pi/6 radians

s = 5pi/6 cm

50. In which quadrants are each trigonometric function positive?

Describe the signs of the coordinate points in each quadrant.

51. Graph the function f(x)=2sin(3x – pi)

52. The temperature of a chemical reaction oscillates between a low of

20° Celsius and a high of 120° Celsius. The temperature is at its lowest

point when the elapsed time is zero (t = 0) and completes one cycle over a

six-hour period.

How long does it take for the chemical to reach its maximum temperature?

53. If sinΘ=3/4, what are the values of cos Θ and tan Θ?

54. If sinΘ=√(3) / 2, and π/2 < Θ < π, what are the values of cosΘ and

tanΘ?

Algebra 2 Segment Two Exam Review Solve by substitution...

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