Final Review Packet JUNE 2011 ALGEBRA 2 FINAL EXAM PART I ...

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NAME:_________________________________________________________________

Final Review Packet

JUNE 2011

ALGEBRA 2 FINAL EXAM

PART I

Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits.

Write your answers on the scantron sheet provided. FOR EACH OF THE 5

QUESTIONS YOU OMIT ON PART I, FILL IN CHOICE (5) ON THE SCANTRON

SHEET.

1. The expression is equivalent to

(1) (2) (3) (4) (5)OMIT

2. If and , what is the value of (1) (2) (3) (4) (5)OMIT

3. What are the values of in the interval that satisfy the equation

(1) (2) (3) (4) (5)OMIT

4. Express as a single trigonometric function.

(1) (2) (3) (4) (5)OMIT

5. Which graph represents the solution set of

(1) (3)

-2 8 -2 8

(2) (4) (5)OMIT

-2 8 -2 8

6. Which function is NOT one-to-one?

(1) {(4,3), (3,2), (2,1), (1,0)} (2) {(2,1), (4,2), (6,2), (8,4)}

(3) {(0,2), (1,3), (4,5),(2,4)} (4) {(5,1), (4,2), (3,3), (2,4)} (5)OMIT

7. In , , s = 12 and t = 14. What is the area of to the nearest square

inch?

(1) (2) (3) (4) (5)OMIT

8. Which graph does NOT represent a function?

(1) (2) (3) (4)

2


(1) (2) (3) (4)

(5)OMIT

10. If

, what is ?

(1)

(2)

(3)

(4)

(5)OMIT

11. The value of the expression is

(1) 8 (2) 4 (3) 9 (4) -10 (5)OMIT

12. For which equation does the sum of the roots equal

and the product of the roots equal 2?

(1) 2x2 – x + 4 = 0 (2) 2x

2 + x – 4 = 0

(3) 2x2 – x – 4 = 0 (4) 2x

2 + x + 4 = 0 (5)OMIT

13. The graph to the right represents which equation below?

(1) y = sin 2x (2) y = 2 sin x

(3) y = ½ sin x (4) y = sin½ x (5)OMIT

14. The expression

is equivalent to

(1)

(2

(3) 4)

(5)OMIT

15. Nine students who went to SUNY Albany were asked how many times they withdrew money

from the ATM in the Campus Center over the last month. Their responses are shown below.

3, 9, 2, 2, 6, 4, 1, 0, 7

Determine the standard deviation for this data to the nearest tenth.

(1) 2.8 (2) 3.0 (3) 34 (4) 3.8 (5)OMIT

3

16. If a function is defined by the equation f(x) = , which graph represents the inverse of that

function?

(5)OMIT

17. Factored completely the expression is equivalent to

(1) (2)

(3) (4) (5)OMIT


(1) (2) (3) (4) (5)OMIT

19. What is the second term in the expansion of (4 – x)4?

(1) 96x2

(2) (3)

(4) (5)OMIT

20. In simplest form the expression

equals

(1) (2)

(3)

(4)

(5)OMIT

4

21. What is the solution of the equation ?

(1) 75 (2) 50 (3)

(4)

(5)OMIT

22. A circle has a radius of 7 inches. In inches, what is the length of the arc intercepted by a

central angle of 2 radians?

(1) 14 (2) (3) 21 (4) 21 (5)OMIT

23. What is the domain of the function ?

(1) x ≥ 3 (2) x > 3 (3) x ≤ 3 (4) x < 3 (5)OMIT

24. What is the equation of the axis of symmetry of the graph of y = 3x2 + 12x – 2?

(1) x = -2 (2) x = 2 (3) y = -2 (4) y = 2 (5)OMIT

25. Which formula can be used to determine the total number of different 12 letter

arrangements that can be formed using the letters in the word CONSTITUTION ?

(1) 12! (2)

(3)

(4)

(5)OMIT

26. Express in factored form.

(1) (2)

(3) (4) (5)OMIT

27. The solution set of |3x - 5| = 7 is

(1) {

} (2) {4} (3) {-

, 4} (4) {-4} (5)OMIT

28. The solution set of is (1) { } (2) { 7 } (3) { -7 } (4) { 25 } (5)OMIT 29. Given the equation solve for the value of x. (1) 40 (2) (3) 22 (4) (5)OMIT

30. If side a = 13 and angle , find side b correct to two decimal places when

angle (1) 20.33 (b) 7.21 (3) 7.60 (4) 10.78 (5)OMIT

5

JUNE 2011 ALGEBRA 2 PART II

Answer all 5 questions from this part. Show work in the space provided.

[Four credits each]

31. What change will be made to the graph of the equation if the equation is changed to

32. Using the formula V = Pert find the value of V for an investment of $2000 at an annual rate

of 4%, compounded continuously after 7 years.

33. Express

with a rational denominator, in simplest radical form.

34. Find the center and radius of the circle with the equation: (x – 3)

2 + (y + 5)

2 = 49.

35. Solve the fractional equation for x:

JUNE 2011 ALGEBRA 2

PART III

Answer 3 out of the 4 questions in this section. All work necessary to the solution of the

question must be written in the space provided and on the graph where necessary. [Each

question selected is worth 10 points]

36. Answer both parts a and b.

a) Solve expressing the result in simplest form.

b) Solve by factoring by grouping.

6

37. The number of items sold based on the weekly selling price in dollars is summarized in the

table below.

Quantity 30 47 38 28 49 23 47 46 39 42

Price 28 22 29 32 20 35 21 20 24 29

a. Find the linear equation of best fit for the given data. Round decimals to three

places.

b. Find the correlation coefficient “r” correct to 4 decimal places for part a.

c. Find the quadratic equation of best fit for the given data. Round decimals to three

places.

d. Find the correlation coefficient “r” correct to 4 decimal places for part c.

e. Use the values of “r” to determine which equation, linear from part a or quadratic

from part c, is a better fit for the given data.

f. Use the equation of best fit found in part e to estimate the price to the nearest

dollar if the quantity sold was 55 items.


a. Two forces have magnitudes of 70 pounds and 120 pounds respectively, and act upon a body

at an angle of between them. Find, to the nearest pound, the resultant force of these two

forces.

b. In ∆XYZ, side x = 8.4, side y = 11.3, and the measure of angle X = 47°. Find, to the nearest

degree, the measure of angle Y.

7


a) On the same set of axes, sketch and label the graphs of the equations

in the interval

b) Using the graphs drawn in part a, determine the number of values in the interval

that satisfy the equation .

8

JUNE 2010


PART I




SHEET.


(1) (2) (3) (4) (5) OMIT

2. If and , what is the value of

(1) (2) (3) (4) (5) OMIT

3. What are the values of in the interval that satisfy the equation

(1) (2) (3) (4) (5) OMIT

4. A survey completed at a local high school asked 1,500 students if they felt the funding for the

after school sports programs should be cut. Every fourth student entering the gymnasium was

surveyed. Which characteristic of the survey could create a bias in the results?

(1) the age of the students surveyed (2) the method of analyzing the data

(3) the method of choosing the students surveyed (4) the size of the sample (5) OMIT

**Note: This question was removed from the curriculum. It will not be on your final.**

5. Which graph represents the solution set of

(1) (3)

-3 4 -3 4

(2) (4)

-3 4 -3 4

(5) OMIT

6. Which function is NOT one-to-one?

(1) {(2,4), (3,6), (4,7), (5,10)} (2) {(3,2), (4,3), (5,4), (6,5)}

(3) {(1,1), (2,2), (3,3),(4,4)} (4) {(2,3), (4,5), (6,7), (7,7)} (5) OMIT

7. In , b = 3 and c = 4. What is the area of to the nearest square

inch?

(1) 3 (2) 4 (3) 5 (4) 6 (5) OMIT

9

8. Which graph does NOT represent a function?

(1) (2) (3) (4)

(5) OMIT


(1) 2 (2) 3 (3) 4 (4)

(5) OMIT


(1) (2) (3) (4) (5) OMIT

11. The value of the expression is

(1) 55 (2) 50 (3) -34 (4) 52 (5) OMIT

12. For which equation does the sum of the roots equal -9 and the product of the roots equal 10?

(1) x2 – 9x + 10 = 0 (2) x

2 + 9x – 10 = 0

(3) x2 + 9x + 10 = 0 (4) x

2 – 9x – 10 = 0 (5) OMIT

13. The graph to the right represents which equation below?

(1) y = 2cosx (2) y = cos2x

(3) y = ½ cos x (4) y = cos ½ x

(5) OMIT

14. The expression

is equivalent to

(1)

(2)

r

11 s

4 (3)

(4)

(5) OMIT

15. The weekly salaries of all 9 workers in a small office are listed below. Determine the

population standard deviation (to the nearest tenth) for the weekly salaries of these 9 workers.

$255, $265, $270, $270, $275, $280, $285, $290, $300

(1) 276.7 (2)13.7 (3) 12.9 (4) 2490 (5) OMIT

10

16. If a function is defined by the equation f(x) = log4x, which graph represents the inverse of

that function?

(5) OMIT

17. The expression is equivalent to:

(1) (2) (3) (4) (5) OMIT


(1) 3 10ab b (2) 3 12ab b (3) (4) (5) OMIT

19. What is the third term in the expansion of (2y – 5)5?

(1) 2000y3

(2) -2000y3

(3) 200y2

(4) -200y2 (5) OMIT

20. For a ≠ 0, 2, -2, the fraction

21

4a

aa

is equivalent to

(1) 1

2a (2)

1

2a (3)

1

2a

(4)

1

2a

(5) OMIT

11

21. What is the solution of the equation ?

(1) 9 (2) 16 (3) 3 (4)

(5) OMIT



(1) 4 (2) 4 (3) 12 (4) 12 (5) OMIT


(1) x ≥ 4 (2) x > 4 (3) x ≤ 4 (4) x < 4 (5) OMIT

24. What is the axis of symmetry of the quadratic equation y = x2 – 8x + 4

(1) x = 8 (2) x = -8 (3) x = -4 (4) x = 4 (5) OMIT

25. Which formula can be used to determine the total number of different eleven-letter

arrangements that can be formed using the letters in the word MATHEMATICS ?

(1) 11! (2)

(3)

(4)

(5) OMIT

26. Express in factored form.

(1) (2) (3) (4)

(5) OMIT

27. The solution set of |3 + 4x| = 1 is

(1) {-

} (2) {-2, -1} (3) {-

, -1} (4) {-1} (5) OMIT

28. The solution set of is (1) { } (2) { 2 } (3) { 5 } (4) { 85 } (5) OMIT 29. Given the equation solve for the value of x. (1) 40 (2) 22 (3) 44 (4) - 40 (5) OMIT

30. If side a = 8 and angle , find side b correct to two decimal places when

angle (1) 12.19 (b) 12.20 (3) 10.74 (4) 10.75 (5) OMIT

12



[Four credits each]

31. What change will be made to the graph of the equation if the equation is changed to


of 3.2%, compounded continuously after 5 years.

33. Express


34. Find the center and radius of the circle with the equation: (x – 5)

2 + (y + 2)

2 = 16.


JUNE 2010 ALGEBRA 2

PART III





a. Two forces have magnitudes of 1350 and 1425 pounds respectively, and act upon a body

at an angle of 137˚ between them. Find, to the nearest pound, the resultant force of these

two forces.

13

b. In ∆XYZ, side x = 13, side y = 9, and the measure of angle X = 56°. Find, to the nearest



a) Solve by completing the square, expressing the result in simplest radical

form.

b) Solve by factoring by grouping.

38. In a small town the police department keeps statistics on the number of speeding tickets

issued and the age of the offending drivers. The table below summarizes the findings.

Age 17 18 21 25 30 35 40 45 50 55 60 65

Tickets 49 49 48 39 31 33 24 25 16 10 5 6

c. Find the linear equation of best fit for the given data. Round decimals to two

places.

d. Find the correlation coefficient “r” correct to 4 decimal places.

e. Use the equation found in part b to estimate the number of tickets citizens aged 23

would receive. Round your answer to the nearest ticket.

14



in the interval


that satisfy the equation

.

15

Practice Final #3

Part I: Multiple Choice. On the final all of these questions will be multiple choice questions. You

will have to answer 25 out of 30 questions (omit 5).

1. Which of the following functions is NOT one-to-one?

(1) {(1,2), (4,5), (6,7)} (3) {(1,4), (2,4), (8,4)}

(2) {(0,0), (1,1), (2,2)} (4) {(9,1), (1,9), (0,3)}

2. Express (sec x)(cot x) as a single trigonometric function.

3. What are the values of in the interval that satisfy the equation:

?

4. If f(x) = x2 + 4 and g(x) = 3x – 4, evaluate (f ○ g)(x)?

5. Draw a graph (using a number line) that represents the solution set of |2x + 6| > 24.

6. The expression (3 + 4i)2 is equivalent to:

7. In ΔQRS, m<R = 28○, s = 15, and q = 18. What is the area of ΔQRS to the nearest square

inch?

8. Which graph does not represent a function?

(1) (3)

(2) (4)

9. What is the third term in the expansion (3 – x)4?

10. Factor completely: x4 – 81.

16

11. Simplify the expression, there should be no negative exponents:

12. Write an equation with integer coefficients where the sum of the roots equals

and the

product of the roots equals 2.

13. Write the equation of the graph of the graph that’s given:

14. Evaluate:

15. Twelve students at St. Francis Prep were asked how many hours during a week they spend on

Facebook. Their responses are shown below:

5, 6, 12, 7, 5, 4, 7, 13, 9, 12, 12, 11

Determine the standard deviation for this data to the nearest tenth.

16. Simplify:

17. If

, what is ?

18. Simplify:

19. Evaluate: log3243

20. Sketch the graph of the inverse of the function y = 8x.

21. What is the solution of the equation log4(2x) = 3?

22. What is the axis of symmetry of the equation y = 2x2 – 16x + 9?




25. Write a formula to determine the total number of different 8 letter arrangements that can be

formed using the letters in the word INTERNET?

17

26. The solution set of |3x – 21| = 33 is:

27. Express x3 – 6x

2 +8x in factored form

28. If side a = 15 and angle A = 72o, find side b to two decimal places when angle B = 26

o.

29. Given the equation sin(2x + 4) = cos (3x – 9) solve for the value of x.

30. The solution set of is:

Part II: Answer all 5 questions from this section. Show all work, including formulas.

31. What change will be made to the graph of y = x2, if the equation is change to y = (x+2)

2 – 9?


of 8%, compounded continuously after 7 years.

33. Express


34. Find the center and radius of the circle with the equation: (x + 8)2 + (y – 9)

2 = 100.


Part III: Answer 3 out of the 4 questions in this section. All work necessary to the solution must

be written in the space provided and on the graph when necessary.

36. Answer both parts a & b.

a. Solve x2 + 8x + 12 = 0 expressing the result in simplest a + bi form.

b. Solve x3 – 6x

2 – 9x + 54 = 0 by factoring by grouping.

18

37. The table shows the amount of medicine for treating a disease in the bloodstream over the 9

hours following a dose of 10 mg. It seems that the rate of decrease of the drug is approximately

proportional to the amount remaining.

Time (hrs) 0 1 2 3 4 5 6 7 8

Drug Amt (mg)

10 8.3 7.2 6.0 5.4 4.4 3.7 2.8 2.5

a. Find the linear equation of best fit for the given data. Round decimals to three

places.

b. Find the correlation coefficient “r” correct to 4 decimal places for part a.

c. Find the quadratic equation of best fit for the given data. Round to 3 decimals.

d. Find the correlation coefficient “r” correct to 4 decimal places for part c.

e. Use the values of “r” to determine which equation, linear from part a or quadratic

from part c, is a better fit for the given data.

f. Use the equation of best fit found in part e to estimate the drug amount to the

nearest tenth after 10 hours has passed.

19


a. Two forces have magnitudes of 80 pounds and 130 pounds respectively, and act upon a body

at an angle of between them. Find, to the nearest pound, the resultant force of these two

forces.

b. In ∆XYZ, side x = 6.7, side y = 10.4, and the measure of angle X = 52°. Find, to the nearest




in the interval


that satisfy the equation

.

20

39. Continued:

21

Older Final Exams – Note the difference in the new test!

JUNE 2009


PART I




SHEET.

1. Given the function f x x( ) 2 10 , find the numerical value of f ( )3 .

(1) –1 (2) –4 (3) 0 (4) −7 (5) omit

2. If x log5 6211, the value of x to the nearest hundredth is:

(1) 5.41 (2) 5.42 (3) 5.43 (4) 5.44 (5) omit

3. The expression 5 22

x b g in expanded form equals:

(1) 25 42x (2) 5 42x (3) 25 5 42x x (4) 25 20 42x x (5) omit

4. The graph of the equation 9 10 152 2x y is a:

(1) ellipse (2) circle (3) parabola (4) hyperbola (5) omit

5. If y varies inversely with x, and y = 5 when x = 6, find the value of y when x = 3.

(1) 10 (2) 5

2 (3)

2

5 (4)

18

5 (5) omit

6. Express 8

5

radians in degree measure.

(1) 72 (2) 144 (3) 288 (4) 576 (5) omit

7. Solve the equation for x: 4 20 84x

(1) {−2} (2) {3} (3) {–3} (4) { } (5) omit

8. Find the solution set for the inequality x x2 3 10 0 .

(1) 2 5x (2) 5 2x (3) x 2 or x 5 (4) x 5or x 2 (5) omit

9. Find the area of a triangle with two adjacent sides of lengths 8.1 and 9.3, and the included

angle measuring 76 . Express your answer to the nearest tenth.

(1) 18.3 (2) 73.1 (3) 36.5 (4) 37.7 (5) omit

10. Solve the equation 2 3 0cosx for all x in the interval 0 2 x .

(1)

3

5

3and (2)

6

7

6and (3)

6

11

6and (4)

3

8

3and (5) omit

11. Find the product: ( )( )3 2 3 i i .

(1) 9 7 i (2) 9 7 i (3) 6 3 i (4) 6 3 2 i (5) omit

22

12. If f x x( ) 3

5 find f 32b g . (1)

1

8 (2) 8 (3)

1

16 (4) 16 (5) omit

13. What is the solution set for the equation x 7 3.

(1) { }16 (2) { }2 (3) { }8 (4) { , }2 8 (5) omit

14. The roots of the equation 7 9 02x x k will be imaginary when k =

(1) 3 (2) 2 (3) 1 (4) 0 (5) omit

15. The value of tan cosb g FHGIKJ

3

2is:

(1) −1 (2) 0 (3) 1 (4) Undefined (5) omit

16. The frequency of the function y x 4 2sin( ) is:

(1) 2 (2) 4 (3) 90 (4) 180 (5) omit

17. Simplify and express in a + bi form: 3

4

i

i.

(1)

3

17

12

17i (2)

1

5

4

5i (3)

3

17

12

17 i (4)

1

5

4

5 i (5) omit

18. Find the value of x, to the nearest degree, given cos .x 3846 .

(1) 23 (2) 66 (3) 67 (4) 68 (5) omit

19. If Z1 = 3 35 i and Z2 = 4 3 i , in which quadrant does Z1 – Z2 lie?

(1) I (2) II (3) III (4) IV (5) omit

20. Reduce the algebraic fraction to lowest terms: x x

x x

2

2

6

12

.

(1) x

x

2

4 (2)

x

x

2

4 (3)

x

x

2

4 (4)

1

2 (5) omit

21. When simplified the expression (tan )(cos ) is equivalent to:

(1) cot (2) sin (3) csc (4) sec (5) omit

22. The expression log x y3 is equivalent to:

(1) log logx y3 (2) 3log logx y (3) log log3x y (4) log log log3 x y (5) omit

23

23. If f x x( ) 1and g x x( ) 2 3 find f g( ( ))6 .

(1) 12 (2) 13 (3) 14 (4) 15 (5) omit

24. Find the value of angle X to the nearest degree if

arc A = 220 and arc B = 50 .

A B

(1) 135 (2) 50 (3) 85 (4) 170 (5) omit X

25. If sin 0and tan 0 , in what quadrant does the terminal side of angle lie?

(1) I (2) II (3) III (4) IV (5) omit

26. Simplify the complex fraction:

1 1

5

x y

xy

(1) x y

5 (2)

x y

xy

2 2

5

(3)

y x

5 (4) 5 5y x (5) omit

27. If log5 3x , find the value of x.

(1) 25 (2) 1

125 (3) 125 (4)

1

25 (5) omit

28. Find the domain of f x x( ) 2 6 .

(1) x 3 (2) x 3 (3) x 3 (4) x 6 (5) omit

29. Solve for all values of x given the equation: 2 9 7x .

(1) 1 8, qm (2) { }8 (3) 8 8, qm (4) 18, qm (5) omit

30. Rationalize the denominator and express the answer in simplest terms:4

8.

(1) 4 8 (2) 4 8

8

(3) 2 (4)

32

8 (5) omit

24



[Four credits each]

31. Solve the following absolute value inequality and graph the solution set on the

real number line: x 2 7 [4]

32. For the equation 4x2 + 7x – 1 = 0, find a) the sum of the roots and b) the product

of the roots. [4]

33. Write in simplest form: 3 48 5 12 . [4]

34. Solve the equation for x, show all work: tan( ) cot( )3 5 6 13x x . [4]

35. Factor the following expression completely: 2x2 – 14x + 24. [4]

25

JUNE 2009 ALGEBRA 2

PART III




36. Solve the following equation and express the roots in simplest a+ bi form.

x2 + 4x + 29 = 0


a) A ship at sea is 3200 miles from one lighthouse and 3600 miles from a second

lighthouse. The angle formed on the ship’s deck between the two lighthouses is 86˚.

Find the distance between the two lighthouses to the nearest mile.

AND b) In acute triangle RST, side r = 15, side s = 18 and m<R = 48˚. Find m<T to the

nearest degree.

26

38. a) On the same set of axes, sketch and label the graphs of the equations y x1

22sin

and y x 21

2cos in the interval 0 2 x .

b) Based on the graphs drawn in part a, determine the number of values of x in the

interval graphed where the two functions are equal.

27

39. The number of rooms in your home is said to be a reliable predictor of your SAT

scores. The following data contains the number of rooms in students’ homes and

their math SAT scores.

Number

of Rooms

3 4 5 6 7 8

Math

Score

500 530 570 610 630 640

a. Find the linear equation of best fit for the given data. Round decimals to two

places.

b. Find the correlation coefficient “r” correct to 4 decimal places.

c. Use the equation found in part b to estimate the SAT math score of a student

living in a 12 room house. Remember SAT scores are reported in increments

of 10.

Final Review Packet JUNE 2011 ALGEBRA 2 FINAL EXAM PART I ...

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