alg 2 first semester exam review ch. 1-6 max

Algebra 2 First Semester Exam ReviewMultiple Choice Identify the choice that best completes the statement or answers the question. ____

____

____

1. Order the numbers 2, 7 , , 0.6448, from least to greatest. 5 a. c. 5 7 7 , 0.6448, 2, , , 0.6448, , ,2 5 5 b. d. 7 , 0.6448, , 2, , 2, , 0.6448, 7 2. Use interval notation to represent the set of numbers 7 x 3. a. (7, 3) c. [7, 3] b. (3, 7] d. {7, 3} 3. Write the set in set-builder notation.8 6 4 2 0 2 4 6 8 x

5

a. ____

c.

b. [3, 4) d. [3, 4] 4. What statement can be determined from the diagram?

Rhombus Square

Parallelogram

a. Every square is a rhombus. b. Every rhombus is a square. ____

c. No parallelogram is a rhombus. d. No parallelogram is a square.2

____

____

5. Find the additive and multiplicative inverse of 3 . 3 5 a. c. additive inverse: 2 ; additive inverse: 3 ; 3 multiplicative inverse: 0 multiplicative inverse: 2 2 3 b. d. additive inverse: 3 ; additive inverse: 2 ; 3 2 multiplicative inverse: 2 multiplicative inverse: 3 6. Identify the property demonstrated by the equation 3(5 + 2) = 15 + 6. a. Commutative Property c. Distributive Property b. Associative Property d. Closure Property 7. Use mental math to find a 11% tax on a $25.00 backpack.

____

a. $11.00 c. $27.50 b. $2.75 d. $2.50 8. Which example shows that the Associative Property does not hold for division? a. c. b. d. 9. Estimate a. 6.5 b. 6.6 to the nearest tenth. c. 6.7 d. 7.0 . c.

____

____ 10. Simplify the expression a. b.

25 49 d. 5 7

____ 11. Simplify a. b. ____ 12. Add. a. b.

by rationalizing the denominator. c. d.

c. d.

____ 13. Write an algebraic expression to represent the number of letters Isabel wrote. Isabel wrote 10 letters to friends each month for x months in a row. a. 10x c. b. 10 x d. ____ 14. Evaluate the expression g + s for g = 9 and s = 3. a. 12 c. b. 6 d. ____ 15. Evaluate for x = 7. a. 28 c. b. 50 d. 10 + x 27 13 8 34

____ 16. Simplify the expression . a. c. b. d. ____ 17. Murphys motorcycle gets 55 miles per gallon of gas on the highway and 45 miles per gallon in the city. The motorcycle holds 8 gallons of gas. Write and simplify an expression for the total number of miles Murphy can travel if he has a full tank of gas but uses 2 gallons on the highway and the rest in the city. a. c. ; 270 miles ; 110 miles b. d. ; 380 miles ; 420 miles

____ 18. Write a. b.

in expanded form. c. d. . c. 4 d. 0 . Assume all variables are nonzero. c. d. . Write the answer in scientific notation. c. 3.06 106 d. 3.06 1012 in expanded form. c. d.

____ 19. Simplify the expression a. 12 1 4

b.

____ 20. Simplify the expression a. b. ____ 21. Simplify the expression a. 3.06 1012 b. 3.06 103 ____ 22. Write the expression a. b.

____ 23. Simplify the expression . Write the answer in scientific notation. a. 1.28 10 5 c. 1.28 10 6 b. 1.03 10 9 d. 1.03 10 5 ____ 24. Give the domain and range of the relation. x 2 8 0 3 y 5 17 0 5

a. D: {3, 0, 2, 8}; R: {5, 0, 5, 17} b. D: {5, 0, 5, 17}; R: {3, 0, 2, 8} c. D: {2, 8, 3, 5, 17, 5}; R: {0} d. D: {3, 2, 8}; R: {5, 5, 17} ____ 25. Determine whether the relation is a function. Antonios age (years) Antonios height (inches) 11 60 12 61 13 62 14 67 15 69 16 69

a. No, the relation is not a function. b. Yes, the relation is a function. ____ 26. Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.

y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

a. Yes, the relation is a function. b. No, the relation is not a function. (0, 4) and (0, 4) ____ 27. Which is an element of the range of the graphed function?y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

a. 3 b. 2 ____ 28. For a. 23 b. 15 , evaluate .

c. 4 d. 0 c. 27 d. 32 .

____ 29. Graph the function

a.6 5 4 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6

y

c.6 5 4 3 2 1 1 2 3 4 5 6 x 6 5 4 3 2 1 1 2 3 4 5 6

y

1

2

3

4

5

6

x

b.6 5 4 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6

y

d.6 5 4 3 2 1 1 2 3 4 5 6 x 6 5 4 3 2 1 1 2 3 4 5 6

y

1

2

3

4

5

6

x

____ 30. The commercial jet that travels from Houston to Miami averages about 375 mi/h. The air distance from Houston to Miami is 968 miles. Write a function to represent the distance d remaining on the trip t hours after takeoff. a. c. b. d. ____ 31. Evaluate a. b. for . c. d.

____ 32. Translate the point (1, 1) right 2 units and down 2 units. Give the coordinates of the translated point.

a.

y

c.

y

(3, 3) (1, 1)x

(1, 1) (1, 1)x

b.

y

d.

y

(3, 3) (1, 1)x

(1, 1) (3, 1)x

____ 33. Use a table to translate the graph 3 units to the left.y 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 x

a.8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8

y

c.8 7 6 5 4 3 2 1

y

1 2 3 4 5 6 7 8

x

8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

x

b.8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8

y

d.8 7 6 5 4 3 2 1

y

1 2 3 4 5 6 7 8

x

8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

x

____ 34. Use a table to perform a vertical stretch of f(x) = x by a factor of 3. Graph the transformed function on the same coordinate plane as the original function. y y a. c.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x 5 4 3 2 5 4

f(x)

3 2 1 1 1 2 3 4 5 1

f(x)

2

3

4

5

x

b.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

d.5 4

y

f(x)

3 2 1

f(x)

1

2

3

4

5

x

5

4

3

2

1 1 2 3 4 5

1

2

3

4

5

x

____ 35. The graph shows Carmens savings each week. She decides to save 2.5 times as much money each week. Sketch a graph that represents the new savings and identify the transformation of the original graph that it represents.50 45 40

Total Savings ($)

35 30 25 20 15 10 5 1 2 3 4 5 6 7 8 9 10

Time (weeks)

a.

50 45 40

Total Savings ($)

35 30 25 20 15 10 5 1 2 3 4 5 6 7 8 9 10

Time (weeks)

The graph represents a vertical stretch by a factor of 2.5.

b.

50 45 40

Total Savings ($)

35 30 25 20 15 10 5 1 2 3 4 5 6 7 8 9 10

Time (weeks)

The graph represents a horizontal stretch by a factor of 2.5. c.50 45 40

Total Savings ($)

35 30 25 20 15 10 5 1 2 3 4 5 6 7 8 9 10

Time (weeks)

The graph represents a vertical compression by a factor of d.50 45 40

.

Total Savings ($)

35 30 25 20 15 10 5 1 2 3 4 5 6 7 8 9 10

Time (weeks)

The graph represents a vertical translation up 2.5 units. ____ 36. Fabric that regularly sells for $4.90 per square foot is on sale for 10% off. Write an equation that represents the cost of s square feet of fabric during the sale. Write a transformation that shows the change in the cost of fabric. a. c. ; ;

b.

;

d.

;

____ 37. Identify the parent function for and describe what transformation of the parent function it represents. a. The parent function is the cubic function, . represents a vertical translation of the parent function 3 units up. b. The parent function is the cubic function, right. c. d. The parent function is the cubic function, The parent function is the cubic function, . . represents a vertical translation of the parent function 3 units down. represents a horizontal translation of the parent function 3 units to the left. ____ 38. Graph the data from the table. Describe the parent function and the transformation that best approximates the data set. x y a.8

.

represents a horizontal translation of the parent function 3 units to the

3 0y

2 1

1 2

6 3

13 4

4

4 4

4

8

12

x

8

Square root function translated 3 units to the left.

b.8

y

4

4 4

4

8

12

x

8

Linear function with a vertical compression of c.8 y

translated 3 units to the left.

4

4 4

4

8

12

x

8

Quadratic function translated 3 units to the left. d.8 y

4

4 4

4

8

12

x

8

Linear function with a vertical compression of translated 3 units to the left. ____ 39. In the deep ocean, the length of a wave in meters is related to the period of the wave in seconds. Graph the relationship between wave period and wavelength and identify which parent function best describes it. (Hint: Although time cannot be negative, the negative portion of this function has been provided for you.)

Wave period (sec) 1 1 2 3 5 a.45 40

Wavelength (m) 1.56 1.56 6.24 14.04 39 c.45 40

Wavelength (m)

30 25 20 15 10 5

Wavelength (m)1 2 3 4 5 6 7 8 9

35

35 30 25 20 15 10 5

1 5

Wave period (sec)

1 5

1

2

3

4

5

6

7

8

9

Lin d.45 40

Wave period (sec)

Qu

ear parent function b.45 40

adratic parent function

Wavelength (m)

30 25 20 15 10 5

Wavelength (m)1 2 3 4 5 6 7 8 9

35

35 30 25 20 15 10 5

1 5

Cu bic parent function uare-root parent function ____ 40. For which function is 3 NOT an element of the range? a. c. b. d.

Wave period (sec)

1 5

1

2

3

4

5

6

7

8

9

Wave period (sec)

Sq

____ 41. Dan paid a total of $25.80 last month for his international calls. He makes international calls only to England. Dan pays $0.06 per minute in addition to $10.98 fixed monthly payment. How many minutes of international calls did Dan make last month? a. 247 minutes c. 419 minutes b. 430 minutes d. 613 minutes ____ 42. Solve a. =4 . c. = 1

= 11 ____ 43. Solve 3n 24 = 14 30n. a. n = 2 b. n=

b.

d. c. d.

=5 n= n=

1 2710 33

11

1 33

5

____ 44. Solve . a. The solution set is all real numbers, or . b. The solution set is the empty set. c. d. ____ 45. Solve and graph 2a 7 > 3. a. a < 210 8 6 4 2 0 2 4 6 8 10

b. a > 210 8 6 4 2 0 2 4 6 8 10

c. a > 510 8 6 4 2 0 2 4 6 8 10

d. a < 510 8 6 4 2 0 2 4 6 8 10

____ 46. Solve and graph 3 a. x 510 9 8 7 6 5 4 3 2 1

.

0

1

2

3

4

5

6

7

8

9

10

b. The inequality has no solution. The solution set is the empty set.10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

c. The solution set is the set of all real numbers.10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

d.

x

7 5

10 9

8

7

6

5

4

3

2

1

0

1

2

3

4

5

6

7

8

9

10

____ 47. Solve the proportion a. x = 32 b. x = 0.03

. c. x = 8 d. x = 9

____ 48. A high school stadium can seat about 80% of the students attending the high school. If there are 405 students enrolled in the high school, how many students can the stadium seat? If necessary, round to the nearest number of students. a. 329 students c. 324 students b. 321 students d. 327 students ____ 49. Lydia is training for the half marathon, a 13-mile-long race. This morning she ran 8 miles in 58 minutes. Assuming she can maintain this pace, how long will it take her to run the half marathon? Round your answer to the nearest minute. a. 36 min c. 94 min b. 63 min d. 152 min ____ 50. a.12

has vertices , , and and on the same grid.y

. c.

is similar toy

with a vertex at

. Graph

C12

C

8

8

F

F4 4

A

4 y

D

8

B

12

x

A

4 y

D

8

B

12

x

b.12

d.C12

F

C

8

8

4

4

A

4

D

8

B

12

x

A

4

D

8

B

12

x

____ 51. A sawyer (person who cuts down trees) wants to know the height of a tree. The sawyer measures the shadow of his friend, who is 5 feet tall and standing beside the tree, and measures the shadow of the tree. If his friends shadow is 12 feet long and the trees shadow is 60 feet long, how tall is the tree? a. 144 feet c. 25 feet b. 1 foot d. 53 feet ____ 52. A recipe for trail mix requires 2 parts peanuts, 3 parts raisins, and 4 parts granola by weight. Chiwa has 30 ounces of peanuts, 63 ounces of raisins, and 40 ounces of granola. How many ounces of trail mix can she make? How many ounces of raisins will she need? a. 90 oz; 30 oz

b. 135 oz; 45 oz c. 113 oz; 38 oz d. 133 oz; 63 oz ____ 53. Determine whether the data set could represent a linear function. x 0 1 2 3 a. b. c. d. f(x) 1 0 1 2

Yes, the data set could represent a linear function. No, the data set does not represent a linear function. The data set is constant. Cannot be determined

____ 54. Graph the line with slope a.15 12 9 6 3 15 12 9 6 3 3 6 9 12 15 y

3

1

that passes through (6, 4). c.15 12 9 6 3 y

3

6

9

12

15

x

15 12 9

6

3 3 6 9 12 15

3

6

9

12

15

x

b.15 12 9 6 3 15 12 9 6 3 3 6 9 12 15

y

d.15 12 9 6 3 3 6 9 12 15 x 15 12 9 6 3 3 6 9 12 15

y

3

6

9

12

15

x

____ 55. Find the intercepts of , and graph the line. a. x-intercept: 2, y-intercept: 3 c. x-intercept: 2, y-intercept: 2

y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10 x 10 8 6 4 10 8 6 4 2 2 2 4 6 8 10

y

2

4

6

8

10

x

b. x-intercept: 4, y-intercept: 3y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10 x

d. x-intercept: 4, y-intercept: 2y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10 x

____ 56. Write the function a.y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6

in slope-intercept form. Then graph the function. c.y 10 8 6 4 2 8 x 10 8 6 4 2 2 4 6 8 10 2 4 6 8 x

b.

d.

y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 x 10 8 6 4 10 8 6 4 2 2 2 4 6 8 10

y

2

4

6

8

x

____ 57. Determine if is vertical or horizontal. Then graph. a. The line is horizontal.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

b. The line is vertical.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

c. The line is horizontal.

y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

d. The line is vertical.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

____ 58. There was $1,400 in Naomis school art and music fund when school began. Then the parents group held a 12-day fundraiser to reach the schools goal of $6,000. Find the average amount of money per day the parents raised. Graph the daily amount of money in the fund during the 12-day parent fundraiser. a. The average amount raised per day is about $383.33.7000 6500 6000 5500 5000 4500

Amount ($)

4000 3500 3000 2500 2000 1500 1000 500 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of Days

b. The average amount raised per day is about $500.00.

7000 6500 6000 5500 5000 4500

Amount ($)

4000 3500 3000 2500 2000 1500 1000 500 1 2 3 4 5 6 7 8 9 10 11 12 13

Number of Days

c. The average amount raised per day is about $383.33.7000 6500 6000 5500 5000 4500

Amount ($)

4000 3500 3000 2500 2000 1500 1000 500 1 2 3 4 5 6 7 8 9 10 11 12 13

Number of Days

d. The average amount raised per day is about $500.00.7000 6500 6000 5500 5000 4500

Amount ($)

4000 3500 3000 2500 2000 1500 1000 500 1 2 3 4 5 6 7 8 9 10 11 12 13

Number of Days

____ 59. Determine whether the data in the table are linear. Explain. Session Length (min) Cost ($) 4 2.90 9 4.65 14 6.40 21 8.85 27 10.95

a. Yes, the rate of change is constant. For example, to the nearest hundredth,

, , and so on. b. No, the ratio of the cost to the session length is not constant. For example, to the nearest hundredth, and . c. No, the rate of change is not constant. For example, and . d. Yes, the difference between successive session lengths is constant. For example, , and so on. ____ 60. Write the equation of the graphed line in slope-intercept form.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

,

a. c. b. d. ____ 61. Find the slope of the line that passes through the points (1, 3) and (9, 7). a. 2 c. 1 b. d. 2 ____ 62. In slope-intercept form, write the equation of the line that contains the points in the table. x y 1 2 5 4 9 6 13

a. c. b. d. ____ 63. After the first three miles, the cost of a taxi ride is a linear function of the trip length. Express the taxi cost as a function of the trip length. Graph the relationship between the taxi cost and the trip length. If a 5-mile ride costs $5.00 and a 10-mile ride costs $8.75, how much does a 16-mile ride cost? a. c.

18 16

18 16

Cost of taxi ride ($)

14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18


14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18

Number of miles

Th d.

Number of miles

Th

e 16-mile ride costs $15.00. b.18 16 18 16

e 16-mile ride costs $13.25.


14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18


14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18

Th Th e 16-mile ride costs $14.00. e 16-mile ride costs $12.50. ____ 64. In slope-intercept form, write the equation of the line that is parallel to y = 2x 9 and passes through (2, 4). 1 1 a. c. y = 2x 5 y = 2x 3 b. y = 2x 8 d. y = 2x 11 ____ 65. Find the slope of each segment and then classify the quadrilateral.

Number of miles

Number of miles

y 6 4

B

A2

6

4

2 2 4

2

4

6

x

C

D6

a. b. c. d.

The slope of and is . The slope of The quadrilateral is a rectangle. The slope of and is . The slope of The quadrilateral is a rectangle. The slope of and is 4. The slope of The quadrilateral is a rectangle. The slope of and is . The slope of The quadrilateral is a rectangle. .y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

and and and and

is

.

is 4. is .

is .

____ 66. Graph the inequality a.

c.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

1

2

3

4

5

x

b.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

d.5 4 3 2 1 1 2 3 4 5 x 5 4 3 2 1 1 2 3 4 5

y

1

2

3

4

5

x

____ 67. Graph 16x + 8y > 32 using intercepts. y a.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

c.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

1

2

3

4

5

x

b.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

d.5 4 3 2 1 1 2 3 4 5 x 5 4 3 2 1 1 2 3 4 5

y

1

2

3

4

5

x

____ 68. Solve a.

for y. Graph the solution. c.

y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x 5 4 3 2 5 4 3 2 1 1 1 2 3 4 5

y

1

2

3

4

5

x

b.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

d.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

____ 69. Graph the inequality a.6 4 2

y

. c.6 4 2

y

6

4

2 2 4 6

2

4

6

x

6

4

2 2 4 6

2

4

6

x

b.6 4 2

y

d.6 4 2

y

6

4

2 2 4 6

2

4

6

x

6

4

2 2 4 6

2

4

6

x

____ 70. Let a. b.

be the transformation, vertical translation 3 units down, of c. d.

. Write the rule for

.

____ 71. Let be a horizontal compression of function. a.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

by a factor of . Write the rule for c.y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

and graph the

b.

d.

y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x 5 4 3 2 5 4 3 2 1 1 1 2 3 4 5

y

1

2

3

4

5

x

____ 72. Let rule for a.

be a vertical shift of .

up 4 units followed by a vertical stretch by a factor of 3. Write the c.

b. d. ____ 73. The Ybarra family is renting a car for a few days. Meinke Rentals charges $20 per day, plus a fixed cleaning fee of $20. The function represents the cost to rent a car from Meinke Rentals for d days. SmartRent charges $25 per day. The function represents the cost to rent a car from SmartRent for d days. Graph and on the same coordinate plane and describe the transformation that takes to . a.150 140 130 120 110 100 90 80 70 60 50 40 30 20 10

Cost ($)

M(d) S(d)

1

2

3

4

5

6

7

Number of days

A vertical stretch by a factor of 1.25, followed by a vertical shift down 20 units.

b.150 140 130 120 110 100 90 80 70 60 50 40 30 20 10

Cost ($)

M(d) S(d)

1

2

3

4

5

6

7

Number of days

A vertical shift down 20 units, followed by a vertical stretch by a factor of 1.25. c.150 140 130 120 110 100 90 80 70 60 50 40 30 20 10

Cost ($)

S(d) M(d)

1

2

3

4

5

6

7

Number of days

A vertical compression by a factor of 0.75, followed by a vertical shift up 20 units. d.150 140 130 120 110 100 90 80 70 60 50 40 30 20 10

Cost ($)

S(d) M(d)

1

2

3

4

5

6

7

Number of days

A vertical shift up 20 units, followed by a vertical compression by a factor of 0.75. ____ 74. Give two different combinations of transformations that would transform into a. 1. A vertical shift 15 units down, followed by a horizontal compression by a factor of . 2. A vertical stretch by a factor of 3, followed by a vertical shift 21 units down. .

b. c.

1. A horizontal compression by a factor of , followed by a vertical shift 15 units down. 2. A vertical shift 21 units down, followed by a vertical stretch by a factor of 3.

1. A horizontal shift 15 units left, followed by a horizontal compression by a factor of . 2. A vertical stretch by a factor of 3, followed by a vertical shift 21 units down. d. 1. A horizontal stretch by a factor of 3, followed by a vertical shift 15 units down. 2. A vertical compression by a factor of , followed by a vertical shift 21 units down. ____ 75. Anchorage, Alaska and Augusta, Georgia have very different average temperatures. This is a table of the average monthly temperature in each city. Make a scatter plot for the temperature data, identify the correlation, and then sketch a line of best fit and find its equation. Jan Anchorage Augusta 15 44 Feb 19 47 Average Temperatures (F) Ma Apr Ma Jun Jul Aug Sep r y 26 26 47 54 58 56 48 56 63 71 78 81 80 75 c. Negative correlationAugusta

Oct Nov Dec 35 64 21 55 16 47

a. Positive correlationAugusta

72

72

60

60

48

48

36 24 36 48 Anchor.

36 24 36 48 Anchor.

b. Positive correlationAugusta

d. Negative correlation

72

60

48

36 24 36 48 Anchor.

Augusta

72

60

48

36 24 36 48 Anchor.

____ 76. There is a known relationship between forearm length (f) and body height (h). The table and accompanying scatter plot show arm lengths and heights from a randomly selected sample of people. Find the correlation coefficient r and the line of best fit. Forearm length (cm) 24 Body height (cm) 157height

27 177

24 164

26 175

32 195

30 178

29 180

28 172

190

180

170

160

150 10 20 30 40 forearm

c. ; r = 0.84 ; r = 0.83 d. ; r = 6.43 ; r = 0.91 ____ 77. The data set shows the amount of funds raised and the number of participants in the fundraiser at the Family House organization branches. Make a scatter plot of the data with number of participants as the independent variable. Then, find the correlation coefficient and the equation of the line of best fit and draw the line. Family House Fundraiser Number of participants Funds raised ($) 6 10 15 20 25 13 15 18 450 550 470 550 650 600 600 650

a. b.

a.

1000 900 800

c.

1000 900 800

Money raised ($)

600 500 400 300 200 100 3 6 9 12 15 18 21 24 27

Money raised ($)

700

700 600 500 400 300 200 100 3 6 9 12 15 18 21 24 27

Number of participants


; b.Number of participants30 27 24

; d.1000 900 800

18 15 12 9 6 3 100 200 300 400 500 600 700 800 900

Money raised ($)

21

700 600 500 400 300 200 100 3 6 9 12 15 18 21 24 27

Money raised ($)


; ____ 78. Estimate the value of r for the scatter plot.y 12 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 12 2 4 6 8 10 x

;

a. 1.00 c. 1.00 b. 2.50 d. 2.50 ____ 79. Solve the compound inequality. Then graph the solution set. or a. {s | s 8 or s > 2}10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 s

b. {s | 8 < s 2}10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 s

c.

{s | 8 s < 2}10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 s

d. {s | s < 8 or s 2}10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 s

____ 80. Solve the equation a. x = 13 b. x = 85 or x = 77 ____ 81. Solve the inequality a.10 8 6 4 2 0 2 4

. c. x = 13 or x = 5 d. x = 85 and graph the solution set. c.6 8 10 10 8 6 4 2 0 2 4 6 8 10

b.10 8 6 4 2 0 2 4 6 8 10

d.10 8 6 4 2 0 2 4 6 8 10

____ 82. Solve a.

and graph the solution set. c.48 40 32 24 16 8 0 8 16 24 32 40 48 48 40 32 24 16 8 0 8 16 24 32 40 48

b.

No solution.

d.48 40 32 24 16 8 0 8 16 24 32 40 48

____ 83. Solve the inequality and graph the solution set for a. No solution. c.

.

2 3

10 8

6

4

2

0

2

4

6

8

10

b.

310 8

2

or6 4

32

10

d.

10 or10 8 6 4

62 0 2 4 6 8 10

0

2

4

6

8

10

____ 84. Let a.

be a horizontal shift ofy 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10

3 units left. Write the rule for c.y 10 8 6 4 2 x 10 8 6 4 2 2 4 6 8 10 2

and graph the function.

4

6

8

10

x

b.y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10 x

d.y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 10 x

____ 85. Translate a.

so that the vertex is at (5, 3). Then graph. c.

y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 x 10 8 6 4 10 8 6 4 2 2 2 4 6 8 10

y

2

4

6

8

x

b.y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 x

d.y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 2 4 6 8 x

____ 86. Stretch the graph of a.24 18 12 6

y

horizontally by a factor of 3. c.24 18 12 6

y

18

12

6 6 12

6

12

18

x

18

12

6 6 12

6

12

18

x

b.24 18 12 6

y

d.24 18 12 6

y

18

12

6 6 12

6

12

18

x

18

12

6 6 12

6

12

18

x

____ 87. Graph a.

.y 8 6 4 2

c.8 6 4 2

y

10

8

6

4

2 2 4 6 8

2

4

6

x

10

8

6

4

2 2 4 6 8

2

4

6

x

b.8 6 4 2

y

d.8 6 4 2

y

10

8

6

4

2 2 4 6 8

2

4

6

x

10

8

6

4

2 2 4 6 8

2

4

6

x

____ 88. Use substitution to determine if (0, 2) is an element of the solution set for the system of equations.

a. (0, 2) is a solution of the system.

b. (0, 2) is not a solution of the system.

____ 89. Use a graph to solve the system y a.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

. Check your answer. c.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

1

2

3

4

5

x

The solution to the system is (2, 4). b.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x y

The solution to the system is (2, 4). d.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x y

The solution to the system is (2, 4).

The solution to the system is (2, 4).

____ 90. Classify the system , and determine the number of solutions. a. This system is inconsistent. It has infinitely many solutions. b. This system is inconsistent. It has no solutions. c. This system is consistent. It has infinitely many solutions. d. This system is consistent. It has one solution. ____ 91. Two snow resorts offers private lessons to their customers. Big Time Ski Mountain charges $5 per hour plus $50 insurance. Powder Hills charges $30 per hour plus $10 insurance. For what number of hours is the cost of lessons the same for each resort? a. 3 hours c. 5 hours b. 4 hours d. 6 hours ____ 92. Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have the same volume of water? What is that volume of water?

a. 5 minutes; 150 gallons b. 5 minutes; 250 gallons

c. 10 minutes; 150 gallons d. 10 minutes; 250 gallons

____ 93. Use substitution to solve the system a. 8 ( 3 , 3) b. (2, 3)

. c.

( 3 , 1) d. (3, 2)

4

____ 94. Use elimination to solve the system a. (1, 4) b. (0, 3)

. c. (3, 0) d. (4, 1)

____ 95. Classify the system , and determine the number of solutions. a. The system is inconsistent and independent and has no solutions. b. The system is inconsistent and dependent and has no solutions. c. The system is consistent and dependent and has infinitely many solutions. d. The system is consistent and independent and has infinitely many solutions. ____ 96. A zookeeper needs to mix a solution for baby penguins so it has the right amount of medicine. Solution A has 20% medicine. Solution B has 4% medicine. How many ounces of each solution is needed to obtain 10 ounces of 8% medicine? a. c. 2 ounces of A and 10 ounces of B ounces of A and ounces of B b. 4 ounces of A and 6 ounces of B d. 2.5 ounces of A and 7.5 ounces of B ____ 97. One equation in a linear system is solution . a. b. . Write another equation so that the system has the unique c. d.

____ 98. Graph the system of inequalities y a.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

. c.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x y

b.5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

y

d.5 4 3 2 1 1 2 3 4 5 x 5 4 3 2 1 1 2 3 4 5

y

1

2

3

4

5

x

____ 99. Minas Catering Service is organizing a formal dinner for 280 people. The hall has two kinds of tables, one that seats 4 people and one that seats 10 people. The hall can contain up to a total of 52 tables. Write and graph a system of inequalities that can be used to determine the possible combinations of tables that can be used for the event so there are enough seats for all the people. a. c.y 72 64 56 48 40 32 24 16 8 8 16 24 32 40 48 56 64 72 80 x 72 64 56 48 40 32 24 16 8 8 16 24 32 40 48 56 64 72 80 x y

b.

d.

y 72 64 56 48 40 32 24 16 8 8 16 24 32 40 48 56 64 72 80 x 72 64 56 48 40 32 24 16 8

y

8

16

24

32

40

48

56

64

72

80 x

____ 100. Graph the system of inequalities, and classify the figure created by the solution region.

a.4 3 2 1

y

4

3

2

1 1 2 3 4

1

2

3

4

x

The shaded region is a plane minus a rectangle. b.4 3 2 1 y

4

3

2

1 1 2 3 4

1

2

3

4

x

There is no region common to all four inequalities. c.4 3 2 1 y

4

3

2

1 1 2 3 4

1

2

3

4

x

The shaded region is a rectangle. d.4 3 2 1 y

4

3

2

1 1 2 3 4

1

2

3

4

x

The region is the entire plane. ____ 101. A shop makes tables and chairs. Each table takes 8 hours to assemble and 2 hours to finish. Each chair takes 3 hours to assemble and 1 hour to finish. The assemblers can work for at most 200 hours each week, and the finishers can work for at most 60 hours each week. The shop wants to make as many tables and chairs as possible. Write the constraints for the problem, and graph the feasible region. Let t be the number of tables and c be the number of chairs. a. c.

c 72 64 56 48 40 32 24 16 8 8 16 24 32 40 48 56 64 72 80 t 72 64 56 48 40 32 24 16 8

c

8

16

24

32

40

48

56

64

72

80

t

b.

d.

c 72 64 56 48 40 32 24 16 8 8 16 24 32 40 48 56 64 72 80 t 72 64 56 48 40 32 24 16 8

c

8

16

24

32

40

48

56

64

72

80

t

____ 102. Maximize the objective function a. No maximum exists. b.

under the constraints c. (10,0) d. (8, 0)

.

____ 103. A small publishing company is planning to publish 2 books this month: book A and book B. The publishing cost is $6 each for book A and $8 each for book B. The total cost can be no more than $7,200. The company cannot publish more than 560 copies of book A and 720 copies of book B. The profit per book A is $10, and the profit per book B is $15. Find the number of books of each type that the company should publish to maximize its profits.

a.1200

y

900

(240, 720)600

(0, 720) (560, 480)

300

(560, 0) (0, 0)300 600 900 1200 x

The objective function is maximized at (240, 720), so the company should publish 240 copies of book A and 720 copies of book B. b.1200 y

900

(240, 720)600

(560, 720)

(0, 720) (560, 480)

300

(560, 0) (0, 0)300 600 900 1200 x

The objective function is maximized at (560, 720), so the company should publish 560 copies of book A and 720 copies of book B.

c.1200

y

900

(240, 720)600

(0, 720) (560, 480)

300

(560, 0) (0, 0)300 600 900 1200 x

The objective function is maximized at (540, 480), so the company should publish 540 copies of book A and 480 copies of book B. d.1200 y

900

(240, 720)600

(0, 720) (560, 480)

300

(560, 0) (0, 0)300 600 900

(1200, 0)1200 x

The objective function is maximized at (1200, 0), so the company should publish 1200 copies of book A and 0 copies of book B. ____ 104. Which point gives the minimum value of in the feasible region shown?

y 7 6 5 4 3

R

U1 3 2 1 1 2 3 1 2T 3 4

2

S5 6 7 x

a. b. ____ 105. Graph (2, 3, 1) in three-dimensional space. a.

c. d. c.

b.

d.

____ 106. Graph the linear equation

in three-dimensional space.

a.

z

(0, 0, 10)>

c.

z

(0, 0, 10)>

(0, 5, 0) (0, 5, 0) (6, 0, 0)y y

(6, 0, 0)

x

x

(0, 6, 0)y

(5, 0, 0)

(5, 0, 0)

or and a solid line for or . If the coefficient of x2 is positive, the vertex is the minimum value. If the coefficient of x2 is negative, the vertex is the maximum value. Step 2 Shade below the parabola for < orFeedback A B C D

and shade above the parabola for > or .

Check the coefficient of x^2. Correct! Check the inequality sign. Check the inequality sign and the coefficient of x^2. 1 DIF: Average REF: Page 366 5-7.1 Graphing Quadratic Inequalities in Two Variables 5-7 Solving Quadratic Inequalities B . NAT: 12.5.4.a

PTS: OBJ: TOP: 173. ANS:

Use a graphing calculator to graph each side of the inequality. Use values of x for which

and

. Identify the

x

y1

y2

y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

3 2 1 0 1 2

0 4 6 6 4 0

4 4 4 4 4 4

5

4

3

2

1

0

1

2

3

4

5

The parabola is at or above the line when x is less than or equal to 2 or greater than or equal to 1. So, the solution set is or . The table supports the answer. The number line shows the solution set.Feedback A B C D

Pick the part of the graph above y = -4. Correct! Check the points of intersection of y = x^2 + x - 6 and y = -4. Check the points of intersection of y = x^2 + x - 6 and y = -4.

PTS: 1 DIF: Average REF: Page 367 OBJ: 5-7.2 Solving Quadratic Inequalities by Using Tables and Graphs NAT: 12.5.4.a TOP: 5-7 Solving Quadratic Inequalities 174. ANS: A Step 1 Write the related equation. Write the equation in standard form. Factor. Step 2 Find the critical values. The critical values are 6 and 8. Step 3 The critical values divide the number line into three intervals: , , or .

?10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5

66

?7

88 9 10

?

Test an x-value in each interval in the original inequality to determine which intervals make the inequality true. The solution isFeedback A B C D

.

Correct! The critical values are correct. Test values of x to find the intervals satisfy the inequality. Subtract values from both sides of the equal sign when solving an equation. Subtract values from both sides of the equal sign when solving an equation. NAT: 12.5.4.a

PTS: 1 DIF: Average REF: Page 368 OBJ: 5-7.3 Solving Quadratic Inequalities Using Algebra TOP: 5-7 Solving Quadratic Inequalities 175. ANS: D The profit must be at least $600. Find the critical values by solving the related equation.

or Use a number line and test an x-value in each of the three regions created by the critical points.

2

4

6

8

10

12

14

16

18

20

22

Try x = 10: 15(10)2 + 330(10) 815 = 985 985 600 Round.Feedback A

Try x = 18: 15(20)2 + 330(20) 815 = 215 215 is not 600

Try x = 4: 15(4)2 + 330(4) 815 = 265 265 is not 600

If the price is 0 dollars then the profit is $815. Use a number line and critical values to

B C D

find the answer. If the price is 0 dollars then the profit is $815. Use a number line and critical values to find the answer. If the price is $19 then the profit is only $40. Use a number line and critical values to find the answer. Correct!

PTS: 1 DIF: Average REF: Page 368 OBJ: 5-7.4 Problem-Solving Application NAT: 12.5.4.a TOP: 5-7 Solving Quadratic Inequalities 176. ANS: B Place the inequality in standard form and use the Quadratic Formula to find its zeros. Add 11 to both sides. Multiplying by reverses the inequality. Substitute the values into the Quadratic Formula. Simplify the discriminant. Find the square root. Solve for x. Factor the inequality. Create a number line and find the sign of each interval+ + + + 5 4 3 - - - - 2 1 0 1 + + + + 2 3

.

The interval which solves the inequality isFeedback A B C D

.

Add 11 to both sides before factoring. Correct! Multiplying by 1 changes the inequality sign. Add 11 to both sides before factoring. DIF: Advanced 4 11 0 14 4 14 NAT: 12.5.4.a 8 11 TOP: 5-7 Solving Quadratic Inequalities

PTS: 1 177. ANS: C x 8 y 5

As the 2nd differences are constant for equally spaced x-values, the data set could represent a quadratic function.Feedback A B C D

The first differences of y-values do not need to be evenly spaced for this to be a quadratic function. The x-values are evenly spaced. Correct! The second differences of y-values are evenly spaced. DIF: Average REF: Page 374 OBJ: 5-8.1 Identifying Quadratic Data TOP: 5-8 Curve Fitting with Quadratic Models .

PTS: 1 NAT: 12.5.2.g 178. ANS: C

Use each point to write a system of equations to find a, b and c in System in a, b, c

(0, 6) (2, 4) (3, 6) Substitute (2) from (1) into both equation (2) and equation (3). (3) (4) Solve equation (4) and equation (5) for a and b using elimination. Then write the function using the values you found for a, b, and c.Feedback A B C D

(1) (2) (3)

(5)

Check the signs when calculating b. You switched the values for a and b. Correct! You switched the values for b and c.

PTS: 1 DIF: Average REF: Page 375 OBJ: 5-8.2 Writing a Quadratic Function from Data NAT: 12.5.2.g TOP: 5-8 Curve Fitting with Quadratic Models 179. ANS: C Enter the data in the chart as two lists in a graphing calculator. Use the quadratic regression feature. Graph the data and function model to be sure the model fits the data. Use the table feature to find the function value at t = 15.

F 35 30 25 20 15 10 5

5

10

15

20

25

30

35

t

A quadratic model is where F is the fuel consumption in miles per gallon and t is the tread height in mm. For the 15 mm tread height, the model predicts fuel consumption of 38 miles per gallon.Feedback A B C D

Fuel consumption is greater than 30 mpg, because 15 mm is between given data for 12 and 20, where corresponding fuel consumption is greater than 30. Solve for fuel consumption, not tread height. Correct! Use the quadratic regression function on your calculator to model the data.

PTS: 1 DIF: Average REF: Page 376 OBJ: 5-8.3 Application NAT: 12.5.2.g TOP: 5-8 Curve Fitting with Quadratic Models 180. ANS: D The real axis is the x-axis, and the imaginary axis is the y-axis. Think of as . Thus the complex number 2 is at .Feedback A B C D

The real axis is the x-axis, and the imaginary axis is the y-axis. The real axis is the x-axis, and the imaginary axis is the y-axis. If the imaginary part is positive, the point lies above the real (or x) axis. Correct!

PTS: 1 DIF: Basic REF: Page 382 OBJ: 5-9.1 Graphing Complex Numbers TOP: 5-9 Operations with Complex Numbers 181. ANS: B The real axis is the x-axis, and the imaginary axis is the y-axis. Think of as . Thus the complex number is at .Feedback A B C D

The real axis is the x-axis, and the imaginary axis is the y-axis. Correct! The real axis is the x-axis, and the imaginary axis is the y-axis. If the imaginary part is positive, the point lies above the real (or x) axis. DIF: Basic REF: Page 382 OBJ: 5-9.1 Graphing Complex Numbers

PTS: 1

TOP: 5-9 Operations with Complex Numbers 182. ANS: D The real axis is the x-axis, and the imaginary axis is the y-axis. Think of the complex number is at .Feedback A B C D

as

. Thus

The real axis is the x-axis, and the imaginary axis is the y-axis. The real axis is the x-axis, and the imaginary axis is the y-axis. If the imaginary part is positive, the point lies above the real (or x) axis. Correct!

PTS: 1 DIF: Basic REF: Page 382 OBJ: 5-9.1 Graphing Complex Numbers TOP: 5-9 Operations with Complex Numbers 183. ANS: A The real axis is the x-axis, and the imaginary axis is the y-axis. Think of as . Thus the complex number is at .Feedback A B C D

Correct! If the imaginary part is positive, the point lies above the real (or x) axis. The real axis is the x-axis, and the imaginary axis is the y-axis. The real axis is the x-axis, and the imaginary axis is the y-axis.

PTS: 1 DIF: Basic REF: Page 382 OBJ: 5-9.1 Graphing Complex Numbers TOP: 5-9 Operations with Complex Numbers 184. ANS: D Find the square root of the sum of the squares of the real and imaginary parts of the complex number. Simplify the square root. 130Feedback A B C D

Take the square root of the sum of the squares of the real and imaginary parts. Take the square root of the sum of the squares of the real and the imaginary parts. Take the square root of the sum of the squares of the real and imaginary parts. Correct!

PTS: 1 DIF: Basic REF: Page 383 OBJ: 5-9.2 Determining the Absolute Value of Complex Numbers TOP: 5-9 Operations with Complex Numbers 185. ANS: C To add complex numbers, add the real parts and the imaginary parts. To subtract complex numbers, subtract the real parts and the imaginary parts. (5 2 ) (6 + 8 ) = (5 (6)) + (5 (5)) = 1 10Feedback A B C

Check whether you should add or subtract the two complex numbers. Add or subtract real parts and imaginary parts. Correct!

D

Add or subtract real parts and imaginary parts.

PTS: 1 DIF: Average REF: Page 383 OBJ: 5-9.3 Adding and Subtracting Complex Numbers TOP: 5-9 Operations with Complex Numbers 186. ANS: C Graph and on the complex plane. Connect each of these numbers to the origin with a line segment. Draw a parallelogram that has these two line segments as sides. The vertex that is opposite the origin represents the sum of the two complex numbers, . Therefore, = .Feedback A B C D

Check the sign of the imaginary parts of the numbers. Plot each term, and then create a parallelogram using the two points and the origin. The sum is the final point opposite the origin. Correct! The real axis is the x-axis, and the imaginary axis is the y-axis. 1 DIF: Average REF: Page 384 5-9.4 Adding Complex Numbers on the Complex Plane 5-9 Operations with Complex Numbers B Distribute. Use Write inFeedback


. form.

A B C D

Use the Distributive Property. Then simplify by using the fact that i squared is equal to 1. Correct! Use the Distributive Property. Then simplify by using the fact that i squared is equal to 1. Use the Distributive Property. Then simplify by using the fact that i squared is equal to 1. 1 DIF: Basic REF: Page 384 5-9.5 Multiplying Complex Numbers 5-9 Operations with Complex Numbers C Rewrite Simplify.Feedback


as a power of

.

A B C D

If n is even, rewrite i^n as a power of i^2. If n is odd, rewrite i^n as a product of i and a power of i^2. If n is even, rewrite i^n as a power of i^2. If n is odd, rewrite i^n as a product of i and a power of i^2.. Correct! If n is even, rewrite i^n as a power of i^2. If n is odd, rewrite i^n as a product of i and a power of i^2. OBJ: 5-9.6 Evaluating Powers of i

PTS: 1 DIF: Average REF: Page 385 TOP: 5-9 Operations with Complex Numbers 189. ANS: C

= = = 2 17

Multiply by the conjugate. Distribute. Use +8 17

.

i

Simplify.

Feedback A B C D

Remember that i^2 = 1 Remember that i^2 = 1 Correct! Remember that i^2 = 1 OBJ: 5-9.7 Dividing Complex Numbers

PTS: 1 DIF: Average REF: Page 385 TOP: 5-9 Operations with Complex Numbers 190. ANS: D = = = =Feedback A B C D

Multiply. Combine like terms. Simplify. .

First, expand the square and multiply. Then, combine like terms and simplify. i squared is equal to 1. First, expand the square and multiply. Then, combine like terms and simplify. Correct! DIF: Advanced TOP: 5-9 Operations with Complex Numbers

PTS: 1 191. ANS: A

Add the exponents of the variables. 3 + 5 = 8 The degree is 8.Feedback A B C D

Correct! Add the exponents of the variables. Add the exponents of the variables. The degree of the monomial is the sum of the exponents of the variables.

PTS: 1 DIF: Basic REF: Page 406 OBJ: 6-1.1 Identifying the Degree of a Monomial TOP: 6-1 Polynomials 192. ANS: A The standard form is written with the terms in order from highest to lowest degree. In standard form, the degree of the first term is the degree of the polynomial. The polynomial has 6 terms. It is a quintic polynomial.Feedback A B C D

Correct! The standard form is written with the terms in order from highest to lowest degree. The standard form is written with the terms in order from highest to lowest degree. Find the correct coefficient of the x-cubed term. REF: Page 407 OBJ: 6-1.2 Classifying Polynomials

PTS: 1 DIF: Average TOP: 6-1 Polynomials 193. ANS: A = =Feedback A B C D

Identify like terms. Rearrange terms to get like terms together. Combine like terms.

Correct! Check that you have included all the terms. When adding polynomials, keep the same exponents. First, identify the like terms and rearrange these terms so they are together. Then, combine the like terms. 1 DIF: Basic REF: Page 407 6-1.3 Adding and Subtracting Polynomials 6-1 Polynomials A NAT: 12.5.3.c


represents the cost, $15.24, of delivering flowers to a destination that is 6 miles from the shop. represents the cost, $22.09, of delivering flowers to a destination that is 11 miles from the shop.Feedback A

Correct!

B C D

You reversed the values of C(6) and C(11). You added all the terms. There is a minus sign before 0.65. Square the number of miles before multiplying by 0.65. DIF: Average REF: Page 408 TOP: 6-1 Polynomialsy 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 x

PTS: 1 NAT: 12.5.3.c 195. ANS: D

OBJ: 6-1.4 Application

From left to right, the graph alternately increases and decreases, changing direction three times. The graph crosses the x-axis two times, so there appear to be two real zeros.Feedback A B C D

How many times does the graph change direction? How many times does the graph cross the x-axis? How many times does the graph change direction? How many times does the graph cross the x-axis? How many times does the graph cross the x-axis? Correct!

PTS: 1 DIF: Average REF: Page 409 OBJ: 6-1.5 Graphing Higher-Degree Polynomials on a Calculator TOP: 6-1 Polynomials 196. ANS: D Use the Distributive Property to multiply the monomial by each term inside the parentheses. Group terms to get like bases together, and then multiply.Feedback A B C D

Multiply the coefficients for each term; don't add. When multiplying like bases, add the exponents. Don't forget to multiply the coefficients for each term. Correct! 1 DIF: Basic REF: Page 414 6-2.1 Multiplying a Monomial and a Polynomial 6-2 Multiplying Polynomials A NAT: 12.5.3.c


= = = =Feedback A B C D

Distribute Distribute Multiply.

and and

. again.

Combine like terms.

Correct! Combine only like terms. Combine only like terms. Check the signs.

PTS: 1 DIF: Average REF: Page 414 OBJ: 6-2.2 Multiplying Polynomials NAT: 12.5.3.c TOP: 6-2 Multiplying Polynomials 198. ANS: A Total revenue is the product of the number of engines and the revenue per engine. . Multiply the two polynomials using the distributive property.

Feedback A B C D

Correct! Multiply each of the terms in the first polynomial by each of the terms in the second polynomial. First, multiply the coefficients. Then add the coefficients of like terms. First, multiply the coefficients. Then add the coefficients of like terms. OBJ: 6-2.3 Application

PTS: 1 DIF: Average REF: Page 415 NAT: 12.5.3.c TOP: 6-2 Multiplying Polynomials 199. ANS: A Write in expanded form. Multiply the last two binomial factors.

Distribute the first term, distribute the second term, and combine like terms.

Feedback A B C D

Correct! To find the product, write out the three binomial factors and multiply in two steps. To find the product, write out the three binomial factors and multiply in two steps. Remember that the second term is negative.

PTS: 1 DIF: Average REF: Page 416 OBJ: 6-2.4 Expanding a Power of a Binomial NAT: 12.5.3.c TOP: 6-2 Multiplying Polynomials 200. ANS: B The coefficients for n = 4 or row 5 of Pascals Triangle are 1, 4, 6, 4, and 1.

= =Feedback A B C D

The variable term and number term exponents must add to 4. Correct! Use row 5 from Pascal's Triangle. Use the numbers from Pascal's Triangle as coefficients for each term.

PTS: 1 DIF: Average REF: Page 417 OBJ: 6-2.5 Using Pascals Triangle to Expand Binomial Expressions TOP: 6-2 Multiplying Polynomials 201. ANS: C measure of leg 1 measure of leg 2 measure of hypotenuse

Feedback A B C D

Multiply both side lengths and the hypotenuse by 3y. The perimeter is the sum of all the side lengths. Correct! Check for algebra mistakes.

PTS: 1 DIF: Advanced TOP: 6-2 Multiplying Polynomials 202. ANS: B To divide, first write the dividend in standard form. Include missing terms with a coefficient of 0. Then write out in long division form, and divide.

50 Write out the answer with the remainder to getFeedback A B C D

.

Remember to include the remainder in the answer. Correct! Be careful when subtracting the terms. Remember to divide by the "2". NAT: 12.5.3.c

PTS: 1 DIF: Average REF: Page 422 OBJ: 6-3.1 Using Long Division to Divide Polynomials TOP: 6-3 Dividing Polynomials 203. ANS: A Write the coefficients of the dividend. Use . 4 1 4 4 5 4 0 16 1 0 4 11

Feedback A B C D

Correct! Bring down the first coefficient. Add each column instead of subtracting. Write the coefficients in the synthetic division format. Some of them are negative numbers. DIF: Basic REF: Page 424 TOP: 6-3 Dividing Polynomials OBJ: 6-3.3 Using Synthetic Substitution

PTS: 1 NAT: 12.5.3.c 204. ANS: A .

Substitute. Use synthetic division. 5 1 12 47 60 5 35 60 1 7 12 0

The width can be represented byFeedback A B C D

.

Correct! When dividing by x + 5, divide by 5 in synthetic division. Add each column instead of subtracting. The degree of the polynomial quotient is always one less than the degree of the dividend. OBJ: 6-3.4 Application

PTS: 1 DIF: Average REF: Page 425 NAT: 12.5.3.c TOP: 6-3 Dividing Polynomials 205. ANS: B Find by synthetic substitution.

SinceA B C

,

is a factor of the polynomial

.

Feedback

(x r) is a factor of P(x) if and only if P(r) = 0. Find P(r) by synthetic substitution. Correct! (x r) is a factor of P(x) if and only if P(r) = 0. Find P(r) by synthetic substitution. 1 DIF: Average REF: Page 430 6-4.1 Determining Whether a Linear Binomial is a Factor 12.5.3.d TOP: 6-4 Factoring Polynomials C Group terms. Factor common monomials from each group. Factor out the common binomial. Factor the difference of squares.

PTS: OBJ: NAT: 206. ANS: = = =

Feedback A B C D

Watch your signs when factoring. Watch your signs when factoring. Correct! In the second group, factor out a negative number. OBJ: 6-4.2 Factoring by Grouping

PTS: 1 DIF: Average REF: Page 431 NAT: 12.5.3.d TOP: 6-4 Factoring Polynomials 207. ANS: A Factor out the GCF.

Write as a sum of cubes.

Factor. =Feedback A B C D

Correct! Check the formula for the sum of cubes. In a sum of cubes, the plus and minus signs alternate. After factoring out the GCF, see if the result can be factored further. 1 DIF: Basic REF: Page 431 6-4.3 Factoring the Sum or Difference of Two Cubes 6-4 Factoring Polynomials A has zeroes at and NAT: 12.5.3.d


The graph indicates factors of

. By the Factor Theorem,

and

are .

. Use either root and synthetic division to factor the polynomial. Choose the root

Write as a product. Factor out 1 from the quadratic. Factor the perfect-square quadratic.

Feedback A B C D

Correct! After identifying the roots, use synthetic division to factor the polynomial. The graph decreases as x increases. How is this represented in the function? The Factor Theorem states that if r is a root of f(x), then x r, not x + r, is a factor of f(x). DIF: Average REF: Page 432 TOP: 6-4 Factoring Polynomials OBJ: 6-4.4 Application

PTS: 1 NAT: 12.5.3.d 209. ANS: A = = =

Rewrite the expression as a difference of cubes. Use Simplify. Combine like terms. .

Feedback A B C D

Correct! Use the formula for factoring a difference of two cubes. Use the formula for factoring a difference of two cubes. Check your answer by multiplying the factors. DIF: Advanced NAT: 12.5.3.d Factor out the GCF, 3x3. Factor the quadratic. Set each factor equal to 0. Solve for x.Feedback

PTS: 1 210. ANS: B

TOP: 6-4 Factoring Polynomials

A B C D

Set the GCF equal to zero. Correct! Set each factored expression equal to zero and solve. Factor out the GCF first. 1 DIF: Average REF: Page 438 6-5.1 Using Factoring to Solve Polynomial Equations 6-5 Finding Real Roots of Polynomial Equations A


is a factor once, and is a factor twice. The root 5 has a multiplicity of 1. The root has a multiplicity of 2.Feedback A B C D

Correct! You reversed the operation signs of the factors. Also, if x a is a factor of the equation, a is a root of the equation. If x a is a factor of the equation, then a is a root of the equation. You reversed the operation signs of the factors. OBJ: 6-5.2 Identifying Multiplicity

PTS: 1 DIF: Average REF: Page 439 TOP: 6-5 Finding Real Roots of Polynomial Equations 212. ANS: A Let x be the width in inches. The length is Step 1 Find an equation. , and the height is

.

Volume is the product of the length, width, and height. Multiply the left side.

Set the equation equal to 0. Step 2 Factor the equation, if possible. Factors of 140: , , , , , , , .

,

,

,

,

Rational Root Theorem

Use synthetic substitution to test the positive roots (length cant be negative) to find one that actually is a root. The synthetic substitution of 5 results in a remainder of 0. 5 is a root. Use the Quadratic Formula to factor The roots are complex. Width = 5 in.Feedback A B C D

.

Width must be a positive real number.

Correct! Remember to subtract 140 from both sides before finding a root. Be careful using synthetic substitution. 6 is not a possible root. OBJ: 6-5.3 Application

PTS: 1 DIF: Average REF: Page 440 TOP: 6-5 Finding Real Roots of Polynomial Equations 213. ANS: B The possible rational roots are Test . 4 31 4 23 The remainder is 0, so Now test . 4 4 100 11 is a root.

. 22 0

23 1 24 6

11 0 is a root. . .

The remainder is 0, so

The polynomial factors to To find the remaining roots, solve

Factor out the common factor to get . Use the quadratic formula to find the irrational roots.

The fully factored equation is The roots areFeedback A B C D

. .

These are the two rational roots. There are also irrational roots. Correct! These are the possible rational roots. Use these to find the rational roots. Be careful when finding the irrational roots. 1 DIF: Average REF: Page 441 6-5.4 Identifying All of the Real Roots of a Polynomial Equation 6-5 Finding Real Roots of Polynomial Equations A (x + 2)(x 7)(x (


+

1 2

)

If r is a zero of

, then

is a factor of

.

+ 5x 14)(x ) 9 9 2 + 2 7 x

1 2

Multiply the first two binomials. Multiply the trinomial by the binomial.

Feedback A B C D

Correct! If r is a zero of P(x), then (x r), not (x + r), is a factor of P(x). The simplest polynomial with zeros r1, r2, and r3 is (x r1)(x r2)(x r3). If r is a zero of P(x), then (x r) is a factor of P(x).

PTS: 1 DIF: Average REF: Page 445 OBJ: 6-6.1 Writing Polynomial Functions Given Zeros TOP: 6-6 Fundamental Theorem of Algebra 215. ANS: B The polynomial is of degree 4, so there are four roots for the equation. Step 1: Identify the possible rational roots by using the Rational Root Theorem.

and Step 2: Graph to find the locations of the real roots.

y 200 160 120 80 40 10 8 6 4 2 40 80 120 160 200 2 4 6 8 10 x

The real roots are at or near 5 and Step 3: Test the possible real roots. Test the possible root of 5:

. Test the possible root of :

The polynomial factors into Step 4: Solve to find the remaining roots.

.

The fully factored equation is The solutions are 5, , i, and 3i.Feedback A B C D

.

The polynomial is of degree 4, so there are 4 roots. Correct! Graph the equation to find the locations of the real roots. Set each factored expression equal to zero and solve! 1 DIF: Average REF: Page 446 6-6.2 Finding All Roots of a Polynomial Equation 6-6 Fundamental Theorem of Algebra A


There are five roots: , , , , and . (By the Irrational Root Theorem and Complex Conjugate Root Theorem, irrational and complex roots come in conjugate pairs.) Since it has 5 roots, the polynomial must have degree 5.

Write the equation in factored form, and then multiply to get standard form.

Feedback A B C D

Correct! i squared is equal to 1, so the opposite is equal to 1. 4x(5) = 20x Only the irrational roots and the complex roots come in conjugate pairs. There are five roots in total.

PTS: 1 DIF: Average REF: Page 447 OBJ: 6-6.3 Writing a Polynomial Function with Complex Zeros TOP: 6-6 Fundamental Theorem of Algebra 217. ANS: B Write an equation to represent the volume of ice cream. Note that the hemisphere and the cone have the same radius, x.

So,

Set the volume equal to Write in standard form. Multiply both sides by .

.

The graph indicates a possible positive root of 4. Use synthetic division to verify that 4 is a root, and write the equation as cm.Feedback A B C

. Since the discriminant of

is

, the roots of

are complex. The radius must be a positive real number, so the radius of the sugar cone is 4

Write the total volume as the sum of the volume of a cone of height 10 cm and the volume of a hemisphere. Then solve for the radius. Correct! Write the total volume as the sum of the volume of a cone of height 10 cm and the

D

volume of a hemisphere. Then solve for the radius. Write the total volume as the sum of the volume of a cone of height 10 cm and the volume of a hemisphere. Then solve for the radius. OBJ: 6-6.4 Problem-Solving Application

PTS: 1 DIF: Average REF: Page 447 TOP: 6-6 Fundamental Theorem of Algebra 218. ANS: C If r is a root of . Distribute.

, then

is a factor of

Multiply the trinomials. Use . Combine like terms. Multiply the binomial and trinomial. Combine like terms.Feedback A B C D

If r is a root of P(x), then (x r) is a factor of P(x). First, multiply the factors. Then, combine like terms to get a polynomial function. Correct! If r is a root of P(x), then (x r) is a factor of P(x). DIF: Advanced TOP: 6-6 Fundamental Theorem of Algebra

PTS: 1 219. ANS: A

The leading coefficient is 5, which is negative. The degree is 4, which is even. So, as , and as , .Feedback A B C D

Correct! The degree is the greatest exponent. For polynomials, the function always approaches positive infinity or negative infinity as x approaches positive infinity or negative infinity. The degree is the greatest exponent.

PTS: 1 DIF: Basic REF: Page 454 OBJ: 6-7.1 Determining End Behavior of Polynomial Functions TOP: 6-7 Investigating Graphs of Polynomial Functions 220. ANS: D As , and as , . is of odd degree with a positive leading coefficient.Feedback A B

The leading coefficient is positive if the graph increases as x increases and negative if the graph decreases as x increases. The degree is even if the curve approaches the same y-direction as x approaches positive or negative infinity, and is odd if the curve increases and decreases in opposite directions. The leading coefficient is positive if the graph increases as x increases and

C

D

negative if the graph decreases as x increases. The degree is even if the curve approaches the same y-direction as x approaches positive or negative infinity, and is odd if the curve increases and decreases in opposite directions. Correct!

PTS: 1 DIF: Basic REF: Page 454 OBJ: 6-7.2 Using Graphs to Analyze Polynomial Functions TOP: 6-7 Investigating Graphs of Polynomial Functions 221. ANS: D Step 1: Identify the possible rational roots by using the Rational Root Theorem. p = 8 and q = 1, so roots are positive and negative values in multiples of 2 from 1 to 8. Step 2: Test possible rational zeros until a zero is identified. Test x = 1. Test x = 1.

is a zero, and Step 3: Factor: The zeros are 1, 2, and 4. .

.

Step 4: Plot other points as guidelines. so the y-intercept is 8. Plot points between the zeros. and Step 5: Identify end behavior. The degree is odd and the leading coefficient is positive, so as . Step 6: Sketch the graph by using all of the information about f(x).Feedback A B C D

and as

The leading coefficient is positive, so x should go to negative infinity as P(x) goes to negative infinity. The y-intercept should be the same as the last term in the equation. The function is cubic, so should have 3 roots. Correct! 1 DIF: Average REF: Page 455 6-7.3 Graphing Polynomial Functions 6-7 Investigating Graphs of Polynomial Functions B on a calculator.


Step 1 Graph

The graph appears to have one local maximum and one local minimum. Step 2 Use the maximum feature of your graphing calculator to estimate the local maximum. The local maximum is about 31.627417. Step 3 Use the minimum feature of your graphing calculator to estimate the local minimum. The local minimum is about 13.627417.Feedback A B C D

You reversed the values of the maximum and minimum. Correct! The constant is a positive number. You forgot to add the constant of the function to the calculator.

PTS: 1 DIF: Average REF: Page 456 OBJ: 6-7.4 Determine Maxima and Minima with a Calculator TOP: 6-7 Investigating Graphs of Polynomial Functions 223. ANS: A Find a formula to represent the volume. Use x as the side length for the squares you are cutting out.

Graph . Note that values of less than 0 or greater than 4.25 do not make sense for this problem. The graph has a local maximum of about 66.1 when . So, the largest open box will have a volume of about 66.1 inches cubed when the sides of the squares are about 1.6 inches long.Feedback A B C D

Correct! Find the x-value for the local maximum. Find the x-value for the local maximum. Find the x-value for the local maximum. OBJ: 6-7.5 Application

PTS: 1 DIF: Average REF: Page 456 TOP: 6-7 Investigating Graphs of Polynomial Functions 224. ANS: A

To graphFeedback A B C D

, translate the graph of

up 2 units. This is a vertical translation.

Correct! f(x) + c represents a vertical translation of f(x). f(x) + c represents a vertical translation of f(x). The sign of c determines whether f(x + c) represents a vertical translation of f(x) |c| units up or down.


1 DIF: Average REF: Page 460 6-8.1 Translating a Polynomial Function 6-8 Transforming Polynomial Functions D

For a function g(x) that reflects f(x) across the y-axis:

+ 7 4x 5Feedback A B C D

This is a reflection of f(x) across the x-axis. To reflect across the y-axis, replace x with (x). A negative number squared is a positive number. The constant remains the same. Correct! 1 DIF: Average REF: Page 461 6-8.2 Reflecting Polynomial Functions 6-8 Transforming Polynomial Functions A


Feedback A B C D

Correct! The transformation is inside the function; this makes a horizontal transformation. The transformation is inside the function; this makes a horizontal transformation. The function makes a different type of horizontal transformation. 1 DIF: Average REF: Page 461 6-8.3 Compressing and Stretching Polynomial Functions 6-8 Transforming Polynomial Functions A


Feedback A B C D

Correct! The left shift value is added to the x value before it is cubed. A shift to the left involves adding, not subtracting. The vertical stretch factor will effect the y-intercept. OBJ: 6-8.4 Combining Transformations

PTS: 1 DIF: Average REF: Page 462 TOP: 6-8 Transforming Polynomial Functions

228. ANS: D

The transformation represents a horizontal shift left of 4 units, which corresponds to making the same profit for selling 4 fewer bicycles.Feedback A B C D

The transformation is f(x + 4), not f(x) + 4. The transformation is f(x + 4), not f(x) + 4. The transformation is a horizontal shift left. Correct!

PTS: 1 DIF: Average REF: Page 462 OBJ: 6-8.5 Application TOP: 6-8 Transforming Polynomial Functions 229. ANS: B The x-intercepts are constant, so the transformation is not a horizontal shift or a horizontal stretch. The graph of is symmetric about the x-axis, so the transformation is not a vertical shift. has a higher maximum and a lower minimum than , showing a vertical stretch. So the transformation is a vertical stretch.Feedback A B C D

The transformed function is symmetric about the x-axis, so the transformation is not a vertical shift. Correct! The x-intercepts are constant, so the transformation is not a horizontal shift. The x-intercepts are constant, so the transformation is not a horizontal stretch.

PTS: 1 DIF: Advanced 230. ANS: A The x-values increase by a constant, 2. Find the differences of the y-values. y 12 5 19 3 1 7 14 16 4 1 21 30 12 5 51 42 7 93 49 142 Not constant Not constant Not constant Constant

First differences Second differences Third differences Fourth differences

The fourth differences are constant. A quartic polynomial best describes the data.Feedback A B C D

Correct! Check your work. The third differences are not constant. Check your work. The second differences are not constant. To find the differences in the y-values, subtract each y-value from the y-value that

follows it. PTS: 1 DIF: Basic REF: Page 466 OBJ: 6-9.1 Using Finite Differences to Determine Degree TOP: 6-9 Curve Fitting by Using Polynomial Models 231. ANS: A Find the finite differences for the y-values.

The third differences of these data are not exactly constant, but because they are relatively close, a cubic function would be a good model. Using the cubic regression feature on a calculator, the function is found to be:

Feedback A B C D

Correct! Find the differences between population values, stopping once you see relatively constant differences. First differences are not relatively constant, so a linear model will not be a good fit. Second differences are not relatively constant, so a quadratic model will not be a good fit.

PTS: 1 DIF: Average REF: Page 467 OBJ: 6-9.2 Using Finite Differences to Write a Function TOP: 6-9 Curve Fitting by Using Polynomial Models 232. ANS: A Let x represent the number of weeks before the election. Make a scatter plot of the data. The function appears to be cubic or quartic. Use the regression feature to check the cubic: quartic: -values.

The quartic function is a more appropriate choice. The data can be modeled by Substitute 5 for x in the quartic model. Based on the model, the number of supporters 5 weeks before the election was 3676.Feedback A B C D

Correct! The quartic function is a more appropriate choice than the cubic function. The quartic function is a more appropriate choice than the quadratic function. The quartic function is a more appropriate choice than the exponential function.

PTS: 1 DIF: Average REF: Page 468 OBJ: 6-9.3 Application TOP: 6-9 Curve Fitting by Using Polynomial Models 233. ANS: A If r is a root of , then is a factor of . Substitute the roots from the graph. Simplify. Multiply by 8 and simplify.Feedback A B C D

Correct! Each factor of the polynomial subtracts a root from x. Find the roots of the graph and subtract these values from x. Multiply these factors together to create the polynomial. Find the zeros of the graph and subtract these values from x. Multiply these factors together to create the polynomial. DIF: Advanced TOP: 6-9 Curve Fitting by Using Polynomial Models

PTS: 1

NUMERIC RESPONSE 234. ANS: 10.8 PTS: 1 235. ANS: 243 DIF: Advanced NAT: 12.5.3.c TOP: 1-3 Square Roots

PTS: 1 DIF: Average NAT: 12.5.3.c TOP: 1-4 Simplifying Algebraic Expressions 236. ANS: 25 PTS: 1 NAT: 12.3.2.e 237. ANS: $28.57 PTS: 1 NAT: 12.3.2.e 238. ANS: 148.7 PTS: 1 NAT: 12.3.2.e 239. ANS: 12 DIF: Average OBJ: 2-2 Proportional Reasoning KEY: proportions | similarity DIF: Average KEY: proportion DIF: Average KEY: proportion OBJ: 2-2 Proportional Reasoning

OBJ: 2-2 Proportional Reasoning

PTS: 1 DIF: Advanced NAT: 12.5.4.g TOP: 3-3 Solving Systems of Linear Inequalities 240. ANS: 0.6

PTS: 1 241. ANS: 2 PTS: 1 242. ANS: 31 PTS: 1 243. ANS:

DIF: Average DIF: Advanced DIF: Average

TOP: 3-5 Linear Equations in Three Dimensions TOP: 4-1 Matrices and Data TOP: 4-4 Determinants and Cramers Rule

PTS: 1 DIF: Average NAT: 12.5.1.e TOP: 5-1 Using Transformations to Graph Quadratic Functions 244. ANS: 5 PTS: 1 DIF: Advanced NAT: 12.5.4.a TOP: 5-3 Solving Quadratic Equations by Graphing and Factoring 245. ANS: 1.25 PTS: 1 246. ANS: 6 PTS: 1 247. ANS: 9 DIF: Advanced DIF: Average NAT: 12.5.4.a TOP: 5-4 Completing the Square

TOP: 5-5 Complex Numbers and Roots

PTS: 1 DIF: Advanced NAT: 12.5.1.e TOP: 5-8 Curve Fitting with Quadratic Models 248. ANS: 16 PTS: 1 249. ANS: 45 PTS: 1 250. ANS: 2 PTS: 1 DIF: Average DIF: Advanced DIF: Advanced TOP: 6-3 Dividing Polynomials TOP: 6-5 Finding Real Roots of Polynomial Equations TOP: 6-7 Investigating Graphs of Polynomial Functions

alg 2 first semester exam review ch. 1-6 max

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