2015-2016 Algebra 1 B Review JANUARYmontgomeryschoolsmd.org/uploadedFiles/curriculum/math...65. The following box plots show the distributions of test scores for two math classes

Algebra 1 B Semester Exam Review

MCPS © 2015–2016

Algebra 1 B

Semester Exam Review

January 2016


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Residual: Difference between the observed (actual) value and the predicted (line of fit) value

Slope-Intercept Form of a linear function: f x mx b

Forms of quadratic functions:

Vertex Form: 2f x a x h k

Standard Form: 2f x ax bx c

Factored Form: f x x d x e

Quadratic Formula: If 2

2 40, then

2

b b acax bx c x

a

Zero-Product Property: If 0a b , then 0a or 0b

Pythagorean Theorem:

In a right triangle, 2 2 2a b c , where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Distance between two points 1 1 2 2, and ,x y x y : 2 22 1 2 1x x y y

Slope of a line containing two points 1 1 2 2, and ,x y x y : 2 1

2 1

y y

x x


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Unit 4, Topic 1

For items 1 through 3, classify each function below as linear, exponential, or quadratic. Justify your answers. 1. x y

1 2 2 5 3 8 4 11

2. x y

1 2 2 5 3 10 4 17

3. x y

1 2 2 4 3 8 4 16

4. A rectangle has a length that is 6 inches longer than its width. If w represents the width, write an expression, in terms of w, for the area of the rectangle.

5. A rectangle has a length that is 4 inches shorter than its width. If w represents the width, write an expression, in terms of w, for the area of the rectangle.


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For items 6 through 8, a function of time is given. In each item, determine the average rate of change on the given interval. Give the units for your answer.

6.

Time (seconds) Distance (feet) 0 0 1 5 2 20 3 45 4 80 5 125

7.

Average speed on the interval 2 5t :

Units:

x

y

Average rate of bacteria growth on the interval 1 6t :

Units:

0 1 2 3 4 5 6 7 8 9 10

Time (hours)

5

10

15

20

25

30

35

40

45

50

Num

ber

of B

acte

ria


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8. 2500d t t t

t in minutes, d t in kilometers

9. The number of weeds on a lawn can be written as the function 25 60W d d , where

d represents the number of days since spring started.

a. Is the rate of change of this function constant? Explain your answer.

b. What is the rate of change?

c. What are the units for the rate of change?

Average speed on the interval 0 4t :

Units:


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10. Jack is inventing a variation on bowling. Here are the first four rows of pins.

Let P r represent the total number of pins in r rows.

a. Complete the table based on the total number of pins.

Number of Rows

(r)

Total Number of Pins P r

1 2 2 5 3 4 5 6

b. What type of function is represented by the table above?

c. Explain why you chose that type of function.

d. Write a function for P r .

e. Jack decides that he will have 12 rows of pins. What is the total number of pins that he will need?

1 row 3 rows2 rows 4 rows


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11. Look at the pattern of dots below.

Figure 1 Figure 2 Figure 3 Figure 4

Let D n be a function that represents the number of dots in figure number n.

a. Complete the table below.

Figure number (n) Number of Dots D n

1 3 2 8 3 4 5 6

b. Which type of function: linear, quadratic, or exponential, is represented by D n ?

Give a reason for your answer.

c. Write the function rule for D n .

d. How many dots will be in Figure 9? Show how you determined your answer.


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Unit 4, Topic 2

In the table below, a square is shown in the first column. The second column tells what change is made to the length of each side of the square. In the third column, write the AREA of the new square in two different ways.

Original Square Change to each side of the original square

AREA of the NEW square, written in two different ways

12.

Add 3

13.

Subtract 7

14.

Multiply by 4

15.

Multiply by 2, then add 5

For items 16 through 18, fill in the number that completes the square.

16. 2 6 ____x x

17. 2 12 ____x x

18. 2 7 ____x x

x

x

x

x


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19. The graph below represents 2y x .

Look at the graphs, labeled I, II, III, and IV below.

Match the equations listed below with the graphs I, II, III, and IV above.

a. ______ 21

3y x b. ______ 24y x

c. ______ 25y x d. ______ 21

2y x

I II

III IV

x

x

x x

x

y y

y y

y


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For items 20 through 24, write the function in the form(s) requested.

20.

21. A quadratic parent function 2f x x whose

graph is translated to the right 4 units and up 5 units

22.

x f x

– 5 0 – 4 – 3 – 3 – 4 – 2 – 3 – 1 0

x

y

O

Vertex Form:

f x

Factored Form:

f x

Standard Form:

f x

Vertex Form:

g x

Standard Form:

g x

Vertex Form:

f x

Factored Form:

f x

Standard Form:

f x


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23. 2 6 7f x x x

24.

For items 25 and 26, sketch the graph of the function, then give the information requested.

25. 2 4 5f x x x

x f x

– 2 40 – 1 10 0 0 1 10 2 40

Standard Form:

f x

x

y

O

Vertex:

Line of Symmetry:

x-intercepts:

y-intercept:

Domain:

Range:

Interval on which f x is increasing:

Interval on which f x is decreasing:

Factored Form:

f x


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26. 22 3 8f x x

For items 27 through 30, add or subtract as indicated.

27. 2 23 4 7 7 3 12x x x x

28. 2 22 5 9 4 7 12x x x x

29. 2 24 11 8 11 15x x x x

30. 2 24 9 12 2 9 11x x x x

x

y

O

Vertex:

Line of Symmetry:

x-intercepts:

y-intercept:

Domain:

Range:

Interval on which f x is increasing:

Interval on which f x is decreasing:


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For items 31 through 36, multiply as indicated. 31. 2 5 4 7x x

32. 3 2 9x x

33. 22 3x

34. 25 3x

35. 7 7x x

36. 3 5 3 5x x


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For each rectangle below, determine the perimeter and the area. The area should be written as a trinomial.

37. 38.

Perimeter ___________________ Perimeter ______________________

Area as a trinomial _______________________ Area as a trinomial ____________________

Factor.

39. 2 8 20x x

40. 2 16 60x x

41. 2 36x

42. 2 121x

43. 23 5 2x x

44. 22 10 12x x

45. 23 21 36x x

3 2x

2 5x 7 3x

7 3x


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Unit 4, Topic 3

For items 46 through 48, use your calculator to graph the function, then state the number of real zeros.

46. 26f x x

47. 2 5f x x x

48. 2 2 1f x x x

49. Jack kicked a football. The height, h t in feet, of the ball after t seconds is given by the

quadratic function 216 64h t t t .

a. After how many seconds does the ball hit the ground? Show how you determined your answer.

b. Does the ball reach its maximum height at 2t seconds? Show how you determined your answer.


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50. An animal makes a leap into the air. A function for the height h t , in meters, of the

animal above the ground after t seconds is given by 25 12.5h t t t .

a. How long is the animal in the air? Show how you determined your answer. b. What is the animal’s maximum height? Show how you determined your answer.


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51. In your own words, what is the zero-product property?

For items 52 through 57, solve the equation using any method.

52. 27 81x 53. 5 3 2 0x x

54. 27 8 1 0x x 55. 2 10 1 0x x

56. 2 6 8x x 57. 2 7 9x


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58. A farmer plants apple trees. The total number of apples can be represented by the

function 2300 5A t t t , where t is the number of trees that he plants.

a. Sketch the graph of 2300 5A t t t on the coordinate plane below. Show the

points where 0,10,20,30,40,50,60t .

b. The farmer wants to be able to harvest at least 4000 apples.

Use your graph above to solve the inequality 2300 5 4000t t .

c. What is the meaning of your solution in the context of this situation?

t

A t

0 10 20 30 40 50 60 70 80 90

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0


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59. The equations 2 4 5y x x and 7y are graphed on the coordinate plane below.

a. What are the solutions to the equation 2 4 5 7x x ?

b. What are the solutions to the inequality 2 4 5 7x x ?

x

y

O


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For items 60 and 61, determine the side of the right triangle marked x.

60. 61.

On the coordinate plane below, three line segments are shown, with their coordinates.

For items 62 and 63, find the distance between each pair of points.

62. 7, 2 and 6,3

63. 6,3 and 2,9

2,9

5

12 x

x 10 7

x

y

O

7, 2

6,3


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Unit 3

64. Ms. Tran looks at the scores on her first Algebra 1 test. They are listed below:

99, 45, 88, 68, 77, 73, 81, 76, 66, 79, 81, 74, 81, 41, 91, 94, 68

She cannot decide how to display these scores, so she makes two different displays.

a. Make a box plot of the data.

b. Make a histogram of the data. Use the intervals shown for your display.

c. Use your displays to describe the data. You should use measures of central tendency, variability and distribution in your description.

0 10 20 30 40 50 60 70 80 90 100

0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99

5

4

3

2

1

Test Scores

Test Scores

Fre

quen

cy


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65. The following box plots show the distributions of test scores for two math classes.

a. From the list below, circle which ones you can NOT determine from the box plots.

median mean range interquartile range individual scores

quartiles distribution (skewness) the number of test scores

b. Based on what you know about box plots, which class performed better on the test? Give at least two reasons for your answer.

c. Which data set has greater variability? Justify your answer.


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66. Look at a scatterplot and the line of best fit below.

A residual for a value of x is the difference between the observed (actual) value of y and the predicted (line of fit) value of y.

a. What is the residual when 3x ?

b. What is the residual when 6x ?

c. What is the residual when 9x ?

67. a. In the 1980’s it was found that the correlation coefficient between the amount of ice cream sold and the number of crimes in New York City was 0.97r . Does this mean that an increase in ice cream sales causes an increase in the number of crimes? Explain your reasoning.

b. Give another example of two variables that might have a high correlation coefficient, but the change in one of the variables does NOT cause a change in the other.

x

y

0 1 2 3 4 5 6 7 8 9 10

100

90

80

70

60

50

40

30

20

10

0


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68. Sammy is interested in the number of visitors that will come to the beach as a function of the temperature. Below is the data and a scatterplot that Sammy has collected.

a. What is the relationship between the temperature and the number of visitors to the beach?

b. Circle the value that best describes the value of r, the linear correlation coefficient. Justify your answer.

1r .89r .76r .05r

This item continues on the next page.

Temperature (t)

Visitors V t

82 2801 84 2861 86 3000 86 3060 87 3121 88 3151 89 3226 92 3150 94 3221 94 3302 96 3269

2700

2800

2900

3000

3100

3200

3300

3400

80 85 90 95 100

Visitors

Temperature oF

At the Beach


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Continuation of item 68 from the previous page.

Here are the results of finding the line of best fit on a calculator.

c. From the information above, write the equation of the line of best fit.

d. What is the slope of the line of best fit? What is its meaning in the context of this situation?

e. What is the y-intercept of the line of best fit? What is its meaning in the context of this situation?

f. What does your line of best fit predict for a temperature of 88 degrees?

g. What is the residual at a temperature of 88 degrees?

(Residual: Difference between the observed (actual) value and the predicted (regression) value)

h. According to the line of best fit, at what temperature will there be no visitors at the beach? Explain how you determined your answer.

LinReg y = ax + b a = 32 b = 256 r = .8944


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69. A carnival game kept track of the ages and what type of prize, if any, that people won at the game. The results are shown in the table below.

Children Adults Total No Prize 24 56 80 Small Prize 18 82 100 Big Prize 8 12 20 Total 50 150 200

a. Of the children who played, what fraction won a big prize?

b. What fraction of the small prize winners were adults?

c. What fraction of the total number of players were children?

d. The percent of children who won a small prize was (less than/equal to/greater than) the percent of adults who won no prize.


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70. Montgomery County middle and high school students were asked if school should start later in the day. Here is some information about the responses.

Yes

No Total

Middle School 30

High School

225 250

Total

350

a. Complete the table.

b. What fraction of high school students said yes?

c. Of the students who said no, what fraction were middle school students?

d. Of all of the students, what fraction were high school students who said no?


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Unit 5

71. Which graph below represents the function 3f x x ?

x

y

x

y

x

y

x

y

A B

C D


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72. Jill takes a Sunday drive in her car. She drives at an average speed of 50 miles per hour for 3 hours. She takes a dinner break for 2 hours. After dinner, she travels at an average speed of 25 miles per hour for the next 4 hours.

Let t represent the number of hours since she started. Let D t represent the total distance that

she has travelled after t hours.

a. What is the domain of t?

b. Sketch a graph of D t on the coordinate axes below.

c. Write a piecewise function for D t .

d. What was Jill’s average speed on the interval 0 9t ? Show how you determined your answer.

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

250

225

200

175

150

125

100

75

50

25

0


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73. Bob uses sugar to make candy. Beginning at noon 0t , he uses sugar at the rate of

100 pounds per hour. At 3 p.m., 3t , he starts using sugar at the rate of 50 pounds per

hour. He stops making candy at 7 p.m. 7t .

Let t represent the number of hours since noon. Let S t represent the total amount of

sugar that Bob has used after t hours.

a. Between noon and 7 p.m., what is the total amount of sugar that Bob uses?

b. On the coordinate graph below, make a continuous graph, showing the total

amount of sugar S t that Bob uses as a function of t.

c. Complete the piecewise function for the total amount of sugar that Bob uses.

_______________ if 0 3

_______________ if 3 7

tD t

t

t 0 1 2 3 4 5 6 7

500

450

400

350

300

250

200

150

100

50

0


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74. Which statement is true about the function f x x ?

A. Both the domain and range is all real numbers.

B. Both the domain and range is all real numbers greater than or equal to zero.

C. The domain is all real numbers; the range is all real numbers greater than or equal to zero.

D. The domain is all real numbers greater than or equal to zero; the range is all real numbers.

75. Look at the graphs of and f x x g x x below.

Which of the following statements is true?

A. For every value of x, x x .

B. For every value of x, x x .

C. If x is an integer, x x , otherwise x x .

D. If x is an integer, x x , otherwise x x .

x

y

O x

y

O

f x x g x x


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For items 76 through 78, sketch the graph of each function

76. 3 if 4

2 1 if 4 3

5 if 3

x

f x x x

x

77. 1g x x

78. 3 2h x x

For items 79 through 81, evaluate 1.6f

79. f x x

80. f x x

81. 3 6.4, 2

2.4, 2

x if xf x

x if x

x

y

x

y

x

y

Documents

2015-2016 Algebra 1 B Review JANUARYmontgomeryschoolsmd.org/uploadedFiles/curriculum/math...65. The following box plots show the distributions of test scores for two math classes