2013-2014 Algebra 1 B Review - Montgomery County Public...

Algebra 1 B Semester Exam Review

MCPS © 2013–2014

Algebra 1 B

Semester Exam Review

2014


MCPS © 2013–2014 Page 1

Residual: Difference between the observed (actual) value and the predicted (regression) 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 3

1. 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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2. 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.

3. Make a sketch of the following types of frequency distributions.

Skewed left Skewed right Normal


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

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

a. What is the residual when 3x ?

b. What is the residual when 6x ?

c. What is the residual when 9x ?

5. 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 .97 . 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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6. 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.

2700

2800

2900

3000

3100

3200

3300

3400

80 82 84 86 88 90 92 94 96 98

Visitors

Temperature oF

At the BeachTemperature

(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


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Continuation of item 6 from the previous page.

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

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

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

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

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

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

g. According to your regression line, 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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7. 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.

8. 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

Complete the table.


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Unit 4, Topic 1

For items 9 through 11, classify each function below as linear, exponential, or quadratic. Use mathematics to justify your answers. 9. x y

1 2 2 5 3 8 4 11

10. x y

1 2 2 5 3 10 4 17

11. x y

1 2 2 4 3 8 4 16

12. 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.

13. 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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14. A rectangle shown below has a perimeter of 40 inches. Its width is 5 inches.

What is the area of the rectangle?

15. A rectangle shown below has a perimeter of 30 feet. Its width is w feet.

What is the area of the rectangle? (the area should be an expression in terms of the variable w)

For items 16 through 18, 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.

16.

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

Average speed on the interval :

Units:

5

w


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17.

18. 2500d t t t

t in minutes, d t in kilometers

x

y

Average rate of bacteria growth on the interval :

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

Average speed on the interval :

Units:


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19. 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 constant rate of change?

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


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20. 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 . The function can either be explicit or recursive.

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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21. 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 the table? Give a reason for your answer.

c. Write the function rule for D n . The rule can be explicit or recursive.

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


MCPS © 2013–2014 Page 14

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

22.

Add 3

23.

Subtract 7

24.

Multiply by 4

25.

Multiply by 2, then add 5

26.

Multiply by 9, then subtract 1

For items 27 through 29, fill in the number that completes the square.

27. 2 6 ____x x

28. 2 12 ____x x

29. 2 7 ____x x

x

x

x

x

x


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30. 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

xx

x

y y

y y

y


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For items 31 through 34, write two equivalent quadratic functions for each representation.

31. 32. A quadratic parent function 2f x x

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

33. 34. 2 6 7f x x x

For items 35 and 36, write one equation for the function represented.

35. 36.

x f x

– 2 40 – 1 10 0 0 1 10 2 40

x f x

– 3 0 – 2 – 3 –1 – 4 0 – 3 1 0

x

y

O

x

y

O


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For items 37 and 38, sketch the graph of the function, then give the information requested.

37. 2 4 5f x x x

38. 22 3 8f x x

x

y

O

x

y

O

Vertex:

Line of Symmetry:

x-intercepts:

y-intercept:

Domain:

Range:

Interval on which is increasing:

Interval on which is decreasing:

Vertex:

Line of Symmetry:

x-intercepts:

y-intercept:

Domain:

Range:

Interval on which is increasing:

Interval on which is decreasing:


MCPS © 2013–2014 Page 18

For items 39 through 42, add or subtract as indicated.

39. 2 23 4 7 7 3 12x x x x

40. 2 22 5 9 4 7 12x x x x

41. 2 24 11 8 11 15x x x x

42. 2 24 9 12 2 9 11x x x x

For items 43 through 48, multiply as indicated. 43. 2 5 4 7x x

44. 3 2 9x x

45. 22 3x

46. 25 3x

47. 7 7x x

48. 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.

49. 50.

Perimeter ___________________ Perimeter ______________________

Area as a trinomial _______________________ Area as a trinomial ____________________

For items 51 through 55, the area of a rectangle is given. Factor the expression as the product of two binomials to find its side lengths.

51. Area: 2 8 20x x

52. Area: 2 16 60x x

53. Area: 2 36x

54. Area: 2 121x

55. Area: 23 5 2x x

56. Factor: 22 10 12x x

57. Factor: 23 21 36x x


MCPS © 2013–2014 Page 20

Unit 4, Topic 3

For items 58 through 60, use your calculator to graph the function, then state the number of real zeros.

58. 26f x x

59. 2 5f x x x

60. 2 2 1f x x x

61. 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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62. 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.


MCPS © 2013–2014 Page 22

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

For items 64 through 69, solve the equation using any method.

64. 27 81x 65. 5 3 2 0x x

66. 27 8 1 0x x 67. 2 10 1 0x x

68. 2 6 8x x 69. 2 7 9x


MCPS © 2013–2014 Page 23

70. 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.

Solve the inequality 2300 5 4000t t .

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

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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71. The equations 2 4 5y x x and 7y 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 72 and 73, determine the side of the right triangle marked x.

72. 73.

For items 74 and 75, the lengths of 3 sides of a triangle are given. Determine whether the triangle is a right triangle.

74. Lengths are 12, 16, and 20

75. Lengths are 2, 3, and 4

5

12 x

x 10 7


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

For items 76 and 77, find the distance between each pair of points.

76. 7, 2 and 6,3

77. 6,3 and 2,9

x

y

O

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