Semester 1 Exam Study Materialskmtanneberg.weebly.com/uploads/5/8/9/0/58903231/semester... · 2018....

ALGEBRA I 2015–2016 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1

2015–2016 Page 1 of 31 Revised September 2015 Clark County School District

18. (2.2) Use the diagram below.

A rectangle’s sides are measured to be 6.2 cm and 9.3 cm. What is the rectangle’s area rounded to the correct number of significant digits?

(A) 57.66 cm2

(B) 57.7 cm2

(C) 58 cm2

(D) 60 cm2

19. (2.3) In the formula F I at , F and I are measured in meters per second and t is measured in seconds. In what units is a measured?

(A) meters

(B) seconds

(C) meters per second

(D) meters per second squared

20. (2.5) What are the coefficients in the expression 3x – 4y +2?

(A) 3x, –4y, and 2

(B) 3 and –4

(C) x and y

(D) 2

21. (2.6) An athlete works out each day for 60 minutes, of which t minutes is spent running at 0.20

, and the rest of the time is spent walking at 0.05 . Which expression represents the total

distance the athlete travels in miles while working out each day? (A)

mi

min

mi

min

0.25 60

9.3 cm

6.2 cm



(B)

(C)

(D)

For questions 22 and 23, use the solution to the equation 2x – 3 = 11 below.

Start: 2x – 3 = 11

Step 1: 2x – 3 + 3 = 11 + 3

Step 2: 2x = 14

Step 3: 1 12 14

2 2x

Step 4: x = 7

22. (2.7) In Step 1, the addition property of equality was applied.

(A) True

(B) False

23. (2.7) In Step 3, the symmetric property of equality was applied.

(A) True

(B) False

24. (2.8) Let the price of a meal at a restaurant be p. The tax and tip on the meal are generally a percentage of the meal’s price. The total cost of the meal is its price plus tax plus tip.

(a) Write an expression for the total cost of a meal where the tax is 8% and the tip is 15%.

(b) Write an expression for the total cost of a meal where the tax is x% and the tip is g%.

(c) David calculates a 15% tip by dividing the meal price by 10, dividing that number by 2,

and then adding the two numbers, i.e. . Explain whether or not this

method is correct.

25. (2.9) Tim was asked to solve the equation for x. His solution is shown below.

Start:

0.25 60t t

0.20 0.05 60t t

0.20 0.05 60t t

10tip 10 2

pp

kx my mx

kx my mx



Step 1:

Step 2:

Step 3:

In which step did Tim make his first mistake when solving the equation?

(A) Step 1

(B) Step 2

(C) Step 3

(D) Tim did not make a mistake.

26. (2.9) The potential energy P of an object relative to the ground is equal to the product of its mass m, the acceleration due to gravity g, and its height above the ground h is represented in the equation

. Solve the formula for height h.

(A)

(B)

(C) h = Pmg

(D) h = P – mg

27. (2.9) In the formula , xf and x0 are both measured in feet and t is measured in seconds.

(a) In what units is v measured?

kx mx my

x k m my

myx

k m

Ph

mg

mgh

P

0fx xv

t



(b) Let x0 = 3,300 ft. Convert x0 to miles. (1 mile = 5280 feet)

(c) Solve the formula for xf.

28. (3.4) An internet business sells U.S. flags for $16.95 each, plus $2.50 shipping per flag. Shipping is free, however, on orders where more than $100.00 of flags are purchased. Which correctly shows the number of flags f that must be purchased to get free shipping?

(A)

(B)

(C)

(D)

29. (3.5) Solve each absolute value equation.

30. (3.7) Some fire extinguishers contain pressurized water. The water pressure should be 162.5 psi (pounds per square inch), but it is acceptable for the pressure to differ from this value by at most 12.5 psi. Write and solve an absolute-value inequality to find the range of acceptable pressures.

31. (4.2) Given . What is ?

16.95 100f

16.95 100f

19.45 100f

16.95 2.50 100f

(a) 6 21x

(b) 18 3 1x

(c) 3 4 31y

(d) 3 14 5x

(A) 12.5 162.5p

150.0 175.0p

(B) 12.5 162.5p

150.0p or 175.0p

(C) 162.5 12.5p

150.0p or 175.0p

(D) 162.5 12.5p

150.0 175.0p

5 2f x x 4f



(A) 18

(B) 54

(C) 20x – 2

(D) 20x – 8

32. (4.2) Kathy has two sets of numbers, A and B. The sets are defined as follows:

A = {1, 2, 3}

B = {10, 20, 30}

Kathy created four relations using elements from Set A for the domains and elements from Set B for the ranges. Which of Kathy’s relations is NOT a function?

(A) {(1, 10), (1, 20), (1, 30)}

(B) {(1, 10), (2, 10), (3, 10)}

(C) {(1, 10), (2, 20), (3, 30)}

(D) {(1, 10), (2, 30), (3, 20)}

33. (4.3) Justin plans to spend $20 on sports cards. Regular cards cost $3.50 per pack and foil cards cost $4.50 per pack. Which inequality shows the relationship between the number of packs of regular cards (r) and the number of packs of foil cards (f) Justin can afford to buy?

(A)

(B)

(C)

(D)

34. (4.3) The exchange rate for U.S. Dollars to Euros is $1.50 = 1 Euro. At a bank, there is a flat $20.00 service fee to exchange dollars for Euros. Which graph shows how many Euros E would be received if an amount D in U.S. Dollars were exchanged at the bank?

3.5 4.5 20f r

3.5 4.5 20r f

3.5 4.5 20f r

3.5 4.5 20r f



35. (4.3) Lana is buying balloons for a party. Small balloons cost 30 cents each; large balloons cost 80 cents each. Lana has $3.00 to spend on balloons.

The number of large balloons L she can buy as a function of the number of small balloons S bought

is given by . What are the domain and range of this function?

(A) domain: all real numbers range: all real numbers

(B) domain: all real numbers, where 0 ≤ S ≤ 10 range: all real numbers, where 0 ≤ L ≤ 3.75

(C) domain: all positive integers range: all positive integers

(D) domain: all integers, where 0 ≤ S ≤ 10 range: all integers, where 0 ≤ L ≤ 3

(A)

(B)

(C) (D)

300 30

80

SL S



36. (4.3) To fix a clogged pipe, Dripmaster Plumbing charges $75 plus $40 per hour. NoClog Plumbers charges $50 plus $70 per hour for the same service. Which function shows the difference in charges between the two companies for a repair taking h hours?

(A) Difference = $20 – $35h

(B) Difference = $25 – $30h

(C) Difference = $25 – $110h

37. (4.3) Steve borrows $4,800 from his parents to purchase a used car. No interest is charged on the loan and Steve will pay his parents $150 per month until the loan is paid off.

(a) Write a function that describes the relationship between the amount Steve owes his parents and the number of months since the loan was made.

(b) What are the domain and range of the function in part (a)? What do these represent in context of the situation?

(c) Graph the function in part (a), identify important points, and explain why they are important.

38. (4.3) Explain why the relation y = x2 is a function even though x = –2 and x = 2 both produce y = 4.

39. (4.6) The first five terms of a sequence are given.

14 17 20 23 26

Which equation describes the nth term of the sequence?

(A)

(B)

( ) 3 11f n n

( ) 11 3f n n



(C)

(D)

40. (4.6) What are the first five terms of the sequence defined as

a(1) = 3

a(n + 1) = a(n) – 4, for n ≥ 1?

(A) –3, –2, –1, 0, 1

(B) –1, –5, –9, –13, –17

(C) 3, –1, –5, –9, –13

(D) 3, –1, 0, 1, 2

41. (4.6) Let g(x) = 2x – 6. Which expression represents g(2x)?

(A) x – 3

(B) 2x – 12

(C) 4x – 12

(D) 4x – 6

42. (4.6) A sequence t is defined as , where n ≥ 1. Which is an equivalent recursive

definition for sequence t?

(A)

(B)

(C)

(D)

43. (4.6) The graph shows the first five terms of an arithmetic sequence whose domain is the positive integers.

( ) 14 17f n n

( ) 17 3f n n

0.57 0.06t n n

1 0.57; 1 0.06, for 1t t n t n n

1 0.51; 1 0.06, for 1t t n t n n

1 0.57; 1 0.51, for 1t t n t n n

1 0.51; 1 0.51, for 1t t n t n n



Which is a definition of the sequence?

(A)

(B)

(C)

(D)

44. (4.6) A sequence t is defined where the first term is –4. Each successive term is 3 more than the term before it.

(a) Write an explicit formula for the sequence t.

(b) A second function is defined as s(n) = 2 + 2n. Compare the rates of change of t(n) and s(n).

(c) For what value(s) of n does t(n) = s(n)? Show your work.

8t n n

8 2t n n

10t n n

10 2t n n



45. (4.7) Sam is beginning an exercise program that begins the first week with 30 minutes of daily exercise. Each week, daily exercise is increased by 5 minutes. Which function represents the number of minutes of daily exercise in week n?

(A) , for n ≥ 2

(B) , for n ≥ 2

(C) , for n ≥ 2

(D) , for n ≥ 2

For questions 46 and 47, use the table.

x 3 5 8 12 17 y 12 16 22 30 40

46. (5.1) The ordered pairs (x, y) form a linear function.

(A) True

(B) False

47. (5.1) The value of y changes by increasingly larger amounts for each change of 1 in x.

(A) True

(B) False

48. (5.2) What are the intercepts of the line with equation 2x – 3y = 30?

(A) (–10, 0) and (0, 15)

(B) (6, 0) and (0, –6)

(C) (15, 0) and (0, –10)

(D) (30, 0) and (0, –30)

49. (5.3) Use the table below.

x f(x) 3 10

(1) 30; ( ) 30f f n n

(1) 30; ( ) 5 30f f n n

(1) 30; ( ) ( 1) 5f f n f n

(1) 30; ( ) 5 ( 1)f f n f n



6 14 9 18

12 22

What is the slope of y = f(x)?

(A) 4

(B)

(C)

(D)

50. (5.3) Which is the graph of y = –2x + 1?

4

3

10

3

22

12



51. (5.3) This graph shows three lines named a, b, and c.

(A)

(B)

(C) (D)



Which ratio of the lines’ slopes equals ?

(A)

(B)

(C)

(D)

1

2

slope of line

slope of line

a

b

slope of line

slope of line

a

c

slope of line

slope of line

b

a

slope of line

slope of line

c

b

x

ya b c



52. (5.3) Use the graph.

What is the slope of the line?

(A)

(B)

(C)

(D)

3

5

5

3

3

5

5

3

x

y



For questions 53 and 54, use this graph that helps convert temperatures from degrees Fahrenheit to degrees Celsius.

Three important temperatures are shown on the graph: –40°F = –40°C, 32°F = 0°C, and 212°F = 100°C.

53. (5.3) A temperature increase of 9°F corresponds to an increase of 5°C.

(A) True

(B) False

54. (5.3) The slope of the line is .

(A) True

(B) False

55. (5.4) When the function f = k + ac is graphed on the axes shown, what quantity corresponds to the intercept on the vertical axis?

(A) f

(B) k

(C) f – k

(D)

1.8F

C

f k

a

°F

°C

c

f



56. (5.4) A line is defined by the equation . Which ordered pair does NOT represent a point

on the line?

(A) (–5, 0)

(B) (0, 3)

(C) (1, )

(D) (5, 5)

57. (5.4) A certain child’s weight was measured at 16.6 pounds. The child then gained weight at a rate

of 0.65 pounds per month. On a graph of weight versus time, what would represent?

(A) The y-intercept of the graph

(B) The x-intercept of the graph

(C) The slope of the graph

58. (5.5) Which is the graph of 2x – 3y < 12?

(A)

(B)

(C)

(D)

23

5y x

17

5

pounds0.65

month

x

y

x

y

x

y

x

y




Which inequality is represented in the graph?

(A) x ≤ 1

(B) x ≥ 1

(C) y ≤ 1

(D) y ≥ 1

For questions 60-62, use the inequality .

60. (5.5) (0, 1) is a solution of the inequality.

(A) True

(B) False


(A) True

(B) False


(A) True

(B) False

12

xy

x

y



63. (5.5) What is the equation of the horizontal line through the point (4, –7)?

(A) x = 4

(B) x = –7

(C) y = 4

(D) y = –7


If and , what is ?

(A) –3

(B) 0

(C) 3

(D) 4

1 1f x g x 2 2g x h x 1 2f x g x

x

y

y=f(x)

y=g(x)

y=h(x)



65. (5.6) The graph shows a line segment.

Which equation best describes the line segment?

(A)

(B)

(C)

(D)

66. (5.7) What is the equation of the line that passes through the points (5, –1) and (4, –5)?

(A)

(B)

(C)

(D)

39

4P k k

318

4P k k

42

3P k k

412

3P k k

5 4 4y x

5 4 4y x

15 4

4y x

15 4

4y x

k

P(k)

(12,18)

(28,30)



For questions 67-69, use the scenario below.

A phone call using a prepaid card consists of a fixed fee to place the call plus an additional fee for each minute of the call.

The cost of an n-minute phone call with a card from Company A is A(n) = $0.99 + $0.25n, where n is a positive integer.

The cost of an n-minute phone call with a card from Company B is shown in the graph below.

67. (6.1) The per minute fee for Company B is greater than Company A.

(A) True

(B) False

68. (6.1) The fixed fee for Company B is greater than Company A.

(A) True

(B) False

69. (6.1) A call using Company B will always cost more than the same length call using Company A.

(A) True

(B) False

n

B(n)

totalcost($)

minutesused



70. (6.2) An online music service charges a $25 start-up fee plus $8 per month for unlimited downloads. The graph illustrates the total cost of a membership for a given number of months.

What would happen to the graph if the start-up fee changed from $25 to $32?

(A) The slope would increase by $7/month.

(B) The slope would decrease by $7/month.

(C) The graph would translate up $7.

(D) The graph would translate down $7.

Totalcost($)

x

y

Numberofmonths



71. (6.2) The graph shows the linear function .

y f x

Which graph shows 1y f x ?

(A)

(B)

(C)

x

y

x

y

x

y

x

y



72. (6.3) The scatterplot below represents the forearm lengths and foot lengths of 10 people.

Based on a linear model of the data, which is the best prediction for the length of a person’s foot if his/her forearm length is 21 centimeters?

(A) 19 cm

(B) 20 cm

(C) 22 cm

(D) 24 cm

Footlength(cm

)

Forearmlength(cm)



73. (6.3) The line of best fit for the scatterplot below is

Predict y when x = 6.

(A) 2.2

(B) 10.5

(C) 11.3

(D) 18.8

ˆ 1.4 2.9y x

0

4

8

12

16

20

x

0 2 4 6 8 10

y



74. (6.3) Which equation best describes fits the data shown in the scatterplot?

(A)

(B)

(C)

(D)

37

5y x

18

3y x

8y x

4y

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y



75. (6.3) The line of best fit for the scatterplot below is

What is the residual for the point (4, 10)?

(A) –1.5

(B) 1.5

(C) 8.5

(D) 10

76. (6.3) A scatterplot is made of a city’s population over time. The equation of the line of best fit is where is the city’s predicted population size and t is the number of years since

2000. What is the meaning of the slope of this line?

(A) In 2000, the city’s population was about 629 people.

(B) In 2000, the city’s population was about 150,000 people.

(C) The city’s population increases by about 629 people each year.

(D) The city’s population increases by about 150,000 people each year.

77. (6.3) The equation , gives the predicted population of a city (in thousands) x years after 1975. What is meaning of the y-intercept?

(A) In 1975, the city’s population was about 120 people.

(B) In 1975, the city’s population was about 31,400 people.

(C) The city’s population decreases by about 120 people each year.

(D) The city’s population decreases by about 31,400 people each year.

ˆ 1.4 2.9y x

ˆ 629 150,000p t p

ˆ 31.4 0.12y x y

0

4

8

12

16

20

x

0 2 4 6 8 10

y



78. (6.3) The equation gives the predicted price of a particular style of television m months after the style first became available. What is the meaning of the P-intercept?

(A) The original price of the television was about $9.50.

(B) The original price of the television was about $509.00.

(C) The price of the television decreases by about $9.50 each month.

(D) The price of the television increases by about $509.00 each month.

79. (6.3) The data below comes from a scatterplot.

x 2 3 4 5 6 7 8 8 8 9 10 10 y 2 8 4 1 10 4 6 10 2 7 3 9

Which best describes the linear relationship between x and y?

(A) Weak or no correlation

(B) Strong positive correlation

(C) Strong negative correlation

For questions 80-82, evaluate the truth of each statement about the correlation coefficient r.

80. (6.3) A value of r near zero indicates there is a weak linear relationship between x and y.

(A) True

(B) False

81. (6.3) A value of r = –0.5 indicates a weaker linear relationship between x and y than a value of r = 0.5.

(A) True

(B) False

82. (6.3) A value of r = 1 indicates that there is a cause-and-effect relationship between x and y.

(A) True

(B) False

ˆ 9.50 509P m P



For questions 83 and 84, use the following scenario.

A linear model describes the relationship between two variables, x and y. The correlation coefficient of the linear fit is r = –0.9.

83. (6.3) The slope of the line of best fit is negative.

(A) True

(B) False

84. (6.3) The linear relationship between x and y is weak.

(A) True

(B) False



85. (6.3) The table shows the amount of rainfall in Seattle during the month of December in the years 1980–1999.

The histogram shows the distribution of rainfall in Seattle during the month of July in the same years, using intervals of 0.5 inches.

a) Create a histogram on the grid above that shows the distribution of rainfall in December using intervals of 1.0 inch.

b) Describe the shapes of the distributions for July and December.

c) How does the mean rainfall for July compare to the median rainfall? Explain.

d) Compare the median rainfalls for July and December over the period 1980–1999.

e) Describe how to compute the standard deviation of the December rainfalls. (You do not have to actually compute it.)

f) Which month’s rainfall, July or December, has the greater standard deviation? Explain.

Monthly Rainfall (inches) Year December 1980 7.4 1981 5.6 1982 6.2 1983 5.0 1984 5.0 1985 1.5 1986 6.8 1987 6.1 1988 7.5 1989 4.8 1990 3.1 1991 3.3 1992 4.1 1993 4.5 1994 8.2 1995 6.4 1996 5.2 1997 2.2 1998 9.0 1999 5.1

Rainfall(inches)

Frequenc

Frequency

December

July



g) One of the rainfall amounts for July was recorded at 2.4 inches. In actuality, it was only 1.4 inches. Explain how this would affect the mean and median of July rainfall.

h) On the grid below, create a scatterplot showing December monthly rainfall over the period from 1980–1999.

i) Describe the relationship between December rainfall and year.

Rainfall(inches)

Year

December



86. (6.5) Two residual plots are shown below.

Plot I

Plot II

Which residual plot(s) would indicate a linear model is appropriate?

(A) Plot I only

(B) Plot II only

(C) Both Plot I and Plot II

(D) Neither Plot I nor Plot II

xresiduals

xresiduals

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