Algebra I Common Core EOC Review 2012-2013 Name______

Algebra I Common Core EOC Review 2012-2013 Name______

Section I: Calculator Inactive

1) Simplify the following.

2) If , solve for T2.

3) Solve 5(x+3) – 3x =55 for x. Use mathematical properties to justify each step in the process.

4) Create a frequency distribution table and histogram for the following set of data:

Age (in months) of First Steps
13 / 9 / 12 / 11
10 / 8.5 / 14 / 9
12.5 / 10 / 13.5 / 9.5
6 / 7.5 / 15 / 9
8 / 11.5 / 10 / 12
10.5 / 11 / 13 / 12.5

5) Which description would fit the graph?

AThe number of pennies Montrell has if he gives away 2 every day.

BThe number of pennies Montrell has if his mother gives him 2every day.

CThe number of pennies Montrell has if he gives away 2 the first day, 4 the next day, 8 the day after that, and so forth.

DThe number of pennies Montrell has if he gets none and gives none away.

6) GreatSmokyMountainNational Park has 484 miles of roads. Of theseroads, 238 miles are paved. If x miles are unpaved, which equation could be used to find the number of miles of unpaved roads in the park?

A238 + x = 484

B484 + x = 238

C238x = 484

D484x = 238

7) The length of a rectangle is 8 cm, and its perimeter is 20 cm. What is the area of the rectangle in

square centimeters?

8) Solve the system:

9) Express 2(x3 – 3x2 + x – 6) – (x – 3)(x + 4) in factored form and use your answer to say for what values of x the expression is zero.

10) Chloe looked at the data below and said, “The median is 37.” Which answer points out Chloe’s mistake?

38, 42, 51, 55, 37, 57, 34, 44, 56

AChloe should have added the numbers and divided by 9. The median is 46.

BChloe did not make a mistake; the median is 37.

CChloe forgot to arrange thenumbers in ascending order. The median is 44.

DThe median is the number which appears the most; there is no median.

11) A business purchases a computer for$2,000. The value of the computer depreciates $400 per year. Which linear equation gives the value y of the computer after xyears?

Ay = 400x + 2,000

By = 2,000x – 400

Cy = 2,000x + 400

Dy = –400x + 2,000

12) Penny saves the same amount ofmoney every month. The equation T = 18M + 50 shows how much money T she has in her account atthe end of every month M. What does the number 18 represent in the equation?

AThe money her uncle gave her to open the account

BThe total amount of money she has in her account

CThe money she saves each month

DThe number of months Penny has been saving money at the bank

13) If the mode of a bar graph is 10, then which statement is true?

AMore bars have height 10 than anyother value.

BThe middle bar has height 10.

CThe tallest bar is 10 taller than theshortest bar

DThere must be 10 bars on the graph.

14) Kelli was to determine the average height of the female population in her school. She used the roster of the school’s girls’ basketball team. What is wrong with this approach?

ABasketball rosters always exaggerate the heights of their team.

BBasketball team members probably tend to be taller than the average.

CShe should have picked at least one other sport team roster to include.

DShe should have included some boys in the sample population.

15) Which equation describes the relationship between x and y in the table below?

x / y
-3 / -14
-1 / -6
1 / 2
3 / 10

16) A homeowner’s monthly telephone bill can be calculated usingb = 0.08m + 32.50 where m is the number of minutes the phone is used each month. Whether a customer uses the phone or not, there is a monthly fee. What is this monthly fee?

A $32.50

B $32.58

C $40.50

D$112.50

17) Based on some old data in a familyalbum, Max decided to graph hisheight over the years and look for atrend. What would be the independentvariable?

Ayear

Bweight

Cincrease in weight over the year

Dheight

Use the following information to answer questions #18 - 19 below.

Shauna saw a total of 30 clams and fish at the seashore one day.

18) If the number of fish Shauna saw was 6 more than twice the number of clams, which equation could she use to find x, the number of clams?

A2x + 6 = 30

Bx + 2x + 6 = 30

Cx + 6 = 30

Dx = 2x + 6

19) How many clams did she see?

A 8

B12

C16

D24

20) The equation F = 5P + 30 is used to calculate the yearly membership fee,F,for Milo’s running club. P is the number of practices attended eachyear. What does the coefficient of Prepresent?

Athe price for a bottle of water

Bthe y-intercept

Cthe one-time yearly fee

Dthe fee per practice

21) What is the rule in the form “y = “ for the NEXT – NOW equation below?

NEXT = NOW – 5, starting at 12

22) What is the NEXT – NOW equation for ?

A NEXT = NOW – 15, starting at 20

B NEXT =–20 NOW, starting at 15

C NEXT = – 15 NOW, starting at 20

D NEXT = NOW – 20, starting at 15

23) What is the equation of the line shown?

Ay = –3x + 2

Cy = 3x

24) Joe accepts an acting role suited to a much heavier person. To fit it, he goes on a weight-gaining diet. The graph represents his weight over a12-week period. The ray intersects the y-axis at the point (0, 155). What does the 155 represent?

AJoe’s weight after the first week

BThe day Joe began the diet

CJoe’s weight at the start of thediet

DJoe's target weight

25) The graph shows the path of a North CarolinaState mini football thrown in the air from a height of6 feet. What is the maximum height the ball reaches?

A 6 feet

B19 feet

C25 feet

D50 feet

26) Which of the following coordinates for point Q will guarantee that line PQ has slope 2.5?

AQ (1, 2.5)

BQ (1, 4.5)

CQ (2, 1)

DQ (4, 1)

27) What is the solution to the equation ?

28) The figure below shows the dimensions of a rectangular area rug. Hanna plans to expand the length and width of the rug by x units on all four sides. Write an expression that represents the area of the rug after the expansion?

2x + 10

x + 5

29) Which of the lines shown is the graph of ? (The scale on each axis is 1.)

30) What is the slope of the line through the points (-2, 4) and (10, 0)?

31) Which is the midpoint of if thecoordinates of the endpoints are A(–7, 2) and D(8, –3)?

32) When 2x – 3y = 6 is solved for y, which equation results?

33) Which quadrants would the graph of y = a + bx pass through if a is negative and b is positive?

AI, II, III

BI, II, IV

CI, III, IV

DII, III, IV

34) Which graph could represent the equation ?

35) A culture of bacteria doubles in population every three hours. If the population of a culture

was 20 at 3:00 p.m., which expression represents its population after 24 hours?

36) What is the length, in units, of the missing side of the triangle below?

A 6

B11

C12

D17

Use the following information to answer questions #37 – 38 below.

Manuel has $1500 saved for a motorcycle. He plans to make deposits to his savings account for the motorcycle each month. Use the graph below to answer questions 41 – 42.

37) What is the slope of the line that contains the points on the graph?

A- 750

B150

C750

D1,500

38) What does the slope of the line represent?

Athe increase in price of the motorcycle

Bthe number of months Manuel will save for the motorcycle

Cthe difference between the cost of the motorcycle and the amount Manuel has saved

Dthe amount Manuel will save each month

39) What is the area of the label on the side of a can of soup if the radius of the can is 2 inches, the height is 4 inches, and the label completely covers the sides? Round to the nearest tenth.

A 8.0 square inches

B12.6 square inches

C16.0 square inches

D50.26 square inches

40) Which is the graph of ?

41) Which equation has a graph that represents exponential decay?

42) Which expression is equivalent to?

A4x2 + 25

B2x2 + 10x + 5

C2x2 + 20x + 25

D4x2 + 20x + 25

43) The Pythagorean Theorem expresses the relation between the legs a and b of a right triangle and its hypotenuse c with the equation a2 + b2 = c2.

a. Why might the theorem need to be solved for c?

b. Solve the equation for c and write a problem situation where this form of the equation might be useful.

44) Solve for radius r.

45) Motion can be described by the formula below, where t = time elapsed, u=initial velocity, a = acceleration, and s = distance traveled:

s = ut+½at2

a. Why might the equation need to be rewritten in terms of a?

b. Rewrite the equation in terms of a.

46) Solve for x or y in each equation or inequality below.

b. 3x > 9

c. ax + 7 = 12

e. < 18

47) If the sum of two numbers is 10 and their difference is 4, what are the numbers? Write a system of equations and solve.

Section II: This is the end of the calculator inactive test questions. You may now use your calculator for the calculator active review questions.

Use the following bowling scores to answer the questions #1-5 below.

70, 78, 83, 90, 110, 110, 122, 124, 128, 130, 145, 156, 174, 180, 205.

48) What is the mean?

A110

B124

C127

D135

49) What is the median?

A110

B124

C127

D135

50) What is the interquartile range?

A 66

B 70

C 90

D110

51) To be an outlier a bowling score would have to be greater than what number?

A 99

B127

C205

D255

52) Solve the system of equations: x+ y = 11 and 3x – y = 5. Use a second method to check your answer.

53) Solve the system of equations:x – 2y + 3z = 5

x + 3z = 11

5y – 6z = 9

54) The opera theater contains 1,200 seats, with three different prices. The seats cost $45 dollars per seat, $50 per seat, and $60 per seat. The opera needs to gross $63,750 on seat sales. There are twice as many $60 seats as $45 seats. How many seats in each level need to be sold?

55) Two friends are driving to the Grand Canyon in separate cars. Suzette has been there before and knows the way but Andrea does not. During the trip Andrea gets ahead of Suzette and pulls over to wait for her. Suzette is traveling at a constant rate of 65 miles per hour. Andrea sees Suzette drive past. To catch up, Andrea accelerates at a constant rate. The distance in miles (d) that her car travels as a function of time in hours (t) since Suzette’s car passed is given by d = 3500t2. Write and solve a system of equations to determine how long it takes for Andrea to catch up with Suzette.

56) Given the following equations determine the x value that results in an equal output for both functions.

57) Graph the solution: y 2x + 3.

58) A publishing company publishes a total of no more than 100 magazines every year. At least 30 of these are women’s magazines, but the company always publishes at least as many women’s magazines as men’s magazines. Find a system of inequalities that describes the possible number of men’s and women’s magazines that the company can produce each year consistent with these policies. Graph the solution set.

59) Graph the system of linear inequalities below and determine if (3, 2) is a solution to the system.

60) If , find

61) Let . Find , , , and

62) If P(t) is the population of Tucsont years after 2000, interpret the statements P(0) = 487,000 and P(10)-P(9) = 5,900.

63) A rocket is launched from 180 feet above the ground at time t = 0. The function that models this situation is given by h = – 16t2 + 96t + 180, where t is measured in seconds and h is height above the ground measured in feet.

a. What is a reasonable domain restriction for t in this context?

b. Determine the height of the rocket two seconds after it was launched.

c. Determine the maximum height obtained by the rocket.

d. Determine the time when the rocket is 100 feet above the ground.

e. Determine the time at which the rocket hits the ground.

f. How would you refine your answer to the first question based on your response to the second and fifth questions?

64) The average rate of change of a function y = f(x) over an interval [a,b] is .

In addition to finding average rates of change from functions given symbolically, graphically, or in a table, you may collect data from experiments or simulations (ex. falling ball, velocity of a car, etc.) and find average rates of change for the function modeling the situation.

a. Use the following table to find the average rate of change of g over the intervals [-2, -1] and [0,2]:

x / g(x)
-2 / 2
-1 / -1
0 / -4
2 / -10

b. The table below shows the elapsed time when two different cars pass a 10, 20, 30, 40 and 50 meter mark on a test track.

For car 1, what is the average velocity (change in distance divided by change in time) between the 0 and 10 meter mark? Between the 0 and 50 meter mark? Between the 20 and 30 meter mark? Analyze the data to describe the motion of car 1.

How does the velocity of car 1 compare to that of car 2?

Car 1 / Car 2
d / t / t
10 / 4.472 / 1.742
20 / 6.325 / 2.899
30 / 7.746 / 3.831
40 / 8.944 / 4.633
50 / 10 / 5.348

65) Examine the functions below. Which function has the larger maximum? How do you know?

66) You buy a $10,000 car with an annual interest rate of 6 percent compounded annually and make monthly payments of $250. Express the amount remaining to be paid off as a function of the number of months, using a recursion equation.

67) A cup of coffee is initially at a temperature of 93º F. The difference between its temperature and the room temperature of 68º F decreases by 9% each minute. Write a function describing the temperature of the coffee as a function of time.

68) The radius of a circular oil slick after t hours is given in feet by , for 0 ≤ t ≤ 10. Find the area of the oil slick as a function of time.

69) An explicit rule for the nth term of a sequence gives an as an expression in the term’s position n; a recursive rule gives the first term of a sequence, and a recursive equation relates an to the preceding term(s). Both methods of presenting a sequence describe an as a function of n.

a) Generate the 5th-11th terms of a sequence if A1= 2 and

b) Use the formula: An= A1 + d(n - 1) where d is the common difference to generate a sequence whose first three terms are: -7, -4, and -1.

c) There are 2,500 fish in a pond. Each year the population decreases by 25 percent, but 1,000 fish are added to the pond at the end of the year. Find the population in five years. Also, find the long-term population.

d) Given the formula An= 2n - 1, find the 17th term of the sequence. What is the 9th term in the sequence 3, 5, 7, 9, …?

e) Given a1= 4 and an= an-1+ 3, write the explicit formula.

70) You are planning to take on a part time job as a waiter at a local restaurant. During your interview, the boss told you that their best waitress, Jenni, made an average of $70 a night in tips last week. However, when you asked Jenni about this, she said that she made an average of only $50 per night last week. She provides you with a copy of her nightly tip amounts from last week (see below). Calculate the mean and the median tip amount.

Day / Tip Amount
Sunday / $50
Monday / $45
Wednesday / $48
Friday / $125
Saturday / $85

a) Which value is Jenni’s boss using to describe

the average tip? Why do you think he chose this value?

b)Which value is Jenni using? Why do you think she chose this value?

c) Which value best describes the typical amount of tips per night? Explain why.

71) Write the expression below as a constant times a power of x and use your answer to decide whether the expression gets larger or smaller as x gets larger.

72) Given that the following trapezoid has area 54 cm2, set up an equation to find the length of the base, and solve the equation.

73) Lava coming from the eruption of a volcano follows a parabolic path. The height h in feet of a piece of lava t seconds after it is ejected from the volcano is given by . After how many seconds does the lava reach its maximum height of 1000 feet?

74) A man-made lake is initially stocked with 500 fish. The population is expected to increase by about 20% each year. If the lake can’t support more than 2,000 fish, in about how many years will the lake become overpopulated with fish?

A 3

B 8

C15

DIt will never become overpopulated with fish.

75) A club is selling hats and jackets as a fundraiser. Their budget is $1500 and they want to order at least 250 items. They must buy at least as many hats as they buy jackets. Each hat costs $5 and each jacket costs $8.

a. Write a system of inequalities to represent the situation.

b. Graph the inequalities.

c. If the club buys 150 hats and 100 jackets, will the conditions be satisfied?

d. What is the maximum number of jackets they can buy and still meet the conditions?

76) Which change in the graph below would causethe median to be 27?

AAdd another state with 19 hazardous waste sites.

BAdd another state with 25hazardouswaste sites.

CAdd another state with 27 hazardouswaste sites.

DAdd another state with 29hazardous waste sites.

77) Alex deposits $1,500 in a new savings account at 2% interest. The equationgives total savings y in the savings account at the end of x years. How much money will Alex have in his account after 5 years?

A$1,502

B$1,656.12

C$1,682.43

D$150,510

78) Bruce, Lola, Sheehan, Lakesha, and Mickey have 36, 48, 40, 61, and 312 stamps in their respective collections. Which measure of central tendency best represents the number of stamps in their collections?

Amean

Bmedian

Cmode

Dmean or mode

Use the box-and-whisker plots to answer questions #79-82 below.

79) What is true about the interquartileranges (IQR)?

AThe IQR for CD burners is 130andfor digital cameras 200.

BThe IQR for CD burners is 250 andfor digital cameras 600.

CThe IQR for CD burners is 170lessthan that for digital cameras.

DThe IQR for CD burners is 200lessthan that for digital cameras.

80) How much does the least expensive CD burner cost?

A $80

B$100

C$120

D$400

81) An outlier for the price of CD burners would be greater than what value?

A$250

B$380

C$395

D$445

82) If 50 digital cameras were includedin this survey, approximately howmany of them cost from $300 to$600?

A13

B25

C37

D50

Use the following information to answer questions #83 – 84 below.

3 notebooks and 5 $1.25 pens cost a total of $13.75.

83) Which equation could you solve to find the cost of each notebook?

Ax + 1.25 = 13.75

B3x + 5(1.25) = 13.75

Cx + 5(1.25) = 13.75

D3x + 1.25 = 13.75

84) How much does each notebook cost?

A$1.25

B$2.00

C$2.50

D$4.25

85) The 1990 population of Australia was about 18.3 million people. The annual rate of growth is estimated at 1%. The table below shows the estimated population, to the nearesttenth of a million, for each year from 1991 to 1996. Which NEXT-NOW equation could be used tocalculate Australia’s populationestimate for any year based on theprevious year’s population?

Year / Estimated Population
1991 / 18.5
1992 / 18.7
1993 / 18.9
1994 / 19.0
1995 / 19.2
1996 / 19.4

ANEXT = .01 NOW

BNEXT = .99 NOW

CNEXT = 1.01 NOW

DNEXT = 18.3 +NOW

86) Monica’s investment of $500 grows at a rate of 10% a year. How muchmoney should Monica have after 4 years?

A$665.60

B$700

C$732.05

D$20,000

87) Matiana’s mom created the equation S = 20T + 10 to predict Matiana’s score on her next 100 point math test based on the number of hours Matiana studies. If the equation works and Matiana studies for 2.75 hours T what will be her score S?