review mid year math 1 name: wise and then cuts to form a...

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Review Mid Year Math 1

Name:____________________________________

1. Erin has a rectangular sheet of paper that measures 8 inches by 10 inches. She folds the sheet in half length-

wise and then cuts to form a triangle as shown.

Which is closest to the length of each longest side of the cut triangle?

A. 5.2 inches B. 6.0 inches

C. 10.8 inches D. 12.8 inches

Which is true regarding the Pythagorean Theorem?

2. A. The sum of the squares of the legs equals the square of the hypotenuse.

B. The sum of the squares of the hypotenuses equals the square of the leg.

C. The sum of the legs equals the hypotenuse.

3.

D. The sum of the hypotenuses equals the leg.

A triangle has sides that measure 5 units, 7 units, and 8 units. Is this triangle a right triangle?

A.

B.

C.

D.

4. Which of the following gives the BEST statement of the Pythagorean theorem?

A. In a right triangle, the square of the length of the hypotenuse equals the sum of the square of the lengths of the

legs.


B. In a right triangle, the square of the length of the hypotenuse equals the difference of the squares of the lengths of

the legs.

C. If the square of the length c of one side of a triangle equals the sum of the square of the lengths of the legs, then

it is a right triangle with hypotenuse of length c.

D. If the square of the length c of one side of a triangle equals the difference of the square of the lengths of the legs,

then it is a right triangle with hypotenuse of length c.

5. A bakery sells chocolate chip cookies and oatmeal cookies in packages of 12 each. On Saturday, the bakery

sold half as many oatmeal cookies as chocolate chip cookies. If the total number of cookies sold on Saturday

was 504, how many packages of chocolate chip cookies were sold?

A. 7

B. 14 C. 28 D. 42

6. The total number of students who could attend a field trip is represented by the variable t. The number of

students in Group A is less than the number in Group B. Group A has 6 students more than the total

number of students, while Group B has 3 less than the total number of students. Which inequality represents

this situation?

A.

B.

C.

D.

7. Ferguson and Carla began at the same time, from points 30 miles apart, to ride their bikes toward each other.

They met in 2 hours. If Carla rode 3 miles per hour faster than Ferguson, at what rate, in miles per hour, did

Carla ride?

A. 6

B. 9 C. 12 D. 18

8. If 6 more than 4 times a number is 14, what is the number?

A. 5

B. 2 C. D. 9. A rabbit weighed 4 ounces when it was born. The rabbit gained 2 ounces each week for the next 12 weeks. Which

equation models the weight of the rabbit, w, x weeks after it was born, where x ≤ 12?

A. w = 6x

B. w = 2x – 4 C. w = 2x + 4 D. w = 4x + 2

10. A business buys a computer for $3,000. After 4 years, the value of the computer is expected to be $250. The value, V,

can be related to the time in years, t, in a linear equation. Which equation models the relationship between V and t?

A. V = 250t

B. V = 12t C. V = 687.50t – 3,000 D. V = –687.50t + 3,000

11. Nicole and her sister each invest $500 in a bank account that earns an annual interest rate of 4%. If y represents the

total amount of money in the account and t represents the time in years since they invested in the account, which

equation represents this situation?


A.

B.

C.

D.

12. Suppose a forest starts with a deer population of 35 deer. The population is increasing at a rate of 12% per year.

Which equation represents the population of deer after x years?

A. y = 12(0.35)x

B. y = 12(1.35)x C. y = 35(0.12)x D. y = 35(1.12)x

13. Nicki needs to purchase AT LEAST 65 party decorations. The Party Palace charges $0.50 per decorative

streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Nicki

purchase with $20.00 at the Party Palace?

A. 36 streamers and 29 balloons

B. 16 streamers and 48 balloons

C. 15 streamers and 51 balloons D. 13 streamers and 53 balloons

14. Write a real-life word problem that can be solved using the system of inequalities below. Define what each of

the variables represents.

x + y ≥ 250

1.25x + 2.25y ≤ 400

15. Laurel needs to purchase AT LEAST 40 party decorations. The Party Palace charges $0.50 per decorative

streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Laurel

purchase with $16.00 at the Party Palace?

A. 22 streamers and 19 balloons

B. 24 streamers and 17 balloons

C. 25 streamers and 14 balloons

D. 28 streamers and 12 balloons

16. Jerry works for a cable television company. He must sell at least 10 television packages over the next week.

Customers have two packages to pick from, Package X and Package Y.

Jerry has to sell at least 2 of each package.

He can sell at most 12 of Package X.

He makes $30 for each Package X he sells.

He can sell no more than 17 of Package Y.

He makes $25 for each Package Y he sells.

Which inequality is a constraint for Jerry’s sales?

A. x ≥ 12


B. y ≥ 2

C. x + y > 10

D. 30x + 25y ≥ 55

17. The electrical resistance of a wire changes with a change in temperature and is given by the relation

where a = temperature coefficient of resistance. Which of these equations can be used to

find the value of a?

A.

B.

C.

D.

18.

The formula that describes an object’s motion is given by where S is the distance traveled, u is the

initial velocity, a is the acceleration, and t is the time. Which equation represents a in terms of the other variables?

A.

B.

C.

D.

19. What values of x

satisfy the inequality

?

A.

B.

C.

D.


20. The equation below is used to find S, the sum of the measures of the interior angles of a polygon with n sides.

Which equation is equivalent when solved for n in terms of S?

A.

B. C.

D.

21. Which graph represents the equation

A.

B.


C.

D.

22. Which graph represents ?


A.

B.

C.


D.

23. The graph of which of the following equations passes through Point S?

A.

B.

C.


D.

24. Which of the following could represent the graph of

A.

B.

C.

D.


25. Two functions are shown below.

f

(

x

)

=

3

x

+

6

g

(

x

)

=

3

(

−

2

)

x

For which value of


x

does

f

(

x

) =

g

(

x

)?

A. −

2

B. 0

C. 1

2

D. 2

26. Two functions are shown below.

f(x) = 2(3)x

g(x) = 4x + 2

What is the difference in the


y

-values of the two unique points where

f

(

x

) =

g

(

x

)?

A. 0

B. 2

C. 4

D. 6

27. If y = 6x + 8 and y = –4x – 2, what is the value of x + y when the two equations are equal?

A. –2

B. –1

C. 1

D. 2


28. A new computer company has its sales increasing by 3% each week. A second computer company has its sales

decreasing by $100 each day. The first company had $500 in sales when the second company had $7,000 in sales.

After approximately how many weeks will the sales for the two companies be the same?

A. 9 weeks

B. 13 weeks

C. 49 weeks

D. 63 weeks

29. A system of inequalities is shown below.

y

<

−

1

2

x

−

2

y

≤

1

2

x

+


2

Which graph shows the solution set to the system?

A.

B.


C.

D.

30. Which of the following graphs represents the equation


A.

B.

C.


D.

31. Which graph represents the solution of this system of inequalities?

A.


B.

C.

D.


32. Which inequality is graphed below?

A. 3x + 4y > 1

B. 3x + 4y < 1

C. 3x – 4y > –1

D. 3x – 4y < –1

33.

What values of x make the inequality true?

A.

B.


C.

D.

34. Which equation is equivalent to

A.

B.

C.

D.

35. If x is an integer, what is the largest value of x that satisfies the inequality below?

A.

B.

C. 0

D. 1

36. For which values of x is the inequality true?

A.

B.


C.

D.

37. Which value of is a solution to ?

A.

B.

C.

D.

38. What is the solution set for ?

A.

B.

C.

D.

39. What are the solutions to the equation

A.

or

B.

or


C.

or

D.

or

40. What is the solution set of the equation

A.

B.

C.

D.

41. Jolene is solving the system of equations shown below.

Which of these systems of equations has the same solution?

/files/assess_files/8d137a18-8b39-40bd-ad1b-6edb5109a055/formula_sheets/FL-

IBTP_Math_Reference_Sheet_Grade_9-12.pdf

FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf


A.

B.

C.

D.

42. Arthur was solving the system of equations below:

Arthur multiplied the first equation (I) by 2 and added the product to the second equation (II). The sum was the

equation seen below:

When Arthur solved for y, he got 3. Substituting 3 into the first equation (I), he found that x was 2.

Use Arthur's answers to show that his solution works for the second equation (II).

/files/assess_files/fa896dc8-764b-4ff1-b4b8-d38df7aaaadb/formula_sheets/FL-




43. A system of equations is given below.

Which of these procedures will eliminate a variable in one of the equations in the system above?

A. Multiply the first equation by 2 then add the result to the second equation.

B. Multiply the first equation by –2 then add the result to the second equation.

C. Multiply the second equation by 2 then add the result to the first equation.

D. Multiply the second equation by –2 then add the result to the first equation.

44. Which system of equations has the same solutions as the system below?

/files/assess_files/f0397209-25e9-4115-a2d6-eb19c15bc50e/formula_sheets/FL-



A.

B.

C.

D.


45. A boiling pot of water (212ºF) is cooling at a rate of 3.5 degrees per hour. A second pot is heated from freezing

(32ºF) at a rate of 7 degrees per hour.

Based on the graph, what is the water’s temperature when the two pots are equal?

A. 7°F

B. 17°F

C. 152°F

D. 212°F

46. Which graph shows the solution of this system of equations?


A.

B.


C.

D.

47. Marcus buys 2 hamburgers and 3 drinks for $8.75. Pam buys 4 hamburgers and 2 drinks for $12.50. How much does

1 hamburger cost?

A. $1.25

B. $1.75

C. $2.25

D. $2.50


48. Emma needs to develop prints of digital pictures she took at a party. She has two options to choose from. An online

digital photo lab charges $0.15 per print and $2.50 for shipping. Another local photo lab charges $0.35 per print, but

there will be no shipping charge.

Part A: Graph the system of linear equations that represents the situation above.

Part B. Use the graph of the two equations from part A to determine the solution to the system of equations. Is it

possible to find an exact solution using the graph? Explain.

Part C. Solve the system of linear equations that represents the given situation algebraically.

Part D. Which of the methods used for solving the system of equations in part B or part C is best for finding the

solution of this system of equations? Explain.

Use words, numbers, and/or pictures to show your work.


49.

Given as the original equation, which equation below demonstrates the Additive Inverse

Property was performed?

A.

B.

C.

D.

50.

Albert rewrote the equation as Which properties did he use to rewrite the equation?

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A. only the division property of equality

B. only the multiplication property of equality

C. the division and subtraction properties of equality

D. the multiplication and subtraction properties of equality


51. Elena solved an equation as shown below.

Solve:

Step

1:

Step

2:

Step

3:

Is Elena’s work correct? For each step of Elena’s work, describe the property of operations that she used and

tell whether or not the step is correct.

52. A visual representation for the equation is shown below.

Which visual representation could model the next step in solving this equation?


A.

B.

C.

D.

53. A new type of cell phone is being released to the public. The function below is used to predict f(t), the total

sales in thousands of units per day based on t, the time in weeks since the date of release.

According to this function, what are the predicted sales on the first day, and what is the predicted rate of

percentage increase per week in the sales amount?

A. 18,000 units on the first day then 40% per week


B. 40,000 units on the first day then 1.18% per week

C. 40,000 units on the first day then 18% per week

D. 118,000 units on the first day then 40% per week

54. Marissa plans to create silk floral arrangements. The expression represents her cost, in

dollars, for the arrangements when she buys v vases, f stems of flowers, b stems of wood bark, and m packages

of marbles for the bottom of the vases. Which statement is true?

A. The term 13v represents the cost of 13 vases.

B. The coefficient 6 represents the cost of b stems of wood bark.

C. The term 8f represents the cost of f stems of flowers at $8 per stem.

D. The coefficient 3 represents the number of packages of marbles she buys.

55. George is filling a swimming pool with volume V cubic units. He observed that at time the volume of the pool

filled is and that at time one-fourth of the pool was left to be filled. What does the expression

represent?

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A. the volume of the pool left to be filled

B.

the volume of the pool filled until time

C.

the volume of water filled in time


D.

the volume of water filled in time

56. The expression represents the cost, in dollars, to purchase n cases of paper, f packages

of hanging folders, p packs of pencils, and d flash drives. Which statement is NOT true?

A. The term 7p represents the cost for 7 packs of pencils.

B. The coefficient 10 represents the cost of each flash drive.

C. The coefficient n represents the cost of one case of paper.

D. The term 13f represents the cost of f packages of hanging folders at $13 per package.

57. A salesperson earns a weekly base salary plus a commission of 20% of all sales over the first $500. This

situation can be represented by the expression . Which of the following describes the

meaning of for this situation?

A. total amount of sales

B. total amount of salary earned

C. total amount of commission earned

D. total amount of sales after the first $500

58.

From the menu, select the option that BEST completes the sentence.


The formula is used to calculate the volume of the following three-dimensional object.

The in the formula stands for

.

59. A baker sells cookies for $1.50 each. If a minimum of two dozen cookies is ordered, the baker gives a 40%

discount for each cookie ordered after the minimum has been met. The cost of an order of cookies after this

discount is given by the expression below.

Which of the following parts of the expression represents the number of cookies to which the discount will be

applied?

A.

B.

C.

D.


60. A theater sells t tickets at a price of p dollars each. The theater conducts a survey and predicts that if the price of each

ticket is changed by $2, the number of tickets sold will change by 15 tickets. If n is the number of times the theater

changes the ticket price by $2, the expression can represent the theater’s total revenue, in dollars.

In this expression, what does represent?

/files/assess_files/076323f0-ffb3-4a79-83e9-d7046cfcdf35/formula_sheets/FL-



A. the number of tickets the theater will sell if the ticket price is increased by $2

B. the number of tickets the theater will sell if the ticket price is increased by $2n

C. the number of tickets the theater will sell if the ticket price is decreased by $15

D. the number of tickets the theater will sell if the ticket price is decreased by $15n

61. Coach Henderson ordered x certificates for the players of three sports teams at a high school.

• of the certificates ordered went to the basketball players

• 66 of the certificates ordered went to the volleyball players

• The remaining certificates ordered went to the football players

Which method could be used to determine the number of certificates Coach Henderson ordered for the

football players?

A.

B.

C.

D.


62. Kevin is saving money for a trip. He already has $150 and plans to save $48 each month. Which equation represents

the amount of money Kevin has saved after n months?

A. an = 198 + 48(n – 1)

B. an = 150 + 48(n – 1)

C. an = 198 + 48(n + 1)

D. an = 150 + 48(n + 1)

63. When Milo buys an order of copper, he pays $45 for the first pound and $42 for each additional pound. Which

of the following expressions represents the total cost, in dollars, of an order of p pounds of copper?

A. 45 + 42p

B. 45 + 42 (p – 1)

C. 45 + 42 (p + 1)

D. 87p

64. The value of a car and the time since its purchase is shown in the table below.

Years Since

Purchased (t)

Value of Car (V)

2 24,463

4 23,018

5 22,327


8 20,377

Which function

best

models the relationship between time and value of the car?

A. V(t) = 24,463(0.97)t

B. V(t) = 24,463 – 0.97t

C. V(t) = 26,000(0.97)t

D. V(t) = 26,000 – 0.97t

65. Which is the graph of 3x – 2y = 4?

A.


B.

C.


D.

66. Which is an equation of the function graphed below?

A. y = 2x2 – 4x – 4

B. y = 2x2 – 4x + 4

C. y = 2x2 + 4x – 4

D. y = 2x2 + 4x + 4


67. The costs of purchasing various numbers of notebooks are shown in the table.

Which graph BEST represents the information shown in the table?

A.


B.

C.

D.


68. Which is the graph of

A.

B.


C.

D.

69. A function, , is defined by the equation . Another function, , is graphed below.


Which statement describing both graphs of and is true?

A. The parabolas have the same vertices.

B. The parabolas open downward.

C. The parabolas have the same y-intercept.

D. The parabolas have the same maximum value.

70.

Exponential function g is defined as and exponential function h is graphed below.


Which statement about the graphs of the two functions is NOT true?

A.

B. Both functions are always decreasing.

C. Both functions have the same y-intercept.

D. The values of both functions are always positive.

71. Quadratic functions f and g are represented in two different ways as shown below.

x g(x)

–3 4

–2 –2

–1 –4

0 –2

1 4

2 14

3 28


Which statement about the graphs of the two functions is true?

A. They intersect at a total of two points.

B. The y-intercept of f is greater than the y-intercept of g.

C. They show that f is decreasing, and g is increasing between and

D. They show that f has a maximum value of 3, and g has a minimum value of –4.

72. A plumber charges a one-time fee for a service call plus a constant amount for each hour worked. The table

shows the total amount charged by the plumber for different numbers of hours of work.

Based on the data in the table, which statement is true?

A. The plumber charges $45 for each hour worked.

B. The plumber charges $68 for each hour worked.

C. The plumber charges $90 for each hour worked.

D. The plumber charges $115 for each hour worked.


73. Describe a real-world situation that could be modeled with the table below.

x y

2 100

3 125

6 200

8 250

74. Given the equation , what are the x-intercept and y-intercept of the graph?

A.

x-intercept = ; y-intercept =

B.


C.


D.


75. Which point is the x-intercept of the line represented by the equation

A.

B.

C.

D.


76. A 3-ounce serving of roasted chicken without the skin contains 140 calories. Based on this information, which

graph shows the relationship between the number of ounces of roasted chicken without the skin and the

number of calories in the chicken?

A.

B.


C.

D.

77. What BEST describes the domain

A.

B.

C.

D.


78. Which expression describes the domain of

A. x ≥ 1

B.

x ≥

C. x ≤ 1

D.

x ≤

79. The art club at a high school is selling baked goods to raise money to paint a mural in the gym. The function

f(x)=0.50x models the profit the club makes for selling x number of baked goods. If the club has 225 baked goods to

sell, what is the domain of the function?

A. 0 ≤ x ≤ 112.50

B. 0 ≤ x ≤ 225

C. x ≤ 225

D. x ≤ 0.50

80. What is the domain of the function

A.

B.

C.

D.


81. In which choice is ynot a function of x?

A. x2 = y + 7

B. y = 7

C.

x y

–5 6

–3

7

0 8

–3 –7

–5 –6

D.

x y

1 2

2 4

3 6

–2 4

–1 2

82. In which graph is y a function of x?

A.


B.

C.


D.

83. In which equation is ynot a function of x?


A.

y

=

2

x

2

−

5

B.

y

2

=

x

+

6

C.

−

4

x

+

y

=

−


3

D.

y

=

2

x

+

3

84. In which equation is y a function of x?

A. 3x2 + y = –4

B. 2x + y2 = 16

C. 4x2 + 4y2 = 36

D. 5x2 – y2 = 28

85. The function f(n)= 10(2)n predicts the population of coyotes in an area n years from 2010. What is the predicted

number of coyotes in the area in 2015?

A. 100

B. 270

C. 320

D. 440


86. Which function has the largest value for f(–3)?

A. f(x) = 2x – 5

B. f(x) = 2 – 4x

C. f(x) = 6 – 3x

D. f(x) = 2x + 10

87. A man’s shoe size is related to his foot length and can be modeled by the equation s = 1.7f – 7.2, where s is shoe size

and f is foot length, in inches. What is the shoe size of a man whose foot measures 9 inches?

A. 6

B. 8

C. 9

1

2

D. 10

1

2

88. Mr. Lanctot was renting an apartment for $800 per month. He was approved for a $76,200 loan to buy a

home. He will make monthly payments on the home loan for 30 years at a 4.8% annual interest rate,

compounded monthly. The formula shown below can be used to determine Mr. Lanctot’s monthly payment on

his home loan.


M = monthly payment, A = amount of the loan, r = monthly interest rate, and n = length of loan in months

Which statement correctly compares Mr. Lanctot’s monthly payment on the home loan and the amount he

pays on rent per month?

A.

The monthly payment on the home loan is about the amount he pays on rent per month.

B. The monthly payment on the home loan is about 5 times the amount he pays on rent per month.

C. The monthly payment on the home loan is about $400 more than the amount he pays on rent per month.

D. The monthly payment on the home loan is about $400 less than the amount he pays on rent per month.

89. The weight of a person on the moon, w, is one-sixth of the weight of the person on Earth. Weight on Earth is

the product of the mass, m, and the acceleration due to gravity,

Which of the following is the independent quantity?

A.

B. 9.8

C. m

D. w

90. The value of Jim’s car, after years can be modeled by the function


Part A. What do the values of 10,000 and 0.91 represent in terms of the context?

Part B. Can the value of ever be negative or 0? Explain why or why not.

Use words, numbers, and/or pictures to show your work.

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91. The function f(t) = 2,000(1.0012)4t models the balance of an investment account after t years. What does the 2,000 in

the function best represent?

A. the initial balance of the investment account

B. the initial cost of opening the investment account

C. the balance of the investment account after t years

D. the number of times the investment account is compounded per year

92. The equation is used to find the height of an object thrown upward from a height of

48 feet at an initial velocity of 32 feet per second. If Trevor sets h equal to 0 and solves the equation,

for t, the solution is 3. Which statement correctly interprets this solution?

A. 3 is the height of the object.

B. 3 is the distance the object has traveled.

C. 3 is the number of seconds until the object strikes the ground.


D. 3 is the number of seconds until the object reaches its maximum height.

93. Which is an equation of a line that is perpendicular to the graph of 9x – 3y = –10?

A. 3x – y = 10

B. 4x + 12y = 11

C. 5x – 15y = 6

D. 6x + 2y = 9

94. Which line passes through the point (6, 8) and is perpendicular to the line x + 3y = 9?

A. x + 3y = 30

B. x – 3y = –18

C. 3x + y = 26

D. 3x – y = 10

95. Which is an equation of a line that is perpendicular to line l graphed below?


A. 3x − 4y = –4

B. 3x + 4y = –36

C. 4x − 3y = 6

D. 4x + 3y = –21

96. Which line passes through the point (–4, 7) and is perpendicular to the line 3x + 4y = 12?

A. y

=

4

3

x


+

37

3

B. y

=

4

3

x

+

5

3

C. y

=

−

3

4

x

+

10

D. y

=

−

3

4


x

+

4

97. Which expression is equivalent to ?

A.

B.

C.

D.

98. A square has an area of 12 square inches. What is the length of a side of the square, in inches?

A.

B.

C. 6

D. 3

99.

If a, b, or c do not equal 0, which of the following is equivalent to

A.


B.

C.

D.

100. What value of n makes true?

A. 4

B. 8

C. 14

D. 32

review mid year math 1 name: wise and then cuts to form a...

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