Algebra I Midterm Review

Name: ______________________ Class: _________________ Date: _________ ID: A

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Algebra 1 Midterm Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1 Use the vertical-line test to determine which graph represents a function.

A C

B D

Name: ______________________ ID: A

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2 What is the graph of y + 2 = ! 23

x + 6( )?

F H

G J

Name: ______________________ ID: A

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3 Find the rate of change. What does rate of change mean in this situation?

A 60; 1 hour to move 60 miles.B 60; the speed is 60 miles per hour.C 30; 1 hour to move 15 miles.D 30; the speed is 30 miles per hour.

Name: ______________________ ID: A

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What is the graph of the equation?

4 !4x + y = !2F

H

G J

Name: ______________________ ID: A

5

5 3x ! y = 1A

C

B D

6 A plumber’s assistant charges a service fee of $40 plus $25 per hour for labor. Write a function rule for the total cost of hiring the assistant for a job that takes x hours. How much would it cost to hire him for a job that takes 4 hours?F y = 40 + 25x; $140 H y = 40x + 25; $185G y = 25x ! 40; $60 J y = 40x ! 25; $135

Name: ______________________ ID: A

6

What is the solution of each equation?

7 3 + 6z = 13 + 6z

A ! 56

C infinitely many solutions

B 2 23

D no solution

8 The formula for the area of a triangle is A = 12 bh. Solve the formula for h. What is the height h of a

triangle with area A = 40 square inches and base b = 20 inches?F h = A

2b, 1 inch H h = 2A

b, 4 inches

G h = 2Ab

, 2 inches J h = A ! 12 ! b, h = 19 1

2 inches

Which number is a solution of the inequality?

9 8 " 8kA 1 B 11 C 3 D 18

10 What are the solutions and graph of the compound inequality below?3n ! 1 > 8 or 4n + 3 < !1F 2 1

3 < n < 12

H n < 1 or n > 3

G n < !1 or n > 3 J n < 12 or n > 2 1

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11 If the data in the table are linear, what is the slope of the line that contains the data?

x !2 !1 0 1y 3 2 1 0

A 1

B ! 23

C –1

D ! 32

Name: ______________________ ID: A

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Write the equation in slope-intercept form. What are the slope and y-intercept?

12 !5x ! 8y = 1

F y = 58

x + 18

;

slope: 18

; y-intercept: 58

H y = ! 58

x ! 18

;

slope: ! 58

; y-intercept: ! 18

G y = 58

x ! 18

;

slope: 58

; y-intercept: ! 18

J y = ! 58

x + 18

slope: 58

; y-intercept: 18

13 !8x + 3y = !10

A y = 83

x + 103

;

slope: 103

; y-intercept: 83

C y = ! 83

x ! 103

;

slope: 83

; y-intercept: 103

B y = 83

x ! 103

;

slope: 83

; y-intercept: ! 103

D y = ! 83

x + 103

slope: 83

; y-intercept: 103

14 What are the names of the properties shown in steps 3 and 4?Step 1 10x ! 3 + 5x = 10x + !3( ) + 5xStep 2 = 10x + 5x + !3( )Step 3 = 10 + 5( )x + !3( )Step 4 = 15x + !3( )Step 5 = 15x ! 3

F Commutative Property of Addition and Distributive PropertyG Distributive Property and SubstitutionH Commutative Property of Addition and Associative Property of AdditionJ Substitution and Identity Property of Addition

What property is illustrated by each statement?

15 7 + (4 + 4) = (7 + 4) + 4A Inverse Property of AdditionB Associative Property of AdditionC Commutative Property of MultiplicationD Commutative Property of Addition

Name: ______________________ ID: A

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16 Use the Distributive Property to rewrite the following expression.–8(4 +5x)F –4 + 12xG –32 – 40xH 32 +40xJ –32 – 3x

What is the simplified form of each expression?

17 4 12 ! 6( ) 2 ÷ 3A 12 B 48 C 8 D 16

18 What is the solution of the proportion?3y ! 8

12 =y5

F !10 G !7 H 340

J 403

19 What is the value of x when !3x + 16 = !23?A –13 C 13B –6 D 6

20 What is the solution of the equation?12 = !2(!9 !3z)F !36 G !1 H 12 J 18

21 The distance traveled by a rock rolling down a hill is shown in the table below.Which equation best represents the relationship between x and y?

Time (x) Distance (y)1 32 63 94 12

A y = 2x + 2 C x = y ! 2B y = 3x D x = 3y

Name: ______________________ ID: A

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22 The scatter plot shows the trend for the number of cars a company rents during a two-week period. Which equation best models the data in the scatter plot?

F y = ! 25

x + 70 H y = 25

x + 70

G y = 52

x ! 70 J y = ! 52

x + 70

23 What is the solution of the equation?

!2 = 3 + z!2

A !2 B 1 C 4 D 7

What is the solution of the equation?

24 5 10x ! 10( ) = !5 !4x + 4( )F 1 G –1 H 0 J 2

25 A dress that normally costs $69.50 is on sale for 45% off. What is the sale price of the dress?A $38.23 C $24.50B $31.28 D $1.54

26 The circulation of a newsletter decreased from 5200 to 3140. Find the percent of decrease in circulation to the nearest percent.F 66% G 40% H 166% J 6%

Name: ______________________ ID: A

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27 What value of x makes the equation below true?

110

x ! 5 = 65

A –650 C 700B 600 D 750

28 A sound studio charges a $100 reservation fee and $52 per hour. Felipe paid a total of $360 to use the sound studio. Write an equation that can be used to find the total number of hours (h) during which Felipe used the studio.F 52 + 100h = 360G 100 + 52h = 360H 100(52+ h) = 360J 52(h + 100) = 360

29 Ed is saving his money in a savings account. She started the account with $150. Each week he will deposit $50. In how many weeks will he have saved $400? A 5 C 20B 10 D 25

30 During Ivan’s last vacation, he used 10 gallons of gas to travel 220 miles. Which proportion can he use to predict the number of gallons g he will use to travel 1,000 miles? To the nearest tenth, what is g?

Fg

10 = 2201000 ; 22.0 gallons H 220

10 = 1000g

; 78.0 gallons

G 22010 = 1000

g; 45.5 gallons J

g10 = 220

1000 ; 45.5 gallons

31 This table represents how a group of elementary students in a school in Boston get to school.

Transportation Mode Number of Elementary Students

bus 28subway 20

car 16foot 11

Approximately what precent of the respondents take the subway to school?A 25% C 52%B 45% D 33%

Name: ______________________ ID: A

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32 This table represents how a group of elementary students in a school in Boston get to school.

Transportation Mode Number of Elementary Students

bus 28subway 20

car 16foot 11

Of 5,000 elementary students in Boston, what is the best estimate of the number of students who will ride the bus to school?F 1150 H 1750G 1600 J 1850

What is the graph of the inequality?

33 h > 72

A

B

C

D

34 Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.

Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed to meet or surpass your goal?

F 135 + 89 + c > 325; c > 101 H 135 + 89 + c " 325; c " 101G 135 + 89 + 325 " c; c " 549 J 135 + 89 + c " 325; c # 549

Name: ______________________ ID: A

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What compound inequality represents the phrase? Graph the solutions.

35 all real numbers that are greater than –8 and less than 8

A –8 < x < 8

B –8 < x < 8

C –8 < x # 8

D –8 # x # 8

36 What are the solutions and graph of the inequality?!12 # 2x ! 4 < 8F x # !4 or x > 6

G !4 # x < 6

H !2 # x < 8

J !8 # x < 2

Let X = {x | x is a whole number less than 15}, Y = { y | y is a multiple of 3}, Z = {z | z is a real number greater than or equal to 5.5}.

37 What is X$Z?A {6,7,8,9,10,11,12,13,14}B {6,9,12,15}C {5,6,7,8,9,10,11,12,13,14,15}D %

Name: ______________________ ID: A

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38 A doctor is examining 3 patients. Which symptoms do all three patients have in common?

F {headaches, hair loss, congestion} H {spasms, memory loss, appetite loss}G {cold sweats, congestion, memory loss} J {fever, joint pain, tiredness}

39 Identify whether the relation between the domain (time) and range (height) is or is NOT a function.

a. b.

A a is a function, b is not a functionB a is not a function, b is a functionC both a and b are functionsD neither a or b are functions

Name: ______________________ ID: A

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40 As a homework assignment, Amy has done a study on the number of hours spent on homework a week and the average grade in a particular math class. She found the relationship to be G = 70 + 3h, where G represents the grade earned and h represents the number of hours spent on homework. If a student spends 6 hours doing math homework each week, what grade can that student expect?F 90 H 86G 88 J 82

41 What is the domain and the range of the function represented by the list of ordered pairs?(!2, 5), (0, 4), (3, 6), (5, 1)ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ

A The domain is 1,4,5,6ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ and the range

is !2, 0, 3, 5ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ

C The domain is !2, 0, 1, 3ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ and the

range is !2,0,1,6ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ

B The domain is !2,0,3,6ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ and the

range is !2, 0, 2, 6ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ

D The domain is !2,0,3,5ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ and the

range is 1, 4, 5, 6ÏÌÓÔÔÔÔ

¸˝̨ÔÔÔÔ

42 What is the range of f(x) = 43

x + 4 for the domain {!1, 3, 7, 9}?

F 83

, 10, 403

, 16ÏÌÓ

ÔÔÔÔÔÔÔ

¸˝˛

ÔÔÔÔÔÔÔ

H 83

, 8, 403

, 16ÏÌÓ

ÔÔÔÔÔÔÔ

¸˝˛

ÔÔÔÔÔÔÔ

G 83

, 7, 403

, 15ÏÌÓ

ÔÔÔÔÔÔÔ

¸˝˛

ÔÔÔÔÔÔÔ

J 83

, 8, 403

ÏÌÓ

ÔÔÔÔÔÔÔ

¸˝˛

ÔÔÔÔÔÔÔ

43 This graph shows the height and distance traveled by a tennis ball.

What is the maximum height of the tennis ball?A 0 feet B about 4.5 feet C about 5.5 feet D about 9 feet

Name: ______________________ ID: A

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44 Use integer coefficients. What is the standard form of the equation below?

(y ! 3) = 23

(x + 6)

F 2x + 3y = 7 H 2x – 3y = –9G 3x – 2y = –21 J 2x – 3y = –21

45 Find the domain and range of the relation and determine whether it is a function.

1A domain: positive integers; range: positive integers; No, it is not a function.B domain: x > –1; range: y > 0; Yes, it is a function.C domain: all real numbers; range: all real numbers; Yes, it is a function.D domain: x " 0; range: y > –1; No, it is not a function.

Name: ______________________ ID: A

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46 Terry pays $210 in advance into her health savings account. She used the account 1 time , and $10 was deducted from the account. After using it 4 times, $40 was deducted from the account. Which graph would you use to represent this situation?F B = 210 ! 2n H B = 210 + 10n

G B = 200 + 10n J B = 40 + 10n

47 Suppose you have two distinct lines. One has slope m , one contains points A and B. Are the lines parallel, perpendicular, or neither? If neither, what is the correct explanation?

m = 12

; A = (0, 0), B = (1, ! 2)

A parallelB perpendicularC Neither; the slopes are NOT equal, and the product of the slopes does NOT equal 1.D Neither; the slopes are equal, and the product of the slopes does NOT equal –1.

Name: ______________________ ID: A

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48 What is the equation for the line that is parallel to the given line and that passes through the given point?y = !3x + 6; (0, 1)F y = 3x + 1 H y = !3x + 1G y = !3x ! 1 J y = !3x + 3

49 What is the equation of a line that is perpendicular to the given line and that passes through the given point?

y = 13

x + 53

; (2, 1)

A y = 3x + 7 C y = !3x + 7

B y = 3x + 53

D y = !3x + 53

50 The table shows the height of a slowly descending air balloon over time. Let y stand for the height of the balloon in feet and let x stand for the time in minutes. Which equation best models the data?

Time (minutes)

Height(feet)

10 234

20 218

40 186

60 154

F y = 250x ! 1.6 H y = !1.6x + 250G y = !1.6x + 234 J y = 10x + 234

ID: A

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Algebra 1 Midterm ReviewAnswer Section

MULTIPLE CHOICE

1 ANS: A STA: MA.912.A.2.3 2 ANS: G STA: MA.912.A.3.8 3 ANS: D STA: MA.912.A.3.11 4 ANS: G STA: MA.912.A.3.8 5 ANS: B STA: MA.912.A.3.8 6 ANS: F STA: MA.912.A.2.13 7 ANS: D STA: MA.912.A.3.1| MA.912.A.3.2 8 ANS: H STA: MA.912.A.3.3 9 ANS: A STA: MA.912.A.3.4 10 ANS: G STA: MA.912.A.3.4 11 ANS: C STA: MA.912.A.3.11 12 ANS: H STA: MA.912.A.3.10 13 ANS: B STA: MA.912.A.3.10 14 ANS: G STA: MA.912.A.3.2 15 ANS: B STA: MA.912.A.3.2 16 ANS: G STA: MA.912.A.3.2 17 ANS: B STA: MA.912.A.3.2 18 ANS: J STA: MA.912.A.5.4 19 ANS: C STA: MA.912.A.3.1 20 ANS: G STA: MA.912.A.3.1 21 ANS: B STA: MA.912.A.10.1 22 ANS: J STA: MA.912.A.3.11 23 ANS: B STA: MA.912.A.3.1 24 ANS: F STA: MA.912.A.3.1| MA.912.A.3.2 25 ANS: A STA: MA.912.A.1.1 26 ANS: G STA: MA.912.A.1.1 27 ANS: C STA: MA.912.A.3.1 28 ANS: G STA: MA.912.A.3.1 29 ANS: D STA: MA.912.A.3.1 30 ANS: G STA: MA.912.A.5.4 31 ANS: D STA: MA.912.A.10.1 32 ANS: J STA: MA.912.A.10.1 33 ANS: A STA: MA.912.A.3.4 34 ANS: H STA: MA.912.A.3.4 35 ANS: A STA: MA.912.A.3.4 36 ANS: G STA: MA.912.A.3.4 37 ANS: A STA: MA.912.D.7.1| MA.912.D.7.2

ID: A

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38 ANS: J STA: MA.912.D.7.1| MA.912.D.7.2 39 ANS: B STA: MA.912.A.2.3 40 ANS: G STA: MA.912.A.2.13 41 ANS: D STA: MA.912.A.2.4 42 ANS: H STA: MA.912.A.2.4 43 ANS: B STA: MA.912.A.2.13 44 ANS: J STA: MA.912.A.3.7 45 ANS: B STA: MA.912.A.2.3| MA.912.A.2.4 46 ANS: F STA: MA.912.A.3.8 47 ANS: B STA: MA.912.G.1.4 48 ANS: H STA: MA.912.A.3.10 49 ANS: C STA: MA.912.A.3.10 50 ANS: H STA: MA.912.A.3.11