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Algebra I Released Items 2002. Equations and Inequalities.

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Algebra I Released Items 2002
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Page 1: Algebra I Released Items 2002. Equations and Inequalities.

Algebra I Released Items

2002

Page 2: Algebra I Released Items 2002. Equations and Inequalities.

Equations and Inequalities

Page 3: Algebra I Released Items 2002. Equations and Inequalities.

Which property justifies the following

statement?If 3a + 3b = 12 then 3(a + b) = 12

1 2 3 4 5

25% 25%25%25%A. Commutative property of multiplication

B. Distributive property for multiplication over addition

C. Multiplicative identity property

D. Associative property of addition

Page 4: Algebra I Released Items 2002. Equations and Inequalities.

A rectangular planter can hold 2,304 cubic inches of soil. The dimensions of

the base of the planter are 24 inches by 12 inches. What is the height of the

planter?

1 2 3 4 5

25% 25%25%25%

A. 4 inchesB. 8 inchesC. 16 inchesD. 192 inches

Page 5: Algebra I Released Items 2002. Equations and Inequalities.

The graph of y = -¾x + 1 is shown. If the line in the graph is shifted up 2 units, which is the equation of the new line?

1 2 3 4 5

25% 25%25%25%

A. y = ¾x + 3B. y = ¾x + 2C. y = -¾x + 2D. y = -¾x + 3

Page 6: Algebra I Released Items 2002. Equations and Inequalities.

What is the solution to 12 – 1/9d = 17?

1 2 3 4 5 d

= -2

43

d =

-45

d =

-3

d =

-5/9

25% 25%25%25%A. d = -243B. d = -45C. d = -3D. d = -5/9

Page 7: Algebra I Released Items 2002. Equations and Inequalities.

Which statement is always true?

1 2 3 4 5

4 +

a =

4 ·

a

a +

(-4

+ 4)

= a

+ 0

a ÷

4 =

4 ÷

a

4 -

a = a

- 4

25% 25%25%25%

A. 4 + a = 4 · aB. a + (-4 + 4) = a +

0C. a ÷ 4 = 4 ÷ aD. 4 - a = a - 4

Page 8: Algebra I Released Items 2002. Equations and Inequalities.

Which is the graph of a line that appears to have a slope of 3 and y-

intercept -2?

1 2 3 4 5

25% 25%25%25%

A. B.

C. D.

Page 9: Algebra I Released Items 2002. Equations and Inequalities.

What is the slope of the line that

contains points (2, 3) and (2, -4)?

1 2 3 4 5 U

ndefin

ed 0 -¼ -4

25% 25%25%25%A. UndefinedB. 0C. -¼D. -4

Page 10: Algebra I Released Items 2002. Equations and Inequalities.

Which best represents the equation of the line shown?

1 2 3 4 5

25% 25%25%25%

A. y = 2x + 1B. y = 2x - 1C. y = -2x + 1D. y = -2x - 1

Page 11: Algebra I Released Items 2002. Equations and Inequalities.

What is the slope of the line represented by the equation -2y =

x - 1?

1 2 3 4 5-2 -½ ½ 2

25% 25%25%25%A. -2B. -½C. ½D. 2

Page 12: Algebra I Released Items 2002. Equations and Inequalities.

Which line on the grid appears to have slope 2/3?

1 2 3 4 5

25% 25%25%25%

A. AB. BC. CD. D

Page 13: Algebra I Released Items 2002. Equations and Inequalities.

An equation for the line shown could be —

1 2 3 4 5

25% 25%25%25%

A. y = xB. y = -xC. y = x - 1D. y = x + 1

Page 14: Algebra I Released Items 2002. Equations and Inequalities.

What is the solution to this system of

equations?

1 2 3 4 5

25% 25%25%25%

A. x = 2, y = 2B. x = 2, y = 3C. x = 2, y = 1D. x = 6, y = -2

Page 15: Algebra I Released Items 2002. Equations and Inequalities.

Kristy is making a rectangular quilt that is 2 feet longer than it is wide. If the perimeter of the quilt is to be 32

feet, what will be its dimensions?

1 2 3 4 5

25% 25%25%25%A. 4 ft by 8 ftB. 5 ft by 7 ftC. 7 ft by 9 ftD. 15 ft by 17 ft

Page 16: Algebra I Released Items 2002. Equations and Inequalities.

Which is most likely the solution to the

system of equations shown in the graph?

1 2 3 4 5

25% 25%25%25%

A. (4, 3)B. (-2, 0)C. (3, 4)D. (1, 0)

Page 17: Algebra I Released Items 2002. Equations and Inequalities.

Which is an equation for the line that

contains the points (-3, 5) and (1, -3)?

1 2 3 4 5

y =

-x +

2

y =

-2x

- 1

y =

-1/2

x –

3/2

y =

3/2

x –

9/2

25% 25%25%25%A. y = -x + 2B. y = -2x - 1C. y = -1/2x – 3/2D. y = 3/2x – 9/2

Page 18: Algebra I Released Items 2002. Equations and Inequalities.

Which is a solution to (2x + 3)2 = 25?

1 2 3 4 5-4 -2 -1 2

25% 25%25%25%A. -4B. -2C. -1D. 2

Page 19: Algebra I Released Items 2002. Equations and Inequalities.

The dimensions of a rectangle are shown in the drawing below. If the area is 28 square units, what is the

value of d?

1 2 3 4 5

25% 25%25%25%A. 2 unitsB. 7 unitsC. 12 unitsD. 14 units

Page 20: Algebra I Released Items 2002. Equations and Inequalities.

What is the solution to 2x + 3 > x - 5?

1 2 3 4 5 x

> -8

/3

x >

-8

x >

-2/3

x >

-2

25% 25%25%25%A. x > -8/3B. x > -8C. x > -2/3D. x > -2

Page 21: Algebra I Released Items 2002. Equations and Inequalities.

Expressions and Operations

Page 22: Algebra I Released Items 2002. Equations and Inequalities.

What is the value of a(b - c) if a = 2, b = -3 and c = -2?

1 2 3 4 5

25% 25%25%25%

A. 2B. -2C. -4D. -10

Page 23: Algebra I Released Items 2002. Equations and Inequalities.

Each week Jessica earns a 2% bonus on any sales she makes over $600. She also receives a

fixed salary of $190 per week. If Jessica sold $1,300 worth of merchandise in a week, which equation could be used to determine her total

earnings, t, for the week?

1 2 3 4 5

t =

(0.0

2)[1

...

t =

190

+ (.

..

t =

(190

+ ..

.

t =

190

+ (.

..

25% 25%25%25%A. t = (0.02)[1.90 + (1,300 - 600)]

B. t = 190 + (0.02)(600)C. t = (190 + 600)(0.02)D. t = 190 + (0.02)(1,300 -

600)

Page 24: Algebra I Released Items 2002. Equations and Inequalities.

Which expression correctly describes x

divided by the sum of y and 7?

1 2 3 4 5

x ÷

y +

7

_ x

__ y

+ 7

x/y

+ 7

y +

7

x

25% 25%25%25%A. x ÷ y + 7B. _ x__

y + 7C. x/y + 7D. y + 7

x

Page 25: Algebra I Released Items 2002. Equations and Inequalities.

Which is equivalent to (2x2)3 ?

1 2 3 4 5 8

x6 6

x6 8

x5 6

x5

25% 25%25%25%A. 8x6

B. 6x6

C. 8x5

D. 6x5

Page 26: Algebra I Released Items 2002. Equations and Inequalities.

The diameter of a barium atom is0.0000004346 millimeters. In

scientificnotation it is —

1 2 3 4 5

25% 25%25%25%A. 43.46 x 108 mmB. 4.346 x 107 mmC. 4.346 x 107 mmD. 4346.0 x 107

mm

Page 27: Algebra I Released Items 2002. Equations and Inequalities.

The length of a rectangular classroom floor is 19 feet less than twice the width. Which expression represents the area of

the classroom floor?

1 2 3 4 5

25% 25%25%25%

A. 3w - 19B. 6w - 38C. 2w2 - 19wD. 2w2 - 19

Page 28: Algebra I Released Items 2002. Equations and Inequalities.

Which is closest to the value of x if

x = 3√11 + 4√11?

1 2 3 4 513

.623

.2 77 132

25% 25%25%25%A. 13.6B. 23.2C. 77D. 132

Page 29: Algebra I Released Items 2002. Equations and Inequalities.

Consider the following models

What polynomial is represented by this diagram?

1 2 3 4 5

25% 25%25%25%

A. 4x2 - 10x - 6B. 4x2 - 2x - 6C. 4x2 + 2x - 6D. 4x2 + 10x + 6

Page 30: Algebra I Released Items 2002. Equations and Inequalities.

Enter question text...

1 2 3 4 5

4 -

x5y2

+ 7

x10y

3

4xy

- x5

y2 +

7x1

0y3

4 -

x5y3

+ 7

x10y

4

4xy

- x2

y3 +

7x3

y4

25% 25%25%25%

A. 4 - x5y2 + 7x10y3

B. 4xy - x5y2 + 7x10y3

C. 4 - x5y3 + 7x10y4

D. 4xy - x2y3 + 7x3y4

Page 31: Algebra I Released Items 2002. Equations and Inequalities.

If the area of a rectangle can berepresented by x2 - 25, which

couldrepresent its length and width?

1 2 3 4 5

25% 25%25%25%A. x - 5, x - 5B. x - 5, x + 5C. x2, -25D. 5, 5

Page 32: Algebra I Released Items 2002. Equations and Inequalities.

Which is the complete factorization of 2x2 + 5x + 3?

1 2 3 4 5 (2

x +

1)(x

+ 2

)

(2x

+ 1)

(x +

3)

(2x

+ 2)

(x +

1)

(2x

+ 3)

(x +

1)

25% 25%25%25%A. (2x + 1)(x + 2)B. (2x + 1)(x + 3)C. (2x + 2)(x + 1)D. (2x + 3)(x + 1)

Page 33: Algebra I Released Items 2002. Equations and Inequalities.

The height of an equilateral triangle can be determined by evaluating the

expression where n is the length of a side of the triangle. To the nearest tenth of an inch,

what is the height of an equilateral triangle with sides of 6.5 inches?

1 2 3 4 5

3.5

in.

4.8

in.

5.6

in.

10.

4 in

.

25% 25%25%25%

A. 3.5 in.B. 4.8 in.C. 5.6 in.D. 10.4 in.

Page 34: Algebra I Released Items 2002. Equations and Inequalities.

Relations and Functions

Page 35: Algebra I Released Items 2002. Equations and Inequalities.

Which equation best describes this graph?

1 2 3 4 5

25% 25%25%25%

A. y = 20 - 4xB. y = x + 14 - x2

C. y = 16 - 2xD. y = x2 - 5x + 18

Page 36: Algebra I Released Items 2002. Equations and Inequalities.

Which equation is satisfied by all the

points in the table?

1 2 3 4 5

25% 25%25%25%A. x - 4y = 10B. 4y - x = 10C. 7y - x = 20D. x - 7y = 20

Page 37: Algebra I Released Items 2002. Equations and Inequalities.

The ordered pairs in the table follow a

quadratic pattern. What is the value of x?

1 2 3 4 5

25% 25%25%25%A. 10B. 6C. 5D. 3

Page 38: Algebra I Released Items 2002. Equations and Inequalities.

What is the domain of the function shown?

1 2 3 4 5

25% 25%25%25%

A. {All real numbers greater than zero}

B. {All real numbers}C. {All real numbers less than -2}D. {All real numbers greater than -

2}

Page 39: Algebra I Released Items 2002. Equations and Inequalities.

What is the apparent range of therelation shown on the grid?

1 2 3 4 5

25% 25%25%25%

A. {-2, 1, 3}B. {-2, 1, 2, 4}C. {1, 2, 3, 4}D. {-2, 2, 3, 4}

Page 40: Algebra I Released Items 2002. Equations and Inequalities.

Which graph appears to contain all the

points in the table?

1 2 3 4 5

25% 25%25%25%

A. B.

C. D.

Page 41: Algebra I Released Items 2002. Equations and Inequalities.

If a varies directly as b and a = 3 when

b = 12, what is the value of a whenb = 18?

1 2 3 4 5

25% 25%25%25%A. 0.25B. 4C. 4.5D. 72

Page 42: Algebra I Released Items 2002. Equations and Inequalities.

Which set of ordered pairs is not a

function?

1 2 3 4 5 {(

-2, 3

), (4

, 1),

(2, 1

), (1

, 5)}

{(1,

4),

(2, 3

), (3

, 2),

(4, 3

)}

{(2,

3),

(3, 2

), (4

, 4),

(5, 2

)}

{(-2

, 3),

(1, 4

), (2

, 3),

(1, 5

)}

25% 25%25%25%

A. {(-2, 3), (4, 1), (2, 1), (1, 5)}

B. {(1, 4), (2, 3), (3, 2), (4, 3)}C. {(2, 3), (3, 2), (4, 4), (5, 2)}D. {(-2, 3), (1, 4), (2, 3), (1,

5)}

Page 43: Algebra I Released Items 2002. Equations and Inequalities.

The stress distribution on a structure is given by s = 2x2 + 4x - 30 where s is

stress in pounds per square inch and x is the distance in feet from a reference

point. At what distance is the stress equal to 0?

1 2 3 4 5

25% 25%25%25%A. 3 ftB. 5 ftC. 6 ftD. 12 ft

Page 44: Algebra I Released Items 2002. Equations and Inequalities.

In which table of ordered pairs does

n vary directly as m?

1 2 3 4 5

25% 25%25%25%

A. B.

C. D.

Page 45: Algebra I Released Items 2002. Equations and Inequalities.

Which is a zero of the functionƒ(x) = 3x - 21?

1 2 3 4 5-2

1 -7 0 7

25% 25%25%25%A. -21B. -7C. 0D. 7

Page 46: Algebra I Released Items 2002. Equations and Inequalities.

A lumber yard sells square scraps of plywood with sides varying from 1 foot to 4 feet. Ed wants

to use some of these pieces to build storage cubes. The relationship between the length of

the side of a cube and the volume of the cube is expressed by the function

ƒ(x) = x3

where x is the length of a side of the cube. What is the range of this function in cubic feet for the

domain given?

1 2 3 4 5

25% 25%25%25%

A. Range varies from 1 to 64B. Range varies from 1 to 16C. {1, 64}D. {1, 16}

Page 47: Algebra I Released Items 2002. Equations and Inequalities.

Statistics

Page 48: Algebra I Released Items 2002. Equations and Inequalities.

4[B] =?

1 2 3 4 5

25% 25%25%25%

A. B.

C. D.

Page 49: Algebra I Released Items 2002. Equations and Inequalities.

Alberto made the box-and-whisker graph of the heights (in inches) of the members of his basketball team. What is the range

of heights of the team members?

1 2 3 4 5

25% 25%25%25%

A. 16 in.B. 9 in.C. 4 in.D. 2 in.

Page 50: Algebra I Released Items 2002. Equations and Inequalities.

Carol went on a 5-day bicycle trip. She rode 23 miles the first day, 22 miles the second, 21 miles the third, 17 miles the fourth, and 17 miles the fifth day. What was the mean number of miles per day

that Carol rode on her 5-day bicycle trip?

1 2 3 4 5 6

mi.

20

mi.

21

mi.

23

mi.

25% 25%25%25%

A. 6 mi.B. 20 mi.C. 21 mi.D. 23 mi.

Page 51: Algebra I Released Items 2002. Equations and Inequalities.

Based on the scatter plot, which x value would best match y = 12?

1 2 3 4 5

25% 25%25%25%

A. 3B. 4C. 48D. 56

Page 52: Algebra I Released Items 2002. Equations and Inequalities.

Which equation best represents the

data shown on the scatterplot?

1 2 3 4 5

25% 25%25%25%

A. y = -3/5x – 2B. y = x/2 + 2C. y = -3/5xD. y = 3/5x + 10/3


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