algebra i released items 2002. equations and inequalities

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

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

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

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

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

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.

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

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

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

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

1 2 3 4 5

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A. AB. BC. CD. D

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

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

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

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)

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

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

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

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

Expressions and Operations

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

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)

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

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

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

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

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

Consider the following models

What polynomial is represented by this diagram?

1 2 3 4 5

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

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

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

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)

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.

Relations and Functions

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

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

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

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}

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}

Which graph appears to contain all the

points in the table?

1 2 3 4 5

25% 25%25%25%

A. B.

C. D.

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

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)}

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

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.

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

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}

Statistics

4[B] =?

1 2 3 4 5

25% 25%25%25%

A. B.

C. D.

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.

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.

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

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