6th Grade Math Diagnostic Quiz

6th Grade Math Test

1 / 14

Find the value of the expression.

24 3⁄5 + 4³ × (8 1⁄5 −2)

423 2⁄5

422 2⁄5

421 2⁄5

420 2⁄5

2 / 14

Michelle makes jewelry boxes containing drawers of equal size. The number of drawers in three different jewelry boxes and the corresponding total volumes of the drawers are shown in the table below.

Write an equation for the relationship between the number of drawers in the jewelry box, d, and the total volume of the drawers in the jewelry box, V. Use your equation to determine the number of drawers in a jewelry box with a total volume of 17.5 cubic inches.

6 drawers

7 drawers

10 drawers

5 drawers

3 / 14

To convert a temperature from degrees Celsius to degrees Fahrenheit, the temperature in degrees Celsius is multiplied by 1.8, and then 32 is added to the product. Write an expression that can be used to convert a temperature from degrees Celsius, C, to degrees Fahrenheit, and then use that expression to convert 25 degrees Celsius to degrees Fahrenheit.

77 degree Fahrenheit.

78 degree Fahrenheit.

67 degree Fahrenheit.

79 degree Fahrenheit.

4 / 14

Which expression is equivalent to the expression below?

g + g + g + g + g + g

A

B

C

D

5 / 14

Which equation has the solution x = 2 ?

2x - 3 = 19

3x + 2 = 8

4x - 4 = −4

5x + 1 = 10

6 / 14

Which two expressions are equivalent for any value of y?

3(3y + 3) and 6y + 6

3(3y + 3) and 9y + 6

9(y + 3) and 12 + 9y

9(y + 3) and 27 + 9y

7 / 14

Kelly saves $5 every week. Which expression represents the amount of money, in dollars, Kelly will save in w weeks?

5 + w

5 − w

5w

5⁄w

8 / 14

Solve the equation below.

0.3r = 2.1

r = 0.7

r = 1.8

r = 7

r = 1.8

9 / 14

What is the solution of the equation below?

x + 8. 63 = 11.001

x = 19.631

x = 10.138

x = 3. 471

x = 2 .371

10 / 14

A museum has an aquarium in the shape of a right rectangular prism that is 22.9 meters long, 7.5 meters wide, and 4.6 meters high. What is the volume, rounded to the nearest cubic meter, of the aquarium?

280

623

790

1288

11 / 14

Erica drew the parallelogram below.

Which expression can Erica use to find the area of the parallelogram?

5 1⁄4 × 4 1⁄5

1⁄2(5 1⁄4 × 4 1⁄5)

2(5 1⁄4 + 4 1⁄2)

5 1⁄4 + 4 1⁄2

12 / 14

The trapezoid shown below has an area of 21.66 square inches

What is the total area of the shaded sections of the trapezoid?

2.09 square inches

4.18 square inches

4.86 square inches

8.74 square inches

13 / 14

The right rectangular prism shown below is made of equal-sized cubes. The side length of each cube is 2 1⁄2 inches.

What is the volume, in cubic inches, of the right rectangular prism?

50

100

250

625

14 / 14

The points plotted on the coordinate grid below show different locations in a city. The grid lines represent the city’s streets.

The city plans to build a parking lot at the location represented by the coordinates(8,4). Which building is the shortest driving distance from the parking lot?

theater

library

museum

post office

Your score is

Find the value of the expression.

24 3⁄5 + 4³ × (8 1⁄5 −2)

Michelle makes jewelry boxes containing drawers of equal size. The number of drawers in three different jewelry boxes and the corresponding total volumes of the drawers are shown in the table below.

Write an equation for the relationship between the number of drawers in the jewelry box, d, and the total volume of the drawers in the jewelry box, V. Use your equation to determine the number of drawers in a jewelry box with a total volume of 17.5 cubic inches.

The expression to convert a temperature from degrees Celsius (C) to degrees Fahrenheit (F) is F = (C × 1.8) + 32

Now, to convert 25 degrees Celsius to Fahrenheit: F = (25 × 1.8) + 32 F = 45 + 32 F = 77

Therefore the correct answer is A. 77 degrees Fahrenheit.

Which expression is equivalent to the expression below?

g + g + g + g + g + g

The expression g + g + g + g + g + g is equivalent to:

Explanation: The expression represents adding the variable g six times, which is the same as multiplying g by 6. Therefore, g + g + g + g + g + g is equivalent to 6g

Therefore, the correct answer is C. 6g

Which equation has the solution x = 2 ?

To find which equation has the solution x = 2,, substitute x = 2 into each equation and see which one is satisfied:

A. 2(2) − 3 = 4 − 3 = 1 ≠ 19 B. 3(2) + 2 = 6 + 2 = 8 C. 4(2) −4 = 8 − 4 = 4 ≠ −4 D. 5(2) + 1 = 10 + 1 = 11 ≠ 10

So, the equation 3x + 2 = 8 is the one that has the solution x = 2.

Therefore, the correct answer is B. 3x + 2 = 8

Which two expressions are equivalent for any value of y?

Kelly saves $5 every week. Which expression represents the amount of money, in dollars, Kelly will save in w weeks?

Explanation: Kelly saves $5 every week, so the total amount of money she saves after w weeks is the product of $5 and the number of weeks (w). Therefore, 5w represents the total savings in dollars after w weeks.

Solve the equation below.

0.3r = 2.1

To solve the equation 0.3r = 2.1 we can isolate the variable r by dividing both sides of the equation by 0.3:

0.3r/0.3 = 2.1/0.3

This simplifies to: r = 2.1/0.3

Now, perform the division: r = 7

Therefore, the correct answer is C. r = 7

This means that when r is equal to 7, the equation 0.3r = 2.1 is true.

What is the solution of the equation below?

x + 8. 63 = 11.001

To find the solution to the equation x + 8.63 = 11.001, we need to isolate the variable x.

Subtract 8.63 from both sides of the equation:

x + 8.63 − 8.63 = 11.001 − 8.63

x = 2.371

Therefore, the correct answer is D. x = 2.371

This means that when x is equal to 2.371, the equation x + 8.63 = 11.001 is true.

A museum has an aquarium in the shape of a right rectangular prism that is 22.9 meters long, 7.5 meters wide, and 4.6 meters high. What is the volume, rounded to the nearest cubic meter, of the aquarium?

To find the volume of the rectangular prism (aquarium), you can use the formula:

Volume = Length × Width × Height

Given:

Length = 22.9 meters Width = 7.5 meters Height = 4.6 meters

Now, substitute these values into the formula:

Volume = 22.9 × 7.5 × 4.6 Volume ≈ 790.35 cubic meters

Rounded to the nearest cubic meter, the volume of the aquarium is: Volume≈790 cubic meters

Therefore, the correct answer is C. 790

This means the volume of the aquarium is approximately 790 cubic meters.

Erica drew the parallelogram below.

Which expression can Erica use to find the area of the parallelogram?

The trapezoid shown below has an area of 21.66 square inches

What is the total area of the shaded sections of the trapezoid?

The right rectangular prism shown below is made of equal-sized cubes. The side length of each cube is 2 1⁄2 inches.

What is the volume, in cubic inches, of the right rectangular prism?

The points plotted on the coordinate grid below show different locations in a city. The grid lines represent the city’s streets.

The city plans to build a parking lot at the location represented by the coordinates(8,4). Which building is the shortest driving distance from the parking lot?

The expression to convert a temperature from degrees Celsius (C) to degrees Fahrenheit (F) is
F = (C × 1.8) + 32

Now, to convert 25 degrees Celsius to Fahrenheit:
F = (25 × 1.8) + 32
F = 45 + 32
F = 77

The expression $g + g + g + g + g + g$ is equivalent to:

Explanation: The expression represents adding the variable $g$ six times, which is the same as multiplying $g$ by 6. Therefore, $g + g + g + g + g + g$ is equivalent to 6g

To find which equation has the solution $x = 2$ ,, substitute x = 2 into each equation and see which one is satisfied:

A.

So, the equation $3 x + 2 = 8$ is the one that has the solution $x = 2$ .

Explanation: Kelly saves $5 every week, so the total amount of money she saves after $w$ weeks is the product of $5 and the number of weeks ( $w$ ). Therefore, $5 w$ represents the total savings in dollars after $w$ weeks.

To solve the equation $0.3 r = 2.1$ we can isolate the variable $r$ by dividing both sides of the equation by 0.3:

This simplifies to:
r = 2.1/0.3

Now, perform the division:
r = 7

Therefore, the correct answer is $C. r = 7$

This means that when $r$ is equal to 7, the equation

To find the solution to the equation x , we need to isolate the variable $x$ .

This means that when $x$ is equal to 2.371, the equation x is true.

$Height = 4.6 meters$

Volume = 22.9 × 7.5 × 4.6
Volume ≈ 790.35 cubic meters

Rounded to the nearest cubic meter, the volume of the aquarium is:
Volume≈790 cubic meters