7th Grade Review

Select all of the following that are proportional relationships.

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If Rectangle ABCD has a width of 4 feet and a length of 5 feet, what must be the length and width of the scaled copy Rectangle WXYZ ? 

• Width: 12 ft, Length: 15 ft

• Width: 6 ft, Length: 9 ft

• Width: 8 ft, Length: 10 ft

Answer explanation

To find the scaled dimensions of Rectangle WXYZ, we can use a scale factor. The original dimensions are 4 ft (width) and 5 ft (length). Scaling by a factor of 3 gives us 12 ft (width) and 15 ft (length), which matches the correct choice.

The figure shows two intersecting lines and measures of the resulting angles. Find the value of x. 

• 58

• 90

• 60

• 30

Answer explanation

The angles formed by intersecting lines are supplementary. If one angle is 90 degrees, the other must be 90 - x. Setting up the equation 90 - x = 32 gives x = 58. Thus, the correct answer is 58.

Which equation shows how to solve the following scenario?  Select all that apply. 

Angle  (x + 2) is supplementary to angle (x - 8)

• x+2+x-8=360

• x+2+x-8=180

• 2x-6=180

• x+2=x-8

Answer explanation

The angles are supplementary, meaning their sum is 180 degrees. Thus, the equation x+2+x-8=180 correctly represents this relationship. Simplifying it leads to 2x-6=180, confirming both are valid equations.

A cube and a square pyramid are shown.

Name a two-dimensional figure that is a cross-section of both the cube and square pyramid using a cut horizontal to the base.

• Circle

• Square

• Oval

• Rectangle

Answer explanation

A horizontal cut through both the cube and the square pyramid will create a rectangle. The cube's cross-section is a square, while the pyramid's is a rectangle, making 'Rectangle' the correct answer.

A bicycle tire has a radius of 13  inches. How far will the bicycle travel in 40 rotations of the tire? Round to the nearest tenth (Use 3.14 for pi)

• 1632.8 in

• 81.64 in

• 3265.6 in

• 5364.6 in

Answer explanation

The circumference of the tire is calculated as C = 2 * pi * radius = 2 * 3.14 * 13 = 81.64 inches. In 40 rotations, the distance traveled is 40 * 81.64 = 3265.6 inches, which is the correct answer.

Calculate the surface area of the triangular prism shown

• 390

• 360

• 450

Answer explanation

To find the surface area of the triangular prism, calculate the area of the triangular base and the three rectangular sides. The total surface area sums to 390, making it the correct choice.

The Graph shows the number of pencils in a jar for 15 days

What is the initial value of the function?

Answer explanation

The initial value of the function represents the number of pencils in the jar at the start, which is 0. The answer choice 12 does not reflect the starting point, making 0 the correct answer.

he graph shows the number of pencils in a jar for 15 days. 

What is the meaning of the initial value?

• The initial value is 12 pencils.

• The initial value is 8 pencils.

• The number of pencils in the jar to begin with is 12.

• The initial value is 10 pencils.

Answer explanation

The initial value represents the starting number of pencils in the jar before any changes occur. In this case, it is 12 pencils, indicating that the jar began with 12 pencils.

The graph shows the number of pencils in a jar for 15 days. 

What is the rate of change of the function?

• -1/2

• 1/2

• 0.5

• -0.5

Answer explanation

The rate of change is calculated as the change in the number of pencils over the change in time. If the graph shows a decrease, the rate is negative. Here, the correct rate of change is -1/2 or -0.5, indicating a decrease.