7th Grade Midterm Review SY23-24

A scaled copy is a copy of a figure that is the same shape but may or may not be the same size

What is a scaled copy?

Multiple Select

Here is a figure that looks like the letter A, along with several other figures. Select ALL of the scaled copies of the original figure.

• Figure 1

• Figure 2

• Figure 3

• Figure 4

What are the characteristics of a scaled copy?

● A scaled copy will have all the same angles as the original shape, even if the side lengths change.
● If a shape is stretched (or squished) in one direction but not the other, it cannot be a scaled copy.
● All straight lines in the original shape remain straight lines in the scaled copy.

Multiple Select

Figure B is a scaled copy of Figure A. Select ALL of the statements that must be true:

• 1. Figure B is larger than Figure A.

• 1. Figure B has the same number of edges as Figure A.

• 1. Figure B has the same perimeter as Figure A.

• 1. Figure B has the same number of angles as Figure A.

• 1. Figure B has angles with the same measures as Figure A.

A scale factor is the number by which we multiply all the lengths in the original figure to create a scaled copy.
In the example, the scale factor from the smaller figure to the larger figure is 1. 5.

What is a scale factor?

Multiple Select

Select ALL the scaled copies of Figure A.

• Figure B

• Figure C

• Figure D

• Figure E

• Figure F

Fill in the Blanks

Fill in the Blanks

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.

What does it mean for two quantities to be proportional?

Multiple Choice

When Deven makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup.

Are cups of milk and tablespoons of chocolate syrup in a proportional relationship?

• Yes

• No

What is a constant of proportionality?

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.

Fill in the Blanks

1. Straight line

2. ​Passes through the origin

Graphs of Proportional Relationships

Multiple Select

Select all of the graphs that could represent a proportional relationship.

• Top Left

• Top Right

• Bottom Left

• Bottom Right

• Determine the y-value when the x-value is 1 .

• Determine the number you need to multiply the x -value by to find the y-value.

  For example, each y-coordinate in the example is 40 times the x-coordinate.

Constant of Proportionality from a Graph

The graph shows how far a car travels using any amount of gas.

The constant of proportionality is 40.

The constant of proportionality tells us the gas mileage of the car, or how far it can travel using 1 gallon of gas.

Meaning of Constant of Proportionality

Multiple Select

Water runs from a faucet into a bucket at a steady rate. The relationship between the amount of water in the bucket and time is proportional.

Select ALL of the true statements.

• The point (1,4) is on the graph for the line.

• The constant of proportionality for this relationship is 4.

• After 20 seconds, there are 5 ounces of water in the bucket.

• After 1 second, there are 4 ounces of water in the bucket.

This graph shows the distance traveled over time by three different turtles.

I can tell from a graph which turtle is moving fastest by comparing steepness of the lines.
When time is on the x-axis, a steeper graph means the turtle is moving at a faster rate.

Comparing Graphs

I can tell from an equation which turtle is moving fastest by looking at the constant of proportionality.

When the equations are all written for t in terms of d, a greater constant of proportionality means the turtle is moving at a faster rate.

Comparing Equations

Multiple Choice

The graph shows the distance two satellites travel over time as they orbit Mars. 1.1 Which line represents the satellite that is traveling faster?

• Satellite A

• Satellite B

• Diameter: A diameter is a line segment that goes from one edge of a circle to the other and passes through the center.

• Radius: A radius is a line segment that goes from the center to the edge of a circle.

Parts of a Circle

Converting between Radius and Diameter

Multiple Choice

What is the radius and diameter of the given circle?

• Radius: 100cm

  Diameter: 200cm

• Radius: 200cm

  Diameter: 100cm

• Radius: 50cm

  Diameter: 100cm

• Radius: 100cm

  Diameter: 50cm

Multiple Choice

What is the radius and diameter of the given circle?

• Radius: 10ft

  Diameter: 20ft

• Radius: 20ft

  Diameter: 10ft

• Radius: 5ft

  Diameter: 10ft

• Radius: 10ft

  Diameter: 5ft

Distance around a circle.

Formulas:

Circumference

Multiple Choice

What is the circumference of a circle with a radius of 35cm? Use 3.14 for pi

• 35 x 3.14 = 109.9

• 70 X 3.14 = 219.8

• 35 x 35 x 3.14 = 3,846.5

• 70 x 70 x 3.14 = 15,386

Space inside a circle.

Formula:

Area

Multiple Choice

What is the area of a circle with a radius of 35cm? Use 3.14 for pi

• 35 x 3.14 = 109.9

• 70 X 3.14 = 219.8

• 35 x 35 x 3.14 = 3,846.5

• 70 x 70 x 3.14 = 15,386