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Geometry: Unit 1

Last updated 9 months ago
19 questions
Note from the author:
GA K-12 Math: Geometry Item Bank, Unit 1
GA ITEM BANK MATH K-12 Geometry Unit 1:
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Unit 1 - Item 1

The length, width, and height of a shipping container are represented by 4x, 3x + 10, and 2x - 1, respectively. When the volume is expressed as a polynomial in standard form, what is the coefficient of the 2nd term?

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Unit 1 - Item 2

Alex has a garden that is in the shape of a rectangle. Its length is twice its width. He decided to make a larger garden that was 5 feet longer and 3 feet wider than his original garden.

If x represents the original width of the garden, what expression represents the difference between the area of his new garden and the area of the original garden?

Draw a visual representation of the two gardens and explain your results.

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Unit 1 - Item 3

Part A: Write an equation to find x, the width of the sidewalk.

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Unit 1 - Item 3

Part B: Describe how your equation models this situation.

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Unit 1 - Item 3

Part C: Determine and state the width of the sidewalk in meters.

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Unit 1 – Item 4

The perimeter of Walker High School’s basketball court is currently 268 feet.

Part A: Write an expression to determine the length and width of the basketball court.

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Unit 1 - Item 4

Part B: What are the length and width of Walker High School’s basketball court?

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Unit 1 - Item 4

Part C: Coach James would like to have a rectangular sideline all the way around the court that is x feet. Write and simplify an equation that would represent the area of the court including the sidelines. Part D: What is the area of the court only if the radius of the center circle is 3 yards and the paint has a length of 6.5 yards? Give your answer rounded to the nearest foot.

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Unit 1 - Item 4

Part D: What is the area of the court only if the radius of the center circle is 3 yards and the paint has a length of 6.5 yards? Give your answer rounded to the nearest foot.

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Unit 1 - Item 5

Shape Selection: Choose a circle, rectangle, and triangle found in the real world as the geometric shapes for this project. Include clear diagrams of these shapes with labeled binomial and/or trinomial dimensions.

Area Calculation
Write polynomial expressions to calculate the area of each shape. Show step-by-step calculations using the polynomial representations.

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Unit 1 - Item 5

Perimeter Calculation: Write polynomial expressions to calculate the perimeter of each shape. Use appropriate polynomial operations to determine the perimeter of the rectangle, triangle, and the circumference of the circle.

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Unit 1 - Item 5

Comparative Analysis in Presentation: Compare and contrast the calculations of area and perimeter across the selected shapes. Discuss the role of polynomials in representing geometric dimensions. Analyze how the formulas differ for each shape and why.

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Unit 1 – Item 6:

Part A
Write an expression to represent the size of the perimeter of the frame Brooks will need to buy.

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Unit 1 – Item 6:

Part B
What does the variable in your expression represent?

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Unit 1 – Item 6:

Part C
Describe how your equation models the situation.

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Each side of this triangle equals 2x^2 + 4x + 6. Complete the puzzle using the algebraic expressions provided to make the sides of the triangle true. Use each expression only once.

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Davis is designing a new office building. The architect presented him with two floor plans to choose from. Davis's goal is to maximize the size of the conference room.

Details about Plan A
  • The offices will have the same dimensions
  • The hallway is 4 ft wide
  • The dimensions of the exterior walls can be represented by the expression 9x + 4ft by the expression 15x ft
  • The length of the conference room is the same as the length of two offices
  • Office 1 and Office 2 have the same dimensions, 6x ft by 4x ft.
  • Office 3 and Office 4 have the same dimensions, 5.5x ft by (x+4) ft.


Unit 1 – Item 8

Explain how Davis should go about determining which floor plan results in the biggest conference room? Be as detailed as possible.

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Unit 1 – Item 9

Using the information above in Item 8, write an email to Davis explaining which floorplan he should choose and why.

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Unit 1 - Item 10

Which of the following operations with polynomials demonstrates closure under multiplication?