PRESENTER:CARLA KIRKLAND

Algebra I Remediation

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MEASUREMENT

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Objective 4c

Represent polynomial operations with area models. (DOK 2)

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19. The figure below is made up of two rectangles.

What is the total area, in square feet, of the figure?

MSATP Alg I, Test 1, 4c

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Question Number 19

Explanation: Rectangle 1: (x + 3)(x + 2) Rectangle 2: (2x)(x + 1)

= x2 + 2x + 3x + 6 = 2x2 + 2x

= x2 + 5x + 6

And Rectangle 1 + Rectangle 2 = Total Figure

(x2 + 5x + 6) + (2x2 + 2x) = 3x2 + 7x + 6

Answer: C

48. A museum has a model of a square pyramid. Each side of the base of the pyramid is 35 meters long. A rope is placed x meters away from the base of the model on all four sides when the display is closed, as shown in the diagram.

Which polynomial represents the perimeter, in meters, of the region enclosed by the rope?

MSATP Alg I, Test 1, 4c

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Question Number 48

Explanation:

The pyramid itself is a square with sides that are designated by 35 + x units. The formula to calculate the perimeter of a square is P = 4s; substitute the units into the formula.

P = 4s

P = 4(35 +2x)

P = 140 + 8x

P = 8x + 140

Answer: B

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MSATP Alg I, Test 1, 4c

59. Jorge drew a rectangle inside a larger rectangle, as shown below.

If x represents any number greater than 2, which of the following expressions represents the area, in square inches, of the shaded region?

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Question Number 59

Explanation: AL – Area of larger rectangle

AS – Area of smaller rectangle

AL – AS – Area of shaded region

AL – AS

= (x + 2)(x) – (x – 2)(x – 1)

= x2 + 2x – (x2 – 3x + 2)

= x2 + 2x – x2 + 3x – 2

= x2 – x2 + 2x + 3x – 2

= 5x – 2

Answer: B

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MSATP, Alg I, Test 2, 4c

51. Monica’s rectangular lawn has a length of 60 feet and a width of 45 feet. She made a flower bed along two sides of the lawn, as shown in the diagram.

Which of the following expressions can be used to find the area, in square feet, of the flower bed?

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Question Number 51

Explanation:

(Area of whole lawn) – (Area of inside lawn) = Area of flower bed

Answer: D

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