Algebra I Remediation
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PRESENTER:
CARLA KIRKLAND
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MEASUREMENT
Objective 4c
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Represent polynomial operations with area
models. (DOK 2)
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
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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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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?
MSATP Alg I, Test 1, 4c
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Question Number 59
Explanation: AL – Area of larger rectangle
AS – Area of smaller rectangle
AL – AS – Area of shaded region
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AS
= (x + 2)(x)
–
(x – 2)(x – 1)
= x2 + 2x
–
(x2 – 3x + 2)
AL
= x2 + 2x – x2 + 3x – 2
= x2 – x2 + 2x + 3x – 2
= 5x – 2
Answer: B
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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?
MSATP, Alg I, Test 2, 4c
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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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