Download Mathematics – Geometry Practice Test Answer and Alignment ... and more Summaries Geometry in PDF only on Docsity!
Mathematics – Geometry
Practice Test Answer and Alignment Document
Online ABO
The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. − The rubrics show sample student responses. Other valid methods for solving the problem can earn full credit unless a specific method is required by the item. − In items where the scores are awarded for full and partial credit, the definition of partial credit will be confirmed during range-finding (reviewing sets of real student work). − If students make a computation error, they can still earn points for reasoning or modeling.
Unit 1
Item Number Answer Key
Evidence Statement Key/Content Scope
Integrated Course Alignment
Part A: 1 Part B: 44
G-GPE.1-2 3
2. G-GPE.6 3
Part A:
Part B: G-CO.C^1
4. A G-SRT.6 2
- G-C.B.Int.1 3
Unit 2
Item Number Answer Key
Evidence Statement Key/Content Scope
Integrated Course Alignment
Part A: see rubric Part B: see rubric
HS.C.13.2 3
- G-SRT.1a 2
- G-SRT.1b 2
4. G-SRT.8 2
5. B^ G-CO.3 1
Part A: see rubric Part B: see rubric HS.C.18.2 None
- B, F G-CO.1 1
- B G-GMD.3 2
- C G-SRT.7-2 2
- See rubric HS.C.14.5 2
Part A: see rubric Part B: see rubric Part C: see rubric
HS.D.2-11 2
12. B, F G-GMD.1 2
13. C G-CO.6 1
Part A: 1326 Part B: B G-Int.1^3
Rubrics start on the next page.
entire block. The volume of the cube is (10 inches) ,^3 or 1, cubic inches. So the volume of each congruent chunk of clay is 500 cubic inches. Each sphere will have a diameter of 4 inches and a radius of 2 inches. The volume of each clay sphere will be 4 3 32 3 3 (2 inches) , or cubic inches. This is approximately 33.5 cubic inches. To find the number of spheres that Daniel can make from the chunk of clay, divide the volume of the full chunk of clay, by the volume of one sphere: 500 33.5 14.9. The result of 14.9 means that there is enough clay in the chunk to make 14 clay spheres because there is not enough clay to make 15 complete spheres. 2 Student response includes 2 of the above elements. 1 Student response includes 1 of the above elements. 0 Student response is incorrect or irrelevant.
Unit 1 #14 Rubric
Score Description 3 Student response includes each of the following 3 elements: Valid values for h 1 (^) and h 2 Valid approach for determining h 1 (^) and h 2 Verification that the design will store at least 2 dump-truck loads of fertilizer
Sample Student Response: Assuming the dump trucks are rectangular prisms, each dump truck stores 288 cubic feet of fertilizer (4 6 12 288). Two dump trucks will store 576 cubic feet of fertilizer. The volume of the storage building needs to be at least 576 cubic feet. The volume of the storage building equals the volume of the cylinder plus the volume of the cone. I used the maximum diameter of 8 feet. 2 2 1 2 2 2 1 2
1 3 1 3
r h r h
h h
I used the maximum total height of 14 feet. Since the volume of a cone involves dividing by 3, I made the height of the cone much smaller than the height of the cylinder.
2 2 1 2 2 2
1 3 1 3
h h Using h 1 (^) 11 feet and h 2 (^) 3 feet, the storage building will have a volume greater than 576 cubic feet. Note: Any two heights that have a sum of 14 and create a volume greater than 576 are acceptable. 2 Student response includes 2 of the above elements. 1 Student response includes 1 of the above elements. 0 Student response is incorrect or irrelevant.
Unit 2 #1 Part A Rubric
Score Description 1 Student response includes the following element: Correct coordinates of point Q in terms of a , b , and c.
Sample Student Response:
(2 a 2 b , 2 ) c or equivalent
Note: Students are not required to show work, but will not be penalized for showing work. 0 Student response is incorrect or irrelevant.
Unit 2 #1 Part B Rubric
Score Description 2 Student response includes each of the following 2 elements: Student states that the midpoint of SQ must be the same as the midpoint of PR Provides evidence using appropriate mathematical strategies, reasoning, and/or approaches that verifies SQ and PR bisect each other
Sample Student Response: SQ bisects PR and PR bisects SQ. I know this because the midpoint of SQ has the same coordinates as the midpoint of PR , as shown.
rectangle. 2 Student response includes 2 of the above elements. 1 Student response includes 1 of the above elements. 0 Student response is incorrect or irrelevant.
Unit 2 #6 Part B Rubric
Score Description 1 Student response includes the following element: Explanation of why the parallelogram is a rectangle or that diagonals are congruent.
Sample Student Response:
ABCD is a rectangle. Because the lengths AE , BE , CE , and DE are all equal to 16, the diagonals are congruent and parallelogram ABCD is a rectangle. 0 Student response is incorrect or irrelevant.
Unit 2 #10 Rubric
Score Description 3 Student has complete valid proof with valid chains of reasoning. Student Sample Response: Given: A ^ B^ ^ is the image of AB^ after a dilation centered at point C and with scale factor k , k 0. Prove: A B k AB.
- A B is the image of AB after a dilation centered at point C and with scale factor k , k 0.[given]
- CA ^ k CA ; CB ^ k CB [definition of dilation]
- CA ; CA
(^) k CB ; CB
(^) k [Division Property of Equality]
4. CA^ CB
CA CB
(^) [Transitive Property of Equality]
- C C [Reflexive Property of Congruence]
- ACB A CB ^ [SAS Triangle Similarity]
- A B^ CA^ CB AB CA CB
(^) (^) [definition of similar polygons]
8. A B
AB
(^) k [Substitution Property of Equality]
- A B^ ^ k AB [Multiplication Property of Equality]
2 Student response contains a valid chain of reasoning but may omit some information. The student must include the SAS Triangle Similarity property correctly. 1 Student response includes valid justified steps, but is an incomplete proof. 0 Student response is incorrect or irrelevant.
Unit 2 #11 Part A Rubric
Score Description 2 Student response includes each of the following 2 elements: The surface area of the roof is approximately 396 square foot Valid work shown
Sample Student Response: The angle consists of two parts – the right angle created by the side of the shed, and the top of the rectangular side and the acute angle used to form a right triangle. For a 125° angle, the right triangle of the roof line has an angle of 35° and an adjacent side of 9. Each side of the roof is a rectangle with one side measuring 18 feet and the other side measuring 9 cos 35 feet. 9 2 18 (^) cos 35 395. The area of the roof is approximately 395.5 square feet. 1 Student response includes 1 of the above elements. 0 Student response is incorrect or irrelevant.
Unit 2 #11 Part B Rubric
Score Description 2 Student response includes each of the following 2 elements: Decision of “no” with valid reason Valid explanation
Sample Student Response: A 10% decrease in the roof area obtained in Part A is about 356 square feet which means one rectangle would have an area of about 178 square feet.
2
1 Student response includes 1 of the above elements. 0 Student response is incorrect or irrelevant.
