Math Assessment - 8th Grade – Standard 8.G.B.6 & 8.G.B.8
Name: ______Class: ______Date: ______
Questions 1-4: Selected Response: Please bubble in the correct response on your scantron. (1 point each)
1. What is the distance between the points (-4, -6) and (8, -10)? Round the answer to the nearest tenth.
a. 18.1 units b. 12.6 units c. 15.2 units d. 16.0 units
2. Joel is trying to prove the Pythagorean Theorem using the proof below.
Proof
1.) a2 + b2 = c2
2.) 22 + 62 = c2
3.) 4 + 36 = c2
4.) 40 = c2
5.) 40 = c2
6.) 6.3245 units = c
Is Joel’s proof correct? If not where did he make his first mistake and how can he fix it?
a) Joel’s proof is not correct. He made his first mistake in step 2 switching the legs of the triangle. He should have had 62 + 22 = c2.
b) Joel’s proof is not correct. He made his first mistake in step 3 finding the product of six squared. He should have found the sum of six and six.
c) Joel’s proof is not correct. He made his first mistake in step 4 finding the sum instead of the product of 4 and 36.
d) Joel’s proof is correct thus far based on his current calculations and use of the Pythagorean Theorem.
3. Jose is trying to prove the Pythagorean Theorem using the proof below.
Proof
1.) a2 + b2 = c2
2.) 62 + 52 = c2
3.) 12 + 10 = c2
4.) 22 = c2
5.) 22 = c2
6.) 4.6904 units = c
Is Jose’s proof correct? If not where did he make his first mistake and how can he fix it?
a) Jose’s proof is correct thus far based on his current calculations and use of the Pythagorean Theorem.
b) Jose’s proof is not correct. He made his first mistake in step 2 switching the legs of the triangle. He should have had 52 + 62 = c2
c) Jose’s proof is not correct. He made his first mistake in step 3 finding the product of six and two and then the product of five and two. He should have found the product of six squared and five squared.
d) Jose’s proof is not correct. He made his first mistake in step 4 finding the sum instead of the product of 12 and 10.
4. Jack is trying to prove the Pythagorean Theorem given the areas from the squares using the proof below.
Proof
1.) a2 + b2 = c2
2.) a2 + 64 = 100
A =100cm2 3.) a2 + 64 +(-64) = 100 - 64
a 4.) a2 = 36
5.) a2 = 36
6.) a = 6 cm
A = 64cm2
Is Jack’s proof correct? If not where did he make his first mistake and how can he fix it?
a) Jack’s proof is not correct. He made his first mistake in step 3 subtracting 64 from each side of the equation. He should have added sixty-four to each side of the equation.
b) Jack’s proof is not correct. He made his first mistake in step 4 finding the sum of one hundred and negative sixty-four. He should have found the sum of one hundred and sixty-four.
c) Jack’s proof is not correct. He made his first mistake in step 5 finding the square root of thirty-six. He should have left the integer at thirty-six instead of solving for the radical.
d) Jack’s proof is correct thus far based on his current calculations and use of the Pythagorean Theorem.
Questions 5-6: Grid-In. Please write your answer and bubble in the correct response on the grid on your scantron. (1 point each)
5. Use the Pythagorean Theorem to determine the distance between the two points on the coordinate plane. Round your answer to the nearest tenths place if necessary.
6. Use the Pythagorean Theorem to determine the diagonal measurement of the front face on the rectangular prism on the coordinate plane. Round your answer to the nearest tenths place if necessary.
Question 7: Constructed Response. Be sure to answer all parts of the constructed response.
(1 point each part)
There is a slide at the local elementary school your little sister loves to ride. She climbs seven feet up the stairs and slides down eleven feet. She then has to walk back to the stairs nine feet to ride again. Does your little sister walking up the stairs, sliding down the slide, and walking back to the stairs form a right triangle?
Part A Answer the essential question – is this scenario a right triangle?
Part B Justify how you determined this is or is not a right triangle using mathematics. Show all steps.
2014-2015 8.G.B.6 & 8.G.B.8 8th grade page 4