***Practice Test****
Name: _______________________________ Date:_________
Pythagorean Theorem Section B:
Items in this section will be reported in the 3.0 section of the proficiency scale .
Calculators Okay
1. Find the area of the given rectangle. Round to the nearest hundredth.
Answer:_______________
2. Calculate the area of the shaded region. The diagonal of the rectangle is the same length as
the diameter of the circle. Use 3.14 for 𝜋. Round all calculations to the
nearest hundredth.
Answer:__________________
0
1
Nothing
Correct
or
No Work
Done.
Correct answer with procedural method
shown(for example, a written explanation that
states the steps used) but no conceptual
explanation given.
or
Incomplete work shown or incorrect answer, and
some conceptual explanation given
or
Correct answer with the procedural method
shown (for example, a written explanation that
states the steps used) and some conceptual
explanation given
or
Incorrect answer due to a minor computational
error with complete conceptual explanation
2
Correct answer and procedural method
with a complete and logical conceptual
explanation, expressed in a clear and wellorganized way.
3. Students in a class are using their knowledge of the Pythagorean Theorem to make conjectures about
triangles. A student makes the conjecture shown below.
A triangle has side lengths x, y and z. If x < y < z and x2 + y2 > z2, the triangle is an acute triangle.
Use Pythagorean theorem to develop a chain of reasoning to justify or refute the conjecture. You must
demonstrate that the conjecture is always true or that there is at least one example in which the conjecture is
not true.
4. Students in a class are using their knowledge of the Pythagorean Theorem to make conjectures about
triangles. A student makes the conjecture shown below.
A triangle has side lengths x, y and z. If x < y < z and x2 + y2 < z2, the triangle is an obtuse triangle.
Use Pythagorean theorem to develop a chain of reasoning to justify or refute the conjecture. You must
demonstrate that the conjecture is always true or that there is at least one example in which the conjecture is
not true.