Exam Questions

Explain what the "drag test" is and explain how you've used it to verify that you've constructed your figure correctly.

Construct the height h of the trapezoid through E (e.g., the perpendicular to TR and PA). Label the height of triangle PEA and the height of triangle TER . What can you say about the ratio in terms of a, b, c, or d?

Write the area of the trapezoid in terms of and .

Use your responses above to explain why triangle PET and triangle EAR must have the same area.

Find a primitive Pythagorean triple with hypotenuse 73. Explain how you are using your knowledge of complex numbers to find the primitive triple.

Suppose that x can be written as the sum of two squares, and y can be written as the sum of two squares.  Prove that xy can be also be written as the sum of two squares.  Hint: how can you use complex numbers to write the sum of two squares as a product?

Use polynomial division to find the equation of a parabola that is tangent to the function at and .