ASSIGNMENT 1·2 for SECTION 001
There are two parts to this assignment. The first part is online at www.mathxl.com. The second part
consists of the questions on this page. You are expected to provide full solutions with complete arguments
and justifications. You will be graded primarily on the correctness, clarity and elegance of your solutions.
Your answers must be typeset or very neatly written. They must be stapled, with your name and student
number at the top of each page.
1. Find the area of the parallelogram with vertices at (4, 5), (11, 9), (−4, 8) and (3, 12).
2. Explain how the Pythagorean theorem is equivalent to the following statement:
sin2 θ + cos2 θ = 1 for any angle θ.
Note that to prove two statements are equivalent, you must prove that each implies the other.
3. A quadratic curve is a curve of the form
y = ax2 + bx + c
where a, b and c are real numbers, with a not equal to zero. A cubic curve is a curve of the form
y = Ax3 + Bx2 + Cx + D
where A, B, C and D are real numbers, with A not equal to zero. What is the maximum number of
times a quadratic curve might intersect a cubic curve?