ASSIGNMENT 1 for SECTION 001
There are three parts to this assignment. Part A is to be completed online before 7:00 a.m. on Friday,
September 17. Part B and Part C, which require full solutions, are to be handed in at the beginning of class
on the same date.
Part A [10 marks]
This part of the assignment focuses on fundamental skills and computations. It can be found online, labelled
A1, at webwork.elearning.ubc.ca — sign in using the MATH110 001 2010W button.
Part B [5 marks]
This part of the assignment is drawn directly from the course texts. It focuses on mathematical exposition;
you will be graded primarily on the clarity and elegance of your solutions.
From the Just-In-Time text, complete the following questions: section 3.2, question 24; and section 4.2,
question 18.
Part C [15 marks]
This part of the assignment consists of more challenging questions. You are expected to provide full solutions
with complete arguments and justifications.
1. Prove Pythagoras’ theorem in a way different than the one shown in class. (One possible method: calculate
the area of the following shape in two ways.)
c
a
b
2. Consider the graph of the distance between Earth and the planet nearest to it, as a function of time. Is
the graph continuous? Put another way, is the graph a single, unbroken curve?
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?