ASSIGNMENT 1 for SECTION 001
This assignment is to be handed in. There are two parts: Part A and Part B.
Part A will be graded for completeness. You will receive full marks only if every question has been completed.
Part B will be graded for correctness. You will receive full marks on a question only if your answer is correct
and your reasoning is clear. In both parts, you must show your work.
Please submit Part A and Part B separately, with your name on each part.
Part A
From The Mathematics Survival Kit:
Complete question 2 on the following pages: 4, 6, 8, 18, 22, 24, 26, 28, 30, 32, 38, 42, 44, 50, 52
From Calculus: Early Transcendentals:
Complete the Diagnostic Test: Algebra and Diagnostic Test: Analytic Geometry
Part B
1. Solve the following equations for x:
3. (a) 2(1 − x) = (x − 1)2 − (x2 − 1)
3. (b) 2(x − 1) = (x − 1)2 − (x2 − 1)
2. Solve
x+a
x+b
=
for x, in terms of a and b.
x−b
x+a+b
3. Find the area of the triangle enclosed by the lines y = 3, y = 2x − 5 and 2x + 3y = 9.
4. Let a, b and c be numbers such that: (i) their average is 2/3; (ii) a = 1 + b; and (iii) c + 2b = 1. What
can c be? Justify your answer.
5. Prove Pythagoras’ theorem.
(Hint: label the edges of the square-inscribed square to the right, and
calculate the area of the larger square in two ways.)