BMath Bachelor of Mathematics Bachelor of Mathematics: Concepts and Theories 3

Question 1

What is the fundamental theorem of calculus (Part 1) about?

Accepted Answer

If F(x) = ∫ₐˣ f(t) dt and f is continuous, then F'(x) = f(x)

Answer

Part 1 of the FTC states that differentiation and integration are inverse operations when f is continuous.

Question 2

In graph theory, a tree with n vertices has exactly how many edges?

Accepted Answer

n − 1

Answer

A tree is a connected acyclic graph; removing any edge disconnects it, and adding any edge creates a cycle, forcing exactly n−1 edges.

Question 3

Which of the following is NOT a valid axiom in Zermelo-Fraenkel (ZF) set theory?

Accepted Answer

The Axiom of Choice

Answer

The Axiom of Choice is independent of ZF; the system including it is called ZFC, not ZF.

Question 4

The Euler characteristic χ of a convex polyhedron satisfies:

Accepted Answer

χ = V − E + F = 2

Answer

Euler's formula for convex polyhedra states vertices minus edges plus faces equals 2.

Question 5

What does it mean for a set S in a metric space to be dense?

Accepted Answer

Every point in the space is a limit point of S or belongs to S

Answer

S is dense if its closure equals the whole space, meaning every open ball around any point of the space meets S.

BMath Bachelor of Mathematics Practice Test