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Graph Theory and Vectors - MYP Questionbank | RevisionDojo

Practice Graph Theory and Vectors with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

In a bipartite graph where one set of vertices is 'Actors' and the other set is 'Movies', an edge exists if an actor appeared in a movie. What does it mean if the Movie-vertex 'The Great Gatsby' has a degree of $15$ ?

Question 2

Solve the following vector equation for $x$ and $y$ :

\begin{pmatrix} x \\ y \end{pmatrix} + 2 \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}

Question 3

Calculate the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \pi \\ 1 \end{pmatrix}$ , giving the answer correct to three significant figures.

Question 4

A delivery driver starts at vertex $A$ , visits vertices $B$ , $C$ , and $D$ in order, and then returns to vertex $A$ . No vertex is repeated, except for the start and end vertex. Which specific term describes this route?

Question 5

In a parallelogram $ABCD$ , the position vectors of three vertices relative to an origin $O$ are $\overrightarrow{OA} = \mathbf{a}$ , $\overrightarrow{OB} = \mathbf{b}$ , and $\overrightarrow{OC} = \mathbf{c}$ . Find the position vector of the fourth vertex, $\overrightarrow{OD}$ .

Question 6

If $|\mathbf{a}| = 5$ , $|\mathbf{b}| = 4$ , and the angle between the two vectors is $60^\circ$ , calculate the dot product $\mathbf{a} \cdot \mathbf{b}$ .

Question 7

Given the vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ , find the vector $\mathbf{a} + 2\mathbf{b}$ .

Question 8

A connected graph $G$ contains at least one vertex with a degree of $1$ . Which of the following statements about $G$ must be true?

Question 9

Let $\mathbf{a}$ and $\mathbf{b}$ be non-zero and non-parallel vectors. Which of the following statements about the vectors $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ is always true?

Question 10

In a connected graph with $n \ge 3$ vertices, the existence of an articulation point (cut vertex) makes a Hamiltonian cycle impossible. Why is this the case?

Type

Difficulty

Question 1

Question 2

Solve the following vector equation for $x$ and $y$ :

\begin{pmatrix} x \\ y \end{pmatrix} + 2 \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}

Question 3

Calculate the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \pi \\ 1 \end{pmatrix}$ , giving the answer correct to three significant figures.

Question 4

Question 5

Question 6

If $|\mathbf{a}| = 5$ , $|\mathbf{b}| = 4$ , and the angle between the two vectors is $60^\circ$ , calculate the dot product $\mathbf{a} \cdot \mathbf{b}$ .

Question 7

Given the vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ , find the vector $\mathbf{a} + 2\mathbf{b}$ .

Question 8

A connected graph $G$ contains at least one vertex with a degree of $1$ . Which of the following statements about $G$ must be true?

Question 9

Let $\mathbf{a}$ and $\mathbf{b}$ be non-zero and non-parallel vectors. Which of the following statements about the vectors $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ is always true?

Question 10

In a connected graph with $n \ge 3$ vertices, the existence of an articulation point (cut vertex) makes a Hamiltonian cycle impossible. Why is this the case?

Type

Difficulty

Question 1

Question 2

Solve the following vector equation for $x$ and $y$ :

\begin{pmatrix} x \\ y \end{pmatrix} + 2 \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}

Question 3

Calculate the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \pi \\ 1 \end{pmatrix}$ , giving the answer correct to three significant figures.

Question 4

Question 5

Question 6

If $|\mathbf{a}| = 5$ , $|\mathbf{b}| = 4$ , and the angle between the two vectors is $60^\circ$ , calculate the dot product $\mathbf{a} \cdot \mathbf{b}$ .

Question 7

Given the vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ , find the vector $\mathbf{a} + 2\mathbf{b}$ .

Question 8

A connected graph $G$ contains at least one vertex with a degree of $1$ . Which of the following statements about $G$ must be true?

Question 9

Let $\mathbf{a}$ and $\mathbf{b}$ be non-zero and non-parallel vectors. Which of the following statements about the vectors $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ is always true?

Question 10

In a connected graph with $n \ge 3$ vertices, the existence of an articulation point (cut vertex) makes a Hamiltonian cycle impossible. Why is this the case?

Graph Theory and Vectors Questionbank