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The number system - MYP Questionbank | RevisionDojo

Practice The number system with authentic MYP MYP Standard 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 the set of real numbers $\mathbb{R}$ , the set of all numbers that are not irrational is:

Question 2

Which of the following is a direct consequence of the nesting property $\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}$ ?

Question 3

Given the universal set of real numbers $\mathbb{R}$ , which of the following expressions is equivalent to $\mathbb{Q}$ ?

Question 4

Which of the following numbers belongs to the set of integers $\mathbb{Z}$ but does not belong to the set of natural numbers $\mathbb{N}$ (assuming the convention $\mathbb{N} = \{1, 2, 3, \dots\}$ )?

Question 5

According to the Nature of Mathematics, which of the following best describes the status of number systems and their conventions, such as whether $0 \in \mathbb{N}$ ?

Question 6

Let $k$ be a real number such that $k \in \mathbb{Q}'$ , where $\mathbb{Q}'$ is the set of irrational numbers. Which of the following statements must be true?

Question 7

Every terminating decimal, such as $0.375$ , can be expressed as a fraction with a denominator that is a power of $10$ , proving it is a rational number.

Determine whether this statement is true or false.

Question 8

The Golden Ratio, $\phi$ , is defined as the positive root of the equation $x^2 - x - 1 = 0$ .

A physicist requires the most appropriate representation of $\phi$ to maintain absolute precision in a mathematical proof. Which form should be used?

Question 9

Fill in the blank: Based on set-builder notation, a number is defined as rational if it can be written in the form $\dfrac{a}{b}$ where $a, b \in \mathbb{Z}$ and _______.

Question 10

Using the algebraic method of shifting powers of 10, express the repeating decimal $0.444\dots$ as a fraction in its simplest form.

Type

Difficulty

Question 1

In the set of real numbers $\mathbb{R}$ , the set of all numbers that are not irrational is:

Question 2

Which of the following is a direct consequence of the nesting property $\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}$ ?

Question 3

Given the universal set of real numbers $\mathbb{R}$ , which of the following expressions is equivalent to $\mathbb{Q}$ ?

Question 4

Which of the following numbers belongs to the set of integers $\mathbb{Z}$ but does not belong to the set of natural numbers $\mathbb{N}$ (assuming the convention $\mathbb{N} = \{1, 2, 3, \dots\}$ )?

Question 5

According to the Nature of Mathematics, which of the following best describes the status of number systems and their conventions, such as whether $0 \in \mathbb{N}$ ?

Question 6

Let $k$ be a real number such that $k \in \mathbb{Q}'$ , where $\mathbb{Q}'$ is the set of irrational numbers. Which of the following statements must be true?

Question 7

Every terminating decimal, such as $0.375$ , can be expressed as a fraction with a denominator that is a power of $10$ , proving it is a rational number.

Determine whether this statement is true or false.

Question 8

The Golden Ratio, $\phi$ , is defined as the positive root of the equation $x^2 - x - 1 = 0$ .

A physicist requires the most appropriate representation of $\phi$ to maintain absolute precision in a mathematical proof. Which form should be used?

Question 9

Fill in the blank: Based on set-builder notation, a number is defined as rational if it can be written in the form $\dfrac{a}{b}$ where $a, b \in \mathbb{Z}$ and _______.

Question 10

Using the algebraic method of shifting powers of 10, express the repeating decimal $0.444\dots$ as a fraction in its simplest form.

Type

Difficulty

Question 1

In the set of real numbers $\mathbb{R}$ , the set of all numbers that are not irrational is:

Question 2

Which of the following is a direct consequence of the nesting property $\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}$ ?

Question 3

Given the universal set of real numbers $\mathbb{R}$ , which of the following expressions is equivalent to $\mathbb{Q}$ ?

Question 4

Which of the following numbers belongs to the set of integers $\mathbb{Z}$ but does not belong to the set of natural numbers $\mathbb{N}$ (assuming the convention $\mathbb{N} = \{1, 2, 3, \dots\}$ )?

Question 5

According to the Nature of Mathematics, which of the following best describes the status of number systems and their conventions, such as whether $0 \in \mathbb{N}$ ?

Question 6

Let $k$ be a real number such that $k \in \mathbb{Q}'$ , where $\mathbb{Q}'$ is the set of irrational numbers. Which of the following statements must be true?

Question 7

Every terminating decimal, such as $0.375$ , can be expressed as a fraction with a denominator that is a power of $10$ , proving it is a rational number.

Determine whether this statement is true or false.

Question 8

The Golden Ratio, $\phi$ , is defined as the positive root of the equation $x^2 - x - 1 = 0$ .

A physicist requires the most appropriate representation of $\phi$ to maintain absolute precision in a mathematical proof. Which form should be used?

Question 9

Fill in the blank: Based on set-builder notation, a number is defined as rational if it can be written in the form $\dfrac{a}{b}$ where $a, b \in \mathbb{Z}$ and _______.

Question 10

Using the algebraic method of shifting powers of 10, express the repeating decimal $0.444\dots$ as a fraction in its simplest form.

The number system Questionbank