IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Number–Including compound and double inequalities
Topic :Number- Weightage : 21 %
All Questions for Topic : Absolute Values,Representing and Solving Inequalities,Including compound and double inequalities,Irrational numbers,Surds, roots and radicals, including simplifying,Standard form (scientific notation),Laws of exponents, including integer and negative exponents,Number systems notation,Direct and Inverse Proportion,Number Sequence(Prediction ,Description)
Question (3 Marks)
The set of rational numbers $(\mathbb{Q})$ and the set of real numbers $(\mathbb{R})$ are added to the Venn diagram as shown below.
Label the Venn diagram by placing the draggable numbers provided into the correct location.
▶️Answer/Explanation
Ans:
To label the Venn diagram representing the sets of natural numbers ($\mathbb{N}$), integer numbers ($\mathbb{Z}$), rational numbers ($\mathbb{Q}$), and real numbers ($\mathbb{R}$), we can place the draggable numbers in the following locations:
$\bullet$ $-\sqrt{7}$: This represents the negative square root of 7. We can place the number $-\sqrt{7}$ inside the region that represents the set of real numbers ($\mathbb{R}$).
$\bullet$ $\frac{22}{7}$: This represents the fraction 22 divided by 7, which is an approximation of the mathematical constant $\pi$. We can place the number $\frac{22}{7}$ inside the region that represents the set of rational numbers ($\mathbb{Q}$).
$\bullet$ $\pi$: Pi is an irrational number, which means it cannot be expressed as a fraction. We can place the symbol $\pi$ inside the region that represents the set of real numbers ($\mathbb{R}$) but outside the region that represents the set of rational numbers ($\mathbb{Q}$).
$\bullet$ $|-2|$: The expression $|-2|$ represents the absolute value of -2, which is 2. We can place the number 2 inside the region that represents the set of real numbers ($\mathbb{R}$).
$\bullet$ $\tan 45^{\circ}$: The tangent of 45 degrees is 1. We can place the number 1 inside the region that represents the set of real numbers ($\mathbb{R}$).
$\bullet$ $2^{\circ}$: This represents 2 degrees. We can place the number $2^{\circ}$ inside the region that represents the set of real numbers ($\mathbb{R}$).
Here is how the draggable numbers should be placed in the Venn diagram:
