IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Static and Probability-Sets ,including notation and operations up to three sets
Topic :Static and Probability- Weightage : 21 %
All Questions for Topic : Sampling techniques,Data manipulation and misinterpretation,Graphical representations (including: bivariate graphs, scatter graphs, box plots, cumulative frequency graphs)
,Lines of best fit,Data processing: quartiles and percentiles,Measures of dispersion: interquartile range,Correlation, qualitative handling,Relative frequency,Response rates,Sets, including notation and operations up to three sets,Probability with Venn diagrams, tree diagrams and sample spaces,Mutually exclusive events,Combined events
Question (8 Marks)
The elements of the universal set $\boldsymbol{U}$ are $\{1,2,3,4,5,6,7,8,9,10\}$.
Consider two subsets of $\boldsymbol{U}$
Set A contains the multiples of $2$ .
Set B contains the multiples of $3$ .
Question (a) : 2 marks
Organize the given numbers in the Venn diagram. Drag the numbers to the correct place.
▶️Answer/Explanation
Ans:
Question (b) : 2 marks
Describe the region $A \cap B^{\prime}$ in context.
▶️Answer/Explanation
Ans:
The region $A \cap B^{\prime}$ represents the elements that belong to set $A$ (multiples of 2) and do not belong to set $B$ (non-multiples of 3). In other words, it represents the numbers that are multiples of 2 but not multiples of 3.
From the given information, we have:
Set $A$: $\{2, 4, 6, 8\}$ (multiples of 2)
Set $B$: $\{3, 6, 9\}$ (multiples of 3)
To find $B^{\prime}$ (the complement of set $B$), we need to consider the elements that are not in set $B$ but are in the universal set $U$. Since $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, the complement of set $B$ will include the elements not present in $\{3, 6, 9\}$ from $U$. Thus, $B^{\prime} = \{1, 2, 4, 5, 7, 8, 10\}$.
Now, we can calculate the intersection $A \cap B^{\prime}$ by considering the common elements between set $A$ and the complement of set $B$. In this case, $A \cap B^{\prime} = \{2, 4, 8\}$.
Therefore, the region $A \cap B^{\prime}$ in context represents the numbers $\{2, 4, 8\}$, which are the multiples of 2 but not multiples of 3 within the universal set $U$.