DP Mathematical Studies Questionbank

• Syllabus

3.5

Sub sections and their related questions

Basic concepts of set theory: elements \(x \in A\), subsets \(A \subset B\); intersection \(A\mathop \cap \nolimits B\); union \(A\mathop \cup \nolimits B\); complement \({A'}\) .

• 10M.1.sl.TZ2.8a: Find \({\text{P}}(A \cap B)\).
• 10M.1.sl.TZ2.8b: Find \({\text{P}}(A|B)\).
• 11N.1.sl.TZ0.5a: Find the number that have both Australian and British passports.
• 11N.1.sl.TZ0.5c: In the Venn diagram below, set A represents the people in the group with Australian passports and...
• 10N.1.sl.TZ0.9a.i: List the elements of the following set. A
• 10N.1.sl.TZ0.9b: Write down one element of \((A \cup B)'\).
• 10N.1.sl.TZ0.9c: One of the statements in the table below is false. Indicate with an X which statement is false....
• 12N.2.sl.TZ0.2c: Write down \(n[T \cap (C \cup I)']\).
• 12M.1.sl.TZ2.4c: Explain, in words, the meaning of the part of the diagram that represents the set \(P \cap F'\).
• 09N.2.sl.TZ0.2A, d: Write down \(n({\text{B}} \cup {\text{C}})\).
• 09M.2.sl.TZ1.2ii, a: Write down \(n(R \cap S \cap B)\).
• 09M.2.sl.TZ1.2ii, c: Describe which groups the pupils in the set \(S \cap B\) like.
• 11M.2.sl.TZ1.2A.e: Find \(n[(S \cup P) \cap A']\).
• 11M.1.sl.TZ2.1a: Write down the number of elements in \(A \cap C\) .
• 13M.1.sl.TZ1.2a: List the elements of (i) U ; (ii) B .
• 07M.1.sl.TZ0.7a: List the members of sets (i) \(B\) (ii) \(C \cap B\) (iii) \(B \cup C′\)
• 07M.2.sl.TZ0.5ii.b: Find (i) \(n(M \cap W)\) (ii) \(n(M′ \cup S)\)
• 07N.1.sl.TZ0.2a: List the elements of the following sets: A,
• 07N.1.sl.TZ0.2b: List the elements of the following sets: B,
• 07N.1.sl.TZ0.2c: List the elements of the following sets: \(A \cup B\) ,
• 07N.1.sl.TZ0.2d: List the elements of the following sets: \(A \cap B'\) .
• 08N.1.sl.TZ0.9c: Write down the number of pupils that do not study Physics.
• 08N.1.sl.TZ0.9d: Find \(n[(P \cup B) \cap C]\) .
• 08M.1.sl.TZ2.9a: Shade \((A \cup B) \cap C'\) on the diagram below.
• 10N.1.sl.TZ0.9a.ii: List the elements of the following set. \(A \cap B'\)
• 13N.1.sl.TZ0.2c: Complete the Venn diagram with all the elements of \(U\).
• 13N.2.sl.TZ0.3a: Draw a Venn diagram, using sets labelled \(E\), \(S\) and \(A\), to show this information.
• 13N.2.sl.TZ0.3b: Calculate the value of \(x\).
• 13N.2.sl.TZ0.3c: Explain, in words, the meaning of \((E \cup S) \cap A'\).
• 13N.2.sl.TZ0.3d: Write down \(n\left( {(E \cup S \cup A)'} \right)\).
• 14M.2.sl.TZ1.2b: There were 25 tourists in the group and every tourist saw at least one of the three types of...
• 14N.1.sl.TZ0.8a: Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate...
• 14N.1.sl.TZ0.8b: State which polygons from Tuti’s list are elements of (i)     \(A \cap B\); (ii)    ...
• 15M.1.sl.TZ1.8a: Complete the Venn diagram with the numbers written on Aleph’s die (\(A\)) and Beth’s die (\(B\)).
• 15M.1.sl.TZ1.8b: Find \(n(B \cap A')\).
• 15M.1.sl.TZ2.6: Consider the following Venn diagrams. Each diagram is shaded differently. In the following...
• 15M.2.sl.TZ2.1a: Copy the following Venn diagram and correctly insert all values from the above information.
• 15M.2.sl.TZ2.1b: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1c: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1d: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1e: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1f: The number of customers that like only mangoes is equal to the number of customers that like only...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17M.1.sl.TZ2.2b: Complete the Venn diagram using the above information.
• 17N.1.sl.TZ0.7a: Complete the Venn diagram for these students.
• 17N.1.sl.TZ0.7b: One of the students who joined the sports club is chosen at random. Find the probability that...
• 17N.1.sl.TZ0.7c: Determine whether the events \(S\) and \(M\) are independent.
• 18M.1.sl.TZ2.9a.i: Write down an expression, in set notation, for the shaded region represented by Diagram 1.
• 18M.1.sl.TZ2.9a.ii: Write down an expression, in set notation, for the shaded region represented by Diagram 2.
• 18M.1.sl.TZ2.9a.iii: Write down an expression, in set notation, for the shaded region represented by Diagram 3.
• 18M.1.sl.TZ2.9b.i: Shade, on the Venn diagram, the region represented by the set \(\left( {H \cup I} \right)'\).  
• 18M.1.sl.TZ2.9b.ii: Shade, on the Venn diagram, the region represented by the set \(J \cap K\).
• 18M.2.sl.TZ2.1a.i: Write down the value of a.
• 18M.2.sl.TZ2.1a.ii: Write down the value of b.
• 18M.2.sl.TZ2.1b.i: Use the tree diagram to find the probability that an employee encountered traffic and was late...
• 18M.2.sl.TZ2.1b.ii: Use the tree diagram to find the probability that an employee was late for work.
• 18M.2.sl.TZ2.1b.iii: Use the tree diagram to find the probability that an employee encountered traffic given that they...
• 18M.2.sl.TZ2.1c.i: Find the value of x.
• 18M.2.sl.TZ2.1c.ii: Find the value of y.
• 18M.2.sl.TZ2.1d: Find the number of employees who, in the last year, did not travel to work by car, bicycle or...
• 18M.2.sl.TZ2.1e: Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).

Venn diagrams and simple applications.

• 10M.1.sl.TZ1.2: The sets \(P\), \(Q\) and \(U\) are defined as U = {Real Numbers} ,  P = {Positive Numbers} and...
• 10M.1.sl.TZ1.6a: Write down the value of q.
• 10M.1.sl.TZ1.6b: Find the value of p.
• 10M.1.sl.TZ1.6c: Calculate the number of members of the fitness club who attend neither the aerobics course (A)...
• 10M.1.sl.TZ1.6d: Shade, on your Venn diagram, \(A' \cap Y\) .
• 10M.1.sl.TZ2.6a: Show this information on the Venn diagram below.
• 10M.1.sl.TZ2.6b: Find the number of students who like both peanut butter and jam.
• 11N.1.sl.TZ0.5b: In the Venn diagram below, set A represents the people in the group with Australian passports and...
• 11N.1.sl.TZ0.5c: In the Venn diagram below, set A represents the people in the group with Australian passports and...
• 10N.2.sl.TZ0.1A.a: Represent this information on a Venn diagram.
• 10N.2.sl.TZ0.1A.b: Find the number of students who had none of the three choices for breakfast.
• 10N.2.sl.TZ0.1A.c: Write down the percentage of students who had fruit for breakfast.
• 10N.2.sl.TZ0.1A.d: Describe in words what the students in the set \(X \cap Y'\) had for breakfast.
• 10N.2.sl.TZ0.1A.e: Find the probability that a student had at least two of the three choices for breakfast.
• 10N.2.sl.TZ0.1A.f: Two students are chosen at random. Find the probability that both students had all three choices...
• 12N.2.sl.TZ0.2a: Draw a Venn diagram to show this information. Use T to represent the set of students who have a...
• 12N.2.sl.TZ0.2b: Write down the number of students that (i) have a computer only; (ii) have an iPhone and a...
• 12N.2.sl.TZ0.2c: Write down \(n[T \cap (C \cup I)']\).
• 12N.2.sl.TZ0.2d: Calculate the number of students who have none of the three.
• 12M.2.sl.TZ1.1a: Draw a Venn diagram to represent this information. Label A the set that represents The Art...
• 12M.2.sl.TZ1.1b: Find the percentage of the population that does not read any of the three newspapers.
• 12M.2.sl.TZ1.1c: Find the percentage of the population that reads exactly one newspaper.
• 12M.2.sl.TZ1.1d: Find the percentage of the population that reads The Art Journal or The Beartown News but not The...
• 12M.2.sl.TZ1.1e: A local radio station states that 83 % of the population reads either The Beartown News or The...
• 12M.1.sl.TZ2.4a: Write down the total number of students in the school.
• 12M.1.sl.TZ2.4b: Write down the number of students who (i) learn violin only; (ii) learn piano or flute or...
• 12M.1.sl.TZ2.4c: Explain, in words, the meaning of the part of the diagram that represents the set \(P \cap F'\).
• 09N.1.sl.TZ0.2: The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and...
• 09N.1.sl.TZ0.14a: Draw a Venn diagram in the space below to illustrate this information.
• 09N.1.sl.TZ0.14b: Find the probability that a student studies Spanish given that she studies one language only.
• 09N.2.sl.TZ0.2A, a: Copy and complete the Venn diagram on your answer paper.
• 09N.2.sl.TZ0.2A, b: Write down the number of students who study Mathematics but not Further Mathematics.
• 09N.2.sl.TZ0.2A, c: Write down the total number of students in the school.
• 09M.2.sl.TZ1.2ii, a: Write down \(n(R \cap S \cap B)\).
• 09M.2.sl.TZ1.2ii, b: Find \(n(R')\).
• 09M.2.sl.TZ1.2ii, c: Describe which groups the pupils in the set \(S \cap B\) like.
• 09M.2.sl.TZ1.2ii, d: Use set notation to describe the group of pupils who like the Rockers and the Bluers but do not...
• 09M.2.sl.TZ1.2ii, e, i: There are 33 pupils in the class. Find x.
• 09M.2.sl.TZ2.1a: Draw a Venn diagram to represent this information.
• 13M.1.sl.TZ1.2b: Write down the elements of U on the Venn diagram.
• 11M.2.sl.TZ1.2A.a: Draw a Venn Diagram, using sets labelled \(A\) , \(S\) and \(P\) , that shows this information.
• 13M.2.sl.TZ1.2a: Draw a Venn diagram to represent the information above.
• 13M.2.sl.TZ2.1a: Draw a Venn diagram to represent the given information using sets labelled C, M and P. Complete...
• 11M.2.sl.TZ1.2A.b: There were 48 customers of Pete’s Eats that day. Calculate the number of people who were...
• 11M.2.sl.TZ1.2A.c: There were 50 customers of Sarah’s Snackbar that day. Calculate the total number of people who...
• 11M.2.sl.TZ1.2A.d: Write down the number of customers of Alan’s Diner that were also customers of Pete’s Eats.
• 11M.2.sl.TZ1.2A.e: Find \(n[(S \cup P) \cap A']\).
• 07N.1.sl.TZ0.8a: Enter the above information on the Venn diagram below.
• 09M.2.sl.TZ2.1b: Find the number of families who own no pets.
• 11M.1.sl.TZ2.1c: Complete the following Venn diagram with all the elements of \(U\) .
• 13M.1.sl.TZ1.2c: Write down \(n (A \cap B)\).
• 13M.2.sl.TZ1.2b: Write down the number of students who study Music but not Economics.
• 13M.2.sl.TZ1.2c: There are 22 Economics students in total. (i) Calculate the number of students who study...
• 13M.2.sl.TZ2.1b: Find the number of families who (i) went to the circus only; (ii) went to the museum and the...
• SPM.2.sl.TZ0.5a: Represent this information on a Venn Diagram.
• SPM.2.sl.TZ0.5b: There were \(28\) students who used a bus to travel to school. Calculate the number of...
• SPM.2.sl.TZ0.5c: Tomoko used a bus to travel to school yesterday. Find the probability that she also walked.
• SPM.2.sl.TZ0.5d: Two students are chosen at random from all \(50\) students. Find the probability that(i)    ...
• 07M.2.sl.TZ0.5ii.a: Complete the diagram, using the information given in the question.
• 07N.1.sl.TZ0.8b: 99 of the students play basketball, 88 sing in the choir and 110 do drama. Calculate the number...
• 07N.1.sl.TZ0.8c: 99 of the students play basketball, 88 sing in the choir and 110 do drama. Calculate the total...
• 08N.1.sl.TZ0.9a: Write down the number of pupils that study Chemistry only.
• 08N.1.sl.TZ0.9b: Write down the number of pupils that study exactly two sciences.
• 08N.1.sl.TZ0.9c: Write down the number of pupils that do not study Physics.
• 08M.2.sl.TZ1.2i.a: Represent this information on a Venn diagram.
• 08M.2.sl.TZ1.2i.b: Calculate the number of students who own none of the items mentioned above.
• 08M.1.sl.TZ2.9a: Shade \((A \cup B) \cap C'\) on the diagram below.
• 08M.1.sl.TZ2.9b: In the Venn diagram below, the number of elements in each region is given. Find...
• 08M.1.sl.TZ2.9c: \(U\) is the set of positive integers, \({\mathbb{Z}^ + }\). \(E\) is the set of even...
• 09M.2.sl.TZ1.2ii, e, ii: There are 33 pupils in the class. Find the number of pupils who like the Rockers.
• 14M.1.sl.TZ2.3a: 4
• 14M.1.sl.TZ2.3b: \(\frac{1}{3}\)
• 14M.1.sl.TZ2.3c: \(\pi \)
• 14M.1.sl.TZ2.3d: \(0.38\)
• 14M.1.sl.TZ2.3e: \(\sqrt 5 \)
• 14M.1.sl.TZ2.3f: \(-0.25\)
• 13N.1.sl.TZ0.2a: List the elements of \(A\).
• 13N.1.sl.TZ0.2b: List the elements of \(B\).
• 13N.1.sl.TZ0.2c: Complete the Venn diagram with all the elements of \(U\).
• 13N.2.sl.TZ0.3a: Draw a Venn diagram, using sets labelled \(E\), \(S\) and \(A\), to show this information.
• 13N.2.sl.TZ0.3b: Calculate the value of \(x\).
• 13N.2.sl.TZ0.3d: Write down \(n\left( {(E \cup S \cup A)'} \right)\).
• 14M.2.sl.TZ1.2a: Draw a Venn diagram to show this information.
• 14M.2.sl.TZ1.2b: There were 25 tourists in the group and every tourist saw at least one of the three types of...
• 14N.1.sl.TZ0.8a: Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate...
• 14N.1.sl.TZ0.8b: State which polygons from Tuti’s list are elements of (i)     \(A \cap B\); (ii)    ...
• 15M.1.sl.TZ1.8a: Complete the Venn diagram with the numbers written on Aleph’s die (\(A\)) and Beth’s die (\(B\)).
• 15M.1.sl.TZ1.8b: Find \(n(B \cap A')\).
• 15M.1.sl.TZ2.6: Consider the following Venn diagrams. Each diagram is shaded differently. In the following...
• 15M.2.sl.TZ2.1a: Copy the following Venn diagram and correctly insert all values from the above information.
• 15M.2.sl.TZ2.1b: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1c: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1d: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1e: The number of customers that like only mangoes is equal to the number of customers that like only...
• 15M.2.sl.TZ2.1f: The number of customers that like only mangoes is equal to the number of customers that like only...
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 17M.1.sl.TZ2.2b: Complete the Venn diagram using the above information.
• 17N.1.sl.TZ0.7a: Complete the Venn diagram for these students.
• 17N.1.sl.TZ0.7b: One of the students who joined the sports club is chosen at random. Find the probability that...
• 17N.1.sl.TZ0.7c: Determine whether the events \(S\) and \(M\) are independent.
• 18M.1.sl.TZ2.9a.i: Write down an expression, in set notation, for the shaded region represented by Diagram 1.
• 18M.1.sl.TZ2.9a.ii: Write down an expression, in set notation, for the shaded region represented by Diagram 2.
• 18M.1.sl.TZ2.9a.iii: Write down an expression, in set notation, for the shaded region represented by Diagram 3.
• 18M.1.sl.TZ2.9b.i: Shade, on the Venn diagram, the region represented by the set \(\left( {H \cup I} \right)'\).  
• 18M.1.sl.TZ2.9b.ii: Shade, on the Venn diagram, the region represented by the set \(J \cap K\).
• 18M.2.sl.TZ2.1a.i: Write down the value of a.
• 18M.2.sl.TZ2.1a.ii: Write down the value of b.
• 18M.2.sl.TZ2.1b.i: Use the tree diagram to find the probability that an employee encountered traffic and was late...
• 18M.2.sl.TZ2.1b.ii: Use the tree diagram to find the probability that an employee was late for work.
• 18M.2.sl.TZ2.1b.iii: Use the tree diagram to find the probability that an employee encountered traffic given that they...
• 18M.2.sl.TZ2.1c.i: Find the value of x.
• 18M.2.sl.TZ2.1c.ii: Find the value of y.
• 18M.2.sl.TZ2.1d: Find the number of employees who, in the last year, did not travel to work by car, bicycle or...
• 18M.2.sl.TZ2.1e: Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).