DP Mathematics: Applications and Interpretation Questionbank

Find the value of $a$.

Write down the value of the median distance in kilometres (km).

Find the value of $b$.

Find $m$.

The first $150$ athletes that completed the race won a prize.

Given that an athlete took between $22$ and $m$ minutes to complete the $5 \text{km}$ race, calculate the probability that they won a prize.

Find the probability that it will take Fiona between $15$ minutes and $30$ minutes to walk to the bus stop.

Find $\sigma$.

Find the probability that the bus journey takes less than $45$ minutes.

Find the probability that Fiona will arrive on time.

This year, Fiona will go to school on $183$ days.

Calculate the number of days Fiona is expected to arrive on time.

Find the probability that the first ball chosen is labelled $\text{A}$.

Find the probability that the first ball chosen is labelled $\text{A}$ or labelled $\text{N}$.

Find the probability that the second ball chosen is labelled $\text{A}$, given that the first ball chosen was labelled $\text{N}$.

Find the probability that both balls chosen are labelled $\text{N}$.

Write down the value of $a$.

$b$.

$c$.

Find an expression, in terms of $b$, for the probability of a person not having blue eyes and having fair hair.

prefers a laptop given that they are $17\text{–}18$ years old.

prefers a tablet.

prefers a tablet or is $14\text{–}16$ years old.

State the conclusion for the test in context. Give a reason for your answer.

is $11\text{–}13$ years old and prefers a mobile phone.

State the null and alternative hypotheses.

Write down the $p$-value.

Write down the number of degrees of freedom.

Write down the ${\chi }^2$ test statistic.

maximum value of $h$.

Find the period of the function.

Find the height of $\text{C}$ above the ground when $t=2$.

At any given instant, find the probability that point $\text{C}$ is visible from Tim’s window.

minimum value of $h$.

Find the time, in seconds, that point $\text{C}$ is above a height of $100 \text{m}$, during each complete rotation.

The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.

At any given instant, find the probability that Tim can see point $\text{C}$ from his window. Justify your answer.

Find the time, in seconds, it takes for the blade $\text{[BC]}$ to make one complete rotation under these conditions.

Write down the amplitude of the function.

Calculate the angle, in degrees, that the blade $\text{[BC]}$ turns through in one second.

Sketch the function $h\left(t\right)$ for $0\le t\le 5$, clearly labelling the coordinates of the maximum and minimum points.

Find the probability that the applicant applied for the Arts programme.

Find the probability that a randomly chosen applicant from this group was accepted by the university.

Two different applicants are chosen at random from the original group.

Find the probability that both applicants applied to the Arts programme.

Determine the probability that fewer than $7$ people will pass this polygraph test.

Calculate the expected number of people who will pass this polygraph test.

Calculate the probability that exactly $4$ people will fail this polygraph test.

Find, to the nearest integer, the expected increase or decrease in the money made by the airline if they decide to sell $74$ tickets rather than $72$.

Find the probability that on any given day Mr Burke chooses a female student to answer a question.

Find the probability he will choose a female student 8 times.

Find the probability he will choose a male student at most 9 times.

Complete the given probability tree diagram for Iqbal’s three attempts, labelling each branch with the correct probability.

Calculate the probability that Iqbal passes at least two of the papers he attempts.

Find the probability that Iqbal passes his third paper, given that he passed only one previous paper.

Draw a tree diagram to represent this information for the first three days of July.

Find the probability that the 3rd July is calm.

Find the probability that the 1st July was calm given that the 3rd July is windy.

One of the players is chosen at random. Find the probability that this player’s score was 5 or more.

Calculate the mean score.

Complete the following tree diagram.

Find the probability that exactly one of the selected balls is green.

Find P(A ∩ B′ ).

Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).

Copy and complete the following tree diagram.

Find the probability that Pablo leaves home before 07:00 and is late for work.

Find the probability that Pablo is late for work.

Given that Pablo is late for work, find the probability that he left home before 07:00.

Two days next week Pablo will drive to work. Find the probability that he will be late at least once.

Find the probability of rolling exactly one red face.

Find the probability of rolling two or more red faces.

Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is $\frac{1}{3}$.

Write down the value of $x$.

Hence, find the value of $y$.

Ted will always have another turn if he expects an increase to his winnings.

Find the least value of $w$ for which Ted should end the game instead of having another turn.

Find the value of $p$;

Find the value of $q$.

A girl is selected at random. Find the probability that she takes economics but not history.

Find the probability, in terms of $n$, that the game will end on her first draw.

Find the probability, in terms of $n$, that the game will end on her second draw.

third draw.

fourth draw.

Hayley plays the game when $n$ = 5. She pays $20 to play and can earn money back depending on the number of draws it takes to obtain a blue marble. She earns no money back if she obtains a blue marble on her first draw. Let M be the amount of money that she earns back playing the game. This information is shown in the following table.

Find the value of $k$ so that this is a fair game.

Find the value of $p$.

Find the value of $q$.

Find $\text{P}\left(A^{\prime }\cup B\right)$.

Find $\text{P}(B)$.

Find $\text{P}(A\cup B)$.

Find $q$.

Find $p$.

Write down the probability of drawing three blue marbles.

Explain why the probability of drawing three white marbles is $\frac{1}{6}$.

The bag contains a total of ten marbles of which $w$ are white. Find $w$.

Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.

Jill plays the game nine times. Find the probability that she wins exactly two prizes.

Complete the Venn diagram for these students.

One of the students who joined the sports club is chosen at random. Find the probability that this student joined both clubs.

Determine whether the events $S$ and $M$ are independent.

Complete the Venn diagram using the given information.

Find the value of x.

Write down the value of $n\left(\left(F\cup H\right)\cap S^{\prime }\right)$.

Write down an expression, in set notation, for the shaded region represented by Diagram 1.

Write down an expression, in set notation, for the shaded region represented by Diagram 2.

Write down an expression, in set notation, for the shaded region represented by Diagram 3.

Shade, on the Venn diagram, the region represented by the set ${\left(H\cup I\right)}^{\prime }$.

Shade, on the Venn diagram, the region represented by the set $J\cap K$.

Write down the value of a.

Write down the value of b.

Use the tree diagram to find the probability that an employee encountered traffic and was late for work.

Use the tree diagram to find the probability that an employee was late for work.

Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.

Find the value of x.

Find the value of y.

Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.

Find $n\left(\left(C\cup B\right)\cap P^{\prime }\right)$.

Write down an expression, in terms of $x$, for the number of children who play only basketball.

Complete the Venn diagram using the above information.

Find the number of children who play only football.

Write down the value of $n(F)$.

In the table indicate whether the given statements are True or False.

On the Venn diagram, shade the region $A\cap (B\cup C{)}^{\prime }$.

Write down the number of sporting activities offered by the school during its school year.

Determine whether rock-climbing is offered by the school in the fall/autumn trimester.

Write down the elements of the set $F\cap W^{\prime }$;

Write down $n(W\cap S)$.

Write down, in terms of $F$, $W$ and $S$, an expression for the set which contains only archery, baseball, kayaking and surfing.

Draw a Venn diagram to represent the given information, using sets labelled $B$, $C$ and $H$.

Show that $x=3$.

Write down the value of $n(B\cap C)$.

Find the probability that this person

(i)     went on at most one trip;

(ii)     went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.

Find the number of students in the school that are taught in Spanish.

Find the number of students in the school that study Mathematics in English.

Find the number of students in the school that study both Biology and Mathematics.

Write down $n\left(S\cap \left(M\cup B\right)\right)$.

Write down $n\left(B\cap M\cap S^{\prime }\right)$.

Find the probability that this student studies Mathematics.

Find the probability that this student studies neither Biology nor Mathematics.

Find the probability that this student is taught in Spanish, given that the student studies Biology.

Place the numbers $2\pi \text{,}-5\text{,}{3}^{-1}$ and $2^{\frac{3}{2}}$ in the correct position on the Venn diagram.

In the table indicate which two of the given statements are true by placing a tick (✔) in the right hand column.

Write down a formula for $A$, the surface area to be coated.

Express this volume in $\text{c}{\text{m}}^3$.

Write down, in terms of $r$ and $h$, an equation for the volume of this water container.

Show that $A=\pi r^2+\frac{1000000}{r}$.

Find $\frac{\text{d}A}{\text{d}r}$.

Using your answer to part (e), find the value of $r$ which minimizes $A$.

Find the value of this minimum area.

Find the least number of cans of water-resistant material that will coat the area in part (g).

Write down the elements that belong to $A\cap B$.

Write down the elements that belong to $A\cap B^{\prime }$.

Write down $n\left(A\cap B^{\prime }\right)$.

Find the probability that Sungwon’s score on her first turn is greater than $4$.

Find the probability that Sungwon scores greater than $4$ on both of her first two turns.

Sungwon will play the game for $11$ turns.

Find the expected number of times the score on a turn is greater than $4$.

State ${\text{H}}_0$, the null hypothesis for this test.

Write down the number of degrees of freedom.

Show that the expected number of children who chose shrimp is $31$, correct to two significant figures.

the ${\chi }_2$ statistic.

the $p$-value.

State the conclusion for this test. Give a reason for your answer.

Calculate the probability that the customer is an adult.

Calculate the probability that the customer is an adult or that the customer chose shrimp.

Given that the customer is a child, calculate the probability that they chose pasta or fish.