DP Mathematics: Applications and Interpretation Questionbank

State the sampling method being used.

Show that $11$ employees are selected for the sample from the national department.

Juliet classifies response $\text{K}$ as an outlier and removes it from the data. Suggest one possible justification for her decision to remove it.

Calculate the number of grade $12$ students who should be in the sample.

The Principal selects the students for the sample by asking those who took part in a previous survey if they would like to take part in another. She takes the first of those who reply positively, up to the maximum needed for the sample.

State which two of the sampling methods listed below best describe the method used.

Stratified          Quota          Convenience          Systematic          Simple random

Identify the type of sampling used by the restaurant manager.

State which of the two sampling methods, systematic or quota, Jason has used.

Determine whether Jason is correct. Support your reasoning.

Show that the test score of $25$ would not be considered an outlier.

Determine if the Netherlands’ score is an outlier for this data. Justify your answer.

State whether the data is discrete or continuous.

Name the type of sampling that best describes the method used by the Principal.

It was not possible to ask every person in the school, so the Headmaster arranged the student names in alphabetical order and then asked every 10th person on the list.

Identify the sampling technique used in the survey.

Find the value of $k$.

State the hypotheses for this t-test.

State the name for this type of sampling technique.

Find the p-value for this t-test.

Calculate the number of volunteers in the sample under the age of 30.

Recalling definitions, such as the Lower Quartile is the $\frac{n+1}{4}th$ piece of data with the data placed in order, find an expression for the Interquartile Range.

State the conclusion of this test, in context, giving a reason.

Give an example of a set of data with 7 numbers in it that does have an outlier, justify this fact by stating the Interquartile Range.

State an assumption that the company is making, in order to use a t-test.

Hence, show that a data set with only 5 numbers in it cannot have any outliers.

The current drug.

The new drug.

Find the value of p.

Find μ, the expected value of X.

Find P(X > μ).

Using this distribution model, find .

Using this distribution model, find the standard deviation of $X$.

an estimate for the mean number of emails received per working day.

an estimate for the standard deviation of the number of emails received per working day.

Give one piece of evidence that suggests Willow’s Poisson distribution model is not a good fit.

Suppose that the probability of Archie receiving more than 10 emails in total on any one day is 0.99. Find the value of λ.

Now suppose that Archie received exactly 20 emails in total in a consecutive two day period. Show that the probability that he received exactly 10 of them on the first day is independent of λ.

Show that $\text{P}(X=3)=0.001$ and $\text{P}(X=4)=0.0027$.

Find the values of the constants $a$ and $b$.

Deduce that $\frac{\text{P}(X=n)}{\text{P}(X=n-1)}=\frac{0.9(n-1)}{n-3}$ for $n>3$.

(i)     Hence show that $X$ has two modes $m_1$ and $m_2$.

(ii)     State the values of $m_1$ and $m_2$.

Determine the minimum value of $x$ such that the probability Kati receives at least one free gift is greater than 0.5.

the standard deviation.

Find the value of the interquartile range.

One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.

Find $(g\circ f)(x)$.

Given that $\underset{x\to +\mathrm{\infty }}{lim}(g\circ f)(x)=-3$, find the value of $b$.

Write down the gradient of the curve of $f$ at P.

Find the equation of the normal to the curve of $f$ at P.

Determine the concavity of the graph of $f$ when and justify your answer.

Find the value of $p$.

Find the value of $a$.

The line $y=kx-5$ is a tangent to the curve of $f$. Find the values of $k$.

Find the value of $p$.

Write down the coordinates of A.

Write down the rate of change of $f$ at A.

Find the coordinates of B.

Find the the rate of change of $f$ at B.

Let $R$ be the region enclosed by the graph of $f$ , the $x$-axis, the line $x=b$ and the line $x=a$. The region $R$ is rotated 360° about the $x$-axis. Find the volume of the solid formed.

Find the gradient of $L$.

Find u.

Find the acute angle between $y=x$ and $L$.

Find $\left(f\circ f\right)\left(x\right)$.

Hence, write down $f^{-1}\left(x\right)$.

Hence or otherwise, find the obtuse angle formed by the tangent line to $f$ at $x=8$ and the tangent line to $f$ at $x=2$.

Consider f(x), g(x) and h(x), for x∈$\mathbb{R}$ where h(x) = $\left(f\circ g\right)$(x).

Given that g(3) = 7 , g′ (3) = 4 and f ′ (7) = −5 , find the gradient of the normal to the curve of h at x = 3.

Find the coordinates of P.

Find $f^{\prime }\left(x\right)$.

Hence, find the equation of L in terms of $a$.

The graph of $f$ has a local minimum at the point Q. The line L passes through Q.

Find the value of $a$.

Find the volume of the container.

Find the value of $p$ and of $q$.

During the interval $p$ < $t$ < $q$, he volume of water in the container increases by $k$ m³. Find the value of $k$.

When $t$ = 0, the volume of water in the container is 2.3 m³. It is known that the container is never completely full of water during the 4 hour period.

Find the minimum volume of empty space in the container during the 4 hour period.

(i)     Find the value of $c$.

(ii)     Show that $b=\frac{\pi }{6}$.

(iii)     Find the value of $a$.

(i)     Write down the value of $k$.

(ii)     Find $g(x)$.

(i)     Find $w$.

(ii)     Hence or otherwise, find the maximum positive rate of change of $g$.

Find $f^{\prime }\left(x\right)$.

The graph of $f$ has a horizontal tangent line at $x=0$ and at $x=a$. Find $a$.

Find the value of $\text{tan}\theta$.

Line $L$ passes through the origin and has a gradient of $\text{tan}\theta$. Find the equation of $L$.

Find the derivative of $f$.

The following diagram shows the graph of $f$  for 0 ≤ $x$ ≤ 3. Line $M$ is a tangent to the graph of $f$ at point P.

Given that $M$ is parallel to $L$, find the $x$-coordinate of P.