DP Mathematics: Applications and Interpretation Questionbank

Calculate the percentage error in using Katya’s four decimal place approximation of $\mathrm{\pi }$, compared to the exact value of $\mathrm{\pi }$ in your calculator.

A triangular field $\text{ABC}$ is such that $\text{AB}=56 \text{m}$ and $\text{BC}=82 \text{m}$, each measured correct to the nearest metre, and the angle at $\text{B}$ is equal to $105°$, measured correct to the nearest $5°$.

Calculate the maximum possible area of the field.

Calculate Katya’s approximation of $\mathrm{\pi }$, correct to four decimal places.

Use the trapezoidal rule with an interval width of $0.4$ to estimate the total amount of carbon dioxide emitted during these two hours.

The real amount of carbon dioxide emitted during these two hours was $72$ tonnes.

Find the percentage error of the estimate found in part (a).

Find an expression for $u_n$.

Calculate the total amount of acceptance fees paid to the university in the first $10$ years.

Calculate the percentage increase in applications from the first year to the second year.

Find $k$.

State whether, for all $n>k$, the university will have places available for all applicants. Justify your answer.

Write down the common ratio of the sequence.

Find the number of student applications the university expects to receive when $n=11$. Express your answer to the nearest integer.

Write down an expression for $v_n$ .

Find, with justification, the largest possible percentage error if the answer to part (a) is recorded as the area of the sector.

Find the upper bound and lower bound of the area of the sector.

Calculate the percentage error in the maximum number of daylight hours Boris recorded in the diagram.

Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the
horizontal, is 85° to the nearest degree.

Use Giovanni's diagram to calculate the length of AX.

Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.

Find the percentage error on Giovanni’s diagram.

Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.

Find the angle of elevation of A from D.

Show that $\text{BD}=93\text{ m}$ correct to the nearest metre.

Calculate angle $\mathrm{B}\hat{\mathrm{C}}\mathrm{D}$.

Find the area of ABCD.

Calculate Abdallah’s estimate for the area.

Find the percentage error in Abdallah’s estimate.

Find the range of the average body weights for these seven species of mammal.

For the data from these seven species calculate $r$, the Pearson’s product–moment correlation coefficient;

For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.

Write down the equation of the regression line $y$ on $x$, in the form $y=mx+c$.

Use your regression line to estimate the average weight of the brain of grey wolves.

Find the percentage error in your estimate in part (d).

Write down the median length of these leaves.

Write down the number of leaves with a length less than or equal to 8 cm.

Write your answer to part (b)(ii) in the form $a\times {10}^k$, where .

Use your graphic display calculator to write down $\overline{y}$, the mean examination score.

Use your graphic display calculator to write down r , Pearson’s product–moment correlation coefficient.

Find the exact value of m and of c for these data.

Use the regression line y on x to estimate Jerome’s examination score.

Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.