DP Mathematics: Analysis and Approaches Questionbank

Find the side length, $s$, where $s>0$, of a square such that $A=P$.

Write down, in terms of $x$ and $n$, an expression for the area, $A_T$, of one of these isosceles triangles.

Find an expression, in terms of $x$ for the travel time $T$, from $\text{A}$ to $\text{B}$, passing through $\text{D}$.

the boat travels directly to $\text{B}$.

the boat is taken from $\text{A}$ to $\text{P}$, and the bus from $\text{P}$ to $\text{B}$.

Find the value of $x$ so that $T$ is a minimum.

Write down the minimum value of $T$.

Write down the minimum total cost for this journey.

Find the new value of $x$ so that the total cost $C$ to travel from $\text{A}$ to $\text{B}$ via $\text{D}$ is a minimum.

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.

Use this model to calculate the circumference of the Moon in kilometres. Give your full calculator display.

Give your answer to part (a) correct to three significant figures.

Write your answer to part (b) in the form $a\times {10}^k$, where 1 ≤ $a$ < 10 , $k\in \mathbb{Z}$.

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

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

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

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).

State whether it is valid to use the regression line to estimate the average weight of the brain of mice. Give a reason for your answer.

Write down the median length of these leaves.

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

Use the graph to find the value of $k$.

Before measuring, the researcher estimated $k$ to be approximately 9.5 cm. Find the percentage error in her estimate.

Calculate the value of $p$. Write down your full calculator display.

Write your answer to part (a)

(i)     correct to two decimal places;

(ii)     correct to three significant figures.

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

Use the above information to write down an equation in $x$ and $y$.

Use the information about the cost of tickets to write down a second equation in $x$ and $y$.

Find the value of $x$ and the value of $y$.

Find the percentage error.

Find the length $\text{AB}$, giving your answer to four significant figures.

Find the total area of the two rectangles that make up the roof.

Find the maximum number of complete panels that can be fitted to the whole roof.

Find the percentage error in her estimate.

Olivia investigates arranging the panels, such that the longer edge of each panel is parallel to $\text{AB}$ or $\text{AC}$.

State whether this new arrangement will allow Olivia to fit more solar panels to the roof. Justify your answer.

Write down an expression for the width of the garden in terms of $x$.

Write down an equation for the perimeter of the garden in terms of $x$.

Find the value of $x$.

Calculate the volume of this hemisphere in cm³.

Give your answer correct to one decimal place.

Write down your answer to part (a) correct to the nearest integer.

Write down your answer to part (b) in the form a × 10^k , where 1 ≤ a < 10 and k ∈ $\mathbb{Z}$.

Use your graphic display calculator to write down $\overline{x}$, the mean project mark.

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.

Show that the point M ($\overline{x}$, $\overline{y}$) lies on the regression line y on x.

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.

In his final IB examination Jerome scored 65.

Calculate the percentage error in Jerome’s estimated examination score.

Calculate the radius of the base of the cone which has been removed.

Calculate the curved surface area of the cone which has been removed.

Calculate the curved surface area of the remaining solid.

Calculate the volume of this pan.

Find the radius of the sphere in cm, correct to one decimal place.

Find the value of $a$.

Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.

Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.

In the context of this model, state what the value of 19 represents.

Calculate the length of side AC in km.

Calculate the area of the park.

Find an expression for the slant height of the cone in terms of r.

The total external surface area of the pencil case rounded to 3 significant figures is 570 cm².

Using your graphic display calculator, calculate the value of r.

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).

Calculate the time, in minutes, it takes for light from the Sun to reach the Earth.

Find the distance from the Earth to Polaris in millions of km. Give your answer in the form $a\times {10}^k$ with and $k\in \mathbb{Z}$.

Find the radius, $r$, of the circular base of the cone.

Find the slant height, $l$, of the cone.

Find the curved surface area of the cone.

Find the value of $a$.

Find the time, in years, for the population to decrease to 20 turtles.

There is a number $m$ beyond which the turtle population will not decrease.

Find the value of $m$. Justify your answer.

Find the volume of one cone-shaped container.

Find the slant height of the cone-shaped container.

Show that the total surface area of the cone-shaped container is 314 cm², correct to three significant figures.

Find the height, $h$, of this cylinder-shaped container.

The factory director wants to increase the volume of coconut water sold per container.

State whether or not they should replace the cone-shaped containers with cylinder‑shaped containers. Justify your conclusion.

Write down the value of x.

Calculate the volume of the paperweight.

1 cm³ of glass has a mass of 2.56 grams.

Calculate the mass, in grams, of the paperweight.

Find the volume, in cm³, of this calculator case.

Find the distance from A to C.

Find the size of angle $\text{B}\stackrel{\wedge }{\text{A}}\text{C}$.

Find the size of angle $\text{C}\stackrel{\wedge }{\text{A}}\text{D}$.

Find the size of angle $\text{A}\stackrel{\wedge }{\text{C}}\text{D}$.

The length of path AD is 287 m.

Find the area of the region ABCD.

Use this exchange rate to calculate the amount of ARS that is equal to 350 AUD.

Calculate the total amount of ARS Jose paid to get 350 AUD.

Find the value of $x$.

Calculate the amount of PEN she receives.

Calculate the amount of USD she receives.

Find the amount of Euros that Claudia receives. Give your answer correct to two decimal places.

Find the value of $r$.

Calculate, in CAD, the total amount John pays for the bicycle.

Find the value of the bicycle during the 5th year. Give your answer to two decimal places.

Calculate, in years, when the bicycle value will be less than 50 USD.

Find the total amount John has paid to insure his bicycle for the first 5 years.

John purchased the bicycle in 2008.

Justify why John should not insure his bicycle in 2019.

Calculate the amount of MXN Harry received.

Calculate the value of the commission, in MXN, that Harry paid.

The exchange rate for this exchange was 1 USD = 17.24 MXN.

Calculate the amount of USD Harry received. Give your answer correct to the nearest cent.

Calculate the amount of VEF that Javier receives.

Calculate the total amount, in USD, that Javier has remaining from his 5000 USD after his trip to Venezuela.

Calculate the amount that Velina receives in DKK.

Calculate the amount, in DKK, that will be left to exchange after commission.

Hence, calculate the amount of USD she receives.

Write down the $x$-coordinate of the point of inflexion on the graph of $y=f\left(x\right)$.