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.

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

Write your answer to part (a)

(i)     correct to two decimal places;

(ii)     correct to three significant figures.

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

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

Calculate the area of the park.

Write down the value of x.

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

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

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

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

Find the value of $a$.

Calculate the amount of MXN Harry received.

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

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

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

Find the area of ABCD.

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

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

Calculate the length of side AC in km.

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

Write down the minimum value of $T$.

Write down the minimum total cost for this journey.

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

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

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

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

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

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.

Find the slant height of the cone-shaped container.

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

Calculate the volume of this hemisphere in cm³.

Give your answer correct to one decimal place.

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

Calculate the amount of USD she receives.

Find the value of $r$.

Write down the median length of these leaves.

Find the value of $a$.

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

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

Calculate the volume of this pan.

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

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.

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

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

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

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

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

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

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

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

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

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.

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

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

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.

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

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

1 cm³ of glass has a mass of 2.56 grams.

Calculate the mass, in grams, of the paperweight.

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

Find the value of $x$.

Calculate the amount that Velina receives in DKK.

Find the percentage error.

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

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

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

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

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

The length of path AD is 287 m.

Find the area of the region ABCD.

Hence, calculate the amount of USD she receives.

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

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

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

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

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

Find the curved surface area of the cone.

Calculate the curved surface area of the remaining solid.

John purchased the bicycle in 2008.

Justify why John should not insure his bicycle in 2019.

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

Calculate the amount of VEF that Javier receives.

Find the value of $x$.

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

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

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 value of this minimum area.

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

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

Calculate the volume of the paperweight.

Calculate the amount of PEN she receives.

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

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.

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.

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.

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

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

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.

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.

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 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.

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.

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

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

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

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

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.

Find the volume of one cone-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.

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 $\text{A}\stackrel{\wedge }{\text{C}}\text{D}$.

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.