DP Mathematics: Analysis and Approaches Questionbank

Write down the value of the iron in the form $a\times {10}^k$ where $1\le a<10 , k\in \mathrm{\mathbb{Z}}$.

Calculate James’s estimate of its volume, in ${\text{km}}^3$.

The actual volume of the asteroid is found to be $6.074\times {10}^6 {\text{km}}^3$.

Find the percentage error in James’s estimate of the volume.

Write down the radius of the planet.

The volume of the planet can be expressed in the form $\mathrm{\pi }\left(a\times {10}^k\right) {\text{km}}^3$ where $1\le a<10$ and $k\in \mathrm{\mathbb{Z}}$.

Find the value of $a$ and the value of $k$.

Find the length, in cm, of this line. Give your answer in the form a × 10^k , where 1 ≤ a < 10 and k ∈ $\mathbb{Z}$.

Write down the length of the Amazon River in cm.

Find the value of x.

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 $k\in \mathbb{Z}$.

Calculate the percentage of the population of Ottawa that speak English but not French.

Calculate the number of people in Ottawa that speak both English and French.

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

Calculate $\sqrt[3]{\frac{p}{q}}$. Give your full calculator display.

Write down your answer to part (a) correct to two decimal places;

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

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

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 .

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 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 , $k\in \mathbb{Z}$.