A sphere with diameter 3 474 000 metres can model the shape of the Moon.

Let $p=\frac{\cos <!--\; \; -->x+\sin <!--\; \; -->y}{\sqrt{w^2-<!--\; -\; -->z}}$,

where $x={36}^{\circ <!--\; \circ \; -->},y={18}^{\circ <!--\; \circ \; -->},w=29$ and $z=21.8$.

For a study, a researcher collected 200 leaves from oak trees. After measuring the lengths of the leaves, in cm, she produced the following cumulative frequency graph.

The researcher finds that 10% of the leaves have a length greater than $k$ cm.

The volume of a hemisphere, V, is given by the formula

V = $\sqrt{\frac{4S^3}{243\mathrm{\pi <!--\; \pi \; -->}}}$,

where S is the total surface area.

The total surface area of a given hemisphere is 350 cm².

Consider the following sets:

The universal set $U$ consists of all positive integers less than 15;
$A$ is the set of all numbers which are multiples of 3;
$B$ is the set of all even numbers.

A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.
A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is removed from the top of the larger cone, as shown in the diagram.

The speed of light is $\text{300}\text{000}$ kilometres per second. The average distance from the Sun to the Earth is 149.6 million km.

A light-year is the distance light travels in one year and is equal to $\text{9}\text{467}\text{280}$ million km. Polaris is a bright star, visible from the Northern Hemisphere. The distance from the Earth to Polaris is 323 light-years.

A type of candy is packaged in a right circular cone that has volume $\text{100 c}{\text{m}}^{\text{3}}$ and vertical height 8 cm.

Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.

The cylinder has a radius of r cm and a height of 12 cm.

The cone has a base radius of r cm and a height of 10 cm.

A calculator fits into a cuboid case with height 29 mm, width 98 mm and length 186 mm.

A solid glass paperweight consists of a hemisphere of diameter 6 cm on top of a cuboid with a square base of length 6 cm, as shown in the diagram.

The height of the cuboid, x cm, is equal to the height of the hemisphere.

A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km. Angle A$\stackrel{\wedge <!--\; \wedge \; -->}{\text{B}}$C is 52°.

Passengers of Flyaway Airlines can purchase tickets for either Business Class or Economy Class.

On one particular flight there were 154 passengers.

Let $x$ be the number of Business Class passengers and $y$ be the number of Economy Class passengers on this flight.

On this flight, the cost of a ticket for each Business Class passenger was 320 euros and the cost of a ticket for each Economy Class passenger was 85 euros. The total amount that Flyaway Airlines received for these tickets was $\text{14}\text{970 euros}$.

The airline’s finance officer wrote down the total amount received by the airline for these tickets as $\text{14}\text{270 euros}$.

The width of a rectangular garden is 4.5 metres shorter than its length, which is $x$ metres.

The perimeter of the garden is 111 m.

Little Green island originally had no turtles. After 55 turtles were introduced to the island, their population is modelled by

$$N\left(t\right)=a\times <!--\; \times \; -->2^{-<!--\; -\; -->t}+10\text{,}t⩾<!--\; ⩾\; -->0\text{,}$$

where $a$ is a constant and $t$ is the time in years since the turtles were introduced.

Claudia travels from Buenos Aires to Barcelona. She exchanges 8000 Argentine Pesos (ARS) into Euros (EUR).

The exchange rate is 1 ARS = 0.09819 EUR. The bank charges a 2% commission on the exchange.

When Claudia returns to Buenos Aires she has 85 EUR left and exchanges this money back into ARS. The exchange rate is 1 ARS = 0.08753 EUR. The bank charges $r$% commission. The commission charged on this exchange is 14.57 ARS.

In this question, give all answers correct to 2 decimal places.

Jose travelled from Buenos Aires to Sydney. He used Argentine pesos, ARS, to buy 350 Australian dollars, AUD, at a bank. The exchange rate was 1 ARS = 0.1559 AUD.

The bank charged Jose a commission of 2%.

Jose used his credit card to pay his hotel bill in Sydney. The bill was 585 AUD. The value the credit card company charged for this payment was 4228.38 ARS. The exchange rate used by the credit card company was 1 AUD = $x$ ARS. No commission was charged.

Daniela is going for a holiday to South America. She flies from the US to Argentina stopping in Peru on the way.

In Peru she exchanges 85 United States dollars (USD) for Peruvian nuevo sol (PEN). The exchange rate is 1 USD = 3.25 PEN and a flat fee of 5 USD commission is charged.

At the end of Daniela’s holiday she has 370 Argentinean peso (ARS). She converts this back to USD at a bank that charges a 4% commission on the exchange. The exchange rate is 1 USD = 9.60 ARS.

Harry travelled from the USA to Mexico and changed 700 dollars (USD) into pesos (MXN).

The exchange rate was 1 USD = 18.86 MXN.

On his return, Harry had 2400 MXN to change back into USD.

There was a 3.5 % commission to be paid on the exchange.

In this question give all answers correct to two decimal places.

Javier takes 5000 US dollars (USD) on a business trip to Venezuela. He exchanges 3000 USD into Venezuelan bolívars (VEF).

The exchange rate is 1 USD $=$ 6.3021 VEF.

During his time in Venezuela, Javier spends 1250 USD and 12 000 VEF. On his return home, Javier exchanges his remaining VEF into USD.

The exchange rate is 1 USD $=$ 8.7268 VEF.

In this question, give all answers to two decimal places.

Velina travels from New York to Copenhagen with 1200 US dollars (USD). She exchanges her money to Danish kroner (DKK). The exchange rate is 1 USD = 7.0208 DKK.

At the end of her trip Velina has 3450 DKK left that she exchanges to USD. The bank charges a 5 % commission. The exchange rate is still 1 USD = 7.0208 DKK .