Give your answers to parts (b), (c) and (d) to the nearest whole number.

Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money.

Option A: Invest the full amount, in USD, in a fixed deposit account in an American bank.

The account pays a nominal annual interest rate of r % , compounded yearly, for the five years. The bank manager says that this will give Harinder a return of 17 500 USD.

Option B: Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.

The exchange rate is 1 USD = 66.91 INR.

The account in the Indian bank pays a nominal annual interest rate of 5.2 % compounded monthly.

A large underground tank is constructed at Mills Airport to store fuel. The tank is in the shape of an isosceles trapezoidal prism, $\text{ABCDEFGH}$.

$\text{AB}=70 \text{m}$ , $\text{AF}=200 \text{m}$, $\text{AD}=40 \text{m}$, $\text{BC}=40 \text{m}$ and $\text{CD}=110 \text{m}$. Angle $\text{ADC}=60°$ and angle $\text{BCD}=60°$. The tank is illustrated below.

Once construction was complete, a fuel pump was used to pump fuel into the empty tank. The amount of fuel pumped into the tank by this pump each hour decreases as an arithmetic sequence with terms $u_1, u_2, u_3, \dots , u_n$.

Part of this sequence is shown in the table.

At the end of the $2\text{nd}$ hour, the total volume of fuel in the tank was $88 200 {\text{m}}^3$.

The following table shows the average body weight, $x$, and the average weight of the brain, $y$, of seven species of mammal. Both measured in kilograms (kg).

The average body weight of grey wolves is 36 kg.

In fact, the average weight of the brain of grey wolves is 0.120 kg.

The marks obtained by nine Mathematical Studies SL students in their projects (x) and their final IB examination scores (y) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.

The equation of the regression line y on x is y = mx + c.

A tenth student, Jerome, obtained a project mark of 17.

John purchases a new bicycle for 880 US dollars (USD) and pays for it with a Canadian credit card. There is a transaction fee of 4.2 % charged to John by the credit card company to convert this purchase into Canadian dollars (CAD).

The exchange rate is 1 USD = 1.25 CAD.

John insures his bicycle with a US company. The insurance company produces the following table for the bicycle’s value during each year.

The values of the bicycle form a geometric sequence.

During the 1st year John pays 120 USD to insure his bicycle. Each year the amount he pays to insure his bicycle is reduced by 3.50 USD.

A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.

A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.

The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.

The temperature, $P$, of the pizza, in degrees Celsius, °C, can be modelled by

$$P(t)=a(2.06{)}^{-<!--\; -\; -->t}+19,t⩾<!--\; ⩾\; -->0$$

where $a$ is a constant and $t$ is the time, in minutes, since the pizza was taken out of the oven.

When the pizza was taken out of the oven its temperature was 230 °C.

The pizza can be eaten once its temperature drops to 45 °C.

A water container is made in the shape of a cylinder with internal height $h$ cm and internal base radius $r$ cm.

The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.

The volume of the water container is $0.5{\text{m}}^3$.

The water container is designed so that the area to be coated is minimized.

One can of water-resistant material coats a surface area of $2000\text{ c}{\text{m}}^2$.

The Tower of Pisa is well known worldwide for how it leans.

Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a diagram showing a non-right triangle, ABC.

On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is 60°. AX is the perpendicular height from A to BC.

Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX, is 3.9 metres.

A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height of 13 cm.

The factory designers are currently investigating whether a cone-shaped container can be replaced with a cylinder-shaped container with the same radius and the same total surface area.

An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths from point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and angle $\text{A}\stackrel{\wedge <!--\; \wedge \; -->}{\text{B}}<!--\; \; -->\text{C}$ is 125°.

The archaeologists plan to build two more straight paths, AD and DC. For the paths to go around the site, angle $\text{B}\stackrel{\wedge <!--\; \wedge \; -->}{\text{A}}<!--\; \; -->\text{D}$ is to be made equal to 85° and angle $\text{B}\stackrel{\wedge <!--\; \wedge \; -->}{\text{C}}<!--\; \; -->\text{D}$ is to be made equal to 70° as shown in the following diagram.

Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.

The lengths of the sides are $\text{AB}=\text{40 m, BC}=\text{115 m, CD}=\text{60 m, AD}=\text{84 m}$ and angle $\mathrm{B}\stackrel{^<!--\; ^\; -->}{\mathrm{A}}\mathrm{D}={90}^{\circ <!--\; \circ \; -->}$.

This information is shown on the diagram.

The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is

$\text{area}=\frac{(\text{AB}+\text{CD})(\text{AD}+\text{BC})}{4}$.

Abdallah uses this formula to estimate the area of his plot of land.

A sector of a circle, centre $\text{O}$ and radius $4.5 \text{m}$, is shown in the following diagram.

A square field with side $8 \text{m}$ has a goat tied to a post in the centre by a rope such that the goat can reach all parts of the field up to $4.5 \text{m}$ from the post.

^{[Source: mynamepong, n.d. Goat [image online] Available at: https://thenounproject.com/term/goat/1761571/
This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
https://creativecommons.org/licenses/by-sa/3.0/deed.en [Accessed 22 April 2010] Source adapted.]}

Let $V$ be the volume of grass eaten by the goat, in cubic metres, and $t$ be the length of time, in hours, that the goat has been in the field.

The goat eats grass at the rate of $\frac{dV}{dt}=0.3 t{\text{e}}^{-t}$.

Eddie decides to construct a path across his rectangular grass lawn using pairs of tiles.

Each tile is $10 \text{cm}$ wide and $20 \text{cm}$ long. The following diagrams show the path after Eddie has laid one pair and three pairs of tiles. This pattern continues until Eddie reaches the other side of his lawn. When $n$ pairs of tiles are laid, the path has a width of $w_n$ centimetres and a length $l_n$ centimetres.

The following diagrams show this pattern for one pair of tiles and for three pairs of tiles, where the white space around each diagram represents Eddie’s lawn.

The following table shows the values of $w_n$ and $l_n$ for the first three values of $n$.

Find the value of

Write down an expression in terms of $n$ for

Eddie’s lawn has a length $740 \text{cm}$.

The tiles cost $\$24.50$ per square metre and are sold in packs of five tiles.

To allow for breakages Eddie wants to have at least $8\%$ more tiles than he needs.

There is a fixed delivery cost of $\$35$.